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coldgirl [10]
3 years ago
10

The diameter d of a sphere is twice the radius r. The volume of the sphere as a function of its radius is given by v(r)= 4/3(3.4

)(r)^3 A) write the diameter d of the sphere as a function of the radius r
Mathematics
1 answer:
Goryan [66]3 years ago
5 0

Answer:

  A)  d = 2r

Step-by-step explanation:

A) The first sentence in the problem statement tells you the diameter is twice the radius:

  d = 2r

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What is the range of the function f(x) = 3x2 + 6x – 8?
timama [110]

Answer:

Range is {y | y ≥ –11}


Step-by-step explanation:

This is quadratic equation.

<em>A quadratic equation's range can be found if we find the vertex.</em>

For quadratic equations that have a positive number in front of  x^{2} , it is upward opening and thus <u>all the numbers greater than or equal to the minimum value of vertex is the range.</u>


The formula for vertex of a parabola is:

Vertex =  (-\frac{b}{2a}, f(-\frac{b}{2a})

Where,

  • a is the coefficient of x^{2}
  • b is the coefficient of x

From our equation given, a=3  and  b=6

Now, x coordinate of vertex is  x=-\frac{b}{2a}\\x=-\frac{6}{(2)(3)}\\x=-\frac{6}{6}\\x=-1

y coordinate of the vertex IS THE MINIMUM VALUE that we want. We get this by plugging in the x value [ x=-1 ] into the equation. So we have:

3(-1)^{2}+6(-1)-8\\=-11


Hence, the range would be all numbers greater than or equal to -11  

Third answer choice is the right one.


6 0
2 years ago
Read 2 more answers
A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which e
kirill115 [55]

We can use the arc length formula to solve this.

Arc length = \frac{q}{360}*2\pi r

Given arc length is 7 and radius is 5, we can plug in the values and solve for q.

7=\frac{q}{360}*2\pi (5)\\7=\frac{q}{360}*10\pi \\7=\frac{10\pi q}{360}\\7=\frac{\pi q}{36}\\7*36=\pi q\\252=\pi q\\q=\frac{252}{\pi}\\q=80.21


ANSWER:

We can use the equation 7=\frac{q}{360}*2\pi (5) to find the value of q. And, the value of q is 80.21°.


3 0
3 years ago
Read 2 more answers
A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: ŷ = 13
Lunna [17]

Answer:

y=6x +135

And for this case the interpretation for the slope would be that for every unit that the height in inches increase then the weight in pounds increase 6 units.

For the intercept of 135 represent the amount initial amount of weight for the scale.

Step-by-step explanation:

We assume that they use least squares in order to create the regression equation

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

With these we can find the sums:

And the slope would be:

m=6

The means for x and y are given by:

\bar x= \frac{\sum x_i}{n}

\bar y= \frac{\sum y_i}{n}

And we can find the intercept using this:

b=\bar y -m \bar x

For this case we know that the line adjusted is:

y=6x +135

And for this case the interpretation for the slope would be that for every unit that the height in inches increase then the weight in pounds increase 6 units.

For the intercept of 135 represent the amount initial amount of weight for the scale.

3 0
3 years ago
Would really appreciate the help. Oh and please tell me how you got the answer.
swat32

Answer:3x-2/6

Step-by-step explanation:When you multiply 1/2 by 6 you would get 3, so 6x is turned to 3x, and when you multiply 1/2 by -2/3, you get -2/6, so your new equation is, (3x-2/6)

4 0
3 years ago
Solve for x
mihalych1998 [28]

Answer:

x=130, x=-77.5, x=1/3

Step-by-step explanation:

1st equation:

1/5x + 24 = 50

1/5x = 26

x = 26(5)

x = 130

2nd equation:

0.4x + 18=-13

0.4x = -31

x=-77.5

3rd equation:

3x - 5/6 = 1/6

3x = 1

x=1/3

7 0
3 years ago
Read 2 more answers
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