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3 years ago

The slope of the line that contains the points (-2, 10) and (3, -5) is -3. What is the y-intercept?

Mathematics

1 answer:

Paladinen [302]3 years ago

7 0

Answer:

The y-intercept of this line is (0, 4)

Step-by-step explanation:

Given that the slope of this line is -3, we know the general form of its equation is y = -3x + b. Arbitrarily choosing the first point, (-2, 10), and substituting -2 for x and 10 for y, we find the y-intercept as follows:

10 = -3(-2) + b, or

10 = 6 + b, or

b = 4 (Answer C)

The y-intercept of this line is (0, 4)

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Answer:

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Step-by-step explanation:

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3 years ago

You place a 16 foot ladder against a building. The angle that the ladder forms with

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Step-by-step explanation:

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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

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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 :

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

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

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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:

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

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

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:

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

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2 years ago

The sum of two numbers is 56, and their difference is 10. What are the numbers?

Elanso [62]

Answer:

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Step-by-step explanation:

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3 years ago

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