Find the value of bx9 when b=8

Find the equation for the inverse of the relation <br> Y=2x+1

Naddik [55]

I thank the answer is 4

8 0

3 years ago

State the name of the property.<br> (24+9)+4=24+(9+4).

nadezda [96]

Associative Property
The parentheses are grouping operators.
Think about the word associate to make it easier

3 0

2 years ago

Read 2 more answers

A right triangle is graphed on a coordinate plane. Find the length of the hypotenuse. Round your answer to the nearest tenth.

Hoochie [10]

Answer:

7.6

Step-by-step explanation:

From the graph, we know the lengths of two legs.

a = 3

b = 7

Knowing this, we can use the Pythagorean Theorem to solve for c, the hypotenuse. (remember, a^2 + b^2 = c^2)

c = √a2 + √b2

= √(7)2 + √(3)2

= √49 + √9

= √58

= 7.6

8 0

3 years ago

Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

7 0

2 years ago

How many solutions does the following equation have?<br> 14x + 12] = 0

Marysya12 [62]

Answer:

$x=-\frac{6}{7}$

It has one solution

Step-by-step explanation:

$14x + 12] = 0\\\\14x+12=0\\\mathrm{Subtract\:}12\mathrm{\:from\:both\:sides}\\14x+12-12=0-12\\\\Simplify\\14x=-12\\\\\mathrm{Divide\:both\:sides\:by\:}14\\\frac{14x}{14}=\frac{-12}{14}\\\\Simplify\\x=-\frac{6}{7}$

8 0

3 years ago