Answer:
a) -2x^2 + 164x
b) 3362 feet
c) (82 , -328)
d) yes
Step-by-step explanation:
y = -2x^2 + 160x
Slope = 4 feet downward for every 1 horizontal foot.
a) h(x) = -2x^2 + 160x - (-4x)
= -2x^2 + 160x + 4x
= -2x^2 + 164x
b) The highest point occurs at the vertex of the parabolic equation. x is the same as the number of the axis of symmetry.
x = -b/2a
From the equation, a = -2 , b= 164
x = -164/ 2(-2)
x = -164/-4
x = 41
Put x = 41 into the value of h(x)
h(x) = -2x^2 + 164x
= -2(41^2) + 164(41)
= -2(1681) + 6724
= -3362 + 6724
= 3362 feet.
The maximum height occurs at 41 feet out from the top of the sloping ground at a height of 3362ft about the top edge of the cliff.
c) h(x) = -2x^2 + 164x
2x^2 - 164x + h = 0 when 0 ≤ x ≤ 41
Solve the equation using the formula (-b+/-√b^2 - 4ac) / 2a
a = 2, b= -164 , c = h
= [-(-164) +/- √(-164)^2 - 4(2)(h) ] / 2(2)
= (164 +/- √26896 - 8h)/ 4
This gives the value of -328 ≤ h ≤ 3362 is used because the rocket hits the sloping ground of (82 , -328)
d) the function still works when it is going down
The radius of circle P is 24 centimeters meanwhile the radius of circle Q is 8 centimeters. Hope this helped
Answer:
x belongs to R+
Step-by-step explanation:
Sqrt(x) has a domain of all positive real numbers greater than 0
Answer:
The answer is (4x - 3)/(x + 6)
Step-by-step explanation:
∵ (4x² - 7x + 3)/(x² + 5x - 6)
Factorize the numerator:
4x² - 7x + 3 = (4x - 3)(x - 1)
Factorize the denominator:
x² + 5x - 6 = (x - 1)(x + 6)
∴ (4x - 3)(x - 1)/(x - 1)(x + 6) ⇒ reduce (x - 1) from in up and down
∴ The answer is (4x - 3)/(x + 6) ⇒ the fourth answer
Answer:
74 feet per second
Step-by-step explanation:
Divide 1,110 by 15 to get 74, which is how many feet the antelope ran per second in its short burst.
Hope this helps!