find the value of the missing sides. leave in rationalized and simplified form. show your work.
Answers
So, in this case, the length of each of the equal sides is: 17 / [tex]\sqrt{2}[/tex] ≈ 12.02
What is triangle?An isosceles triangle is a triangle in which two sides have the same length. This means that two of the three angles in the triangle are also equal in measure. The side that is not congruent to the other two sides is called the base of the triangle, and the angles opposite the congruent sides are called the base angles. In an isosceles triangle, the base angles are always equal in measure.
Isosceles triangles are a common shape in geometry and can be found in many real-world applications. They have special properties that make them useful in various fields of mathematics, such as trigonometry and geometry. For example, the base angles of an isosceles triangle are always equal, so if you know the measure of one of the base angles, you can determine the measure of the other base angle using the fact that the sum of the angles in a triangle is 180 degrees.
given by the question.
In an isosceles triangle with two equal angles of 45 degrees and a third angle of 90 degrees, the two equal sides are opposite the 45 degree angles, and the third side is opposite the 90 degree angle. Let's call the length of the missing side "x".
Using the Pythagorean theorem, we know that in a right triangle with legs of equal length (which is the case for the two 45-degree angles), the length of the hypotenuse is. [tex]\sqrt{2}[/tex] times the length of the legs.
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Related Questions
What is the height of the building shown below? Round to the nearest tenth if necessary.
62.9 feet
132 feet
123.5 feet
77.7 feet
Answers
Answer:
77.7
Step-by-step explanation:
if you know, you know. laso make sure your calculator is on degrees and not radians
Question 4 X Suppose that starting today, you make deposits at the beginning of each quarterly period for the next 40 years. The first deposit is for 400, but you decrease the size of each deposit by 1% from the previous deposit. Using an nominal annual interest rate of 8% compounded quarterly, find the future value (i.e. the value at the end of 40 years) of these deposits. Give your answer as a decimal rounded to two places (i.e. X.XX).
Answers
if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.
The first step in solving this problem is to calculate the amount of each quarterly deposit. We know that the first deposit is $400, and each subsequent deposit decreases by 1% from the previous deposit. This means that each deposit is 99% of the previous deposit. To calculate the size of each deposit, we can use the following formula:
deposit_ n = deposit_(n-1) * 0.99
Using this formula, we can calculate the size of each quarterly deposit as follows:
deposit_1 = $400
deposit_2 = deposit_1 * 0.99 = $396.00
deposit_3 = deposit_2 * 0.99 = $392.04
deposit_4 = deposit_3 * 0.99 = $388.12
...
We can continue this pattern for 40 years (160 quarters) to find the size of each quarterly deposit.
Next, we need to calculate the future value of these deposits using an nominal annual interest rate of 8% compounded quarterly. We can use the formula for compound interest to calculate the future value:
[tex]FV = PV * (1 + r/n)^(n*t)[/tex]
where FV is the future value, PV is the present value (which is zero since we are starting with deposits), r is the nominal annual interest rate (8%), n is the number of times the interest is compounded per year (4 since we are compounding quarterly), and t is the number of years (40).
We can substitute the values into the formula and solve for FV:
[tex]FV = $400 * (1 + 0.08/4)^(440) + $396.00 * (1 + 0.08/4)^(439) + $392.04 * (1 + 0.08/4)^(4*38) + ... + $1.64 * (1 + 0.08/4)^4[/tex]
After solving this equation, we get a future value of $143,004.54, rounded to two decimal places. This means that if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.
This calculation highlights the power of compound interest over long periods of time. By making regular contributions and earning interest on those contributions, our investment grows exponentially over time. It also shows the importance of starting early and consistently contributing to an investment over time in order to achieve long-term financial goals.
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Suppose that A is the set of sophomores at your schooland B is the set of students in discrete math at your school.Express each of the following sets in terms of A and B.a. The set of sophomores taking discrete math at yourschool.That’s the intersection A ∩ B.b. The set of sophomores at your school who are nottaking discrete math.This is the difference A − B. It can also be expressed byintersection and complement A ∩ B.c. The set of students at your school who either are sophomores or are taking discrete math.The union A ∪ B.d. The set of students at your school who either are notsophomores or are not taking discrete math.Literally, it’s A ∪ B. That’s the same as A ∩ B.
Answers
Set of sophomores taking discrete math = A ∩ B. Set of sophomores not taking discrete math = A - B or A ∩ B^c. Set of students who are sophomores or in discrete math = A ∪ B. Set of students who are not sophomores or not in discrete math = (A ∩ B)^c or A ∪ B^c.
The set of sophomores taking discrete math at your school is the intersection of the set of sophomores A and the set of students in discrete math B. So, it can be expressed as A ∩ B.
The set of sophomores at your school who are not taking discrete math is the difference between the set of sophomores A and the set of students in discrete math B. So, it can be expressed as A - B or A ∩ B^c, where B^c is the complement of B (i.e., the set of students who are not in discrete math).
The set of students at your school who either are sophomores or are taking discrete math is the union of the set of sophomores A and the set of students in discrete math B. So, it can be expressed as A ∪ B.
The set of students at your school who either are not sophomores or are not taking discrete math is the complement of the intersection of the set of sophomores A and the set of students in discrete math B.
This can be expressed as (A ∩ B)^c or as A ∪ B^c, where B^c is the complement of B (i.e., the set of students who are not in discrete math). Note that this set includes all students who are either juniors, seniors, or not enrolled in discrete math.
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find the value of the derivative (if it exists) at
each indicated extremum
Answers
Answer:
The derivative does not exist at the extremum (-2, 0).
Step-by-step explanation:
Given function:
[tex]f(x)=(x+2)^{\frac{2}{3}}[/tex]
To differentiate the given function, use the chain rule and the power rule of differentiation.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule of Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Power Rule of Differentiation}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}$\\\end{minipage}}[/tex]
[tex]\begin{aligned}\textsf{Let}\;u &= x+2& \implies f(u) &= u^{\frac{2}{3}}\\\\\implies \dfrac{\text{d}u}{\text{d}{x}}&=1 &\implies \dfrac{\text{d}y}{\text{d}u}&=\dfrac{2}{3}u^{(\frac{2}{3}-1)}=\dfrac{2}{3}u^{-\frac{1}{3}}\end{aligned}[/tex]
Apply the chain rule:
[tex]\implies f'(x) = \dfrac{\text{d}y}{\text{d}{u}} \cdot \dfrac{\text{d}u}{\text{d}{x}}[/tex]
[tex]\implies f'(x) = \dfrac{2}{3}u^{-\frac{1}{3}} \cdot1[/tex]
[tex]\implies f'(x) = \dfrac{2}{3}u^{-\frac{1}{3}}[/tex]
Substitute back in u = x + 2:
[tex]\implies f'(x) = \dfrac{2}{3}(x+2)^{-\frac{1}{3}}[/tex]
[tex]\implies f'(x) = \dfrac{2}{3(x+2)^{\frac{1}{3}}}[/tex]
An extremum is a point where a function has a maximum or minimum value. From inspection of the given graph, the minimum point of the function is (-2, 0).
To determine the value of the derivative at (-2, 0), substitute x = -2 into the differentiated function.
[tex]\begin{aligned}\implies f'(-2) &= \dfrac{2}{3(-2+2)^{\frac{1}{3}}}\\\\ &= \dfrac{2}{3(0)^{\frac{1}{3}}}\\\\&=\dfrac{2}{0} \;\;\;\leftarrow \textsf{unde\:\!fined}\end{aligned}[/tex]
As the denominator of the differentiated function at x = -2 is zero, the value of the derivative at (-2, 0) is undefined. Therefore, the derivative does not exist at the extremum (-2, 0).
Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 146 minutes with a standard deviation of 15 minutes. Consider 49 of the races. Let X = the average of the 49 races.Find the probability that the average of the sample will be between 143 and 147 minutes in these 49 marathons. (Round your answer to four decimal places.)Find the 60th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)______ minFind the median of the average running times._____min
Answers
The probability that the average of 49 marathons is between 143 and 147 minutes is 0.5980. The 60th percentile is 148.25 minutes, and the median is 146 minutes.
The average of a sample of 49 marathons will be approximately normally distributed with mean = 146 minutes and standard deviation = 15/sqrt(49) = 15/7.
To find the probability that the average of the sample will be between 143 and 147 minutes, we can standardize the values:
z1 = (143 - 146) / (15/7) = -1.4
z2 = (147 - 146) / (15/7) = 0.4667
Then, using a standard normal distribution table or calculator, we find:
P(-1.4 < Z < 0.4667) = P(Z < 0.4667) - P(Z < -1.4)
= 0.6788 - 0.0808
= 0.5980
So the probability that the average of the sample will be between 143 and 147 minutes is 0.5980.
To find the 60th percentile for the average of these 49 marathons, we need to find the z-score such that the area to the left of the z-score is 0.6. Using a standard normal distribution table or calculator, we find:
P(Z < z) = 0.6
z = 0.25
Then, we can solve for the corresponding value of X:
0.25 = (X - 146) / (15/7)
X = 148.25
So the 60th percentile for the average of these 49 marathons is 148.25 minutes.
To find the median of the average running times, we note that the median of a normal distribution is equal to its mean. Therefore, the median of the average running times is 146 minutes.
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(b) Write 5 as a percentage.
Answers
Answer:
5 as a percentage of 100 is 5/100 which is 5%
in excercises 7 and 8 find bases for the row space and null space of a. verify that every vector in the row(a) is orthogonal to every vector in null(a)
Answers
The bases for the row space and null space of A, we put A into reduced row echelon form and solve for the null space. The dot product of basis vectors shows they are orthogonal.
To find the bases for the row space and null space of A, we perform row operations on A until it is in reduced row echelon form:
[ 1 -1 3 | 5 ] [ 1 -1 3 | 5 ]
[ 2 1 -5 | -9 ] -> [ 0 3 -11 | -19]
[-1 -1 2 | 2 ] [ 0 0 0 | 0 ]
[ 1 1 -1 | -1 ] [ 0 0 0 | 0 ]
The reduced row echelon form of A tells us that there are two pivot columns, corresponding to the first and second columns of A. The third and fourth columns are free variables. Therefore, a basis for the row space of A is given by the first two rows of the reduced row echelon form of A:
[ 1 -1 3 | 5 ]
[ 0 3 -11 | -19]
To find a basis for the null space of A, we solve the system Ax = 0. Since the third and fourth columns of A are free variables, we can express the solution in terms of those variables. Setting s = column 3 and t = column 4, we have:
x1 - x2 + 3x3 + 5x4 = 0
2x1 + x2 - 5x3 - 9x4 = 0
-x1 - x2 + 2x3 + 2x4 = 0
x1 + x2 - x3 - x4 = 0
Solving for x1, x2, x3, and x4 in terms of s and t, we get:
x1 = -3s - 5t
x2 = s + 2t
x3 = s
x4 = t
Therefore, a basis for the null space of A is given by the vectors:
[-3 1 1 0]
[ 5 2 0 1]
To verify that every vector in the row space of A is orthogonal to every vector in the null space of A, we compute the dot product of each basis vector for the row space with each basis vector for the null space:
[ 1 -1 3 | 5 ] dot [-3 1 1 0] = 0
[ 1 -1 3 | 5 ] dot [ 5 2 0 1] = 0
[ 0 3 -11 | -19] dot [-3 1 1 0] = 0
[ 0 3 -11 | -19] dot [ 5 2 0 1] = 0
Since all dot products are equal to zero, we have verified that every vector in the row space of A is orthogonal to every vector in the null space of A.
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_____The given question is incomplete, the complete question is given below:
in excercises 7 and 8 find bases for the row space and null space of a. verify that every vector in the row(a) is orthogonal to every vector in null(a). a = [ 1 -1 3 5 2 1 0 1 -2 -1 -1 1]
Hence, determine the circumstances of the base base of a coffee tin
Answers
Answer:
We can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
Step-by-step explanation:
What is function?
A function is a relation between a dependent and independent variable.
Mathematically, we can write → y = f(x) = ax + b.
Given is to find the diameter and height of the tin can.
Assume the density of coffee as {ρ}. We can write the volume of the tin can as -
Volume = mass x density
Volume = 750ρ
We can write -
πr²h = 750ρ
r = √(750ρ/πh)
D = 2r
D = 2√(750ρ/πh)
Now, we can write the circumferance as -
C = 2πr
C = 2π√(750ρ/πh)
Therefore, we can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
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A contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning?
Select ALL of the models that can be used to simulate this event.
A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections
E) a bag of 12 black chips and 60 red chips
Answers
Answer:
I'm pretty confident that the answer is E
A child's toy is in the shape of a square pyramid. The pyramid stands 20 inches tall and each side of the base measures 24 inches.
Half of the surface area of the pyramid is black and the remainder is yellow.
What is the surface area of the toy that is yellow?
Answers
Answer: 1704 square inches
Step-by-step explanation:
The surface area of a square pyramid is given by the formula:
Surface Area = base area + 4 × (1/2 × slant height × base length)
The base area of the pyramid is:
base area = length × width = 24 in × 24 in = 576 in²
The slant height of the pyramid can be found using the Pythagorean theorem:
slant height = sqrt(20² + 12²) = 236/5 in
Therefore, the surface area of the whole pyramid is:
Surface Area = 576 in² + 4 × (1/2 × 236/5 in × 24 in) = 1152 in² + 2256 in² = 3408 in²
Half of this area is black, so the area that is yellow is:
Yellow Area = 1/2 × 3408 in² = 1704 in²
Therefore, the surface area of the toy that is yellow is 1704 square inches.
in a popular shopping Centre waiting time for an ABC bank ATM machine is found to be uniformly distributed between 1 and 5 minutes what is the probability of waiting between 2 and 4 minutes to use the ATM
Answers
so here we get two outcomes one is 2 and other is 4.
so there is total 2 outcomes.
total no. of possibility is 5
so the probability of waiting between 2 and 4 minutes to use the ATM is 2/5.
8. for each of the given sample data sets below, calculate the mean, variance, and standard deviation. (a) 79, 52, 64, 99, 75, 48, 52, 24, 76 mean
Answers
The value for mean, variance, and standard deviation for the given set of data is 63.22, 794.04, and 28.17, respectively.
The method to calculate the various operations are:
Mean:
= (79 + 52 + 64 + 99 + 75 + 48 + 52 + 24 + 76) / 9 = 63.22
Mean is a measure of central tendency found by adding all the observations and dividing the result by the number of frequency or the total number of data set values.
Variance:
= ((79 - 63.22)² + (52 - 63.22)² + (64 - 63.22)² + (99 - 63.22)² + (75 - 63.22)² + (48 - 63.22)² + (52 - 63.22)² + (24 - 63.22)² + (76 - 63.22)² / (9-1) = 794.04
(Here, 63.22 is the mean calculated earlier)
Standard deviation:
= √(Variance)
=√(794.04) = 28.17
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Complete question is:
For each of the given sample data sets below, calculate the mean, variance, and standard deviation. (a) 79, 52, 64, 99, 75, 48, 52, 24, 76 mean =_______
variance = __________
standard deviation =_________
Homer's car weighs 4,000 pounds. How many tons does
Homer's car weigh?
Answers
Answer:2
Step-by-step explanation:
Answer:
2 Tons
Step-by-step explanation:
Homer’s car weighs 2 tons because there are 2,000 pounds in a ton and 4,000 divided by 2,000 equals 2
A baseball team plays in a stadium that holds 60000 spectators. With the ticket price at $9 the average attendance has been 23000. When the price dropped to $7, the average attendance rose to 30000. Assume that attendance is linearly related to ticket price. What ticket price would maximize revenue?
Answers
Answer:
Step-by-step explanation:
We can start by assuming that the relationship between the ticket price and attendance is linear, so we can write the equation for the line that connects the two data points we have:
Point 1: (9, 23000)
Point 2: (7, 30000)
The slope of the line can be calculated as:
slope = (y2 - y1) / (x2 - x1)
slope = (30000 - 23000) / (7 - 9)
slope = 3500
So the equation for the line is:
y - y1 = m(x - x1)
y - 23000 = 3500(x - 9)
y = 3500x - 28700
Now we can use this equation to find the attendance for any ticket price. To maximize revenue, we need to find the ticket price that generates the highest revenue. Revenue is simply the product of attendance and ticket price:
R = P*A
R = P(3500P - 28700)
R = 3500P^2 - 28700P
To find the ticket price that maximizes revenue, we need to take the derivative of the revenue equation and set it equal to zero:
dR/dP = 7000P - 28700 = 0
7000P = 28700
P = 4.10
So the ticket price that would maximize revenue is $4.10. However, we need to make sure that this price is within a reasonable range, so we should check that the attendance at this price is between 23,000 and 30,000:
A = 3500(4.10) - 28700
A = 5730
Since 23,000 < 5,730 < 30,000, we can conclude that the ticket price that would maximize revenue is $4.10.
for 50 points! On your OWN PIECE OF PAPER, make a stem-and-leaf plot of the following set of data and then find the range of the data.
83, 71, 62, 86, 90, 95, 61, 60, 87, 72, 95, 74, 82, 54, 99, 62, 78, 76, 84, 92
Answers
Here is the stem and leaf plot:
5 4
6 0, 1, 2, 2
7 1, 2, 4, 6, 8
8 2, 3, 4, 6, 7,
9 0, 2, 5, 5, 9
The range is 45.
What is a stem and leaf plot?A stem-and-leaf plot is a table that is used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf. The stem is the tens digit and the leaf is the units digit. For example, in the number 54, 5 is the stem and 4 is the leaf.
Range is used to measure the variation of a dataset by finding the difference between the highest number and the lowest number.
Range = highest value - lowest value
99 - 54 = 45
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£4100 is deposited into a bank paying 13.55% interest per annum , how much money will be in the bank after4 years
Answers
Answer:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the amount of money in the account after the specified time period
P = the initial principal amount (the amount deposited)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period in years
In this case:
P = £4100
r = 13.55% = 0.1355
n = 1 (interest is compounded once per year)
t = 4 years
Plugging these values into the formula, we get:
A = £4100(1 + 0.1355/1)^(1*4)
A = £4100(1.1355)^4
A = £4100(1.6398)
A = £6717.58
Therefore, the amount of money in the account after 4 years will be £6717.58.
fine the exact value of sin(45-30)
Answers
Estimated answer: 0.650
Can someone please
Help me on these
Answers
Answer:
34. (c) 12
35. (a) -12
36. (a) 51
37. (a) 13
Step-by-step explanation:
34.)
[tex] \implies \: \sf\dfrac{4}{xx + 2} = \dfrac{6}{2xx - 3} \\ \\ \implies \: \sf4(2xx - 3) = 6(xx + 2) \\ \\ \implies \: \sf 8xx - 12 = 6xx + 12 \\ \\ \implies \: \sf 8xx - 6xx = 12 + 12 \sf \\ \\ \implies \: \sf 2xx = 24 \\ \\ \implies \: \sf xx = \dfrac{24}{2} \\ \\ \implies \: \sf xx = 12 \\ [/tex]
Hence, Required answer is option (c) 12.
35.)
[tex] \implies \: \sf \dfrac{xx - 2}{2} = \dfrac{3xx + 8}{4} \\ \\ \implies \: \sf2(3xx + 8) = 4(xx - 2) \\ \\ \sf 6xx + 16 = 4xx - 8 \\ \\ \implies \: \sf 6xx - 4xx = - 8 - 16 \\ \\ \implies \: \sf 2xx = - 24 \\ \\ \implies \: \sf xx = \dfrac{ - 24}{2} \\ \\ \implies \: \sf xx = - 12 \\ [/tex]
Hence, Required answer is option (a) -12.
36.)
[tex] \implies \: \sf\sqrt{xx - 2} = 7 \\ \\ \implies \: \sf xx - 2 = {(7)}^{2} \\ \\ \implies \: \sf xx - 2 = 49 \\ \\ \implies \: \sf xx = 49 + 2 \\ \\ \implies \: \sf xx = 51[/tex]
Hence, Required answer is option (a) 51.
37.)
[tex] \implies \: \sf \sqrt{2xx - 10} = 4 \\ \\ \implies \: \sf 2xx - 10 = {(4)}^{2} \\ \\ \implies \: \sf 2xx - 10 = 16 \\ \\ \implies \: \sf 2xx = 16 + 10 \\ \\ \implies \: \sf 2xx = 26 \\ \\ \implies \: \sf xx = \dfrac{26}{2} \\ \\ \implies \: \sf xx = 13 \\ [/tex]
Hence, Required answer is option (a) 13.
Jonathan and Amber went to the store together to buy school supplies.
Jonathan purchased 2 notebooks and 5 elastic book covers for $6.75. Amber
purchased 4 notebooks and 2 elastic book covers for $7.50. What is the price
of a single notebook?
P
The price of a single notebook is $
Answers
Answer:
The answer is 1.5$
Step-by-step explanation:
Let the price of 1 notebook be x$ and 1 elastic book cover be y$
In first case,
2x+5y=$6.75
2x = $6.75-5y
x=($6.75-5y)/2------------- eqn i
In second case,
4x+2y=$7.50
4×($6.75-5y)/2 +2y=$7.50 [From eqn i]
($27-20y)/2 +2y=$7.50
($27-20y+4y)/2=$7.50
($27-16y)/2=$7.50
$27-16y=$7.50×2
$27-16y=$15
$27-$15=16y
$12=16y
y=$12/16
y=$0.75
The price of single elastic book cover is $0.75
Substituting the value of y in eqn i we get
x=($6.75-5y)/2
x=($6.75-5×$0.75)/2
x=($6.75-$3.75)/2
x=$3/2
x=$1.5
Hence, the price of single notebook is $1.5 Ans
Hey mate, please mark me as brainliest if you got the answer.
if sin0<0 and cos>0, then the terminal point is determined by 0 is in:
Answers
the terminal point of the angle determined by sin(0) < 0 and cos(0) > 0 is in the fourth quadrant.
why it is and what is trigonometry?
If sin(0) < 0 and cos(0) > 0, then we know that the angle 0 is in the fourth quadrant of the unit circle.
In the unit circle, the x-coordinate represents cos(θ) and the y-coordinate represents sin(θ). Since cos(0) > 0, we know that the terminal point of the angle is to the right of the origin. And since sin(0) < 0, we know that the terminal point is below the x-axis.
The fourth quadrant is the only quadrant where the x-coordinate is positive and the y-coordinate is negative, so that is the quadrant where the terminal point of the angle lies.
Therefore, the terminal point of the angle determined by sin(0) < 0 and cos(0) > 0 is in the fourth quadrant.
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It focuses on the study of the functions of angles and their applications to triangles, including the measurement of angles, the calculation of lengths and areas of triangles, and the analysis of periodic phenomena.
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Calculate the derivative of the following function and simplify.
y = [tex]e^{x} csc x[/tex]
Answers
Answer:
To find the derivative of this function, we'll use the product rule and the chain rule. Let's begin by writing the function in a more readable form using parentheses:
y = e^x * csc(x) * (1 / x) * csc(x)
Now we can apply the product rule, letting u = e^x and v = csc(x) * (1 / x) * csc(x):
y' = u'v + uv'
To find u' and v', we'll need to use the chain rule.
u' = (e^x)' = e^x
v' = (csc(x) * (1 / x) * csc(x))'
= (csc(x))' * (1 / x) * csc(x) + csc(x) * (-1 / x^2) * csc(x) + csc(x) * (1 / x) * (csc(x))'
= -csc(x) * cot(x) * (1 / x) * csc(x) - csc(x) * (1 / x^2) * csc(x) - csc(x) * (1 / x) * csc(x) * cot(x)
= -csc(x) * [cot(x) * (1 / x) + (1 / x^2) + (cot(x) / x)]
Now we can substitute these into the product rule formula:
y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (1 / x) - (1 / x^2) - (cot(x) / x)] + e^x * (-csc(x) * cot(x) * (1 / x) * csc(x) - csc(x) * (1 / x^2) * csc(x) - csc(x) * (1 / x) * csc(x) * cot(x))
Next, we can simplify this expression. One way to do this is to factor out common terms:
y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (1 / x) - (1 / x^2) - (cot(x) / x)] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + (cot(x) / x)]
Now we can simplify further by combining like terms:
y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (2 / x) - (1 / x^2)] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + (cot(x) / x)]
= e^x * csc(x) * (1 / x) * csc(x) * [-2cot(x) / x - 1 / x^2 - cot(x) / x^2] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + cot(x) / x]
At this point, the derivative is simplified as much as possible.
(please could you kindly mark my answer as brainliest)
Find the matrix A of the linear transformationT(M)=[8097]M[8097]−1from U2×2 to U2×2 (upper triangular matrices) with respect to the standard basis for U2×2 given by{[1000],[0010],[0001]}.
Answers
The matrix A of the linear transformation T(M) with respect to the standard basis for U2×2 is given by:
T([1000]) = [8 0]
[0 0]
T([0010]) = [0 0]
[0 9]
T([0001]) = [0 1]
[0 0]
To find the matrix A of the linear transformation T(M), we need to apply T to each basis vector of U2×2 and express the result as a linear combination of the basis vectors for U2×2. We can then arrange the coefficients of each linear combination as the columns of the matrix A.
Let's begin by finding T([1000]). We have:
T([1000]) = [8097][1000][8097]^-1
= [8 0]
[0 0]
To express this result as a linear combination of the basis vectors for U2×2, we need to solve for the coefficients c1, c2, and c3 such that:
[8 0] = c1[1000] + c2[0010] + c3[0001]
Equating the entries on both sides, we get:
c1 = 8
c2 = 0
c3 = 0
Therefore, the first column of the matrix A is [8 0 0]^T.
Next, we find T([0010]). We have:
T([0010]) = [8097][0010][8097]^-1
= [0 0]
[0 9]
Expressing this as a linear combination of the basis vectors for U2×2, we get:
[0 0] = c1[1000] + c2[0010] + c3[0001]
Equating the entries on both sides, we get:
c1 = 0
c2 = 0
c3 = 0
Therefore, the second column of the matrix A is [0 0 0]^T.
Finally, we find T([0001]). We have:
T([0001]) = [8097][0001][8097]^-1
= [0 1]
[0 0]
Expressing this as a linear combination of the basis vectors for U2×2, we get:
[0 1] = c1[1000] + c2[0010] + c3[0001]
Equating the entries on both sides, we get:
c1 = 0
c2 = 1
c3 = 0
Therefore, the third column of the matrix A is [0 1 0]^T.
Putting all of this together, we have:
A = [8 0 0]
[0 0 1]
[0 0 0]
Therefore, the matrix A of the linear transformation T(M) is:
T([1000]) = [8 0]
[0 0]
T([0010]) = [0 0]
[0 9]
T([0001]) = [0 1]
[0 0]
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You need 1 1/4 cups of sugar to make cookies. To make 16 cookies you will need how many cups
of sugar
Answers
If you need 1 1/4 cups of sugar to make cookies, that is the amount of sugar needed for one batch of cookies. To find out how much sugar is needed to make 16 cookies, we can set up a proportion:
1 1/4 cups sugar is needed to make 1 batch of cookies
x cups sugar is needed to make 16 cookies
We can solve for x by cross-multiplying:
1 1/4 * 16 = x
20/4 = x
5 = x
Therefore, you will need 5 cups of sugar to make 16 cookies.
The pulse rate of the male population is known to be normal, with a mean of 73 BPM and a standard deviation of 11.3. Find the sample size necessary to be within 2 BPM of the population mean with 95% confidence.
Answers
sample size of n=33
Step by step explanation:
We can use the formula for the margin of error for a confidence interval:
Margin of error = z* (sigma / sqrt(n))
Where z* is the z-score corresponding to the desired confidence level, sigma is the population standard deviation, and n is the sample size.
In this case, we want to find the sample size n such that the margin of error is no more than 2 BPM with 95% confidence. Since the sample size is unknown, we can use a t-distribution instead of the standard normal distribution to find the appropriate critical value.
The critical value for a 95% confidence interval with n-1 degrees of freedom is t=2.064 (from a t-distribution table).
Plugging in the known values, we have:
2 = 2.064 * (11.3 / sqrt(n))
Solving for n, we get:
n = (2.064 * 11.3 / 2)^2 = 32.59
Rounding up to the nearest whole number, we need a sample size of n=33 to be within 2 BPM of the population mean with 95% confidence.
? Answer the question below. Type your response in the space provided. What do you call the materials that help you achieve your goals?
Answers
Answer:
Acquired resources
Step-by-step explanation:
Acquired resources
C Select the correct answer. Which equation is equivalent to the given eq -4(x - 5) + 8x = 9x - 3
Answers
Answer:
-4(x - 5) + 8x = 9x - 3
Simplifying the left side:
-4x + 20 + 8x = 9x - 3
4x + 20 = 9x - 3
Subtracting 4x from both sides:
20 = 5x - 3
Adding 3 to both sides:
23 = 5x
Dividing both sides by 5:
x = 23/5
Therefore, the equation equivalent to the given equation is:
5x - 23 = 0
10 POINTS!! ASAP please help me find the area and also the outer perimeter!!!
Answers
Answer:
area of semi circle =pi r^2/2
3.14*6*6/2=56.2
area of rectangle=lb
=20*12=240
240+56.2=296.2
rounding it it will become 300 ft sqr
perimeter of rectangle without including 4th side=20+12+20=52
perimeter of semicircle=pi r+d (d is not needed here)
3.14*6=18.84
so total perimeter=52+18.84=70.84ft
Step-by-step explanation:
4 x 1 1/5= multiply. Write the product as a mixed number.
Answers
4 4/5.
Step by step explanation:
To multiply 4 by 1 1/5, we can first convert the mixed number 1 1/5 to an improper fraction:
1 1/5 = 6/5
Now we can multiply 4 by 6/5:
4 x 6/5 = 24/5
To write the product as a mixed number, we need to express 24/5 as a whole number plus a proper fraction. We can do this by dividing 24 by 5:
24 ÷ 5 = 4 with a remainder of 4
So, 24/5 can be written as 4 4/5. Therefore, the product of 4 and 1 1/5 is:
4 x 1 1/5 = 4 4/5.
please assist with this question...
Answers
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
(a)
the experimental probability is just using the actual experience to predict any future results.
the total number of cases was 20, and the number of desired cases (yellow) was 12.
so, the experimental probability of landing on yellow is
12/20 = 3/5 = 0.600
(b)
the theoretical probability of a totally fair spinner landing on yellow is 2 out of 5 possibilities, so
2/5 = 0.4000
(c)
the correct statement is the first one.
with a more or less balanced (fair) spinner the experimental numbers should get closer and closer to the theoretical numbers, the more spins we make.
Mark is 19 years old. He buys 50/100/50 liability insurance, and collision and comprehensive insurance, each with $750 deductibles. What is his total annual premium? Round to the nearest dollar. Do not state the units. Be sure to show your work
Answers
After answering the provided question, we can conclude that As a result, function Mark's annual premium is $1,500.
what is function?In mathematics, a function appears to be a connection between two numerical sets in which each individual of the first set (widely recognized as the domain) matches a particular member of the second set (called the range). In other words, a function takes input by one set and provides output from another. The variable x has frequently been used to represent inputs, and the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 represents a linear model whereby each x-value yields a unique value of y.
To determine Mark's total annual premium, add the premiums for liability insurance and collision/comprehensive insurance together.
Mark purchases liability insurance with coverage limits of 50/100/50. This means that his policy will pay up to $50,000 per person for bodily injury, $100,000 for bodily injury per accident, and $50,000 for property damage per accident.
Total Annual Premium: To determine Mark's total annual premium, add together his liability and collision/comprehensive insurance premiums:
Liability Premium + Collision/Comprehensive Premium = Total Annual Premium
Annual premium total = $500 + $1,000
$1,500 is the total annual premium.
As a result, Mark's annual premium is $1,500.
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