Four boxes shown in order from largest volume to smallest

Find (fºg)(1) f(x) = x² - 1 g(x) = √x A.0 B.1 C.4 √2 D. √8

Savatey [412]

Given:

The function are

$f(x)=x^2-1$

$g(x)=\sqrt{x}$

To find:

The value of $(f\circ g)(1)$ .

Solution:

We have,

$f(x)=x^2-1$

$g(x)=\sqrt{x}$

We need to find the value of $(f\circ g)(1)$ .

$(f\circ g)(1)=f(g(1))$ $[\because (f\circ g)(x)=f(g(x))]$

$(f\circ g)(1)=f(\sqrt{1})$ $[\because g(x)=\sqrt{x}]$

$(f\circ g)(1)=f(1)$

$(f\circ g)(1)=(1)^2-1$ $[\because f(x)=x^2-1]$

$(f\circ g)(1)=1-1$

$(f\circ g)(1)=0$

The value of $(f\circ g)(1)$ is 0.

Therefore, the correct option is A.

4 0

2 years ago

If 3 dozen cookies require 1 cup of sugar, write a direct variation equation in two variables that represent this situation. Mak

PIT_PIT [208]

Answer:

Step-by-step explanation:

10 multiply 1/3 makes three full cups. Fu*kin* idiot

5 0

3 years ago

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that

juin [17]

Answer:

The Taylor series of f(x) around the point a, can be written as:

$f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....$

Here we have:

f(x) = 4*cos(x)

a = 7*pi

then, let's calculate each part:

f(a) = 4*cos(7*pi) = -4

df/dx = -4*sin(x)

(df/dx)(a) = -4*sin(7*pi) = 0

(d^2f)/(dx^2) = -4*cos(x)

(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4

Here we already can see two things:

the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.

so we only will work with the even powers of the series:

f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....

So we can write it as:

f(x) = ∑fₙ

Such that the n-th term can written as:

$fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}$

6 0

3 years ago

Would the answer for 36 be $9.88 or $9.75?

ludmilkaskok [199]

total bill before any discounts $13.

she is a student, so she gets 20% off.

she brought an item of clothing, so she gets 5% off.

so she's really getting 20% + 5% off, namely 25% off her bill.

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 13}}{\left( \cfrac{25}{100} \right)13\implies 3.25}~\hfill \stackrel{\textit{bill with all discounts}}{13-3.25\implies 9.75}$

6 0

3 years ago

ANSWER ASAP The ratio of red marbles to blue marbles in a jar is 3 to 8. There are 40 blue marbles in the jar. How many red marb

bogdanovich [222]

If the ratio of red marbles to blue marbles in a jar is 3 to 8, the meaning is for every 3 red marbles there are 8 blue marbles.
3 red marbles------------------8 blue marbles.

ratio=3/8

we have 40 blue marbles; we have to compute the number of red marbles.

1) Method 1; by the rule three.

3 red marbles-----------------8 blue marbles
x----------------------------------40 blue marbles

x=(3 red marbles * 40 blue marbles) / 8 blue marbles=15 red marbles.

answer: B. 15

Method 2: the ratio of red marbles to blue marbles is
ratio=number of red marbles / number of blue marbles
ratio=3/8

if we want to compute the number of red marbles we have to multiply the number of blue marbles by this ratio.

number of red marbles=ratio (red/blue)* number of blue marbles
number of red marbles=(3/8)*40=15

Answer: B.15

5 0

3 years ago