Which expression is equivalent to (r^-7)^6

Mathematics

2 answers:

WITCHER [35]3 years ago

7 0

Answer:

$r^{-42}$

Step-by-step explanation:

(r⁻⁷)⁶ = r⁽⁻⁷⁾ˣ⁶

= (r)⁻⁴²

Lostsunrise [7]3 years ago

5 0

Answer:

${r}^{ - 42}$

hope this helps you..!

Step-by-step explanation:

$({r}^{ - 7}) ^{6} \\ = {r}^{ (- 7) \times 6} \\ = {r}^{ - 42}$

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Emma ran 3 miles in 27 minutes how long would it take her to run 5 miles?

Marizza181 [45]

It will take her 45 minutes to run 5 miles,because 27/3=9 and 9•5=45

4 0

3 years ago

Two consecutive even intergers whose sum is 110

Harrizon [31]

Consecutive even integers are 2 apart
they are
x and x+2

sum is 110
x+x+2=110
2x+2=110
minsu 2 both sides
2x=108
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7 0

3 years ago

Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,

kompoz [17]

If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

$V_{flask}=V_{sphere}+V_{cylinder}.$

Use following formulas to determine volumes of sphere and cylinder:

$V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,$

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

$V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;$
$V_{cylinder}=\pi r^2h=\pi \cdot \left(\dfrac{1}{2}\right)^2\cdot 3=\dfrac{3\pi}{4}\approx 2.36;$
$V_{flask}=V_{sphere}+V_{cylinder}\approx 47.71+2.36=50.07.$

Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

$V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.$