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xxMikexx [17]
3 years ago
14

A person is purchasing a new golf club bag. The compartment for the golf balls is approximately the shape of a rectangular prism

with the dimensions of 8 inches by 11 inches by 5 inches. Assuming golf balls are spherical with a 1.68 inch diameter, how many golf balls should fit in the compartment bag?
Mathematics
1 answer:
Akimi4 [234]3 years ago
5 0

Answer:

The answer to your question is: 161 balls

Step-by-step explanation:

Data

rectangular prism = 8 in x 11 in x 5 in

diameter golf balls = 1.68 in     radius = 1.68/ 2 = 0.84 in

Formula

Volume rectangular prism = l x w x h

Volume sphere = (4/3)π r³

Process

Volume rectangular prism = 8 x 11 x 5 = 400 in³

Volume balls = (4/3) (3.1416) (0.84)³ = 2.48

# of balls in the compartment = volumen rectangular prism / volume balls

# of balls in the compartment = 400 / 2.48 = 161. 29

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Consider the graph of the line y = x – 4 and the point (−4, 2).
Hitman42 [59]

Answer:

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c. The slope of the line perpendicular to the given line is -1

d. A point on the line perpendicular to the given line, passing through (−4, 2), is (3,-5)

Step-by-step explanation:

The equation of the line in Slope-intercept form  is:

y=mx+b

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a. For the line y = x - 4

You can identify that:

m=1

 By definition, two lines are parallel if they have the same slope. Then, the  slope of a line parallel to the given line is:

m=1

b. The equation of the line in Point-slope form is:

y -y_1 = m(x - x_1)

Where m is the slope and (x_1,y_1)  is a point of the line.

Given the point (-4,2), substitute this point and the slope of the line into the equation:

 y -2 = (x +4)

Give a value to "x", substitute it into this equation and solve for "y":

For x=1 :

y -2 = (1 +4)

y= 5+2

y= 7

Then, you get the point (1,7)

c. The slopes of perpendicular lines are negative reciprocals, then the  slope of a line perpendicular to the given line is:

m=-\frac{1}{1}\\\\m=-1

d. Given the point (-4,2), substitute this point and the slope of the line into the equation:

 y -2 = -1(x +4)

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Give a value to "x", substitute it into this equation and solve for "y":

For x=3 :

y -2 = -(3 +4)

y= -7+2

y= -5

Then, you get the point (3,-5)

8 0
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Well, "minus 6 x cubed minus y squared minus 3 x y" translates to:

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Then, if we insert the values for x and y, we get:

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When we distribute and multiply:

144-16-24

And once we combine like terms:

104<em> is the answer</em>


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Step-by-step explanation:

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Step-by-step explanation:

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