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Serggg [28]
3 years ago
11

A cylinder has a volume of 400 cubic feet. If the height of the cylinder is 25 feet, what is the radius of the cylinder? Use 3.1

4 for pi
Mathematics
1 answer:
Hatshy [7]3 years ago
6 0

Answer:V = pi x r2 x h, so solving for r you get

V/pi x h = r2

400/(3.14 x 25) = r2

5.09554 is r2, so you gotta take the square root of both sides and you get:

2.26

Step-by-step explanation:

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Explain why the square root of a number is defined to be equal to that number to the 1/2 power<br>​
denis23 [38]

Answer:

Because square root is essentially the same thing as the power to a half

sqrt(x) is the same as (x)^1/2

4 0
3 years ago
The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2). On a coordinate plane, line A B has points (4, 1) and (n
GarryVolchara [31]

Answer:

(-1,1),(4,-2)

Step-by-step explanation:

Given: The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).

To find: coordinates of vertex of the right angle

Solution:

Let C be point (x,y)

Distance between points (x_1,y_1),(x_2,y_2) is given by \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

AC=\sqrt{(x-4)^2+(y-1)^2}\\BC=\sqrt{(x+1)^2+(y+2)^2}\\AB=\sqrt{(4+1)^2+(1+2)^2}=\sqrt{25+9}=\sqrt{34}

ΔABC is a right angled triangle, suing Pythagoras theorem (square of hypotenuse is equal to sum of squares of base and perpendicular)

34=\left [ (x-4)^2+(y-1)^2 \right ]+\left [ (x+1)^2+(y+2)^2 \right ]

Put (x,y)=(-1,1)

34=\left [ (-1-4)^2+(1-1)^2 \right ]+\left [ (-1+1)^2+(1+2)^2 \right ]\\34=25+9\\34=34

which is true. So, (-1,1) can be a vertex

Put (x,y)=(4,-2)

34=\left [ (4-4)^2+(-2-1)^2 \right ]+\left [ (4+1)^2+(-2+2)^2 \right ]\\34=9+25\\34=34

which is true. So, (4,-2) can be a vertex

Put (x,y)=(1,1)

34=\left [ (1-4)^2+(1-1)^2 \right ]+\left [ (1+1)^2+(1+2)^2 \right ]\\34=9+4+9\\34=22

which is not true. So, (1,1) cannot be a vertex

Put (x,y)=(2,-2)

34=\left [ (2-4)^2+(-2-1)^2 \right ]+\left [ (2+1)^2+(-2+2)^2 \right ]\\34=4+9+9\\34=22

which is not true. So, (2,-2) cannot be a vertex

Put (x,y)=(4,-1)

34=\left [ (4-4)^2+(-1-1)^2 \right ]+\left [ (4+1)^2+(-1+2)^2 \right ]\\34=4+25+1\\34=30

which is not true. So, (4,-1) cannot be a vertex

Put (x,y)=(-1,4)

34=\left [ (-1-4)^2+(4-1)^2 \right ]+\left [ (-1+1)^2+(4+2)^2 \right ]\\34=25+9+36\\34=70

which is not true. So, (-1,4) cannot be a vertex

So, possible points for the vertex are (-1,1),(4,-2)

7 0
3 years ago
Read 2 more answers
Point M is the midpoint of segment AB. Find the X Coordinate of the midpoint M if A (5.1,4.6) and B (7.9,2.5). Round to the near
JulsSmile [24]

Answer:

6.5

Step-by-step explanation:

  5.1+7.9=13

13 divided by 2

     = 6.5

     

4 0
2 years ago
WILL GIVE BRAINLIEST. If x+y=3 and 3x+5y=13, then x-y is equal to?
Alex17521 [72]

Answer:

(1,2)

y=2

x=1

Step-by-step explanation:

x+y=3

3x+5y=13

solve the equation

x=3-y

3x+5y=13

substitute the value of x into an equation

3(3-y)+5y=13

distribute

9-3y+5y=13

add -3y to 5y

9+2y=13

subtract 9 from both sides

2y=4

divide both sides by 2

y=2

substitute the value of y into an equation

x=3-2

subtract 3 to 2

x=1

--------

(1,2)

--------

6 0
2 years ago
Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which t
Svetllana [295]

Answer:

The expected change in reaction time for a 1°F increase in temperature is 4.39 hours.

The expected change in reaction time for a 8°F increase in temperature is 4.32 hours.

Step-by-step explanation:

The simple linear regression line is used to determine the changes in the dependent variables when the independent variable is changed.

The general form of the simple linear regression line is:

y=\alpha +\beta x

The simple linear regression model for the reaction time of a certain chemical process based on the temperature (°F) in the chamber in which the reaction takes place is:

y=4.40-0.01\ x

Here,

<em>y</em> = reaction time (in hours)

<em>x</em> = temperature (°F)

Compute the expected change in reaction time for a 1°F increase in temperature as follows:

y=4.40-0.01\ (1^{\text{o}})

  =4.40-0.01\\=4.39\ \text{hours}

The expected change in reaction time for a 1°F increase in temperature is 4.39 hours.

Compute the expected change in reaction time for a 8°F increase in temperature as follows:

y=4.40-0.01\ (8^{\text{o}})

  =4.40-0.08\\=4.32\ \text{hours}

The expected change in reaction time for a 8°F increase in temperature is 4.32 hours.

7 0
3 years ago
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