A charge Q1 = –1.6 x 10–6 coulomb is fixed on the x–axis at +4.0 meters, and a charge Q2 = + 9 x 10–6 coulomb is fixed on the y–axis at +3.0 meters, as shown on the diagram above. a. i. Calculate the magnitude of the electric field E1 at the origin O due to charge Q1. ii. Calculate the magnitude of the electric field E2 at the origin O due to charge Q2. iii. On the axes below, draw and label vectors to show the electric fields E1 and E2 and also indicate the resultant electric field E at the origin.
Answers
a. The magnitude and direction of the electric field E at the origin O due to the two charges is 2.29 × 10⁴ N/C.
b. The electric potential V at the origin is zero
a. To find the electric field at the origin, we need to consider the electric forces that each charge exerts on a positive test charge placed at that point. The magnitude of the electric field E at the origin is given by the formula:
E = k * |Q₁| / r₁² + k * |Q₂| / r₂²,
where k is Coulomb's constant, |Q₁| and |Q₂| are the magnitudes of the charges, and r₁ and r₂ are the distances from each charge to the origin.
In this case, Q₁ = − 1.6 × 10⁻⁶ C and Q₂ = + 9 × 10⁻⁶ C, so the magnitude of the electric field at the origin is:
E = k * |Q₁| / r₁² + k * |Q₂| / r₂²
= 9 × 10⁹ N·m²/C² * |− 1.6 × 10⁻⁶ C| / (4 m)² + 9 × 10⁹ N·m²/C² * |+ 9 × 10⁻⁶ C| / (3 m)²
= 2.29 × 10⁴ N/C.
b. To find the electric potential at the origin, we need to integrate the electric field from infinity to the point in question. The electric potential V at the origin is given by the formula:
V = − ∫ E · dr
where the integral is taken along any path from infinity to the origin. Since the electric field is conservative, the value of the integral does not depend on the path taken.
Therefore, we can choose a path that goes straight from infinity to the origin, and the integral simplifies to:
V = − ∫ E · dr = − E ∫ dr = − E x r,
where r is the distance from the origin to the point where the test charge is located. Since we are interested in the potential at the origin, we set r = 0 and obtain:
V = 0.
Therefore, the electric potential at the origin is zero, which means that the potential energy of a test charge placed at the origin is the same as the energy of a charge at infinity.
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Complete Question:
A charge Q₁ = − 1.6 × 10⁻⁶ C is fixed on the x-axis at +4 m, and a charge Q₂ = + 9 × 10⁻⁶ C is fixed on the y-axis at +3.0 m.
a. Calculate the magnitude and direction of the electric field E at the origin O due to the two charges. Draw and clearly label this vector on a coordinate axis.
b. Calculate the electric potential V at the origin.
Related Questions
PLEASE HELP!!! 40 points.
Answers
Answer:
D. 7/5
Step-by-step explanation:
In right triangle ABC with right angle C,
sinA = 4/5 = cosB
cosA = 3/5 = sinB
sinB + cosB = 3/5 + 4/5 = 7/5
Please help fast!! Find the slope of a line parallel to the line whose equation is 3x+18y=−486.
Fully simplify your answer.
Answers
Answer: -1/6
Step-by-step explanation:
Put the equation into y = mx + b (slope) form.
3x + 18y = -486
18y = -3x - 486
y = -1/6x - 27
If the line is parallel to this line, the slope must be the same.
Give an example to show that if d is not prime and n2 is divisible by d, then n need not be divisible by d.
Answers
If d is not a prime number and n^2 is divisible by d, it does not necessarily mean that n is also divisible by d, example is d = 6 and n = 3, where n^2 = 9 is divisible by 6, but n = 3 is not divisible by 6.
A prime number is a positive integer greater than 1 that has exactly two distinct factors: 1 and itself. For example, 2, 3, 5, 7, 11, 13, and 17 are all prime numbers.
If a number d is not prime, then it has at least one factor other than 1 and itself. Let's assume that d is not prime, and let p be a factor of d such that p is not equal to 1 or d. Then, by definition, p divides d evenly with no remainder.
Consider the case where d = 6 and n = 3.
Here, d is not a prime number, and n^2 = 9, which is divisible by d since 9 is a multiple of 6. However, n = 3 is not divisible by d = 6, as 6 does not divide 3 evenly.
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A bicycle wheel is 63m in diameter. how many metres does the bicycle travel for 100 revolutions of the wheel. (pie=²²/⁷
Answers
Answer:
19782m
Step-by-step explanation:
1 revolution = circumference
circumference = π * diameter
π = 3.1416
Then
circumference = 3.1416 * 63
= 197.92m
1 revolution = 197.82m
100 revolutions = 100*197.82m
= 19782m
Answer:
19.8 km
Step-by-step explanation:
To find:-
The distance travelled in 100 revolutions .Answer:-
We are here given that,
diameter = 63mWe can first find the circumference of the wheel using the formula,
[tex]:\implies \sf C = 2\pi r \\[/tex]
Here radius will be 63/2 as radius is half of diameter. So on substituting the respective values, we have;
[tex]:\implies \sf C = 2\times \dfrac{22}{7}\times \dfrac{63}{2} \ m \\[/tex]
[tex]:\implies \sf C = 198\ m \\[/tex]
Now in one revolution , the cycle will cover a distance of 198m . So in 100 revolutions it will cover,
[tex]:\implies \sf Distance= 198(100)m\\[/tex]
[tex]:\implies \sf Distance = 19800 m \\[/tex]
[tex]:\implies \sf Distance = 19.8 \ km\\[/tex]
Hence the bicycle would cover 19.8 km in 100 revolutions.
the c on the left has blank1 - word answer please type your answer to submit electron geometry and a bond angle of
Answers
The CH3-CIOI-CNI molecule contains three carbon atoms with different electron geometries and bond angles. The CH3 and CIOI carbon atoms have tetrahedral geometry with a bond angle of approximately 109.5 degrees, while the CNI carbon atom has a trigonal planar geometry with a bond angle of approximately 120 degrees.
Using this Lewis structure, we can determine the electron geometry and bond angle for each carbon atom in the molecule as follows.
The carbon atom in the CH3 group has four electron domains (three bonding pairs and one non-bonding pair). The electron geometry around this carbon atom is tetrahedral, and the bond angle is approximately 109.5 degrees.
The carbon atom in the CIOI group has four electron domains (two bonding pairs and two non-bonding pairs). The electron geometry around this carbon atom is also tetrahedral, and the bond angle is approximately 109.5 degrees.
The carbon atom in the CNI group has three electron domains (one bonding pair and two non-bonding pairs). The electron geometry around this carbon atom is trigonal planar, and the bond angle is approximately 120 degrees.
Therefore, the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI are:
CH3 carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees
CIOI carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees
CNI carbon atom trigonal planar geometry, bond angle of approximately 120 degrees
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_____The given question is incomplete, the complete question is given below:
Determine the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI
State whether the triangles could be proven congruent as SSS or SAS Theorem.
Answers
Using SSS theorem of congruency in triangles, we can prove that in all the cases, each triangle is congruent to the other.
What do you mean by congruent triangles?Whether two or more triangles are congruent depends on the size of the sides and angles. A triangle's size and shape are consequently determined by its three sides and three angles. If the pairings of the respective sides and accompanying angles are equal, two triangles are said to be congruent. Both of these are the exact same size and shape. Triangles may satisfy a number of distinct congruence requirements.
The SSS criterion is also known as the Side-Side-Side criterion. This standard states that two triangles are congruent if the sum of the three sides of each triangle is the same.
Here in the question,
It is given that the two sides of each triangle are equal to the corresponding sides of the other triangle.
Now as two sides of a triangle is equal to the two sides of another triangle, it is obvious that he third side will be equal to the corresponding sides of the other triangle.
Now as per the SSS criteria, as all the sides are equal to the corresponding sides of the other triangle, the triangle are congruent.
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A bag has 4 blue marbles, 3 green marbles, and 5 red
marbles. You select 2 marbles one at a time without
replacement.
Determine the probability the first marble is blue and
the second marble is green Round your answer to
the hundredths place.
Answers
The probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
There are 12 marbles in total in the bag, so the probability of selecting a blue marble on the first draw is 4/12.
After the first marble is drawn, there are 11 marbles left in the bag, so the probability of selecting a green marble on the second draw, given that the first marble was blue and has already been removed, is 3/11.
To determine the probability of both events occurring together, we multiply the probabilities. Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is:
(4/12) * (3/11) = 0.0909
Rounding to the hundredth place, the probability is approximately 0.09.
Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.
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Let S be the universal set, where:
S={1,2,3,...,18,19,20}
Let sets A and B be subsets of S, where:
Answers
The elements in the set (A∩B¹) = {2,11,12,} and (B∩A¹) ={5,7,8,9,13,15,16,18}
What is set theory?You should understand that Set theory is a branch of mathematical logic that studies sets, which can be informally described as collections of objects such as numbers, alphabets and variables.
The universal set
S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}
A = {1,2,6,11,12,19,20}
B = {1,5,6,7,8,9,13,15,16,18,19,20}
S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}
B¹ = {2.3.4.10.11.12.14.17)
A = {1,2,6,11,12,19,20}
(A∩B¹) = {2,11,12,}
The elements of (B∩A¹) is
S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}
A = {1,2,6,11,12,19,20}
A¹ = {3,4,5,7,8,9,10,13,14,15,16,17,18}
B = {1,5,6,7,8,9,13,15,16,18,19,20}
(B∩A¹) = {5,7,8,9,13,15,16,18}
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Between 11pm and midnight on Thursday night Mystery pizza gets an average of 4.2 telephone orders per hour
URGENT
Answers
a. In this exercise, we are given that Mystery Pizza has an average οf 4.2 teIephοne orders per hour between 11 P.M. and midnight on Thursday night. Nοw using these given vaIues, we wiII caIcuIate the probabiIity that at Ieast 30 minutes wiII eIapse before having the next teIephone οrder.
Hοw can we calculate the probability of the expected time for an event to occur?Accοrding to probabiIity theory and statistics, the exponentiaI distributiοn is the probabiIity distribution of time between occurrences in the Poissοn distribution. It is a distribution of probabiIities that frequentIy correIates to the amount of time before a specific event takes pIace. It is a prοcess in which events take pIace continuousIy, independentIy, and at an average pace that remains constant throughout the process.
In caIcuIating the area under the curve of its graph (CDF), we wiII have to use the fοIIowing formuIa for the mean and the standard deviation,
Mean and Standard Deviatiοn:
[tex]$\begin{array}{r}{\mu={\frac{1}{\lambda}};}\\ {\sigma={\frac{1}{\lambda}}\,.}\end{array}$[/tex]
where,
x is the randοm variabIeλ is the rate parameter, aIsοthe mean time between the eventFirst, let us calculate the mean and standard deviation using the given Pοisson mean [tex]$\lambda=4.2.$[/tex] Using the fοrmula, we have,
[tex]$\begin{aligned}\rm{\mu=\sigma={\frac{1}{\lambda}}}\\ {={\frac{1}{4.2}\\{=0.2381}\end{aligned}$[/tex]
Sο we have the mean and the standard deviation of 0.2381 hours.
Nοw, we wiII caIcuIate the probabiIity that at Ieast 30 minutes or 0.50 hοurs wiII eIapse before the next teIephone order. Keep in mind that we are caIcuIating the probabiIity for "more than" the x so we wiII use the right-taiIed formuIa for this which is given by,
Right-tailed area(Mοre than x) :
[tex]$P(X\gt x)=e^{-\lambda x};$[/tex]
where,
x is the randοm variableλ is the rate parameter, alsο the mean time between the eventsUsing the fοrmula, we have:
[tex]$\begin{array}{r l}{P(X\gt 0.50)=e^{-\lambda x}}\\ {=e^{-42(0.50)}}\\ {=0.1225\,.}\end{array}$[/tex]
Therefοre, we can concIude that there is a 12.25% chance that at Ieast 30 minutes or 0.5 hours wiII eIapse before another teIephone order.
b. Next, we wiII caIcuIate the probabiIity that Iess than 15 minutes wiII eIapse befοre the next teIephone order. Remember that we are caIcuIating the probabiIity of Iess than x. This means that we wiII be using the fοrmuIa for the Ieft-taiIed area which is given by,
Left-tailed area(Less than οr equal to x):
[tex]$P(X\leq x)=1-e^{-\lambda x}$[/tex]
where,
x is the randοm variableλ is the rate parameter, alsο the mean time between the eveUsing the fοrmula, we have:
[tex]$\begin{array}{r l}{P(X\leq0.25)=1-e^{-\lambda x}}\\ {=1-e^{-42(0.25)}}\\ {=1-0.3499}\\ {=0.6501\,.}\end{array}$[/tex]
Therefοre, there is a 65.01% that Iess than 15 minutes wiII eIapse before the next teIephοne caII.
c. In this part, we wiII caIcuIate the probabiity that between 15− 30 minutes wiII eIapse befοre the next teIephone order. MathematicaIIy, we have,
[tex]$P(0.25\lt X\lt 0.5)=P(X\lt 0.50)-P(X\lt 0.25)$[/tex]
Frοm part a, we have the value for P(X>0.50) which is 0.1225. Now using the cοmplement rule, we can get P(X<50}
[tex]$\begin{array}{c}{{P(X\lt 50)=1-P(X\gt 50)}}\\ {{=1-0.1225=0.8775\,.}}\end{array}$[/tex]
We have nοw the value of P(X<0.50) which is 0.8775.
We can nοw get the P(0.25<X<0.50) by subtracting P(X<0.50) by P(X<0.25) frοm part b.. So we have,
[tex]$\begin{array}{r}{P(0.25\lt X\lt 0.50)=P(X\lt 0.50)-P(X\lt 0.25)}\\ {=0.8775-0.6501}\\ {=0.2274\,.}\end{array}$[/tex]
Sο we have P(0.25<X<0.50)=0.2274. Therefore, we can concIude that there is a 22.74% chance that between 15 and 30 minutes wiII eIapse before having a teIephone order.
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What is the measure of angle ABC?
Answers
Please help !!!! Given m∥n, find the value of x.
(3x+5) (x-25) = 180 degrees
Answers
Answer:
Step-by-step explanation:
[tex](3x+5)+(x-25)=180 \text{ \ (angles on a straight line are supplementary)}[/tex]
[tex]4x-20=180[/tex]
[tex]4x=200[/tex] (+20 both sides)
[tex]x=50[/tex] (÷4 both sides)
4x-20=180
4x-20+20=180+20
4x=200
Divide both sides by the same factor
Cancel terms that are in both the numerator and denominator
Divide the numbers
4
x
4
=
200
4
4
4
=
2
0
0
4
x
=
50
=
5
0
Sara is a salesperson for Camera's Etc., which is a retailer for high-end digital cameras. Historically. Sara has averaged selling 2.7 extended warranties per day for cameras that she sells. Assume the number of camera warranties that Sara
sells per day follows the Poisson distribution. Complete part A
a. What is the probability that Sara will sell four extended warranties tomorrow?
The probability that Sara whassell four extended warranties tomorrow is___
(Round to four decimal places as needed.)
Answers
Answer:
The probability that Sara whassell four extended warranties tomorrow is 0.1046
Step-by-step explanation:
Please hit brainliest if this helped! If you have any questions, please comment.
We can use the Poisson probability formula to calculate the probability of selling 4 extended warranties tomorrow:
P(X = k) = (e^(-λ) * λ^k) / k!
where λ is the average number of extended warranties sold per day and k is the number of extended warranties sold.
In this case, λ = 2.7 and k = 4. So, plugging in the values, we get:
P(X = 4) = (e^(-2.7) * 2.7^4) / 4!
P(X = 4) ≈ 0.1046
Therefore, the probability that Sara will sell four extended warranties tomorrow is approximately 0.1046, rounded to four decimal places.
in a class if 108 students, 60 like football, 53 like Tennis and 10 like neither. calculate the number of students who like football but not tennis
Answers
Answer:
60 - 10 = 50
;
;
;
;
;
;
;
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3x + y = 6
Y + 2 = x
Answers
Answer: x = 2, y = 0
Step-by-step explanation:
Assuming you need help solving for x or y, and the capital Y is y, we have the system of equations:
3x + y = 6
y + 2 = x
Substituting x for y + 2 gives us
3(y + 2) + y = 6
3y + 6 + y = 6
4y = 0
y = 0
Plugging y = 0 in for the second equation gives us
x = 0 + 2, or x = 2
The Nutty Professor sells cashews for $6.80 per pound and Brazil nuts for $4.20 per pound. How much of each type should be used to make a 35 pound mixture that sells for $5.31 per pound?
Answers
The Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts tο make a 35 pοund mixture that sells fοr $5.31 per pοund.
Assume the Nutty Prοfessοr makes a 35-pοund mixture with x pοunds οf cashews and (35 - x) pοunds οf Brazil nuts.
The cashews cοst $6.80 per pοund, sο the tοtal cοst οf x pοunds οf cashews is $6.8x dοllars.
Similarly, Brazil nuts cοst $4.20 per pοund, sο (35 - x) pοunds οf Brazil nuts cοst 4.2(35 - x) dοllars.
The tοtal cοst οf the mixture equals the sum οf the cashew and Brazil nut cοsts, which is:
6.8x + 4.2(35 - x) (35 - x)
When we simplify, we get:
6.8x + 147 - 4.2x
2.6x + 147
The mixture sells fοr $5.31 per pοund, sο the tοtal revenue frοm selling 35 pοunds οf the mixture is:
35(5.31) = 185.85
When we divide the tοtal cοst οf the mixture by the tοtal revenue, we get:
2.6x + 147 = 185.85
Subtractiοn οf 147 frοm bοth sides yields:
2.6x = 38.85
When we divide by 2.6, we get:
x ≈ 14.94
Tο make a 35-pοund mixture that sells fοr $5.31 per pοund, the Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts.
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I’m having a hard time understanding how to get the Domain and Range. If you help please
Answers
Answer:
[-1,inf) and [-2,inf)
Step-by-step explanation:
Domain is all the X coordinates that the function will pass through. it starts at -1 and goes to inf so [-1,inf) is the domain. The range is all the Y coordinates the function will pass through. It starts at -2 and goes up to inf so [-2,inf) and that is your answer
NEED HELP ASAP 10 PONTS!!! please help me find the area and the perimeter!!!! i beg you at this point.
Answers
Answer: Area = 113.14 ft sq. Perimeter =
Step-by-step explanation:
break down the figure and solve area and perimeter for each
triangle = A = 1/2bh
A = 1/2 (8) (6)
A = 24 ft sq.
square = A = LW
A = (8) (8)
A = 64 ft sq
semi circle = A = 1/2 TT r^2
A = 1/2 (3.14) (4)^2
A = 1/2 (3.14) (16)
A = approximately 25.14 ft sq
rounded to hundredths
total AREA = 24 + 64 + 25.14 = 113.14
now we can find perimeter by breaking down the figures again
triangle
we know one leg is 6 ft and the other is 8 ft
we need to find the hypoteneuse using Pythagorean theorem.
a^2 + b^2 = c^2
6^2 = 8^2 = c^2
36 + 64 = c^2
100 = c^2
√100 = √c^2
10 ft = c
square
given two sides are 8ft and 8ft
semi circle - P is the same as circumference
P = ( 1/2 ) 2 π r
P = (1/2) (2) (3.14) (4)
P = 12.56
total PERIMETER = 12.56 + 8 + 8 + 6 + 10 = 44.56 ft
i attached a print screen showing my breakdowns
please help asap!!!!!!!
Answers
To remove the y-term in the given linear equation in two Variable multiply the equation by 4 then add these two equations.
What is linear equation in two Variable;
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. Yet, there are two solutions to a linear equation with two variables.
According to given question;
5X+8y=5 ……..eqn 1.
3x-2y=3 ………eqn 2.
Multiply by 4 in the eqn 2.
We get
12x-8y=12 ……..eqn 3 .
When we add eqn 1 and eqn 3 we get ;
17x =17
X =1
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After eliminating the y-term in the given equations i.e 5x+8y=5 and
3x-2y=3, The solution to the system of equations is x = 1, y = 0.
What is elimination method?The elimination method is the technique used to solve systems of linear equations. It involves adding or subtracting equations in a system to eliminate one variable and find the value of the other variable.
To eliminate the y-term in these equations, you can multiply the second equation by 4, which will give you:
12x - 8y = 12
Now, you can add this equation to the first equation:
5x + 12x + 0y = 5 + 12
Simplifying the left side gives you 17x, and simplifying the right side gives you 17. So, you have the equation:
17x = 17
Solving for x gives you x = 1.
Now that you have found the value of x, you can substitute it into one of the original equations to solve for y. Using the first equation, you get:
5(1) + 8y = 5
Simplifying this equation gives you:
8y = 0
Solving for y gives you y = 0.
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Please indicate which is the best answer to complete the figure below.
Answers
Answer:b
Step-by-step explanation:
Jason invested $5,500 in an account paying an interest rate of 1 7/8 % compounded quarterly. Kayden invested $5,500 in an account paying an interest rate of 1 3/8 % compounded annually. After 8 years, how much more money would Jason have in his account than Kayden, to the nearest dollar?
Answers
Using compounding we know that the additional amount Jason has more than Kayden is $249.48.
What is compounding?Calculating interest on the principal borrowed as well as any prior interest.
In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one.
So, the amount of Jason after 8 years:
Amount: $5500
Interest: 1.875%
Compounded: Quarterly
Using a compounding calculator:
Amount after 8 years: $6,387.85
The amount of Kayden:
Amount: $5500
Interest: 1.375%
Compounded: Quarterly
Using a compounding calculator:
Amount after 8 years: $6,138.37
The additional amount Jason got: 6,387.85 - 6,138.37 = $249.48
Therefore, using compounding we know that the additional amount Jason has more than Kayden is $249.48.
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Answer:253
Step-by-step explanation:
Decrease R450 in the ratio 9:8
Answers
The value of R500 decrease to ratio 9:8 is x = 400.
What is cross multiplication?By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we may write in a percentage to determine the values of unknown variables.
Given that, decrease R450 in the ratio 9:8.
Let 9 = 450
Then 8 will have the value = x.
That is,
9 = 450
8 = x
Using cross multiplication we have:
9x = 450(8)
x = 50(8)
x = 400
Hence, the value of R500 decrease to ratio 9:8 is x = 400.
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the expression the quantity cosecant squared of theta minus 1 end quantity over cotangent of theta simplifies to which of the following?
Answers
Students were asked to simplify the expression using trigonometric identities:
A. student A is correct; student B was confused by the division
B. 3: cos²(θ)/(sin(θ)csc(θ)); 4: cos²(θ)
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names.
Each student correctly made use of the trigonometric identities
cosec(θ) = 1/sin(θ)
1 -sin²(θ) = cos²(θ)
A.
Student A's work is correct.
Student B apparently got confused by the two denominators in Step 2, and incorrectly replaced them with their quotient instead of their product.
The transition from Step 2 can look like:
[tex]\frac{(\frac{1-sin^2\theta}{sin\theta} )}{cosec\theta} =\frac{1-sin^2\theta}{sin\theta} .\frac{1}{cosec\theta} =\frac{cos^2\theta}{(sin\theta)(cosec\theta)}[/tex]
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Complete question:
Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given. (In image below)
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)
Can someone please tell me what 5 divided by 1/3 is?
Answers
Answer:
15.
The trick to working out 5 divided by 1/3 is similar to the method we use to work out dividing a fraction by a whole number.All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator.
So, the answer to the question "what is 5 divided by 1/3?" is
15!
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3/3 x 5/1 / 1/3 =15/3 / 1/3 = 15
answer: 15
Assuming that the equation defines a differential function of x, find Dxy by implicit differentiation. 4)2xy-y2 = 1 5) xy + x + y = x2y2
Answers
For the equations 2xy - y^2 = 1 and xy + x + y = x^2y^2 using implicit differentiation the value Dxy is given by Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3 respectively.
Equation 2xy - y^2 = 1,
Differentiate both sides of the equation with respect to x,
Treating y as function of x and then differentiate again with respect to x.
Using implicit differentiation,
First, differentiate both sides with respect to x,
2y + 2xy' - 2yy' = 0
Next, solve for y',
⇒2xy' - 2yy' = -2y
⇒y' (2x - 2y) = -2y
⇒y' = -y/(x - y)
Now, differentiate again with respect to x,
y''(x - y) - y'(2x - 2y) = y/(x - y)^2
Substitute the expression we obtained for y' in terms of y and x,
y''(x - y) - (-y/(x - y))(2x - 2y) = y/(x - y)^2
Simplify and solve for y'',
y''(x - y) + (2xy - 3y^2)/(x - y)^2 = 1/(x - y)^2
The expression for Dxy is,
Dxy = (1 - 2xy + 3y^2)/(x - y)^3
For the equation xy + x + y = x^2y^2,
Differentiate both sides of the equation with respect to x,
Using implicit differentiation,
First, differentiate both sides with respect to x,
⇒y + xy' + 1 + y' = 2xyy'
Solve for y',
⇒xy' - 2xyy' + y' = -y - 1
⇒y' (x - 2xy + 1) = -y - 1
⇒y' = -(y + 1)/(x - 2xy + 1)
Now, differentiate again with respect to x,
y''(x - 2xy + 1) - y'(2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2
Substitute the expression we obtained for y' in terms of y and x,
y''(x - 2xy + 1) - (-y - 1)/(x - 2xy + 1)^2 (2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2
Simplify and solve for y''
y''(x - 2xy + 1) - (2y^2 - 2xy - 2y)/(x - 2xy + 1)^2 = (y + 1)/(x - 2xy + 1)^2
The expression for Dxy is,
Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3
Therefore , the value of Dxy using implicit differentiation for two different functions is equal to
Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3
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Participant A did 120 jumping jacks in 10 minutes. Participant B did 140 jumping jacks in 14 minutes. Which participant had the greater jumping jack rate?
Answers
Answer: Participant A
Step-by-step explanation:
if you divide 120 by 10 you would get 12 jumping jacks per minute and if you divide 140 by 14 you would get 10 jumping jacks per minute
Given the equation x² + 4x + y²-2y = 20: (HINT: Type in the equation is the desmos calculator and get the answers from the graph.)
What is the radius of the circle?
What is the center of the circle?
Answers
Answer:
The radius of the circle is 3.
The center of the circle is (-2, 1).
Step-by-step explanation:
Rewrite the equation in standard form:
We need to rewrite the given equation in standard form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. To do this, we complete the square for both the x and y terms.
x² + 4x + y²-2y = 20
(x² + 4x + 4) + (y² - 2y + 1) = 20 + 4 + 1
(x + 2)² + (y - 1)² = 25
Identify the center and radius:
Now that we have the equation in standard form, we can identify the center and radius of the circle.
The center is the point (-2, 1), which we can read directly from the equation.
The radius is the square root of the number on the right side of the equation, which is 5. Therefore, the radius is sqrt(5) or approximately 2.236.
Alternatively, we can also use the Desmos graphing calculator to plot the equation and visually determine the center and radius. When we plot the equation, we see that it forms a circle with center (-2, 1) and radius 3.
Write the function in factored form. Check by multiplication.
y = - 4x³ - 16x² +84x
y= (Factor completely.)
Answers
Answer:
Step-by-step explanation:
We can factor out a common factor of -4x from the equation:
y = -4x(x² + 4x - 21)
To factor the quadratic expression in the parentheses, we need to find two numbers that multiply to -21 and add to 4. These numbers are 7 and -3:
y = -4x(x + 7)(x - 3)
To check our work, we can multiply the three factors:
y = -4x(x + 7)(x - 3) = -4x(x² + 4x - 21) = -4x³ - 16x² + 84x
So the factored form is y = -4x(x + 7)(x - 3), and the check shows that we have factored the equation correctly.
TERM 1 ASSIGNMENT GRADE 7 Question 3 3.1. Calculate the following WITHOUT using a calculator; 3.1.1 6234 ×32
Answers
Answer: 6234 × 32 = 199488.
Step by step:
To calculate 6234 × 32 without using a calculator, you can use the traditional multiplication method as follows:
6234
x 32
-------
12468 (2 x 6234)
+ 62340 (3 x 6234 with a zero added)
--------
199488
Cody has $7 dollars. he wants to buy at least 4 snacks. Hot dogs (x) and $2 each. Peanuts (y) are $1 each. which ordered pair is a solution
Answers
Since we can't find an ordered pair (x, y) that satisfies all the conditions, there is no solution to this problem.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true. Equations can be used to model relationships between variables, solve real-world problems, and make predictions.
Here,
Let's start by defining the variables:
x: number of hot dogs
y: number of peanuts
We need to find an ordered pair (x, y) that satisfies the following conditions:
x and y are both integers
x is greater than or equal to 0
y is greater than or equal to 0
2x + y ≤ 7 (total cost of snacks can't exceed $7)
x ≥ 4 (at least 4 snacks)
We can use trial and error to find a suitable ordered pair. Let's start with x = 4 and see if we can find a corresponding y value that satisfies the conditions:
If x = 4, then the total cost of hot dogs is 4 * $2 = $8.
We need to spend no more than $7, so we have $7 - $8 = -$1 left for peanuts.
Since we can't spend a negative amount of money, there is no solution for x = 4.
Let's try x = 5:
If x = 5, then the total cost of hot dogs is 5 * $2 = $10.
We have $7 - $10 = -$3 left for peanuts, so there is no solution for x = 5 either.
Finally, let's try x = 6:
If x = 6, then the total cost of hot dogs is 6 * $2 = $12.
We have $7 - $12 = -$5 left for peanuts, so there is no solution for x = 6 either.
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Complete question:
Cody has $7 dollars. he wants to buy at least 4 snacks. Hot dogs (x) and $2 each. Peanuts (y) are $1 each. Find the solution for this question of equation?
a water park sold 1679 tickets for total of 44,620 on a wa summer day..each adult tocket is $35 and each child ticket is $20. how many of each type of tixkwt were sold?
Answers
Therefore , the solution of the given problem of unitary method comes out to be the attraction sold 943 child tickets and 736 adult tickets on that particular day.
What is an unitary method?It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.
Here,
Assume the attraction sold x tickets for adults and y tickets for kids.
Based on the supplied data, we can construct the following two equations:
=> x + y = 1679 (equation 1, representing the total number of tickets sold)
=> 35x + 20y = 44620 (equation 2, representing the total revenue generated)
Using the elimination technique, we can find the values of x and y.
When we divide equation 1 by 20, we obtain:
=> 20x + 20y = 33580 (equation 3)
Equation 3 is obtained by subtracting equation 2 to yield:
=> 15x = 11040
=> x = 736
When we enter x = 736 into equation 1, we obtain:
=> 736 + y = 1679
=> y = 943
As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.
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