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2 years ago

6

A scuba diver descends 80 feet, rises 25 feet, descends 12 feet, and then

1 answer:

cluponka [151]2 years ago

3 0

Answer: That would be 15ft

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Determine the area of the given region under the curve <br> (1/x^4) [1,2]

Nikolay [14]

Answer:

$\displaystyle \frac{7}{24}$

General Formulas and Concepts:

<u>Algebra I</u>

Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

<u>Calculus</u>

[Area] Limits of Riemann's Sums - Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Step-by-step explanation:

<u>Step 1: Define</u>

<u /> $\displaystyle f(x) = \frac{1}{x^4} \\ \ [1, 2]$ <u />

<u />

<u>Step 2: Find Area</u>

[Integral] Set up area: $\displaystyle \int\limits^2_1 {\frac{1}{x^4}} \, dx$
[Integral] Rewrite: $\displaystyle \int\limits^2_1 {x^{-4}} \, dx$
[Integral] Reverse Power Rule: $\displaystyle \frac{-1}{3x^3} \bigg| \limits^2_1$
[Area] Fundamental Theorem of Calculus: $\displaystyle \frac{7}{24}$

Topic: Calculus

Unit: Basic Integration/Riemann Sums

Book: College Calculus 10e

6 0

2 years ago

. The two bottles are similar in shape. The larger bottle holds 100 m/ of perfume. Calculate how many millilitres of perfume the

FromTheMoon [43]

Answer:

The smaller bottle holds 12.5 ml of perfume.

====================

<h2>Given</h2>

Two bottles of similar shape;
Larger bottle has volume of 100 ml;
The length of larger bottle is 10 cm;
The length of smaller bottle is 5 cm.

<h2>To find </h2>

The volume of smaller bottle.

<h2>Solution</h2>

Find the scale factor, the ratio of corresponding dimensions:

$k = 5/10 = 1/2$

We know the volume is the function of three dimensions, therefore the ratio of volumes is the cube of the scale factor:

$V_{small}/V_{large} = k^3\\$

Substitute the known values and find the volume of small bottle:

$V_{small}/100= (1/2)^3\\$
$V_{small}/100= 1/8$
$V_{small}= 1/8*100=12.5$

The smaller bottle holds 12.5 ml of perfume.

4 0

1 year ago

Read 2 more answers

Given the functions below, find g(5) + h(2).<br> g(x) = 2x - 5<br> h(x) = 4x + 5

Ksju [112]

G(5) = 2(5)-5=5
h(2)=4(2)+5=13

So, g(5)+h(2)=13+5=18.

4 0

1 year ago

Read 2 more answers

Triangle GCH is similar to triangle DCE. Find CH

soldier1979 [14.2K]

Answer:

x = 65

Step-by-step explanation:

if two triangles are similar then we can use the similarity ratio to find the length of CH

60/156 = x/169 cross multiply expressions

156x = 10140 divide both sides by 156

x = 65

5 0

3 years ago

Can some one help me match these ?

Anastaziya [24]

This is the order....

8 0

3 years ago