Find all the powers of 4 in the range 4 Through 1000

Mathematics

2 answers:

Delvig [45]3 years ago

8 0

We want to find all 4^x less than 1000 and greater than or equal to 4. They are 4, 4*4, 4*4*4... or 4, 16, 64, 256.

Anettt [7]3 years ago

7 0

(4⁰ = 1 too small)

4¹ = 4

4² = 16

4³ = 64

4⁴ = 256

(4⁵ = 1,024 too big)

You might be interested in

The triangle shown is a right triangle. Create the equation to be used to find the missing lengths.

telo118 [61]

The equation used to find the missing lengths:
9 = __SR (5^2 + x^2)__
As long as it is a right triangle, this is called the Pythagorean Theorem
${9}^{2} = {x}^{2} + {5}^{2} \\ \sqrt{ {9}^{2} } = \sqrt{( {x}^{2} + {5}^{2} )} \\ 9= \sqrt{( {x}^{2} + {5}^{2} )}$

** FYI- if you wanted to SOLVE FOR THE MISSING SIDE X, then just switch around the original equation solving in terms of x:
${9}^{2} = {x}^{2} + {5}^{2} \\ {x}^{2} = {9}^{2} - {5}^{2} \\ x= \sqrt{( {9}^{2} - {5}^{2})} = \sqrt{(81 - 25)} \\$
$x = \sqrt{56} = \sqrt{(8 \times 7)} \\ x= \sqrt{(4 \times 14)} = \sqrt{4}\times \sqrt{14} \\ x = 2 \sqrt{14}$

6 0

3 years ago

The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the

Scorpion4ik [409]

Answer:

Step-by-step explanation:

This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.

We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of

$S=4\pi r^2$

In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that

d = 2r so

$\frac{d}{2}=r$ Now we can have the equation in terms of diameter instead of radius. Rewriting:

$S=4\pi(\frac{d}{2})^2$ which simplifies to

$S=4\pi(\frac{d^2}{4})$ and a bit more to

$S=\pi d^2$ (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.

$\frac{dS}{dt}=\pi*2d\frac{dD}{dt}$ Now let's look at the problem and see what we are given as far as information.

The rate at which the surface area changes is -3.8, and we are looking for $\frac{dD}{dt}$ , the rate at which the diameter is changing, when the diameter is 13. Filling in: