The remainder when 9234 is divided by 52 is 30
the quotient is 177 R 30
What is quotient, in math?Division is onw of the mathematical operators that is applied in sharing.
The quotient is the result of dividing two numbers by each other, the number being divided is the dividend while the number dividing is the divisor.
As in the case of 9234 is being divided by 52, the dividend is 9234, while the divisor is 52 the result of the division is the quotient.
the division is done to get
9234 / 52
= 177 30/52
the remainder from the division involving 9234 and 52 is 30, the mixed number is 177 30/52
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if a crew of six workers completes a job in 15 hours how long will it take 10 workers to complete the same job
As no. of crews and time are inversely proportional 10 workers will finish the job in 10 hours.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, A crew of six workers completes a job in 15 hours.
We know more crew will finish the job in less no. of hours so they are inversely proportional.
So, C = k/t.
6 = k/15.
k = 90.
Now, C = 10 hence,
10 = 90/t.
t = 90/10.
t = 10 hours.
So, They can finish in 10 hours.
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State the degree and leading coefficient of the polynomial in one variable. If it is not a polynomial in one variable, explain why.
n+8
degree =
leading coefficient =
Answer: The degree of a polynomial is the highest exponent of the variable in the polynomial. The leading coefficient of a polynomial is the coefficient of the term with the highest degree.
In the expression "n + 8", the highest degree of the variable is 1 and the coefficient of the term with the highest degree is 1. Therefore, the degree of the polynomial is 1 and the leading coefficient is 1.
So, the degree of the polynomial is 1 and the leading coefficient is 1.
Note: If the expression had included terms with higher degrees of the variable, such as "n^2 + 3n + 8", the degree of the polynomial would have been 2 and the leading coefficient would have been 1.
write x^2+10x+12 in the form (x+a)^2-b
Answer:
(x+5)^2 - 13
Step-by-step explanation:
If you work out the target expression, you get:
(x+a)^2-b = (x+a)(x+a)-b = x^2 + 2ax + a^2 - b
so 2ax must be 10x, hence a = 5
also a^2 - b must be 12, and with a being 5, this means b = 25-12 = 13
Answer:
[tex](x+5)^2 - 13[/tex]
Step-by-step explanation:
In order to convert the given quadratic [tex]x^2 + 10x + 12[/tex] into the form [tex](x+a)^2 - b[/tex], you need to put the given quadratic into vertex form.
⭐What is vertex form?
a way you can rewrite a quadratic equation[tex](x-h)^2 + k[/tex]-(-h) = x-value of the vertex+k = y-value of the vertex⭐How do you rewrite a quadratic in vertex form?
you partially complete the squareI will demonstrate how to "partially complete the square" with the given quadratic.
Given: [tex]x^2 + 10x + 12 = 0[/tex]
Subtract the constant from the LHS and RHS.
[tex]x^2 + 10x = -12[/tex]
Divide the coefficient of the middle term by 2, square that result, and add it to the LHS and RHS.
[tex](\frac{10}{2})^2\\(5)^2\\= 25[/tex]
[tex]x^2 + 10x + 25 = -12 + 25[/tex]
[tex]x^2 + 10x + 25 = 13[/tex]
Write the LHS into the polynomial identity: [tex](a+b)^2[/tex] by factorising
[tex]x^2 + 5x + 5x + 25 = 13[/tex]
[tex]x(x + 5) + 5(x + 5) = 13[/tex]
[tex](x+5)(x+5) = 13[/tex]
[tex](x+5)^2 = 13[/tex]
Subtract 13 from the LHS and RHS.
[tex](x+5)^2 - 13[/tex]
That's it!
⭐if this response helped you, please mark it the "brainliest"!⭐
Enter the missing values below.
83
18xy +48x y
25
(3x+8y²)
According to the given algebraic expression the missing value is [tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex].
What is the formula for algebraic expressions?An equation that includes constants, variables, and a few algebraic procedures is said to be algebraic. A good example of an algebraic equation is 3x2 2xy + d. So, three different sorts of fundamental building blocks make up an algebraic expression: Correlation (i.e. integers) (i.e. numbers)
Which five algebraic expressions are there?The subsequent five categories provide further categorization of various algebraic expression forms. These include the monomial, polynomial, binomial, trinomial, and multinomial.
Briefing:[tex]$6.3 x^2x^6 y^3+8.6 x^2 y^3y^2[/tex]
[tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex]
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The complete question is-
[tex]\\$factor the algebraic expression.\\$$18 x^8 y^3+48 x^2 y^5=x-y-\left(3 x^6+8 y^2\right)\\\\$Enter the missing values below\\\\$18 x^8 y^3+48 x^2 y^5=\square x\square y\square (3 x^6+8 y^2)$$[/tex]
The manager of a food company wants to conduct a survey to find out whether consumers like or dislike a new brand of soup that was recently launched. Which of the following data collection methods is mostly likely to get unbiased results? a. Ask distributors who supply the products to local retailers about the popularity of different soup brands. b. Ask the employees in the company which soup is the best. c. Ask customers who visit retailers within a 15 mile radius of the company headquarters. d. Ask customers who visit the grocery store nearest to the manager's house which soup they like the best.
Option c is most likely to get unbiased results.
The best option for collecting unbiased data in this case would be option c: asking customers who visit retailers within a 15 mile radius of the company headquarters. This method would involve sampling a diverse group of customers who are not affiliated with the company in any way, and therefore are likely to provide more objective feedback about the new brand of soup.
Option a, asking distributors who supply the products to local retailers about the popularity of different soup brands, could be biased because the distributors may have their own interests in promoting certain brands over others.
Option b, asking the employees in the company which soup is the best, could also be biased because the employees may have a vested interest in the success of the company and its products, and therefore may not provide completely objective feedback.
Option d, asking customers who visit the grocery store nearest to the manager's house which soup they like the best, could also be biased because it may not be representative of the overall customer base for the soup. It is important to sample a diverse group of customers in order to get a more accurate sense of how the new brand of soup is being received.
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The National Weather Service says that the mean daily high temperature for October in a large Midwestern city is 56 degree F. A local weather service suspects that this value is not accurate and wants to perform a hypothesis test to determine whether the mean. is actually lower than 56 degree F. A simple of mean daily high temperatures for October over past 37 years yields x = 54 degree F. Assume that the population standard deviation is 5.6 degree F. Perform the hypothesis test at the 1% significance level.
The result of the hypothesis test is that we cannot say if the mean is lower than 56.
Hypothesis are ,
H0 : ц = ц 1
H1 : ц ≠ ц 1
It is to be tested whether the mean daily high temperature for October in a large Midwestern city is actually lower than
56 F or not.
Then the test statistic is equal to minus 2.64610 degrees of tritomas degree of to equal to 1 equal to 29 point,
The appropriate conditions to be sufficed before performing the one-sample z-test are:
(i) The measurement of the sample drawn for the observation must be extensive. The desired threshold is 30.
(ii) Each observation should have an equal opportunity of getting selected in the sample.
(iii) The data need to be normal.
On performing the analysis we conclude that it can not be said with 99 % confidence that the true mean temp is less than 56 F.
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The restaurant has 25 boxes of ketchup.
Each box has 250 packets of ketchup.
How many packets of ketchup does the restaurant have?
Answer: 6,250
Step-by-step explanation: As the equation states there are 25 boxes with 250 packs of ketchup take the 25 boxes and multiply the 250 packets
250x25=6,250
show that if \lamdba is in the point spectrum, the the conjugate is in the union of the point and residual spectra of the adjoint
We are given that [tex]\overline\lambda[/tex] is in the point spectrum and we are to prove that the conjugate is the union of the point and residual spectra of the adjoint.
If [tex]\overline\lambda[/tex] ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v ∈ D(T∗).
Hence, for all u ∈ D(T) we have -
⟨Tu,v⟩ = ⟨u,T∗v⟩ = ⟨u,[tex]\overline\lambda[/tex]⟩ = λ⟨u,v⟩,
⟨(T−λ)u,v⟩ = 0, for all u ∈ D(T)
If λ ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v∈D(T∗).
Hence, for all u∈D(T), we have ⟨Tu,v⟩=⟨u,T∗v⟩=⟨u,[tex]\overline\lambda[/tex]v⟩=λ⟨u,v⟩,
and therefore,
⟨(T−λ)u,v⟩=0, for all u∈D(T)
i.e. the range of T−λ is not dense and we will have λ ∈ σr(T) ∪ σp(T).
Hence, proved.
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the value of y varies directly with x.when y=75 x=1/2 what is the value of y when x equals 2 1/4
The value of y from the equation y = 150x when x = 2(1/4) is 337.5.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 is an equation.
We have,
y varies directly with x.
y ∝ x
y = kx
Now,
y = 75 when x = 1/2
75 = k(1/2)
k = 75 x 2
k = 150
Now,
y = kx
y = 150x
When x = 2(1/4) = 9/4
y = 150 x 9/4
y = 337.5
Thus,
The value of y is 337.5.
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Use spherical coordinates to Find the average distance from a point in a ball of radius a to its center.
The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A
Given the radius in the question = a
The integration of the total distance before dividing the volume will be =
⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a\cdot a^2\sin\theta\,da\,d\theta\,d\phi[/tex]
⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a^3\sin\theta\,da\,d\theta\,d\phi[/tex]
⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}\int_0^\pi \sin\theta\,d\theta\,d\phi[/tex]
⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}1\,d\phi[/tex]
⇒ [tex]\pi A^{4}[/tex]
Let us divide the average distance by the ball's volume,
⇒ [tex]\frac{\pi a^4}{(4/3)\pi a^3}[/tex]
⇒ [tex]{\frac{3a}4}[/tex]
By the use of the Parcly Taxel's way,
Let the radius of the ball be = A
f(x) = probability density function
Distance = D from the given point to the center.
P( D < a )
[tex]\begin{align}P(D\leq r)&= \frac{ \frac 43 \pi r^3 }{\frac 43 \pi R^3}=\frac {r^3}{R^3}, \ \ \ 0\leq r\leq R. \end{align}[/tex][tex]\frac{\frac{4}{3} \pi a^{3} }{\frac{4}{3} \pi A^{3} } = \frac{a^{3} }{R^{3} }[/tex]. 0 [tex]\leq[/tex] a [tex]\leq[/tex] A
Therefore, The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A
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Solve for X : x + (7 x5) = 25
please help its holding back my grade 50 points
Answer:
X=54
Step-by-step explanation:
equate both the equations since angles of opposite sides are equal
2x+2=3x-52
3x-2x= 52+2
x=54
answer:
x=54
Step-by-step explanation:
2x+2=3x-52
move the 2x to 3x because x can't be negative
and add 52 to 2 so x=54
the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .
The quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant b^2 - 4ac is either positive or zero .
Given :
the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .
Quadratic equation :
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.
Formula :
= -b ± [tex]\sqrt{b^2 - 4ac / 2a}[/tex]
Discriminant = b^2 - 4ac
if b^2 - 4ac = 0 or positive value then only the formula give us the coordinates of the points of intersection of a line .
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Given f(x)=3x+4 find f(4)
Answer:
Step-by-step explanation:
To find f(4), you can substitute 4 for x in the equation f(x) = 3x + 4. This gives you:
f(4) = 3(4) + 4
= 12 + 4
= 16
Therefore, f(4) = 16.
19 points all i have really..Gavin is hoping to buy his first car in 3 years. He is considering two options to help him save and grow his money. If he currently has $800, should he deposit his money into a savings account that is compounded annually at an interest rate of 9% or in a savings account that is compounded quarterly at an interest rate of 3%?
Gavin should deposit his money into a savings account that is compounded annually at an interest rate of 9%.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
Given that the current balance is $800.
There were two types of schemes.
First scheme offer compounded annually at an interest rate of 9%
Second scheme offer compounded quarterly at an interest rate of 9%.
The formula of compound interest annually is
A = P(1+r)^t
P = principal = 800
r = rate of interest = 9% = 0.09
t = time = 3 year
A = 800(1+0.09)³
A = 1036.02.
The formula of compound interest annually is
A = P(1+(r/n))^tn
P = principal = 800
r = rate of interest = 3% = 0.03
t = time = 3 year
n = 4
nt = 4×3 =12
A = 800(1+0.03/4)¹²
A = 875.04
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convert the following equation into standard form.
Y= -2x+6
Answer:
x = 3+y
Step-by-step explanation:
is your ans .................
Need help fast thank you
Help me with this math please. Help me quick please.
Answer:
f(x) = 5/2x
Step-by-step explanation:
The parent function for the given equation is f(x) = 1/2x. When this function is vertically stretched by a factor of 5, the resulting function will be f(x) = 5/2x. This means that for any value of x, the output of the transformed function will be 5 times greater than the output of the parent function.
For example, if x = 2, then f(x) = 1/2 * 2 = 1 for the parent function, and f(x) = 5/2 * 2 = 5 for the transformed function. Similarly, if x = 3, then f(x) = 1/2 * 3 = 1.5 for the parent function, and f(x) = 5/2 * 3 = 7.5 for the transformed function.
tell me if this helped :)
I need help with my math homework
The multiplications, applying the associative property, are given as follows:
1. (5 x 2) x 3 = 10 x 3 = 30.
2. 4 x (3 x 3) = 4 x 9 = 36.
3. (6 x 1) x 4 = 6 x 4 = 24.
4. 5 x (2 x 4) = 5 x 8 = 40.
5. (2 x 2) x 8 = 4 x 8 = 32.
6. 3 x (2 x 2) = 3 x 4 = 12.
7. (4 x 2) x 4 = 8 x 4 = 32.
8. 6 x (3 x 3) = 6 x 9 = 54.
What is the associative property of multiplication?The associative property of multiplication defines that the order in which the factors are multuiplied does not change the product.
In this problem, we have to consider that the parenthesis gives the precedence of the factors, meaning that the terms inside the parenthesis are multiplied first, and their result should be placed on the blanks below the parenthesis.
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Figure 1 and 2 are shown in the coordinate below.
Saorise claims the there is a sequence of transformations that Carries figure 1 onto figure 2. Select all actions that she could take to justify this claim
A. show that a rotation of 180° counterclockwise about the origin carries Figure 1 onto Figure 2
B. show that a reflection over the x-axis followed by a reflection over the y-axis carries Figure 1 onto Figure 2
C. show that a translation of 4 units right followed by a translation of 5 units down carries Figure 1 onto Figure 2
D. show that a rotation of 90° clockwise about the origin followed by a reflection over the x-axis carries Figure 1 onto Figure 2
Answer:
A and B
Step-by-step explanation:
actually the 180° rotation does the same as the reflection over the x-axis and then the reflection over the y-axis.
Subtract.
−135−(−278)
Enter your answer as a simplified fraction by filling in the boxes.
Answer:143
Step-by-step explanation: When subtracting a negative number from a negative number(a minus sign followed by a negative turns the two signs into a positive sign) you are then adding a positive
A subscription to a program normally costs $36 but is on sale for 25% off. A 7% tax is added at checkout. What is the total cost? $28.89 $45.59 $9.00 $27.00
Answer:
$28.89
Step-by-step explanation:
he subscription is on sale for 25% off, so the cost is $36 - (25% * $36) = $36 - $9 = $27.
Then, a 7% tax is added at checkout, so the total cost is $27 + (7% * $27) = $27 + $1.89 = $28.89.
Therefore, the total cost is $28.89.
Answer:
Step-by-step explanation:
36 will be 27 and 7% of 27 should be added 1,89 so 28,89
Please help asap
Which of the following expressions is equivalent to -6(2x+5)?
(1). -12x-30
(2). -42x
(3). 3-3(4x+11)
(4). -2(6x+15)
A. 1 only
B. 2 and 3
C. 1,3,4
D. 1,2,3,4
Answer:
1st & 4th answers are correct.
Step-by-step explanation:
-6 ( 2x + 5 )
Solve the brackets.
- 12x - 30
We can also write the answer like this.
Take -2 out of the brackets.
- 12x - 30 → -2 ( 6x + 15 )
Therefore, 1st & 4th answers are correct.
Calculate the average rate of change between x=-1 and x=1.
Between x=-1 and x=1, the average rate of change is 1.
What is meant by average rate of change?It represents the average change in the function's per-unit value during that time period. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity. As the slope of the straight line that links the two spots, the average rate of change between the two points is determined. Use the formula:
(f(b)-f(a))/(b-a) to get the average rate of change of f(x) between x=a and x=b.
Given line in the figure passes through the points A(4, 0), B(-1, -5)
Let the equation of the line be:
y=mx+ c
Slope m=(-5-0)/(-1-4)
m=1
Therefore, y=x+ c
It passes through (4, 0)
y+ c=0
c=-4
y=x-4=f(x)
f(-1)= -1-4=-5
f(1)= 1-4=-3
The average rate of change=(f(b)-f(a))/(b-a)
=(f(1)-f(-1))/1-(-1)
= -3-(-5)/(1+1)
=2/2
=1
Therefore, Between x=-1 and x=1, the average rate of change is 1.
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y=-3x+2 and 6x+2y=10
There is no solution to the given system of equations which is the correct answer would be an option (A).
The system of equations is given in the question as:
y = -3x+2 and 6x+2y = 10
These are two equations in the form y = mx + b, where m is the slope and b is the y-intercept.
The first equation, y = -3x + 2, has a slope of -3 and a y-intercept of 2.
The second equation, 6x + 2y = 10, can be rewritten in slope-intercept form as y = -3x + 5. This has a slope of -3 and a y-intercept of 5.
Since both equations have the same slope, they are parallel to each other. This means that they will never intersect, and there is no solution to this system of equations.
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The question seems to be incomplete the correct question would be:
Which statement is true about this system of equations?
y = -3x+2 and 6x+2y = 10
A. there is no solution
B. there is one solution
C. there is many infinite solutions
Modeling multiplication and division fraction pls help
The area of each section is 3/4 square feet. To solve the give question use division operation.
What is mixed fraction?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.
Given that the area of the garden is [tex]5\frac{1}{4}[/tex] square feet.
Now convert the mixed fraction with improper fraction:
[tex]5\frac{1}{4}[/tex] = [(5×4) + 1]/4
[tex]5\frac{1}{4}[/tex] = 21/4
We have to divide the area 7 equal area.
Thus divide 21/4 by 7.
21/4 ÷ 7
To convert the division sign into multiplication sign, take the reciprocal of 7:
21/4 × 1/7
= (21 × 1)/(4 × 7)
Divide the denominator and numerator by 7:
= 3/4
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in a homicide case different witnesses picked the same man from a line up. the line up contained 5 men. if the identifications were made by random guesses, find the probability that all witnesses would pick the same person. round to seven decimal places.
Rounding to seven decimal places, the probability that one individual would be selected by all witnesses is 0.0000128.
Six different witnesses chose the same individual from a lineup in a homicide case. There were 5 guys in the lineup. The likelihood that each of the six witnesses would choose the same person if the identifications were done based just on guesswork.
P = 1 ÷ 5 is the likelihood that a witness will choose a certain individual at random.
The likelihood that all seven witnesses would select the same subject is P = [tex](\frac{1}{5})^{7}[/tex]= 0.0000128.
Simply put, the probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes to determine how likely they are if we are unclear about how an event will turn out.
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8. The number 86.345 correct to one decimal place is
Answer:
86.3
Step-by-step explanation:
86.345
step 1
identify their place values
8 — Tens
6 — Units
.3 — tenth( 1 decimal place)
.34 — Hundredth (2 decimal place)
.345 — Thousandth ( 3 decimal place)
to one decimal place is
= 86.3
remember 4 is a round down number so .345 can't actually affect the 3
i hope this answered helped.
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Find all values of x for which f(x)=3x^4+4x^3-120x^2+120 has local maxima and minima, as well as the inflection points. Please show all of your work.
The Local maxima and minima will be at X = 0 , 4 , -5 and point of inflation will be at [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].
What is Maxima and Minima ?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.
Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.
The peaks and minima of the function that appear in a certain interval are known as local maxima and minima. The value of a function at a place in a certain interval for which the values of the function near that point are always smaller than the value of the function at that point would be considered a local maximum. Local minima, on the other hand, would be the value of the function at a location where the values of the function nearby are higher than the value of the function at that location.
When the concavity of a function's graph (or picture) changes, a point of inflection is identified. We need to determine where the second derivative of the function switches from negative to positive, or vice versa, in order to determine this in algebra. So, we calculate the provided function's second derivative.
The fuction is :
[tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]
So for local Maxima and minima first derivatives should be zero
Therefore,
[tex]\frac{d}{dx}\\[/tex] ([tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex] ) = 0
⇒ [tex]12x^{3} + 12x^{2} - 240x = 0[/tex]
⇒ [tex]x^{3} + x^{2} - 20x = 0[/tex]
⇒[tex]x(x^{2} + x - 20) = 0 \\[/tex]
⇒x(x-4)(x+5) = 0
For x = 0, 4 , -5 there is a local maxima or minima.
Now for Point of Inflation second derivative is zero
Therefore,
[tex]\frac{d^{2} }{dx^{2} }[/tex] ( [tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]) = 0
⇒ [tex]\frac{d}{dx}[/tex][tex]12x^{3} + 12x^{2} - 240x = 0[/tex]
⇒ [tex]36x^{2} + 24x - 240 = 0[/tex]
⇒[tex]3x^{2} + 2x - 20 = 0[/tex]
⇒ x = [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex]
So the point of inflations are [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].
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Sketch the curve with the given vector equation by finding the following points. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) r(t) = (t, 9 – t, 2t) r(-9) (x, y, z) r(0) (x, y, z) r(9) (x, y, z)
For sketching the graph we need to know the coordinate of the vector which are r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩
Given:-
x = t − 2,
y = t² + 1 ⇒ t = x + 2
⇒ y = (x + 2)2 + 1
⇒ y = x² + 4x + 5
For find r′(t) we have to ,
r′(t) = ⟨1, 2t⟩
To sketch the position vector r(t) and the tangent vector r′(t) for t = 1.
r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩
See the above figure. The red vector is r(1) and the blue one is r′(1)
To learn more about the vectors
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