A basketball player scored 26 points in one game. In basketball, some baskets are worth 3 points, some are worth 2 points, and free-throws are worth 1 point. He scored four more 2-point baskets than he did 3-point baskets. The number of free-throws equaled the sum of the number of 2-point and 3-point shots made. How many free-throws, 2-point shots, and 3-point shots did he make?

Answer:

A.2 B.4 C.3 D.4 E.6

Step-by-step explanation:

1/2 ÷ 3/4 = 1/2 x 4/3 (flip 3/4 and keep 1/2)

If you multiply 1/2 x 4/3 you will get 4/6.

Answer and Step-by-step explanation:

Let x and y be two positive integers and their sum is 14:

X + y = 14

And the sum of square of this number is:

f = x2 + y2

 = x2+ (14 – x)2

Differentiate with respect to x, we get:

F’(x) = [ x2 + (14 – x)2]’ = 0

        2x + 2(14-x)(-1) = 0

        2x +( 28 – 2x)(-1) = 0

     2x – 28 +2x = 0

        2x + 2x = 28

         4x = 28

       X = 7

Hence, y = 14 – x = 14 -7 = 7

Now taking second derivative test:

F”(x) > 0

For x = y = 7,f reaches its maximum value:

(7)2 + (7)2 = 49 + 49

                   = 98

F at endpoints x Є [ 0, 14]

F(0) = 02 + (14 – 0)2

       =  196

F(14) = (14)2 + (14 – 14)2

  = 196

Hence the sum of squares of these numbers is minimum when x = y = 7

And maximum when numbers are 0 and 14.

Final answer:

To find two positive integers such that their sum is 14, and the sum of their squares is minimized, we need to consider all possible pairs of positive integers and calculate their sums of squares. The pair (6, 8) has the minimum sum of squares of 100. To find two positive integers such that their sum is 14, and the sum of their squares is maximized, the pairs (1, 13) and (2, 12) both have the maximum sum of squares of 170. Since we need to find two positive integers, the pair (1, 13) is the answer.

Explanation:

To find two positive integers such that their sum is 14 and the sum of their squares is minimized, we need to consider all possible pairs of positive integers that add up to 14 and calculate their sums of squares. Let's list all the pairs:

• 1 and 13: 1^2 + 13^2 = 170
• 2 and 12: 2^2 + 12^2 = 148
• 3 and 11: 3^2 + 11^2 = 130
• 4 and 10: 4^2 + 10^2 = 116
• 5 and 9: 5^2 + 9^2 = 106
• 6 and 8: 6^2 + 8^2 = 100
• 7 and 7: 7^2 + 7^2 = 98

From the list, we can see that the pair (6, 8) has the minimum sum of squares, which is 100.

Similarly, to find two positive integers such that their sum is 14 and the sum of their squares is maximized, we need to again consider all possible pairs and calculate their sums of squares. Let's list the pairs:

• 1 and 13: 1^2 + 13^2 = 170
• 2 and 12: 2^2 + 12^2 = 148
• 3 and 11: 3^2 + 11^2 = 130
• 4 and 10: 4^2 + 10^2 = 116
• 5 and 9: 5^2 + 9^2 = 106
• 6 and 8: 6^2 + 8^2 = 100
• 7 and 7: 7^2 + 7^2 = 98

From the list, we can see that the pair (1, 13) and the pair (2, 12) both have the maximum sum of squares, which is 170. Since we need to find two positive integers, the pair (1, 13) is the answer.

Learn more about Optimization Problems here:

brainly.com/question/32781677

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Answer:

73.3

Step-by-step explanation:

Using the SOH CAH TOA identity

EF = hypotenuse= x

FG = opposite

GE = adjacent  = 50feet

Cos 47 = adj/hyp

Cos 47 = 50/x

x = 50/cos47

x = 50/0.6819

x = 73.32

hence the length of EF is 73.3 feet to the nearest tenth