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4 years ago

Describe how to transform (^6 sqrt x^5)^7 into an expression with a rational exponent.

1 answer:

5 0

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-------------------------------\\\\
\left(\sqrt[6]{x^5}\right)^7\implies \left( x^{\frac{5}{6}} \right)^7\implies x^{\frac{5}{6}\cdot 7} \implies x^{\frac{5\cdot 7}{6}}\implies x^{\frac{35}{6}}$

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The scale factor for the reduction is . The length of A = 20 (one-fifth) = 4 feet What is the length of B? B = feet

notka56 [123]

Answer:

1/5 5

Step-by-step explanation:

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3 years ago

Read 2 more answers

A positive real number is 1 more than another. When -2 times the smaller is added to the square of the larger, the result is 33.

Naya [18.7K]

Answer:

The smaller number is 4√2 and the larger number is (4√2 + 1).

Step-by-step explanation:

Let the two numbers be x and y, where y is the larger of the two numbers.

Since y is the larger number, it is one more than the smaller number. So:

$y=x+1$

When negative two times the smaller is added to the square of the larger, the result is 33. In other words:

$-2x+y^2=33$

Substitute:

$-2x+(x+1)^2=33$

Solve for x. Square:

$-2x+(x^2+2x+1)=33$

Simplify:

$x^2+1=33$

Subtract one from both sides:

$x^2=32$

And take the square root of both sides:

$x=\pm\sqrt{32}=\pm 4\sqrt{2}$

Since y is positive, we can ignore the negative case. So, the smaller number is:

$x=4\sqrt{2}\approx5.66$

And the larger number is:

$y = 4\sqrt{2} + 1 \approx6.66$

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3 years ago

Katy is going to select a card from the group of cards shown. What is the probability that Katy will select a card labeled 5?

grandymaker [24]

Answer:

1/2

Step-by-step explanation:

well, there are 10 cards altogether

then, count how many 5's there are.

there are 5.

therefore, 5/10 or 1/2

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3 years ago

a number rounded to the nearest hundred thousand is 400,000. The same number rounded to the nearest ten thousand is 350,000. Wha

spayn [35]

Answer:

360000

Step-by-step explanation:

Well, we know the number must be above 350,000 because it was rounded up to 400,000. In order for the number to round down to 350,000 the number would have to be between 350,000-354999. So, the number could be any number in between those two numbers.

For example: The number COULD be 351,000 but, that is not the only possible answer.

but the answer would be 360000.

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3 years ago

A storage tank will have a circular base of radius r and a height of r. The tank can be either cylindrical or hemispherical (ha

Neko [114]

Answer:

Volume: $\frac{2}{3}\pi r^3$

Ratio: $\frac{2}{9}r$

Step-by-step explanation:

First of all, we need to find the volume of the hemispherical tank.

The volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

where

r is the radius of the sphere

V is the volume

Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:

$V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3$

Now we want to find the ratio between the volume of the hemisphere and its surface area.

The surface area of a sphere is

$A=4 \pi r^2$

For a hemisphere, the area of the curved part of the surface is therefore half of this value, so $2\pi r^2$ . Moreover, we have to add the surface of the base, which is $\pi r^2$ . So the total surface area of the hemispherical tank is

$A'=2\pi r^2 + \pi r^2 = 3 \pi r^2$

Therefore, the ratio betwen the volume and the surface area of the hemisphere is

$\frac{V'}{A'}=\frac{\frac{2}{3}\pi r^3}{3\pi r^2}=\frac{2}{9}r$

6 0

3 years ago