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SVETLANKA909090 [29]
3 years ago
11

PLZ HELP ASAP!!! NEED TO FINISH!!!! BRAINLIEST ANSWER IF CORRECT!

Mathematics
1 answer:
scZoUnD [109]3 years ago
4 0

Answer:

about 10,652 balls

Step-by-step explanation:

The length of the court is 94 ft × 12 in/ft = 1128 in. That is 1128/8.5 ≈ 132.7 times the diameter of a ball.

The width of the court is 50 ft × 12 in/ft = 600 in. That is 600/8.5 ≈ 70.6 times the diameter of a ball.

When the balls are hexagonally packed, their row spacing is only (√3)/2 ≈ 0.866 times the ball diameter, so by cutting out one ball per row on alternate rows, about 15% more rows can be put in place. That is, there can be 81 rows of balls, alternating between 132 and 131 balls per row.

The number of balls that fit in that arrangement is ...

  132×81 - 40 = 10,652

___

Since there is some extra space beyond the last row, the balls can be "randomized" and a few more balls added, probably at least 2 or 3.

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The table of values represents the function g(x) and the graph shows the function f(x).
snow_tiger [21]
<h2>Hello!</h2>

The answer is:

The first and second options:

f(x) and g(x) intersect at exactly two points.

The x-intercepts of f(x) are common to g(x)

<h2>Why?</h2>

To find the correct option (or options) , we need to remember the following:

- When a function intercepts the y-axis, it means that the "x" coordinate will be equal to 0.

- When a function intercepts the x-axis, it means that the "y" coordinate will be equal to 0.

Now, to find the correct option, we also need to compare the graphed function (f(x))  to the given table (g(x)).

So, discarding each of the given options to find the correct option, we have:

- First option, f(x) and g(x)  intersect at exactly two points: True.

From the graph we can see that f(x) intercepts the x-axis at two points (-1,0) and (1,0), also, from the table we can see that g(x) intercepts the x-axis at the same two points (-1,0) and (1,0), it means that the functions intersect at exactly two points.

Hence,  we have that f(x) and g(x)  intersect at exactly two points.

- Second option, the x-intercepts of f(x) are common to g(x): True.

From the graph we can see that f(x) intercepts the x-axis at two points (-1,0) and (1,0), also, from the table we can see that g(x) intercepts the x-axis at the same two points (-1,0) and (1,0), so, both functions intercepts the x-axis at common points.

Hence,we have that the x-intercepts of f(x) are common to g(x)

- Third option, he minimum value of f(x) is less than the minimum value of g(x): False.

From the graph, we can see that the minimum value of f(x) is located at the point (0,-1), also, from the given table for g(x) we can see that there are values below the point (2,-3), meaning that the minimum value of f(x) is NOT less than the minimum value of g(x).

Hence, we have that the minimum value of f(x) is NOT less than the minimum value of g(x).

- Fourth option, f(x) and g(x) have the same y-intercept: False.

We can see that for the function f(x) the y-intercept is located at (0,-1) while from the given table, we can see the y-intercept for the function g(x) is located at (0,1)

Hence,  we have that f(x) and g(x) have differents y-intercepts.

Therefore, the correct answers are:

The first and second options:

f(x) and g(x) intersect at exactly two points.

The x-intercepts of f(x) are common to g(x)

Have a nice day!

Note: I have attached an image for better understanding.

8 0
3 years ago
The school cafeteria served 2,680 cups of milk in March and 1,480 cups of milk in April. How many quarts of milk did the cafeter
nignag [31]

Answer:

<h2 />

Step-by-step explanation:

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8 0
3 years ago
Write an expression that represents the area of only the red shaded region in terms of x
julsineya [31]

Answer:

(9 × 3x+7) - (5 × x+2)

Step-by-step explanation:

Red area

9 × 3x + 7

white area

5 × x+2

7 0
3 years ago
The reduce feature on a copy machine is set at 84%. The picture being copied is 4.5 inches wide. What will be the width of yhe r
snow_tiger [21]

Answer:

The answer is 3.825 inches, the reduced picture will be 84% of the size of the original

8 0
3 years ago
Read 2 more answers
Find the number b such that the line y = b divides the region bounded by the curves y = 36x2 and y = 25 into two regions with eq
Gemiola [76]

Answer:

b = 15.75

Step-by-step explanation:

Lets find the interception points of the curves

36 x² = 25

x² = 25/36 = 0.69444

|x| = √(25/36) = 5/6

thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

8 0
3 years ago
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