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Norma-Jean [14]

3 years ago

9

You buy 2 pairs of shoes in a sale. You pay the full price of $48 for the first pair, and you get the second pair for half this

price. What fraction of the full price do you pay for 2 pairs of shoes?

1 answer:

KonstantinChe [14]3 years ago

6 0

3/4...........................................................................

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What is the value of y

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Deanna is a dog groomer. On Monday, she groomed 12 dogs in 8 hours. On Tuesday, she groomed 9 dogs in 6 hours. On Wednesday, she

svetoff [14.1K]

Answer:

Step-by-step explanation:

Monday: 12 dogs / 8 hours = 1.5 dogs/hour

Tuesday: 9 dogs/ 6 hours = 1.5 dogs/hour

Wednesday: 6 dogs/ 6 hours = 1 dog/hour

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Find the quotient 17)------ 3145

madreJ [45]

185 * 17 = 3145 so that means 3145 / 17 = 185

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3 years ago

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

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