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2 years ago

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My base is 10. My exponent is an odd number. If you write a multiplication sentence to show my value, it will have fewer than 4

factors of 10. My value is greater than 10. What number am I?

1 answer:

svet-max [94.6K]2 years ago

4 0

. The number is either 10^1 or 10^3 or 10^ 5 or . . . .

<span>If it is more than 10, then it is not 10^1. The next possibility is 10^3which is 1000, which has factors 2, 5, 10, 20, 25, 40, 50, 80, . . . . . </span>

<span>What constitutes a "multiplication sentence" exactly ? This is not a standard mathematical term. Do you mean "reduce it to its prime factors" ? </span>

<span>1000 = 2 x 2 x 2 x 5 x 5 x 5 </span>

<span>which is a lot more than 4 factors. Or not, if you write it as 2³ x 5³. </span>

<span>But you could say the same about 100 000 = 2^5 x 5^5 </span>

<span>or about 10 000 000 = 2^7 x 5^7 </span>

<span>Take your pick. This is a very badly stated question. </span>

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3 years ago

Which expressions are equivalent to ? Check all that apply.

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Answer:

6.2+8.7+8.9x

Step-by-step explanation:

For expressions to be equivalent, they must simplify to the same lowest form. 8.9x+6.2+8.7 simplifies to 8.9x +14.9.

Each of the expressions below must simplify to 8.9x + 14.9 to be equivalent.

9x+6+9 = 9x + 15 NO

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3 years ago

Read 2 more answers

Points A, B, C, and D form the rectangle ABCD. E, F, and H are three points of another rectangle EFGH. Where does the fourth poi

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3 years ago

A right circular cylinder is inscribed in a sphere with diameter 4cm as shown. If the cylinder is open at both ends, find the la

SOVA2 [1]

Answer:

$8\pi\text{ square cm}$

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

$S=2\pi rh$

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

$4^2 = (2r)^2 + h^2$ ( see in the below diagram ),

$16 = 4r^2 + h^2$

$16 - 4r^2 = h^2$

$\implies h=\sqrt{16-4r^2}$

Thus, the surface area of the cylinder,

$S=2\pi r(\sqrt{16-4r^2})$

Differentiating with respect to r,

$\frac{dS}{dr}=2\pi(r\times \frac{1}{2\sqrt{16-4r^2}}\times -8r + \sqrt{16-4r^2})$

$=2\pi(\frac{-4r^2+16-4r^2}{\sqrt{16-4r^2}})$

$=2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})$

Again differentiating with respect to r,

$\frac{d^2S}{dt^2}=2\pi(\frac{\sqrt{16-4r^2}\times -16r + (-8r^2+16)\times \frac{1}{2\sqrt{16-4r^2}}\times -8r}{16-4r^2})$

For maximum or minimum,

$\frac{dS}{dt}=0$

$2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})=0$

$-8r^2 + 16 = 0$

$8r^2 = 16$

$r^2 = 2$

$\implies r = \sqrt{2}$

Since, for r = √2,

$\frac{d^2S}{dt^2}=negative$

Hence, the surface area is maximum if r = √2,

And, maximum surface area,

$S = 2\pi (\sqrt{2})(\sqrt{16-8})$

$=2\pi (\sqrt{2})(\sqrt{8})$

$=2\pi \sqrt{16}$

$=8\pi\text{ square cm}$

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2 years ago

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neonofarm [45]

Answer:

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Step-by-step explanation:

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2 years ago