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4 years ago

What is the answer to -2+5n=4n+2

1 answer:

8 0

-2 + 5n = 4n + 2 Given
-4 + 5n = 4n Subtract 2 from both sides
-4 = -n Subtract 5n from both sides
4 = n Divide both sides by -1

Answer:
n = 4

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Solve. Dante's mom made 2 liters of cocoa. Dante and his 7 friends each drank a serving of cocoa. If each serving is 235 millili

blsea [12.9K]

Answer:

120 millimeters or 0.12 liters

Step-by-step explanation:

To solve this question :

we have to convert liters to millimeters
multiply the serving of coca by the number of people that consumed the coca
subtract the answer gotten from the step above from 2 litters

1 liter = 1000 millimeter

2 liters = 2 x 1000 = 2000mm

8 people drank cocoa = 8 x 235 = 1880mm

Amount of cocoa left over = 2000 - 1880 = 120mm or 0.12 liters

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3 years ago

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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 :

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

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

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

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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2 years ago

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Answer:

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