Hello from MrBillDoesMath!
Discussion:
The slope of the tangent to the curve y = 4x^3 is given by the first derivative.
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y' = 4 (3x^2) = 12x^2
At (-3,-108), the slope is 12x^2 = 12(-3)^2 = 12*9 = 108
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y = mx + b
From the first part, m = 108 so y = 108x + b.
Substituting y = -108 when x = -3 gives
-108 = 108(-3) + b => add 3* 108 to both sides
-108 + 108(3) = b => as 3 -1 = 2
108*2 = b = 216
y = 108x + 216
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Thank you,
MrB
Answer:
13.5 meters
Step-by-step explanation:
As the rectangle has 4 sides and the length is three times the width, each pair of a long side and a short side has a perimeter of 18 meters. As the ratio is 3:1, there are 4 parts in 18 meters, and 18 divided by 4=4.5. As the length covers 3 parts, and there are 4.5 meters per part, 4.5x3=13.5. The length of the rectangle is 13.5 meters. Hope it helps!
Try a calculator and doing some googling of numbers divisible by six. There's a great calculator site called calculator soup! ( Yes it's really called calculator soup )
Volume = 3.14xradius squared x height so it’s 3.14 x 6x6 x8 = 904.32
y = (x - 2)(x + 5) First I would multiply (x - 2) and (x + 5) together
y = x² + 5x - 2x - 10
y = x² + 3x - 10
Next I would plug in a number for x to find its y value. I will plug in 0
y = 0² + 3(0) - 10
y = -10
(0, -10) [this is the y-intercept (the y value when x = 0)]
Your answer is Graph A because the y-intercept is (0,-10)
