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3 years ago

9) Simplify 5^12 ÷ 5^3 A. 5^4 B. 5^9 C. 1^4 D. 1^9

Mathematics

1 answer:

Mashcka [7]3 years ago

5 0

When you divide powers, you subtract them.

12-3=9

B. 5^9 is the answer.

I hope this helps!
~kaikers

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Find the volume. Round your answer to the nearest hundredth.

barxatty [35]

Answer:

c. 162.56 cm3

Step-by-step explanation:

This

volume = L × W × H

7.6 × 6.9 × 3.1 = 162.56 cm3

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3 years ago

Use linear approximation to approximate 25.3‾‾‾‾√ as follows. Let f(x)=x√. The equation of the tangent line to f(x) at x=25 can

loris [4]

Answer:

Approximation f(25.3)=5.03 (real value=5.0299)

The approximation can be written as f(x)=0.1x+2.5

Step-by-step explanation:

We have to approximate $f(25.3)=\sqrt{25.3}$ with a linear function.

To approximate a function, we can use the Taylor series.

$f(x)=\sum_1^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n$

The point a should be a point where the value of f(a) is known or easy to calculate.

In this case, the appropiate value for a is a=25.

Then we calculate the Taylor series with a number of terms needed to make a linear estimation.

$f(x)\approx f(a)+\frac{f'(a)}{1!}(x-a)$

The value of f'(a) needs the first derivate:

$f'(x)=\frac{1}{2\sqrt{x}}\\\\f'(a)=f'(25)=\frac{1}{2\sqrt{25}}=\frac{1}{2*5}=\frac{1}{10}$

Then

$f(x)\approx f(25)+\frac{1}{10}(x-25)=\sqrt{25} +\frac{1}{10}(x-25)\\\\f(x)\approx 5+\frac{1}{10}(x-25)$

We evaluate for x=25.3

$f(25.3)\approx 5+\frac{1}{10}(25.3-25)\\\\f(25.3)\approx 5+\frac{1}{10}(0.3)=5.03$

If we rearrange the approximation to be in the form mx+b we have:

$f(x)\approx 5+\frac{1}{10}(x-25)=5+0.1x-2.5\\\\f(x)\approx 0.1x+2.5$

Then, m=0.1 and b=2.5.

6 0

4 years ago

Which is pattern 12,24,36,48

den301095 [7]

T(n)=n×12, where n=the nth term in the sequence and where 12=a constant. always by 12

4 0

3 years ago

Read 2 more answers

Can someone help me answer this Fraction word problem and give step by step how to give the answer?

Dmitry [639]

This answer maybe long, but it includes all the essential steps to make it easy
This problem shows that the fraction of the time worked by three individuals need to be = to one person working full time.
It just means that the fractions need to add up to one. Since we got to know that one person works 1/2 the time on the project and the other works 1/3 of the time, let us use a variable to represent the amount of time the last person needs to work to have a total of 1.
This is quite easy:
variable = t(representative of the last person)
step 1: 1=1/2+1/3+t
step 2: keep the variable alone at one side
1-1/2-1/3=t
this step on a calculator will be easy, but dont have a calculator? Thats fine!
Lets have a common denominator
2 and 3 can be 6
1/1*(6/6)-1/2*(3/3)-1/3*(2/2)=t
6/6-3/6-2/6=t
step 3: just subtracts and get the answer
1/6=t
In conclusion, the third person must be working 1/6 the time on the project

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3 years ago

The population density of the world is calculated by finding the ratio of the total number of people in the world to the area of

Romashka [77]

Answer:

Step-by-step explanation:

A = Surface area of the Earth = $1.5\times 10^8\ \text{km}^2$