The base of a right rectangular pyramid has length 14 cm, width 12 cm, and height 13 cm. Describe a cross section that could b
1 answer:
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Answer:
p =1
q = 9
Step-by-step explanation:
f(x) = 2x³ - px² + 2qx + q
(x - 3) is a factor of f(x)
⇒f(3) = 0
2(3)³ - p*3² - 2q*3 +q = 0
2*27 - 9p - 6q + q = 0
54 - 9p - 5q = 0
-9p - 5q = -54 -------------------(I)
(2x - 1) is a factor of f(x)
2x - 1 = 0
2x = 1
f(1/2) = 0
1 - p = 0
-p = -1
p = 1
Substitute p =1 in equation (I)
-9*1 - 5q = -54
-9 - 5q = -54
-5q = -54 + 9
-5q = -45
q = -45/(-5)
q = 9
So with this, we will be using proportions. To solve for x, our proportion will be
Firstly, cross-multiply:
Next, subtract 36 on both sides:
Next, replace -9x with 3x-12x
Next, factor x^2+3x and -12x-36 separately: . After, rewrite it as
Next, solve for x separately in the two parentheses:
Since we can't have a negative length, x = 12.
To solve for y, our proportion will be
Firstly, cross-multiply:
Next, just square root each side, and your answer will be (rounded to hundredths)
In short, x = 12 and y = 10.39.