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3 years ago

Solve 25^3k= 625. With the steps please! I'll be give you 90 points (I need help, okay)!

Mathematics

1 answer:

nordsb [41]3 years ago

7 0

Answer:

k =(2/3)

Step-by-step explanation:

25 ^ (3k) = 625

Replace 25 with 5^2 and 625 with 5^4

5^2^3k = 5^4

We know that a^b^c = a^(b*c)

5^(2*3k) = 5^4

5^ (6k) = 5^4

The bases are the same, so the exponents must be the same

6k = 4

Divide each side by 6

6k/6 = 4/6

k = 2/3

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Could i get help solving n + 6 < –1.5 ?

Svetradugi [14.3K]

Subtract 6 and then you will get n< -4.5

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4 years ago

What is b. If the number as a fraction is 56/90.

MA_775_DIABLO [31]

The answer is: " 28 " .
___________________________________________________
" Twenty-eight (28) students said they would vote for Brianna."
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Explanation:
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We are given, in the problem, that there are "45 students total" .
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The fraction: $\frac{56}{90} ;$

can be reduced as follows:

$\frac{56}{90} = (56÷2) / (90÷2) = [tex] \frac{28}{45}$ .
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Thus, "28 students out of 45 students voted for Brianna" .
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The answer is: "28 students" .
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3 years ago

What does the unit rate represent

Furkat [3]

Answer: rate is a ratio that is used to compare different kinds of quantities. A unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

7 0

3 years ago

A tennis ball is in a cylindrical container. The ball has a radius of 5 inches and the cylinder has a height of 8 inches. How mu

Nostrana [21]

Answer:

104.7 in^3

Step-by-step explanation:

Step one:

given data

The ball has a radius of 5 inches and

the cylinder has a height of 8 inches

Step two:

The volume of the cylinder

$v= \pi r^2 h$

substitute our data

$v= 3.142*5^2*8\\\\v=628.4in^3$

The volume of the ball

$v=4/3 \pi r^3$

substitute our data

$v= 4/3 *3.142*5^3\\\\v= 523.7 in^3$

The space will have a volume of

=628.4-523.7

=104.7 in^3

7 0

3 years ago

Find the general solution to the differential equation modeling how a person learns:

Luda [366]

Here we want to solve differential equations, we will see that the general solution is:

$y = A*e^{-t} + 100$

We want to solve the differential equation:

$\frac{dy}{dt} = 100 - y$

From this is pretty clear that y is an exponential function, with an exponent of -1*t.

We can write it generally as:

$y = A*e^{-t} + B\\\\\frac{dy}{dt} = -A*e^{-t}$

Then if we set B = 100 we get:

$y = A*e^{-t} + 100\\\\\frac{dy}{dt} = -A*e^{-t} \\\\\frac{dy}{dt} = -A*e^{-t} - 100 + 100 = -y + 100$

So we just found the general form of the function.

Now we have two cases:

A) y(0) = 35

$y(0) = A*e^{-0} + 100 = 35\\= A + 100 = 35\\\\A = 35 - 100 = -65$

In this case, the function is:

$y = -65*e^{-t} + 100$

B) y(0) = 125

$125 = A*e^0 + 100\\\\\125 - 100 = A\\\\25 = A$

In this case, the function is:

$y = 25*e^{-t} + 100$

Now we want to see which one of the two can represent how a person learns. Just look at the graph below:

The green line is the one for y(0) = 35, and the blue one is for y(0) = 125.

Notice that for small values of t, the blue function is really large, thus it can't really model how a person learns (is larger for smaller values of t than for larger values).

So y(0) = 35 represents better how a <em>person can learn</em> (but not exactly, because you can see that it eventually becomes almost constant, which is something that really does not happen) so the correct option is <u>D: none of the above.</u>

If you want to learn more, you can read:

brainly.com/question/353770

3 0

3 years ago