A parachutists descends 32 feet in 2 seconds. Express the rate of the parachutist's change in helght

What is dy/dx if y = (x2 + 2)3(x3 + 3)2? A. 3(x2 + 2)2(x3 + 3)2 + 2(x2 + 2)2(x3 + 3) B. 2x(x3 + 3)2 + 3x2(x2 + 2)3 C. 6x(x2 + 2)

Vlada [557]

We want to find $\displaystyle{ \frac{dy}{dx}$ , for

$\displaystyle{ y=(x^2+2)^3(x^3+3)^2$ .

Recall the product rule: for 2 differentiable functions f and g, the derivative of their product is as follows:

$(fg)'=f'g+g'f$ .

Thus,

$y'=[(x^2+2)^3]'[(x^3+3)^2]+[(x^3+3)^2]'[(x^2+2)^3]\\\\ =3(x^2+2)^2(x^3+3)^2+2(x^3+3)(x^2+2)^3$

Answer: A) $3(x^2+2)^2(x^3+3)^2+2(x^3+3)(x^2+2)^3$ .

8 0

4 years ago

Kelly runs a bakery that sells Chocolate Blizzards and Mint Breezes. The bakery must make at least 25 dozen and at most 45 dozen

drek231 [11]

Yeah Thanks I love to see that and the answer A

3 0

3 years ago

Recall that Rn denotes the right-endpoint approximation using n rectangles, Ln denotes the left-endpoint approximation using n r

pogonyaev

Answer:

$R_5=1.12$

Step-by-step explanation:

We want to calculate the right-endpoint approximation (the right Riemann sum) for the function:

$f(x)=x^2+x$

On the interval [-1, 1] using five equal rectangles.

Find the width of each rectangle:

$\displaystyle \Delta x=\frac{1-(-1)}{5}=\frac{2}{5}$

List the x-coordinates starting with -1 and ending with 1 with increments of 2/5:

-1, -3/5, -1/5, 1/5, 3/5, 1.

Since we are find the right-hand approximation, we use the five coordinates on the right.

Evaluate the function for each value. This is shown in the table below.

Each area of each rectangle is its area (the y-value) times its width, which is a constant 2/5. Hence, the approximation for the area under the curve of the function f(x) over the interval [-1, 1] using five equal rectangles is:

$\displaystyle R_5=\frac{2}{5}\left(-0.24+-0.16+0.24+0.96+2)= 1.12$