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Liono4ka [1.6K]

2 years ago

7

Simplify 10^9 ÷ 10^7

2 answers:

vesna_86 [32]2 years ago

7 0

Answer:

100

Step-by-step explanation:

Hope it helps

Aneli [31]2 years ago

6 0

Answer:

10^2

Step-by-step explanation:

10^9/10^7 is the same as 10^9*10^-7 if you multiply two same bases you can add there exponents. So, 9+(-7)=2. So, it’s 10^2

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Find the coordinates of the vertices of each figure after the given transformation.

zhannawk [14.2K]

Answer:

uhm sorry this is really hard maybe answer 2

Step-by-step explanation:

7 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

Writing lan's car can go 180 miles on 5 gallons of gas. During a drive last weekend, lan used

MrRissso [65]

Answer:

288 miles

If we have the distance, we divide by 36 instead to find how many gallons of gas he used.

Step-by-step explanation:

180/5=36 miles per gallon

8 gallonsx36 miles per gallon=288 miles

pls mark brainliest

6 0

2 years ago

What is the distance between point A(-3,2) and point B(5,-1)

Gnoma [55]

Remember the distance formula

$S=\sqrt{(5+3)^{2}+(-1-2)^{2} }$

$S=\sqrt{8^{2}+(-3)^{2} }$

$S=\sqrt{64+9}$

$S=\sqrt{73}$

8 0

3 years ago

Give the center and radius of the circle. (x - 5)2 + y2 = 16

olasank [31]

Answer:

Centre: (5,0)

Radius: 4

Step-by-step explanation:

r² = 16

r = 4

7 0

3 years ago