In how many distinct ways can the 11 letters in engineering be arranged

Use f(x) = 2 x and f-'(x) = 2x to solve the problems.

Marrrta [24]

Answer:

a) 1

b) 2

c) 2

Step-by-step explanation:

a) $f(2)$ means find the output for $\frac{1}{2}x$ when $x=2$ .

$\frac{1}{2}(2)$

$\frac{2}{2}$

$1$

b) $f^{-1}(1)$ means find the output for $2x$ when $x=1$

$2(1)$

$2$

c) If $f$ and $f^{-1}$ are truly inverses then $f(f^{-1}(u))=u$ and $f^{-1}(f(u))=u$ as long as $u$ satisfies the domains.

So we should be able to conclude that $f^{-1}(f(2))=2$ with no work.

However, I will also show work.

$f^{-1}(f(2))$

$f^{-1}(1)$ since $f(2)=1$ from part a.

$2$ since $f^{-1}(1)=2$ from part b.

6 0

2 years ago

the volume of a prism with equilateral triangular cross-section is 270cm^3 . If the length if the prism is 10 root 3 cm, what is

stepan [7]

Given:

The volume of a prism with equilateral triangular cross-section is 270cm³.

Length of the prism = $10\sqrt{3}$ cm

To find:

The length of the side of the equilateral triangular cross-section.

Solution:

Formulae used:

Area of an equilateral triangle is

$Area=\dfrac{\sqrt{3}}{4}a^2$

Where a is the side length of equilateral triangle.

Volume of prism is

$V=Bh$

Where, B is base area and h is the height of the triangular prism.

Cross section of the prism is an equilateral triangular so the base area of the prism is $\dfrac{\sqrt{3}}{4}a^2$ sq. cm.

The volume of the prism is

$V=\dfrac{\sqrt{3}}{4}a^2\times 10\sqrt{3}$

$270=\dfrac{10(3)}{4}a^2$

$270=\dfrac{30}{4}a^2$

$270=7.5a^2$

Divide both sides by 7.5.

$\dfrac{270}{7.5}=a^2$

$36=a^2$

$\pm \sqrt{36}=a$

$6=a$

It takes only positive value because the side cannot be negative.

Therefore, the length of the side of the equilateral triangular cross-section is 6 cm.

5 0

2 years ago

barb ate six cheeseburgers in the last four months. How many do you perdict she will eat in two years?

hichkok12 [17]

36 :))) 4 x 3 = 12... 6 x 3 = 18 x 2 = 36!!
Hope this helps!!

5 0

3 years ago

Target sells a pack of iTunes gift cards for $40. Sam's Club sells them for $38.88. What is the percent decrease from Target's p

patriot [66]

We have been given that target sells a pack of iTunes gift cards for $40. Sam's Club sells them for $38.88. We are asked to find the percent decrease from Target's price to Sam's Club's price.

We will use percent decrease formula to solve our given problem.

$\text{Decrease percent}=\frac{|\text{Final}-\text{Initial}|}{\text{Initial}}\times 100\%$

$\text{Decrease percent}=\frac{|38.88-40|}{40}\times 100\%$

$\text{Decrease percent}=\frac{|-1.12|}{4}\times 10\%$

$\text{Decrease percent}=\frac{1.12}{4}\times 10\%$

$\text{Decrease percent}=0.28\times 10$

$\text{Decrease percent}=2.8\%$

Therefore, the percent decrease from Target's price to Sam's Club's price is 2.8%.

3 0

2 years ago

Can i please help me I don't understand

Step2247 [10]

There are two ways for finding p, here is one way:

1/2 = 4p

Multiply both sides by 2:
1 = 8p

Divide both sides by 8:
0.125 = p

Answer:
p = 0.125

Hope it helped :)

6 0

3 years ago

Read 2 more answers