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3 years ago

PLEASE HELP!!! Explain how you got the answer! Will give brainliest to best answer!

Mathematics

2 answers:

Angelina_Jolie [31]3 years ago

7 0

You want one non-zero digit in front of the decimal. Count how many times the decimal must move to be behind the first non-zero digit. This is the power on the ten. If it moves to the left, the power is negative. If you must move it to the right it is positive.

I counted 7 moves to get to behind the 6.

6.85 x 10^ -7

Feliz [49]3 years ago

5 0

The correct answer is 6.85 x 10-7 . Check the exponent of the 10 then move the decimal point that many places to the left.

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Michael got a loan for the Playstation 5. His loan was $600. At a 3.75% interest rate he had to pay $7.50 in interest. How long

Semmy [17]

Answer:

4 mo.

Step-by-step explanation:

I = PRT P = 600 R = .0375 I = 7.50

7.50 = 600(.0375)T

7.5 = 22.5T

T = 7.5/22.5 = 1/3 yr = 4 mo.

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2 years ago

What is the area of a circle with the diameter of 8

Mars2501 [29]

Area = πr^2
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3 years ago

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$

We have to find the equation of tangent line to the given curve at point $(-3\sqrt3,1)$

By using implicit differentiation, differentiate w.r.t x

$\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0$

Using formula : $\frac{dx^n}{dx}=nx^{n-1}$

$\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}$

$\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}$

$\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$

Substitute the value x= $-3\sqrt3,y=1$

Then, we get

$\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}$

$\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}$

Slope of tangent=m= $\frac{1}{\sqrt3}$

Equation of tangent line with slope m and passing through the point $(x_1,y_1)$ is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

The equation of tangent line is given by

$y-1=\frac{1}{\sqrt3}(x+3\sqrt3)$

$y-1=\frac{x}{\sqrt3}+3$

$y=\frac{x}{\sqrt3}+3+1$

$y=\frac{x}{\sqrt3}+4$

This is required equation of tangent line to the given curve at given point.

8 0

3 years ago

The difference of sample means of two populations is 55.4, and the standard deviation of the difference of sample means is 28.1.

Anna [14]

Answer:

The difference of the two means is not significant, so the null hypothesis must be rejected.

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3 years ago

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The volume of the shape below is 6 square units. Determine the volume of the shape in two different ways.

REY [17]

The volume of the shape is 6 cubic units

<h3>How to determine the volume of the shape?</h3>

<u>Method 1</u>

From the figure, we can see that:

There are 6 cubes in the figure
The dimensions of the cubes are equal
The volume of each cube is 1 cubic unit

So, the volume of the shape is

Volume = Number of cubes * Volume of each cube

Substitute the known values in the above equation

Volume = 6 * 1

Evaluate

Volume = 6

<u>Method 2</u>

From the figure, we can see that:

There are 6 cubes in the figure
2 cubes at the top and 4 at the bottom
The dimensions of the cubes are equal
The volume of each cube is 1 cubic unit

So, the volume of the shape is

Volume = Top cubes + Bottom cubes

This gives

Volume = 2 * Volume of each cube + 4 * Volume of each cube

Substitute the known values in the above equation

Volume = 2 * 1 + 4 * 1

Evaluate

Volume = 6

Hence, the volume of the shape is 6 cubic units