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3 years ago

Find the product. Simplify your answer. a/a^2-16 × a+4/a^2

Mathematics

1 answer:

miss Akunina [59]3 years ago

7 0

Answer:

$\frac{1}{a(a-4)}$

Step-by-step explanation:

Factor the denominator of the first fraction

a² - 16 ← is a difference of squares and factors as

a² - 16 = (a - 4)(a + 4), thus fraction becomes

$\frac{a}{(a-4)(a+4)}$ × $\frac{a+4}{a^2}$

Cancel the factor (a + 4) on numerator/denominator and the a and a², leaving

$\frac{1}{a(a-4)}$

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At 2 PM, a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03 PM, the temperature reading yiel

Alexeev081 [22]

Use Law of Cooling:
$T(t) = (T_0 - T_A)e^{-kt} +T_A$
T0 = initial temperature, TA = ambient or final temperature

First solve for k using given info, T(3) = 42
$42 = (80-20)e^{-3k} +20 \\ \\ e^{-3k} = \frac{22}{60}=\frac{11}{30} \\ \\ k = -\frac{1}{3} ln (\frac{11}{30})$

Substituting k back into cooling equation gives:
$T(t) = 60(\frac{11}{30})^{t/3} + 20$

At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
$T(t) = (x-80)(\frac{11}{30})^{t/3} + 80 \\ \\ 71 = (x-80)(\frac{11}{30})^{\frac{10-t}{3}} + 80$
Solve for x:
$x = -9(\frac{11}{30})^{\frac{t-10}{3}} + 80$
Sub back into original cooling equation, x = T(t)
$-9(\frac{11}{30})^{\frac{t-10}{3}} + 80 = 60 (\frac{11}{30})^{t/3} +20$
Solve for t:
$60 (\frac{11}{30})^{t/3} +9(\frac{11}{30})^{\frac{-10}{3}}(\frac{11}{30})^{t/3} = 60 \\ \\ (\frac{11}{30})^{t/3} = \frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}} \\ \\ \\ t = 3(\frac{ln(\frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}})}{ln (\frac{11}{30})}) \\ \\ \\ t = 4.959$

This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM

8 0

4 years ago

What is the median of the data below? 45, 19, 23, 67, 28, 35, 46, 21, 58, 60, 23, 51

VLD [36.1K]

To find the median, you will need to list the data from least to greatest and find the middle number.

19, 21, 23, 23, 28, 35, 45, 46, 51, 58, 60, 67

Cross out a number on both sides until you reach the middle number. In this case, we are left with 2 numbers that are in the middle since there is an even amount of numbers.

When you reach the time where you have two middle numbers, we have to find the average of those two numbers. Our two middle numbers are 35 and 45. Since we have to find the average of those two numbers, we can add them. (35 + 45 = 80). Now, since we have two middle numbers, we have to divide them by 2.
$80 \div 2 = 40$

Answer: $\fbox {Median = 40}$

4 0

3 years ago

Read 2 more answers

a recipe calls for three cups of cheese to make nachos for six people .how much cheese is needed to make nachos for two dozen pe

zubka84 [21]

First, let's figure out how many cups of cheese we need for one dozen people.
There are 12 people in one dozen.

3 cups of cheese = x cups of cheese
6 people 12 people


that means we will need 6 cups of cheese for 12 people, or one dozen.

However, we want to make nachos for two dozen people.

6 cups of cheese for one dozen x 2 dozen = 12 cups of cheese

You need 12 cups of cheese to make nachos for two dozen people.

3 0

4 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B4%7D%20%20-%206%20%7Bx%7D%5E%7B3%7D%20%20%2B%2022%20%7Bx%7D%5E%7B2%7D%20%20-%2

alexira [117]

Answer:

x = 2, 1 + 3i, 1 − 3i

Step-by-step explanation:

Find the Roots (Zeros)

x^4 − 6x^3 + 22x^2 − 48x + 40

Set x^4 − 6x^3 + 22x^2 − 48x + 40 equal to 0. x^4 − 6x^3 + 22x^2 − 48x + 40 = 0

Solve for x.

Factor the left side of the equation.

Factor x^4 − 6x^3 + 22x^2 − 48x + 40 using the rational roots test.

(x − 2) (x^3 − 4x^2 + 14x − 20) = 0

Factor x^3 − 4x^2 + 14x − 20 using the rational roots test.

(x − 2) (x − 2) (x2 − 2x + 10) = 0

Combine like factors.

(x − 2)2 (x^2 − 2x + 10) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

(x − 2)^2 = 0

x^2 − 2x + 10 = 0

Set (x − 2)^2 equal to 0 and solve for x.

Set (x − 2)^2 equal to 0.

(x − 2)^2 = 0

Solve (x − 2)^2 = 0 for x.

x = 2

Set x^2 − 2x + 10 equal to 0 and solve for x.

Set x^2 − 2x + 10 equal to 0. x^2 − 2x + 10 = 0

Solve x^2 − 2x + 10 = 0 for x.

Use the quadratic formula to find the solutions.

−b ± (√b^2 − 4 (ac) )/2a

Substitute the values a = 1, b = −2, and c = 10 into the quadratic formula and solve for x.

2 ± (√(−2)^2 − 4 ⋅ (1 ⋅ 10))/2 ⋅ 1

Simplify.

Simplify the numerator.

x = 2 ± 6i/ 2.1

Multiply 2 by 1

x = 2 ± 6i/2⋅1

Simplify

2 ± 6i/2

x = 1 ± 3i

The final answer is the combination of both solutions.

x = 1 + 3i, 1 − 3i

The final solution is all the values that make (x − 2)2 (x2 − 2x + 10) = 0 true.

x = 2, 1 + 3i, 1 − 3i

3 0

3 years ago

Please solve need help!

lions [1.4K]

Answer:

ST 45

Step-by-step explanation:

9x=4x+25

5x=25

x= 5

plug back in 9(5)

4 0

3 years ago

Find the product. Simplify your answer. a/a^2-16 × a+4/a^2​

Find the product. Simplify your answer. a/a^2-16 × a+4/a^2