Given the function y=-\frac{3\sqrt{x^5}}{4},y=− 4 3 x 5 ​ ​ , find \frac{dy}{dx}. dx dy ​ . Express your answer in radical form without using negative exponents, simplifying all fractions.

Answers

Answer 1

Given:

The function is:

[tex]y=-\dfrac{3\sqrt{x^5}}{4}[/tex]

To find:

The value of [tex]\dfrac{dy}{dx}[/tex].

Solution:

We have,

[tex]y=-\dfrac{3\sqrt{x^5}}{4}[/tex]

It can be written as

[tex]y=-\dfrac{3}{4}x^{\frac{5}{2}}[/tex]        [tex][\because \sqrt[n]x=x^\frac{1}{n}][/tex]

Differentiate with respect to x.

[tex]\dfrac{dy}{dx}=-\dfrac{3}{4}\times \dfrac{5}{2}x^{\frac{5}{2}-1}[/tex]       [tex][\because \dfrac{d}{dx}x^n=nx^{n-1}][/tex]

[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{5-2}{2}}[/tex]

[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{3}{2}}[/tex]

[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}\sqrt{x^3}[/tex]

Therefore, the value of [tex]\dfrac{dy}{dx}[/tex] is [tex]-\dfrac{15}{8}\sqrt{x^3}[/tex].


Related Questions

If the number of hours you hours you work is proportional to the amount of money you earn per hour, which og tye following statements is true?​

Answers

Answer:

it should be a

Step-by-step explanation:

if you work for $10 an hour, and work for 2 hours, you make $20 but if you double the hours worked, so 4 hours, you make $40, which is double the hours, and double the money

CAN SOMEONE PLEASE HELP ME

Answers

corresponding angles are angles that the transversal line cuts across two straight lines and are congruent

Find an equation for the line below

Answers

I’ve attached my work below...
Hope this helps!
y=-1/2x+4.5
y=mx+b
first do rise over run so it goes down 3 units and to the right 6 units then you simplify 3/6 to the smallest fraction which would be 1/2 and since the line is going down horizontally the slope(1/2) would be negative then you simply see where the line crosses the y-axis and that is the "b"(4.5) for the equation now all you gotta do is plug in the numbers and you get
y=-1/2x+4.5

You buy a car for $8,000 that depreciates at a rate of 11% a year. How much is the car worth after 5 years?

Answers

The correct answer for this question would be about $4,467.2 according to my estimation.

If it’s not correct, I’m sorry, but if it is, please mark the brainliest!!

Plz, answer this question plz!

Answers

Answer:

the second option im pretty sure

Answer:

4/48. I don't know for sure, but I think B is the correct answer

i need help with 5 pls!!! I’ll give brainliest:)

Answers

EZ THATS 3RD GRADE MATH ANSWER IS 154

Find the sum.
5y+2/xy^2 + 2x-4/4xy

Answers

[tex]\frac{5y+2}{xy^2}[/tex]+[tex]\frac{2x-4}{4xy}[/tex]=[tex]\frac{xy+8xy+4}{2xy^2}[/tex]

or just (xy+8y+4)/2xy^2 if u can't see the equation

The value of the expression using sum will be (8y + xy + 4) / (2xy²).

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ [(5y + 2) / (xy²)] + [(2x - 4) / (4xy)]

Simplify the expression, then we have

⇒ [(5y + 2) / (xy²)] + [(2x - 4) / (4xy)]

⇒ [4(5y + 2) / (4xy²)] + [y(2x - 4) / (4xy²)]

⇒ [(20y + 8) / (4xy²)] + [(2xy - 4y) / (4xy²)]

⇒ (20y + 8 + 2xy - 4y) / (4xy²)

⇒ (16y + 2xy + 8) / (4xy²)

⇒ (8y + xy + 4) / (2xy²)

The value of the expression using sum will be (8y + xy + 4) / (2xy²).

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ5

I can’t download anything so if anyone can find a way to help with this I’d be grateful (^_^)

Answers

It's hard to explain by words so sorry if you don't understand. For the graphing part, starting from (-3, 0), plot points in (1, 2), (6, 3), and connect them. The end of a line should be (10, 3.5). You will understand better if you use graphing calculator.

The answer of a second question is {x|x is greater or equal to -3.

The marked price of a refrigerator is $1660. John has a coupon for 15% off. Find the selling price of the refrigerator with the coupon

Answers

Answer:

answer is selling price=$1411

Step-by-step explanation:

discount percentage=100%-15%=85%

Ok thank you That helped me too

leaf plot.
Name
Stem & Leaf Plots DOL
1. The total number of cupcakes sold in a fund-raiser is shown in the stem and
STEM
LEAF
1| 2 3 5 5 5 5
2| 34 479
3| 0 2 5 6 77
Which statement is best supported by the data in the stem and leaf plot?
A. The range of the number of cupcakes sold is 27.
B. The range of the number of cupcakes sold is 19.
6 The most common number of cupcakes sold is 15.
D. The most common number of cupcakes sold is 30.

Answers

Answer:

C.

Step-by-step explanation:

there are 4 15's, which is the most thing repeated.

CCCCCCCCCCCCCCCCCCCC

The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):

A graph with two linear functions; f of x passes through 5, 0 and 10, 10, and g of x passes through negative 3, 0 and 2, 10.

Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)

Part B: Solve for k in each type of transformation. (4 points)

Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Answers

Answer:

A linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If this line passes through the points (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

We know that line f(x) passes through points (5, 0) and (10, 10)

Then the slope of f(x) is:

a = (10 - 0)/(10 - 5) = 10/5 = 2

then:

f(x) = 2*x + b

again, knowing that f(10) = 10   (because this line passes through point (10, 10) )

10 = 2*10 + b

10 = 20 + b

10 - 20 = b = -10

Then the equation of this line is:

f(x) = 2*x - 10

Now for g(x) we know that it passes through (-3, 0) and (2, 10)

then the slope is:

a = (10 - 0)/(2 - (-3)) = 10/5 = 2

g(x) = 2*x + b

And knowing that g(2) = 10   (because this line passes through point (2, 10) )

10 = 2*2 + b

10 = 4 + b

10 - 4 = b

6 = b

then:

g(x) = 2*x + 6

Then the equations are:

f(x) = 2*x  - 10

g(x) = 2*x + 6

A) One transformation may be a vertical translation, and the other can be a horizontal translation.

This is a vertical translation, which is defined as:

For a function f(x), a vertical translation of k units is written as:

g(x) = f(x) + k

If k is positive, the translation is upwards

if k is negative, the translation is downwards.

And an horizontal translation of k units is written as:

g(x) = f(x - k)

if k is positive, the translation is to the right

if k is negative, the translation is to the left.

B)

For the vertical translation we have:

g(x) = f(x) + k

2*x + 6 = 2*x  - 10 + k

6 = -10 + k

6 + 10 = k

16 = k

For the horizontal translation we have:

g(x) = f(x - k)

2*x + 6 = 2*(x - k) - 10

2*x + 6 = 2*x - 2*k - 10

6 = -2*k - 10

6 + 10 = -2*k

16 = -2*k

16/-2 = k

-8 = k

C)

The transformations are:

g(x) = f(x) + 16

or

g(x) = f(x - (-8))

) 0 Solve the following equation for x. - 4 (1 – 3x) + 4x = -100 what is x?​

Answers

Step-by-step explanation:

4 (1 – 3x) + 4x = -100

4-12x+4x=-100

-12x+4x=-100-4

-8x=-104

x=-104/-8

x=13

Answer:

x = − 12

Step-by-step explanation:

luis has a cooler full of soda. For every 5 cans of coke there are 3 cans of sprite. if there are 25 cans of coke, how many cans of sprite are there?

Answers

Answer: 15 cans of sprite

Step-by-step explanation:

5 cans of coke and 3 cans of sprite

then its

25 cans of coke and 15 cans of sprite

What is the number in What is 95% of 60

Answers

Answer:

57

Step-by-step explanation:

57 is 95% of 60

(See image below for more information)

Hopefully this helps :3 Sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

-Bee~

The volume of a rectangular prism is 300 ft 3 . If the area of the base is 12 ft 2 , what is its height?

15 feet
24 feet
12 feet
25 feet

Answers

Answer: pretty sure 25 feet

Step-by-step explanation:

Solve for x'if3 - 2x 35-*.​

Answers

Answer:

-16..

Step-by-step explanation:

the question is not clear

choosing a purple green black or silver bike having 10, 18, 21 or 24 speeds

Answers

Answer:

for me the good one is black with 18 speed

Answer:

Black with 18 speeds

Step-by-step explanation:

help me please help me please

Answers

2=10
3 =15
7=35
1=5
Constant of 1 is 5
5+10=15+15=30+30=60+60=120+120=240+240=480+480=960

look at this table
is this relation a function​

Answers

Answer:

i believe function !

Step-by-step explanation:

cuz im smart

Answer:

No

Step-by-step explanation:

The tables shows two inputs that are the same value which is not possible in a function

Let’s say we are using 12 inch diameter balloons filled with helium to lift objects off of the surface.

*Let’s say that 5 balloons can lift 60 grams of weight.

What is the unit rate for weight/balloon? ________

Answers

Answer:

its 12

Step-by-step explanation:

Calculate the area of the right - angled triangle with base of 18cm and height 6.5cm

Answers

Answer:

area = 58.5 cm²

Step-by-step explanation:

area = 18 x 6.5 x 0.5 = 58.5 cm²

HELPPPPPPP MEEEEEEEEEE

Answers

Answer:

A. (0,1) and (1,2)

Step-by-step explanation:

I graphed it

from a point 12 ft from the base of a building, the angle of elevation from the ground to the top of the building is 70 degrees. Which is the closest to the height of the building​

Answers

Answer:

c 33ft .....

Step-by-step explanation:

c is correct

The possible height of the building is 33 ft.

What is Angle of Elevation?

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

Here, Let the height of the building be x ft

           Base = 12ft.

          Angle of Elevation = 70⁰

Now, tan α = perp. / base

         tan 70⁰ = x/12

         2.74 = x/12

          x = 12 X 2.75

          x = 33

Thus, the possible height of the building is 33 ft.

Learn more about Angle of Elevation from:

https://brainly.com/question/21137209

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.necesito resolver estas operaciones con factorial ayuda por favor



- A= (4ǃ+2ǃ+3ǃ)/(3ǃ+2ǃ)


2. (6ǃ-4ǃ)/2ǃ

2ǃx3ǃx4ǃ/(5ǃ+4ǃ)


R = 10ǃx8ǃ/(6ǃ+5ǃ)


((x+5)ǃ(x+3)ǃ)/((x+4)ǃ+(x+3)ǃ)=6ǃ

Answers

Answer:

A. 4

B. 348

C. 2

D. 174182400

E. x = 2

Step-by-step explanation:

Given - A= (4ǃ+2ǃ+3ǃ)/(3ǃ+2ǃ)

             B = (6ǃ-4ǃ)/2ǃ

             C = 2ǃx3ǃx4ǃ/(5ǃ+4ǃ)

             D = 10ǃx8ǃ/(6ǃ+5ǃ)

             E -  ((x+5)ǃ(x+3)ǃ)/((x+4)ǃ+(x+3)ǃ)=6ǃ

Proof -

A.

(4! + 2! + 3! )/ (3! + 2!) = [4×3×2! + 2! + 3×2!] / [3×2! + 2!]

                                  = 2! [ 4×3 + 1 + 3] / 2! [3 + 1]

                                  = [12 + 1 + 3] / [4]

                                  = [16] / [4] = 4

⇒(4! + 2! + 3! )/ (3! + 2!) = 4

B.

(6ǃ-4ǃ)/2ǃ = [6×5×4! - 4!] / 2!

              = 4! [6×5 - 1] / 2!

              = 4×3×2! [ 30 - 1] / 2!

              = 12 [29] = 348

⇒(6ǃ-4ǃ)/2ǃ = 348

C.

2ǃx3ǃx4ǃ/(5ǃ+4ǃ) = 2!×3!×4! / [ 5×4! + 4!]

                         = 2!×3!×4! / 4! [ 5 + 1]

                         = (2×1) × (3×2×1) / 6

                         = 12 / 6 = 2

⇒2ǃx3ǃx4ǃ/(5ǃ+4ǃ) = 2

D.

10ǃx8ǃ/(6ǃ+5ǃ) = 10!×8! / [ 6×5! + 5!]

                      = (10×9×8×7×6×5×4×3×2×1) ×(8×7×6×5!) / 5! [6 + 1]

                      = (10×9×8×7×6×5×4×3×2×1) ×(8×7×6) / [7]

                      = (10×9×8×7×6×5×4×3×2×1) ×(8×6)

                      = 174182400

⇒10ǃx8ǃ/(6ǃ+5ǃ) = 174182400

E.

((x+5)ǃ(x+3)ǃ)/((x+4)ǃ+(x+3)ǃ)=6ǃ

[(x+5)(x+4)(x+3)! (x+3)!] / [ (x+4)(x+3)! + (x+3)! ] = 6!

[(x+5)(x+4)(x+3)! (x+3)!] / (x+3)!  [ (x+4)+ 1] = 6!

[(x+5)(x+4)(x+3)! / (  [ x+ 5 ] = 6!

(x+4)(x+3)! = 6!

(x+4)! = 6!

x+ 4 = 6

x = 6 - 4

x = 2

Note :

x! = x(x-1)(x-2).......(4)(3)(2)(1)


Enter 14% as a fraction in simplest form.

Answers

Answer:

0.14 or 7/50

Step-by-step explanation:

Does anyone know it?!

Answers

Answer:

x = 136º

Step-by-step explanation:

Answer:

x = 136º

Step-by-step explanation:

It is congruent to the angle with the measure of 136 degrees, so it will be 136.

Hope that helps!

jenna buys a clay pot at an art studio for $12. she rents a space at the studio per hour to decorate the pot​

Answers

What’s the full question?

Work out the mean for the data set below: 58002, 58003, 58002, 58003, 58003, 58005, 58003

Answers

Step-by-step explanation:

Mean x¯¯¯ 58003

Median x˜ 58003

Mode 58003

Range 3

Minimum 58002

Maximum 58005

Count n 7

Sum 406021

Quartiles Quartiles:

Q1 --> 58002

Q2 --> 58003

Q3 --> 58003

Interquartile

Range IQR 1

Outliers 58005

copy machine goes brr

help solve please!!!!

Answers

Answer:

60 squared cm

Step-by-step explanation:

If half of the top of the shape is 3, that means the whole top is 6.

6 x 10 = 60

Area = Length x Width

So, 3cm is only half so I think it would have to be changed to 6cm to be the full width. Then, is length X width, so 6 X 10 meaning it would be 60cm^2, I think.

What is the data range of the data below 625, 638, 619, 677, 638, 659

Answers

Answer:

58

Step-by-step explanation:

The range is the difference between the highest and the lowest numbers in the number set.

The highest number in this set is 677 and the lowest number is 619.

677 - 619 = 58

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