Let F(x)=f(x5) and G(x)=(f(x))5. You also know that a4=10,f(a)=2,f′(a)=4,f′(a5)=4 Then F′(a)= and G′(a)=__
Answers
the required values are:F'(a) = 200000G'(a) = 640 Hence, the required answer is F′(a) = 200000 and G′(a) = 640.
Let's use the chain rule of differentiation to calculate F'(a).F(x) = f(x⁵)
Using the chain rule, we get:F'(x) = f'(x⁵) × 5x⁴
Applying this to F(x), we get:F'(x) = f'(x⁵) × 5x⁴Also, substituting x = a, we get:F'(a) = f'(a⁵) × 5a⁴We know that f'(a⁵) = 4 and a⁴ = 10.
Substituting these values, we get:F'(a) = 4 × 5 × 10⁴ = 200000
Now, let's use the chain rule of differentiation to calculate G'(a).G(x) = (f(x))⁵Using the chain rule, we get:G'(x) = 5(f(x))⁴ × f'(x)
Applying this to G(x), we get:G'(x) = 5(f(x))⁴ × f'(x)
Also, substituting x = a, we get:G'(a) = 5(f(a))⁴ × f'(a)
We know that f(a) = 2 and f'(a) = 4.
Substituting these values, we get:G'(a) = 5(2)⁴ × 4 = 640
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Related Questions
Find the value of z.
Answers
Answer:
it depends on what is z for, if it's for the whole triangle then i would think it would be 2z - 4 10 and 7 added or multiplied. Or it could be 2z -4 witch would be z = 2
Karen Sullivan delivers newspapers for the Tribune dispatch. She receives 18.2 cents per paper, six days a week (for the daily paper), and $.70 for the Sunday paper. She delivers 124 daily papers each day and 151 Sunday papers each week what is your total pay.
Answers
Answer:
About $241.11
Step-by-step explanation:
So, Karen receives 18.2 cents per paper.
She delivers 124 paper per day.
In other words, on days other than Sunday, she will make a total of:
\(18.2(124)=2256.8\text{ cents}\)
On Sunday, each paper is sold for $0.70 or 70 cents. She also sells 151 Sunday papers. Thus, on a Sunday, she will make a total of:
\(70(151)=10570\text{ cents}\)
Therefore, in one week, she will do the first equation six times and the Sunday equation once. Thus, her total pay will be:
\(6(2256.8)+10570=24110.8\text{ cents}\approx\$241.11\)
find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→[infinity] x tan(2/x)
Answers
The limit is :lim x→[infinity] x tan(2/x)= 2
To determine the limit:
lim x→[infinity] x tan(2/x)
Using derivatives, the L'hospital rule can be used to evaluate limits involving indeterminate forms.
A limit with an ambiguous form is one that does not provide enough information to determine the original limit.
It is a crucial rule in Calculus.
We can use derivatives to find the value of certain types of limits using this rule.
L'Hospital's rule can be applied.
To do so, we take the denominator's and numerator's derivatives with respect to x.
lim x→[infinity] x tan(2/x)
= lim x → ∞ tan(2/x)/1/x
[as x → ∞, 1/x→0]
=>2 lim 1/x → 0 tan(2/x)/2/x
=> 2 lim Ф → 0 sec²2Ф
=> 2× sec²0
=> 2
Therefore,
lim x→[infinity] x tan(2/x)= 2
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true or false: 3x^2+5x^3=8x^3
Answers
Answer:
false
Step-by-step explanation:
A sweatshirt is discounted 30%. If the discount is $9, what was the original price of the sweatshirt? Please show your work.
Answers
Answer:
$30
Step-by-step explanation:
Let the price of sweatshirt be $x.
Discount percentage = 30%
Discount in dollars = 30% of $x
Discount in dollars = 30/100 of $x = $ 30x/100
Given that discount in $ is 9
thus
30x/100 = 9
x = 9*100/30 = 30
Thus, the original price is $30
Determine if the lines through each pair of points are parallel, perpendicular, or neither.(5, 10) and (1, 6), (2,-6) and (-1, -3)-parallel-perpendicular -neither
Answers
Perpendicular
Explanation:Find the slope for the points (5, 10) and (1, 6)
\(x_1=5,\text{ y}_1=10,\text{ x}_2=1,\text{ y}_2=6\)The slope is calculated below
\(\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ \\ m_1=\frac{6-10}{1-5} \\ \\ m_1=\frac{-4}{-4} \\ \\ m_1=1 \end{gathered}\)For the points (2,-6) and (-1, -3)
\(\begin{gathered} m_2=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ m_2=\frac{-3-(-6)}{-1-2} \\ \\ m_2=\frac{-3+6}{-3} \\ \\ m_2=\frac{3}{-3} \\ \\ m_2=-1 \end{gathered}\)Note that:
\(\begin{gathered} m_1m_2=1(-1) \\ \\ m_1m_2=-1 \end{gathered}\)Since the product of the two slopes is -1, the lines through the pairs of points are perpendicular
The sum of Sharon's and John's ages is . Sharon is times as old as John. If you let Sharon's age and John's age, then the problem can be represented by a system of equations. Which of the following shows a graph of this system and the solution to this problem?
Answers
Answer:
A
Step-by-step explanation:
Im pretty sure its A because
55ish plus 15ish equals 70 which is their ages combined
55-60 is also 4 x 15
Graph A shows the system and solution to the system. Option A is correct.
The sum of Sharon's and John's ages is 70. Sharon is times as old as John. The system of equations regarding the problem is determined.
The equation is the values of two expressions that are equal.
Let the age of Sharon's be x and Jhon's be y.
The sum of Sharon's and John's ages is 70.
x + y = 70 - - - - (1)
Sharon is times as old as John.
x = 4 y
Now put x = 4y in equation 1
4y + y = 70
5y = 70
y = 70/5
y = 14
Now put y = 14 in x = 4y
x = 4*14
x = 56
The solution of a system of equations is (14, 56) shown in graph 1.
Thus, graph A shows the system and solution to the system. Option A is correct.
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What is the relationship between the diameter d and circumference c of a circle
Answers
Answer:
π × d
Step-by-step explanation:
The relationship between the diameter and circumference is that the circumference is equal to π multiplied by the diameter. This means that our answer is π × d, or the third option
A triangle has sides with lengths of 10, 15, and 6 feet. Find the perimeter of a similar triangle whose shortest side is 7
Answers
Answer:
P = 36 1/6 feet
Step-by-step explanation:
you can create the following proportion:
6 / 7 = 10 / x
cross-multiply:
6x = 70
x = 11 2/3
use the same ratio to write a second proportion to find the last side:
6 / 7 = 15 / x
cross-multiply:
6x = 105
x = 17 1/2
Perimeter = 7 + 11 2/3 + 17 1/2 = 28 7/6 + 7 = 29 1/6 + 7 = 36 1/6 feet
What is the range of the function f (1) 4 when the domain is {-3, 0. 4)? {-10. 0. 4) G. {-10. -4.4) H
Answers
Range of a function are the output values of the function:
since the domain is (-3, 0, 4), then we have to substite x with this values:
f(x)=2(-3)-4
f(x)=-6-4
f(x)=-10
f(x)=2(0)-4
f(x)=-4
f(x)=2(4)-4
f(x)=4
Range of the function is (-10, -4, 4)
3a(12+5a-1a^²=
how do u do it
Answers
Answer:
36a + 15a^2 - 3a^3
Step-by-step explanation:
I recommend using a calculator. It helps a lot.
If you're not going to do that, then all you do is multiply the 3a by the 12, tha 5a, and the 1a.
(Projectile Motion) Mary is outside her apartment building. She needs to pass her key to John, who is 6 m above the ground floor of the building. Mary has no time to run upstairs, so she throws the key towards John. Suppose the height, h m, of the key above the ground floor at time t seconds is given by h = -11t² + 20t + 1. Is it possible for John to catch the key? Justify your answer.
Answers
-11t^2 + 20t + 1 = 6
-11t^2 + 20t - 5 = 0
Now we can use the quadratic formula to solve for t:
t = (-b ± √(b^2 - 4ac)) / 2a
where a = -11, b = 20, and c = -5
t = (20 ± √(20^2 - 4(-11)(-5))) / 2(-11)
t = (20 ± √(400 + 220)) / -22
t = (20 ± √620) / -22
t = (20 ± 2√155) / -22
t = (20 ± 2√3 * 5^2) / -22
t = (20 ± 2 * 15) / -22
t = (20 ± 30) / -22
t = (-10 ± 30) / -22
t = (-10 + 30) / -22 = 20 / -22 = -15 / 11
t = (-10 - 30) / -22 = -40 / -22 = 20 / 11
There are two solutions for t: -15 / 11 and 20 / 11. However, the time can not be negative as it represents the amount of time that has passed. Therefore, the only valid solution is t = 20 / 11.
So, the key reaches John's height at t = 20 / 11 seconds, which means it is possible for John to catch the key
a circle is inscribed in a triangle with side lengths 8, 138,13, and 1717. let the segments of the side of length 88, made by a point of tangency, be rr and ss, with r
Answers
The ratio of \(r:s = 1:3\).
Label our triangle ABC where,
AB=17, AC=13, and BC=8.
Let L, J, and K be the tangency points of BC, AC, and AB respectively.
Let \(AK=x\), which implies \(AJ=x\). Thus \(KB=BL=17-x\) and \(JC=LC=13-x\)
\(\because BL+LC = (17-x)+(13-x) = 8 & x = 11\)
\(\therefore r:s = CL:BL = 13-x:17-x = 2:6\)
\(\text{Hence, } r:s = 1:3\)
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help is highly appreciated
Answers
Answer:
Step-by-step explanation:
2-(-1\8)±-7\4 then
2 plus 1\8 plus -7\4
2 plus 1\8 plus -14\8
2 -13\8
2= 16/8
3\8?
Answer:
3/8
Step-by-step explanation:
Substitute given information into given equation
b=2, c=-7/4
2-(-1/8) + - 7/4
Make 2 into 16/8 (by multiplying it by 8/8 To make denominator the same)
16/8 -(-1/8) + -7/4
17/8 (Because when negative and negative will make positive)
17/8+ -7/4
Make -7/4 into -14/8 (by multiplying it by 2/2 To make denominator the same)
17/8 -14/8 (Because negative and positive will make negative)
3/8 is the final answer
I hope this helps, dont hesitate to ask for any question.
Mark me as brainliest is appreciated.Tq!!
A company sells a regular version of software for $17.45 and a deluxe version for $21.95. The company gives a bonus to any salesperson who sells at least
100 units and has at least $2000 in total sales. Complete parts a through c below.
a. Write a system of inequalities that describes the requirements a salesperson must meet to receive the bonus. Let R represent the number of regular
units sold and D represent the number of deluxe units. Choose the correct system of inequalities below.
OA.
O C.
O A.
AD
R+Dz 100
17.45R+21.95D z 2000
120-
R+Dz 100
17:45R+21.95D = 2000
b. Solve the system by graphing. Let the horizontal axis be the regular version and the vertical axis be the deluxe version. Choose the correct graph
below.
B.
AD
B.
120-
O D.
O C.
AD
R+D≤ 100
17.45R+21.95D ≤ 2000
120-
R+D≤ 100
17.45R+21.95D z 2000
Q
D.
AD
120-
Answers
The graph of the system of inequalities is a circle with center (0,0) and radius of 100 units for the regular version and 2000/21.95 units for the deluxe version.
What is inequality?Inequality in math is a mathematical statement that states two expressions are not equal. It can be written using symbols such as <, >, or ≠. Inequality statements are used to compare values or expressions and to describe ranges of values that satisfy certain conditions.
The salesperson must sell at least 100 units of either the regular or deluxe version and their total sales must be at least $2000 in order to receive the bonus.
The company offers a bonus to salespeople who can meet certain sales goals. This encourages salespeople to be more motivated to sell the product and to increase their overall sales. It also helps the company increase their profits by providing incentives for salespeople to increase their sales. By offering the bonus, the company is able to attract more salespeople who are willing to work hard and reach their sales goals in order to receive the bonus. This allows the company to increase their market share and their profits.
The bonus also helps to retain existing salespeople who might otherwise be tempted to leave the company. By offering the bonus, the company is able to reward loyal salespeople who have consistently performed well and have contributed to the company's success. This helps the company to maintain a stable and productive sales team, which is beneficial for the company's long-term success.
Overall, offering a bonus to salespeople who meet certain sales goals is a beneficial strategy for the company. It encourages salespeople to be more motivated and increase their sales, while also helping the company to attract and retain quality salespeople. This helps the company to grow and increase their profits in the long run.
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A vase contains 60 marbles, all of which are red or orange. if the ratio of red marbles to orange ones is 1:5, what is the total number of red marbles in the vase?
Answers
The total number of red marbles in the vase are 10.
What is the ratio?A ratio is described as a comparison between two amounts with the same unit to determine the amount of 1 quantity is contained in the other. Ratios are divided into two sorts.
The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groupings.
Now, according to the question;
Let 'x' be the red marbles in the vase.
Let 'y' be the orange marbles in the vase.
The total number of marbles in the vase are 60
x + y = 60 (equation 1)
The ratio of red marbles to orange ones is 1:5.
Thus, x/y = 1/5
cross multiplying;
5x = y
or y = 5x
substitute the value of y in equation 1;
x + y = 60 (equation 1)
x + 5x = 60
6x = 60
x = 10 (red marbles)
Thus, the number of red marbles in the vase are 10.
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What is the circumference of a circle with a diameter of 24 inches ?
Answers
Answer:
75.4
Step-by-step explanation:
The circumference of the circle whose diameter is 24 inches is 75.36 inches.
We have,
A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius).
Given:
The diameter of the circle, d = 24 inches,
Calculate the circumference of the circle as shown below,
we know that,
Circumference is:
C = 2 × π r
= π d
so, we get,
C = π × 24
Calculate the circumference as shown below,
C = 3.14× 24
we know that,
24x3.14 = 75.36
C = 75.36
Thus, the circumference is 75.36 inches.
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find the value of x for which the fraction 4x +9/7x
Answers
Answer:
x = 3
Step-by-step explanation:
Here ,
4x + 9 =7x
--> 4x - 7x = -9
--> -3x = -9
--> ≠ x = -9/3
--> x = 3
10.) In a simple linear regression analysis on n=100 observations, the following results are produced:
SST= 500, SSE= 100
Which of the following is true?
14.) In a simple regression analysis, if the standard error of estimate is 15 and the number of observations is 10 then the sum of the residual squared must be 120.
15.) In a multiple regression problem involving 35 observations and five explanatory variables
SST= 900 and SSE is 460. The value of the F ratio for testing the significance of this model is 15.56.
Please show Excel work.
Answers
The value of the F ratio for testing the significance of this model is not 15.56.
For question 10, in a simple linear regression analysis, SST represents the total sum of squares, which measures the total variation in the dependent variable. SSE represents the sum of squared errors, which measures the variation that is not explained by the regression model.
To determine which statement is true, we need to compare the values of SST and SSE.
Now let's move on to question 14. The standard error of estimate is a measure of the variability of the observed values around the regression line. It is not directly related to the sum of the residual squared.
Therefore, the statement that the sum of the residual squared must be 120 is not necessarily true.
Lastly, for question 15, the F ratio is used to test the overall significance of a multiple regression model. It compares the explained variation (SST - SSE) with the unexplained variation (SSE) and takes into account the number of observations and number of explanatory variables.
Given that SST is 900 and SSE is 460, we can calculate the F ratio as follows:
F = ((SST - SSE) / number of explanatory variables) / (SSE / (number of observations - number of explanatory variables))
F = ((900 - 460) / 5) / (460 / (35 - 5))
F = 440 / 460
F ≈ 0.9565
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Jon borrows 5.50 from his friends to pay for snacks, and 12.75 from his sister to go the movies. How much does he need to repay
Answers
Answer:
18.25
Step-by-step explanation:
Add 5.50 and 12.75
5.50 + 12.75 = 18.25
Answer: 18.25
Step-by-step explanation:
A parachutist's speed during a free fall reaches 50 meters per second. What is this speed in feet per second? At this speed, how many feet will the parachutist fall during 15 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Please make sure to show your work, thanks! :)
Answers
Answer:
3280
Step-by-step explanation:
50 m ≅ 164 ft (3s.f.)
50 m/s ≅ 164 ft/s
distance after 20 s:
d = 164 ft/s ⋅ 20 s
= 3280 ft
solve for x 7 x + 6 / 4 = 2 x − 3 / 5 Give your answer as an improper fraction in its simplest form.
Answers
x = -14/9 is the solution to the equation ( 7x + 6 )/4 = ( 2x − 3 )/5 in a simplified improper fraction form.
What is the value of x in the given equation?Given the data in the question;
( 7x + 6 )/4 = ( 2x − 3 )/5x = ?To solve for x, first we cross multiply
( 7x + 6 )/4 = ( 2x − 3 )/5
5( 7x + 6 ) = 4( 2x − 3 )
Remove the parenthesis using distributive property
7x×5 + 6×5 = 2x×4 − 3×4
35x + 30 = 8x - 12
Collect like terms by moving all terms containing x to the left and all constant terms to the right side of the equation.
35x - 8x = -12 - 30
27x = -12 - 30
27x = -42
Divide both sides by 27
27x/27 = -42/27
x = -42/27
x = -14/9
Therefore, the value of x in the given equation ( 7x + 6 )/4 = ( 2x − 3 )/5 is -14/9.
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Answer:
2/3
Step-by-step explanation:
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Answers
Answer:
Hey! so the answer is X=7 and Y=6
Step-by-step explanation:
if you look at the pattern you'll see it adds up to 7 and 6 everytime so those are the answers.
Hoped this helped Im Eve btw. Hope you have a great day and consider marking this brainliest Thank you so much if you do! ✨
I need more assistance :D Instructions: Using the image, find the distance between the points given on the graph.
Answers
Answer:
I usually explain even in the answer.
So we use som\(\sqrt{x}\)ething called distance formula which is branched of Pythagorean theorem.
But we dont need to as it just makes it more complicated. We need to find split into 2 vectors, one vertical, and horizontal. The horizontal is 5 long.
The vertical is 1, you can find them by calculating how long is it and how tall.
Use pythogorean theorem from the formula and do 5^2+1^2 = c^2
25+1 = 26, so the answer is √26
I am pretty sure answer is right. Always take abolute value
√26
Two families go to a zoo.
The Smith family of two adults and three children pay £61.
The Jones family of three adults and five children pay £96.
Work out the cost of an adult ticket and the cost of a child ticket.
In your working, let 'a' stand for an adult ticket and 'c' stand for a child ticket.
Answers
Answer:
child = $9
adult = $17
Step-by-step explanation:
Two families go to a zoo. The Smith family of two adults and three children pay £61. The Jones family of three adults and five children pay £96. Work out the cost of an adult ticket and the cost of a child ticket. In your working, let 'a' stand for an adult ticket and 'c' stand for a child ticket.
Family 1: 2a + 3c = 61
Family 2: 3a + 5c = 96
solve family 1 in terms of a:
2a + 3c = 61
subtract 3c from both sides:
2a + 3c - 3c = 61 - 3c
2a = 61 - 3c
divide both sides by 2:
2a/2 = (61 - 3c)/2
a = 61/2 - 3/2c
plug [a = 61/2 - 3/2c] into Family 2 equation:
3a + 5c = 96
3(61/2 - 3/2c) + 5c = 96
multiply:
3(61/2 - 3/2c) + 5c = 96
91.5 - 4.5c + 5c = 96
subtract 91.5 from both sides:
91.5 - 4.5c + 5c - 91.5 = 96 = 91.5
- 4.5c + 5c = 4.5
combine left side:
0.5c = 4.5
divide both sides by 0.5:
0.5c/0.5 = 4.5/0.5
c = 9
Now solve for a. We will use Family 1 equation:
2a + 3c = 61 where c = 9
2a + 3(9) = 61
2a + 27 = 61
subtract 27 from both sides:
2a + 27 - 27 = 61 - 27
2a = 34
divide both sides by 2:
2a/2 = 34/2
a = 17
__________________________________________
Let's check out numbers:
where c = 9 and a = 17
Family 1: 2a + 3c = 61
2(17) + 3(9) = 61
34 + 27 = 61
61 = 61
Family 2: 3a + 5c = 96
3(17) + 5(9) = 96
51 + 45 = 96
96 = 96
HELLLLPPPP MEEEEEE!!!!!!
Answers
Answer:
B I believe correct me if I'm wrong
Oscar charges $25 for the first hour of tutoring and $15 for each additional hour or fraction of an hour counting as a whole hour.
The rates that Latoya charges for x hours of tutoring are modeled with the function shown.
f(x)=30x,0≤x≤3
20x,3 6
(Imagine this stuff above as a piecewise function)
Complete to make a true sentence.
____ will charge $ ____ more to tutor for 5.5 hours.
Answers
Answer and explanation:
Since Oscar charges $25 for the first hour and $15 for every additional hour or fraction of an hour, his function would be :
f(x)= 25x 0 is less than or equal to x and x is less than or equal to 1
Latoya charges $30 for the first three hours and $20 for every additional hour or fraction of an hour. The function :
f(x)= 30x
0 is less than or equal to x and x is less than or equal to 3
Given that each taught their students for 5.5 hours, their charges would be :
For Oscar,
The first hour = 25×1= $25
4.5 hours left= 15×4.5= $67.5
Total charge for 5.5 hours= $67.5+$25= $92.5
For Latoya,
The first three hours= 30×3=$90
2.5 hours left= 2.5×20= $50
Total charge for 5.5 hours= $90+$50= $140
Therefore Latoya will charge $47.5 more to tutor for 5.5 hours.
Question 6(Multiple Choice Worth 4 points)
(02.05 LC)
Which of the following statements best describes the effect of replacing the
graph of y = f(x) with the graph of y = f(x) + 20?
The graph of y = f(x) will shift left 20 units.
The graph of y = f(x) will shift down 20 units.
The graph of y = f(x) will shift up 20 units.
The graph of y = f(x) will shift right 20 units.
Answers
Answer:
the graph will shift 20 units up
make y the subject of formula 2y=3x-2
Answers
Answer:
\(2y = 3x - 2 \\ y = \frac{3x - 2}{2} \\ y = \frac{3}{2} x - 1 \\ thank \: you\)
Answer:
y=3x-2÷2
Step-by-step explanation:
2y=3x-2
solution
cross multiple 2y=3x-2 and make y the subject of the formula,so y now is equal to 3x minus 2 divided by 2.0.5 ( 5 − 7 x ) = 8 − ( 4 x + 6 )
Answers
Answer:
Well,
\(0.5(5-7x)=8-(4x+6)\\-3.5x+2.5=-4x+2\\0.5x+2.5=2\\0.5x=-0.5\\x=-1\)
Step-by-step explanation:
Hope this helps!^^
Answer: -1
Step-by-step explanation:
first you want to simplify 0.5 (5-7x) which will get you 2.5 - 3.5x
then you will do the same for the other side move the xs to one side then treat it like any other problem