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3 years ago

Apply the laws of exponents, calculate the result and express the result in scientific notation, and as a decimal: (8.1*10^-4)^2

Mathematics

1 answer:

AfilCa [17]3 years ago

4 0

<h3>Answer:</h3>

the result in scientific notation is 6.561×10⁻⁷
the result as a decimal is 0.000 000 656 1

<h3>Explanation:</h3>

The rules of exponents say the exponent outside parentheses applies to each factor inside parentheses.

... (8.1*10^-4)^2 = 8.1^2 × (10^-4)^2

... = 65.61 × 10^-8

... = 6.561 × 10^-7 . . . . adjust to scientific notation with one digit left of the decimal point

The exponent of -7 means the decimal point in the decimal number is 7 places to the left of where it is in scientific notation. That is ...

... 6.561 × 10^-7 = 0.0000006561

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An open box with a square base is to have a volume of 18 ft^3.

kotegsom [21]

Answer:

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Step-by-step explanation:

a) Volume V = x2h, where x is side of square base and h is hite.

Then surface area S = x2 + 4xh because box is open.

b) From V = x2h = 6 we have h = 6/x2.

Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.

We get S as function of one variable x. To get minimum we have to find derivative S' = 2x - 24/x2 = 0, from here 2x3 - 24 = 0, x3 = 12, x = (12)1/3 ≅ 2.29 ft.

Then h = 6/(12)2/3 = (12)1/3/2 ≅ 1.14 ft.

To prove that we have minimum let get second derivative: S'' = 2 + 48/x3, S''(121/3) = 2 + 48/12 = 6 > 0.

And because by second derivative test we have minimum: Smin = (12)2/3 + 4(12)1/3(12)1/3/2 = 3(12)2/3 ≅ 15.72 ft2

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3 years ago

Solve for x.<br> y=x-6<br> y=9<br> Simplify your answer as much as p

lukranit [14]

Step-by-step explanation:

$y + 6 = x \\ y = 9 \\ x = 9 + 6 \\ x = 15$

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3 years ago

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Given sin(−θ)=−1/6 and tanθ=−√35/35 What is the value of cosθ?

murzikaleks [220]

Answer:

$cos(\theta)=-\frac{\sqrt{35} }{6}$

Step-by-step explanation:

Recall the negative angle identity for the sine function:

$sin(- \theta)=-sin(\theta)$

Then, we can find the value of $sin(\theta)$ :

$sin(\theta)=-sin(-\theta)\\sin(\theta) =-(-\frac{1}{6} )\\sin(\theta)= \frac{1}{6}$

Now recall the definition of the tangent function:

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

Therefore, now that we know the value of $sin(\theta)$ , we can solve in this equation for $cos(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\\-\frac{\sqrt{35} }{35} =\frac{1/6}{cos(\theta)} \\cos(\theta)=-\frac{\frac{1}{6} }{\frac{\sqrt{35} }{35} } \\cos(\theta)=-\frac{35}{6\,\sqrt{35} } \\cos(\theta)=-\frac{\sqrt{35} }{6}$

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3 years ago

In 1992, Jason bought a gallon of gas for $1.17. Yesterday, he bought a gallon of gas for $2.23. What is the percentage increase

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Answer:

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Step-by-step explanation:

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my dudes could you help me cause im really bad at math heres the problem choose all the values that make the inequality true. 28

Lubov Fominskaja [6]

Answer:

0, 5, 10

Step-by-step explanation:

You can solve the inequality to determine what values to select.

28 -7x ≤ -4(-7x -7) . . . . . . given

28 -7x ≤ 28x +28 . . . . . . eliminate parentheses*

-7x ≤ 28x . . . . . . . . . . . . . subtract 28 from both sides

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0 ≤ x . . . . . . . . . . . . . . . . . divide by 35

So, all values that are 0 or greater will make the inequality true:

0, 5, 10

_____

* Parentheses are eliminated using the distributive property. The factor outside parentheses multiplies each of the terms inside. Pay attention to signs.

-4(-7x -7) = (-4)(-7x) +(-4)(-7) = 28x +28

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