A fruit bag contains apples and bananas. If 17 out of 25 of the fruit are apples. What percent are bananas?

Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y = ta

Irina-Kira [14]

Answer:

The inner function is $u = \pi x$ .

The outer function is $f(u) = \tan{u}$ .

$\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}$

Step-by-step explanation:

The inner function is the one we apply the outer function to.

So

$y = \tan{\pi x}$

We apply the outer function tangent to $\pi x$ .

So, the inner function is $u = \pi x$ .

The outer function is $f(u) = \tan{u}$ .

The derivative of a compositve function

$y = f(u)$ in which $u = g(x)$ is given by the following function.

$y^{\prime} = f^{\prime}(u)*g^{\prime}(x)$

So

$f(u) = \tan{u}$

$f^{\prime}(u) = \sec^{2}{u}$

$u = g(x) = \pi x$

$g^{\prime}(x) = \pi$

So

$y^{\prime} = f^{\prime}(u)*g^{\prime}(x)$

$\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}$

7 0

3 years ago

Kyra is playing a card game. Black cards are worth points while red cards take points away. What is her score if she has a black

nexus9112 [7]

Answer:

-22

Step-by-step explanation:

20-42=22

4 0

4 years ago

Read 2 more answers

You have $5600. The best interest rate you can find is 3%

EleoNora [17]

Answer:

18 years

Step-by-step explanation:

The formula for computing accrued amount A for a principal of P at an interest rate of r(in decimal) compounded n times in a year for t years is given by

$A = P(1 + \frac{r}{n})^{nt}$

Note that r is percentage converted to decimal. So 3% = 3/100 = 0.03

We can rearrange the above equation to:

$\frac{A}{P} = (1 + \frac{r}{n})^{nt}$

Taking logs on both sides

$log(\frac{A}{P}) = log(1 + \frac{r}{n})^{nt}$

This gives

$log(\frac{A}{P}) =nt \times log(1 + \frac{r}{n})\\So,\\nt = \frac{log(\frac{A}{P})}{ log(1 + \frac{r}{n})}$

In this particular problem, n = 4, , A= 9600, P = 5600, r =0.03, so r/n = 0.03/4 = 0.0075

1 + r/n = 1+0.0075 = 1.0075

4t = log(9600/5600)/log(1.0075) = log(1.714) / log(1.0075) = 0.234 /0.00325 = 72

t = 72/4 = 18 years

4 0

2 years ago

A drinking straw is 1 cm in diameter and 15 cm long.<br><br> What is the volume of the straw?

Neporo4naja [7]

Answer: 11.775

If you plug in the radius (0.5 because the radius is half of the diameter) and the height to the formula for volume of a cylinder you will get pi•0.5 squared•15 which when solved is 11.775.

3 0

3 years ago

What are the zeros of the polynomial function y=2x^3-7x^2+2x+3?

zlopas [31]

$y = 2 {x}^{3} - 7 {x}^{2} + 2x + 3$

By inspection 1 is a root of y ,
Hence , (x-1) is a factor of y ,

$\dfrac{2 {x}^{3} - 7 {x}^{2} + 2x + 3 }{x - 1} = 2 {x}^{2} - 5x - 3 \\ \\ 2 {x}^{2} - 5x - 3 = (2x + 1)(x - 3)$

Hence , the 2 other roots are -1/2 and 3 , and the above graphs confirms the same.

Hope it helps you :)

7 0

3 years ago