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3 years ago

Simplify this expression. 6^7 ÷ 6^5 A. 30 B. 35 C. 36 D. 42

Mathematics

2 answers:

bulgar [2K]3 years ago

6 0

Answer:

C 36

Step-by-step explanation:

When we have to exponents to the same base, and we are dividing them, we can subtract the exponents

a^b ÷ a^c = a^ (b-c)

6^7 ÷ 6^5 = 6^(7-5)

= 6^(2)

= 36

Dima020 [189]3 years ago

3 0

ANSWER

C. 36

EXPLANATION

The given expression is

${6}^{7} \div {6}^{5}$

Recall that,

${a}^{m} \div {a}^{n} = {a}^{ m - n}$

We apply this property to get,

${6}^{7}\div {6}^{5} = {6}^{7 - 5}$

This will give us,

${6}^{7}\div {6}^{5} = {6}^{2}$

${6}^{7}\div {6}^{5}= 36$

The correct choice is C.

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the temperature in an experiment is increased at a constant rate over a period of time until the temperature reaches 0 degrees c

dsp73

Answer:

x = 28 (So it takes 28 hours for the temperature to reach 0°C.)

y = -70 (So the temperature when the experiment begins is −70°C.)

Step-by-step explanation:

To find the the x value, you remove the y value or replace it with 0.

0 = 5/2x - 70

Next you move the variable.

70 (2/5) = x (multiply 70 by 2 to get 140 and divide that by 5)

And now you simplify to get:

To find the y value, you remove the x value or replace it with 0.

y = 0 - 70

And now you simplify to get:

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2 years ago

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2 years ago

Sean places 28 tomato plants in rows. All rows contain the same number of plants. There are netween 5 and 12 plants in each row.

IrinaVladis [17]

Answer:

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Step-by-step explanation:

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3 years ago

Find the volume of the solid.

dmitriy555 [2]

In Cartesian coordinates, the region (call it $R$ ) is the set

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In the plane $z=2$ , we have

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which is a circle with radius $\sqrt2$ . Then we can better describe the solid by

$R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx$

While doable, it's easier to compute the volume in cylindrical coordinates.

$\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}$

Then we can describe $R$ in cylindrical coordinates by

$R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}$

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1 year ago

Through (-4,6) and parallel to y=-3x+4

liraira [26]

Y=mx+b
parallel lines will have the same slope.

using the points (-4,6) and the slope for the parallel line -3 we can find b (the y intercept) for the line.

6 = (-3)(-4) + b
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-12 + 6 = -12 + 12 +b
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y = -3x -6

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2 years ago