If a child weighs 83 pounds, how many ounces does she weigh?

Find dy/dx by implicit differentiation. y cos x = 5x2 + 3y2

lbvjy [14]

Step 1:
Start by putting $\frac{d}{dx}$ in front of each term

$\frac{d}{dx}[y cos x]= \frac{d}{dx}[5x^2]+ \frac{d}{dx}[ 3y^2]$
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Step 2:

Deal with the terms in 'x' and the constant terms
$\frac{d}{dx}[ycosx]= 10x+ \frac{d}{dx} [3y^2]$
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Step 3:

Use the chain rule for the terms in 'y'
$\frac{d}{dx}[ycosx]=10x+6y \frac{dy}{dx}$
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Step 4:

Use the product rule on the term in 'x' and 'y'
$(y) \frac{d}{dx} cos x+(cos x) \frac{d}{dx}y =10x+6y \frac{dy}{dx}
$
$y(-siny)+(cosx) \frac{dy}{dx} =10x+6y \frac{dy}{dx}$
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Step 5:

Rearrange to make $\frac{dy}{dx}$ the subject
$-y sin(y)+cos(x) \frac{dy}{dx} =10x+6y \frac{dy}{dx}$
$cos(x) \frac{dy}{dx}-6y \frac{dy}{dx}=10x+y sin(y)$
$[cos(x) - 6y] \frac{dy}{dx}=10x + y sin(y)$
$\frac{dy}{dx}= \frac{10x+ysin(y)}{cos(x)-6y}$ ⇒ Final Answer

5 0

4 years ago

The area of the following equilateral triangle is 62.4 square feet that is he height

Vikentia [17]

The height of this triangle would be 10.4

In order to find this, you first must find the length of the sides. Using a manipulated formula for area of an equilateral triangle, we can determine the lengths of the side. Below if the formula.

S = $\frac{2}{3}3^{\frac{3}{4}} \sqrt{A}$

In this, S is the length of the side and A is the area. So we plug in and get:

S = $\frac{2}{3}3^{\frac{3}{4}} \sqrt{62.4}$

S = $\frac{2}{3}3^{\frac{3}{4}} 7.89$

S = 12

Now that we have the side as 12, we can use the Pythagorean Theorem to find the height. If you split a equilateral triangle down the middle, you are left with two right triangles. Using this right triangle, the hypotenuse would be 12, the first leg would be 6 (half of the base) and the height would be the other leg. So we plug in and solve.

$a^{2} + b^{2} = c^{2}$

$6^{2} + h^{2} = 12^{2}$

$36 + h^{2} = 144$

$h^{2} = 108$

h = 10.4

5 0

3 years ago

Podría alguien ayudarme, es para mañana.

Ludmilka [50]

Answer:..$.$!:

Step-by-step explanation:

5 0

3 years ago

Which could be the first step in simplifying this expression (x^3x^-6)^2

exis [7]

If you follow PEMDAS
P-parentheses
E-exponent
M-multiplication
D-divide
a-addition
s-subtraction
then you should look in the parentheses and multiplying 3x should be your first step IF you know x
hope this helps :)

5 0

3 years ago

Read 2 more answers

Please help me complete 5 and 6

Rina8888 [55]

1. Parenthesis:
(15)8 - 4 + 2 + 1
Multiply:
120 - 4 + 2 + 1
Subtract:
116 + 2 + 1
Add:
119, the answer is A.
2. 8 x 15 = 120
120 / 2 = 60
6 x 15 = 90
90 + 60 = 150
The answer is A.
Hope this helps!

8 0

3 years ago