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Lorico [155]
4 years ago
9

What is the weight in ounces of a 3/4 pound fish

Mathematics
2 answers:
g100num [7]4 years ago
7 0
It would be 12 ounces.
mariarad [96]4 years ago
6 0
12 ounces would be it

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Please help me with these calculus bc questions
zhannawk [14.2K]

4. Compute the derivative.

y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1

Find when the gradient is 7.

4x - 1 = 7 \implies 4x = 8 \implies x = 2

Evaluate y at this point.

y = 2\cdot2^2-2-1 = 5

The point we want is then (2, 5).

5. The curve crosses the x-axis when y=0. We have

y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4

Compute the derivative.

y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}

At the point we want, the gradient is

\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}

6. The curve crosses the y-axis when x=0. Compute the derivative.

\dfrac{dy}{dx} = 3x^2 - 4x + 5

When x=0, the gradient is

\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}

7. Set y=5 and solve for x. The curve and line meet when

5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92

Compute the derivative (for the curve) and evaluate it at these x values.

\dfrac{dy}{dx} = 4x + 7

\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}

\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}

8. Compute the derivative.

y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b

The gradient is 8 when x=2, so

2a\cdot2 + b = 8 \implies 4a + b = 8

and the gradient is -10 when x=-1, so

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2 years ago
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