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3 years ago

Convert 3 miles to feet. A. 15,840 feet B. 1,584 feet C. 3,279 feet D. 9,372 feet

Mathematics

1 answer:

andreev551 [17]3 years ago

7 0

Answer:

A. 15,840 feet

Step-by-step explanation:

1 mile = 5,280 feet (I think "five tomatoes" is helpful: five tomatoes --> five-two-eight-oh)

multiply both sides of equation by 3: 1 * 3 = 5,280 * 3

simplify: 3 miles = 15,840 feet, which means A is the answer

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Answer:

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Step-by-step explanation:

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x=81/3=27

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2 years ago

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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 :

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

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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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3 years ago

How do you solve this question?

dezoksy [38]

What is the x interval??

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4 years ago

Convert 3 miles to feet. A. 15,840 feet B. 1,584 feet C. 3,279 feet D. 9,372 feet​

Convert 3 miles to feet. A. 15,840 feet B. 1,584 feet C. 3,279 feet D. 9,372 feet