What is the measure of R

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

Nikolay [14]

Answer:

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

General Formulas and Concepts:

Algebra I

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

Calculus

[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:

Step 1: Define

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

Step 2: Find Area

[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

3 years ago

the ratios of the sides of a triangle are 3:2:4. if the shortest side is 26cm, what is the length of the longest side?

zalisa [80]

Answer: 52

Divide 26/2 and you get 13, and then multiply 13 by 4. Think of it as a proportion.

4 0

3 years ago

Need some math help please!

Harrizon [31]

The answer is x=-3 and y=13

3 0

3 years ago

Read 2 more answers

In a standard television set, the screen height is 0.75 times the screen width. If a television set measures 34 inches along the

S_A_V [24]

We can solve this by using the Pythagorean theorem which is below:

$a^2 + b^2 = c^2$

Or we can say
 $w^2 + h^2 = d^2$
w = widht
h = height
d = diagonal measure

With that said, we know the height is .75 times the width so .75w. We also know d = 34, which is our diagonal measure.
w = don't know yet but need to find
h = .75w
d = 34
Now lets plugin the information we know into our equation

 $w^2 + h^2 = d^2$
$w^2 + (.75w)^2 = 34^2$
Now lets to the math
$w^2 + (.75w)^2 = 34^2$
$w^2 + (.75w)^2 = 1156$
$w^2 + .5625w^2 = 1156$
Combine like terms
$w^2 + .5625w^2 = 1156$
$1.5625w^2 = 1156$
Divide both sides of the equal sign by 1.5625
$\frac{1.5625w^2}{1.5625} = \frac{1156}{1.5625}$
$w^2 = 739.84$
Now take the square root on both sides of the equal sign
$\sqrt{w^2} = \sqrt{739.84}$
$w = 27.2$

So the width is 27.2
We can check this by putting 27.2 back into our original equation
$w^2 + (.75w)^2 = 34^2$
$27.2^2 + (.75\times 27.2)^2 = 34^2$

3 0

3 years ago

To make concrete, the ratio of cement to sand is 1 : 3. If cement and sand are sold in bags of equal mass, how many bags of ceme

kotykmax [81]

Answer:

5 bags of cement are required.

Step-by-step explanation:

Since to make concrete, the ratio of cement to sand is 1: 3, if cement and sand are sold in bags of equal mass, to determine how many bags of cement are required to make concrete using 15 bags of sand the following calculation must be done:

Cement = 1

Sand = 3

3 = 15

1 = X

15/3 = X

5 = X

Therefore, 5 bags of cement are required.

3 0

3 years ago

What is the measure of R​

What is the measure of R