Pls help I will give Brainliest

Find dx/dt when y=2 and dy/dt=1, given that x^4=8y^5-240<br><br> dx/dt=

katrin2010 [14]

Answer:

The value of $\frac{dx}{dt}$ is $\frac{160}{x^3}$ .

Step-by-step explanation:

The given equation is

$x^4=8y^5-240$

We need to find the value of $\frac{dx}{dt}$ .

Differentiate with respect to t.

$4x^3\frac{dx}{dt}=8(5y^4)\frac{dy}{dt}-0$ $[\because \frac{d}{dx}x^n=nx^{n-1},\frac{d}{dx}C=0]$

$4x^3\frac{dx}{dt}=40y^4\frac{dy}{dt}$

It is given that y=2 and dy/dt=1, substitute these values in the above equation.

$4x^3\frac{dx}{dt}=40(2)^4(1)$

$4x^3\frac{dx}{dt}=40(16)(1)$

$4x^3\frac{dx}{dt}=640$

Divide both sides by 4x³.

$\frac{dx}{dt}=\frac{640}{4x^3}$

$\frac{dx}{dt}=\frac{160}{x^3}$

Therefore the value of $\frac{dx}{dt}$ is $\frac{160}{x^3}$ .

4 0

3 years ago

Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v, and w.

brilliants [131]

Answer:2

Step-by-step explanation:

5 0

2 years ago

Sarah would like to purchase a new camera that costs x dollars. She also wants to

Cerrena [4.2K]

The price of camera Sarah can afford given a savings of $500 and cost of camera lens of $130 is $370

Cost of a new camera = $x
Cost of camera lens = $130
Amount Sarah saved = $500

<h3>The equation</h3>

The cost of new camera = Amount Sarah saved - Cost of camera lens

x = $500 - $130

x = $370

Therefore, the approximation of $370 to 2 decimal point is $370.00

Learn more about equation:

brainly.com/question/16863577

5 0

3 years ago

Are these functions? (Explanation please)

Gnom [1K]

Answer:

1 is not a function because it is not a consistent pattern

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

3

leva [86]

Answer: The correct answer is:

______________

→ Choice: [C]: " $\frac{2}{1} * \frac{7}{-2}$ " .

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Step-by-step explanation:

______________

Note that this problem contains multiplication and division.

WIth multiplication and division;

the order of operations we perform is from "left side to right side" in the expression; in the order in which the operation occurs:

As such:

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The given problem:

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" $\frac{-3}{4} * \frac{7}{-2}$ ÷ $\frac{3}{-8}$ " ;

Is treated as:

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" $(\frac{-3}{4} * \frac{7}{-2})$ ÷ $\frac{3}{-8}$ " ;

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So, we start with:

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" $\frac{-3}{4} * \frac{7}{-2}$ " ;

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→ $\frac{-3}{4} * \frac{7}{-2} = \frac{(-3*7)}{[4*(-2) ]} = \frac{-21}{-8}$ ;

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Simplify:

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" $\frac{-21}{-8} = \frac{(-1)*21}{(-1) *8}$ " ;

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→ The "(-1)'s " cancel out:

{since: "(-1)/(-1) = 1 "} ;

→ And we have: " $\frac{21}{8}$ " ;

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Now, continue with the problem, and divide this value by: " $\frac{3}{-8}$ " ;

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" $\frac{21}{8}$ ÷ $\frac{3}{-8}$ " ;

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Note that dividing by a number is the same as multiplying by the reciprocal of that said number:

______________

The reciprocal of " $\frac{3}{-8}$ " ; is: " $\frac{-8}{3}$ : l

As such:

" $\frac{21}{8}$ ÷ $\frac{3}{-8}$ " ;

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= " $\frac{21}{8} * \frac{-8}{3}$ "

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Now, let us simplify:

Note: The "8" and the "-8" ;

The "8" can be changed to "1" ; and the "-8" can be changed to "-1" ;

since: "-8 ÷ 8 = 1 " ; and since: "8 ÷ 8 = 1 " ;

Note: The "3" and the "21" ;

The "3" can be changed to "1"; and the "21" can be changed to "7" ;

since: "21 ÷ 3 = 7 " ; and since: "3 ÷ 3 = 1 " ;

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And we can we rewrite the expression:

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→ " $\frac{7}{1} * \frac{-1}{1}$ " ;

which equals: " 7 * -1 " ; which equals " - 7 ".

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Now, the problem has 4 (four) answer choices. Which expression [i.e. which answer choice] is equal to: " -7 " ??

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Consider Choice [A]: " $\frac{1}{2} * \frac{7}{2}$ " ; which equals: " $\frac{(1*7)}{(2*2)} = \frac{7}{4} = 1\frac{3}{4}$ " ;

" $1\frac{3}{4} \neq -7$ ."

Rule out: "Choice [A]."

______________

Consider Choice: [B]: " $\frac{2}{1} * \frac{7}{2}$ " ; which equals: " $\frac{(2*7)}{(1*2)} = \frac{14}{2} = 7$ ; " $7\neq -7$ ."

Rule out: "Choice: [B]."

______________

Consider Choice: [C]: " $\frac{2}{1} * \frac{7}{-2}$ " ; which equals: " $-7$ ; " $-7 = -7$ ".

Choice [C]: seems correct!

______________

Consider Choice: [D]: " $\frac{-1}{2} * \frac{7}{-2}$ " ; which equals:

" $\frac{(-1*7)}{(2*-2)} = \frac{-7}{-4} = \frac{(-1)*7}{(-1)*4}$ ;

→ cancel out the "(-1)'s" ;

→ {since: "(-1) / (-1) = 1 " ;

to get:

→ " $\frac{7}{4}$ " ; which equals:

→ " $1\frac{3}{4}$ " ; " $1\frac{3}{4} \neq -7$ . "

Rule out: "Choice: [D]."

______________

The correct answer is:

______________

Choice: [C]: " $\frac{2}{1} * \frac{7}{-2}$ " .

______________

Hope this is helpful to you!

Wishing you the best!

______________

4 0

3 years ago