Tamiya's flower garden has 15 rows of 32 red rose flowers each
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The college GPA for a high school GPA of 3.1 and a college board score of 500 will be 2.801
The equation to predict college GPA is :
where x1 is high school GPA and x2 is college board score.
According to the question, here x1= 3.1 and x2= 500
So, we will plug the values of x1 and x2 into the above equation..
So, the college GPA for a high school GPA of 3.1 and a college board score of 500 is 2.801
Answer:
a. (30 - 2x)(16 - 2x)x. b. length 21.2 cm , width = 7.2 cm and height x = 4.4 cm
Step-by-step explanation:
a. Let x be the side of the squares to be cut from each corner. Since we have two corners on each side, the length of the resulting box from the 30 cm by 16 cm sheet is L = 30 - 2x. Its breadth is B = 16 - 2x. The height of the resulting box is x. So its volume V = LBx = (30 - 2x)(16 - 2x)x.
b. To find the maximum value of V, we differentiate V with respect to x and equate it to zero.
So, dV/dx = 0
d(30 - 2x)(16 - 2x)x/dx = 0
-2(16 - 2x)x + (-2)(30 - 2x)x + (30 - 2x)(16 - 2x) = 0
32x + 4x² - 60x - 4x² + 480 - 60x - 32x + 4x² = 0
4x²- 120x + 450 = 0
x²- 30x + 112.5 = 0
Using the quadratic formula, we find x. So, with a = 1, b = - 15 and c = 112.5,
x ≅ 25.61 or 4.4
V = (30 - 2x)(16 - 2x)x
Substituting the values of x into L and B, we have )x
L = (30 - 2x) = (30 - 2(25.61)) = 30 - 51.22 = -21.22
B = (16 - 2x) = (16 - 2(25.61)) = 16 - 51.22 = -35.22
Since L and B cannot be negative, we use the other value for x = 4.4, So
L = (30 - 2x) = (30 - 2(4.4)) = 30 - 8.8 = 21.2
B = (16 - 2x) = (16 - 2(4.4)) = 16 - 8.8 = 7.2
So V = LBx = 21.2 × 7.2 × 4.4 = 671.62 cm³