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4

A ball is thrown into the air, and its height (in meters) above the ground at time t (in seconds) is given by h(t) = 4.9t^2 + 15t + 2. What is its initial velocity?

A. 4.9 m/s

B. 15 m/s

C. 2 m/s

D. 0 m/s

Correct Answer :

B. 15 m/s


Related Questions

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4

What is the antiderivative of e^(2x) with respect to x?

A. e^(2x) + C

B. (1/2)e^(2x) + C

C. (1/2)e^(2x^2) + C

D. (1/4)e^(2x) + C

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4

What is the integral of vx with respect to x?

A. (2/3)x^(3/2) + C

B. (1/2)x^(3/2) + C

C. 2vx + C

D. x^(3/2) + C

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4

Which of the following is an exact differential equation?

A. dy/dx = 2xy

B. dy/dx = x^2 + y^2

C. dy/dx = e^x

D. dy/dx = y^2 - x^2

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4

What does the definite integral ?(a to b) f(x) dx represent geometrically?

A. The average value of f(x) on [a, b]

B. The area between the curve y = f(x) and the x-axis on [a, b]

C. The derivative of f(x) at x = a

D. The slope of the tangent line to the curve y = f(x) at x = b

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4

What is the equation of the tangent plane to the surface z = 2x^2 + 3y^2 at the point (1, -1, 5)?

A. z = 2x - 3y + 5

B. z = 2x + 3y - 5

C. z = 2x - 3y - 5

D. z = 2x + 3y + 5

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4

In parametric equations, what do the variables x and y depend on?

A. Time t

B. Angle ?

C. Radius r

D. Both a and b

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4

If f(x) = 3x^2 - 2x + 1, what is the value of f(4)?

A. 25

B. 33

C. 41

D. 49

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4

If h(x) = e^(2x), what is h'(x)?

A. 2e^(2x)

B. e^(2x)

C. 2e^(x)

D. e^(x)

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4

What is the area under the curve y = sin(x) from x = 0 to x = p?

A. 0

B. 1

C. p

D. 2p

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4

Which type of differential equation is represented by the equation dy/dx = k*y, where k is a constant?

A. Separable

B. Linear

C. Exact

D. Homogeneous

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4

In three-dimensional space, what are the coordinates of the origin?

A. (0, 0, 0)

B. (1, 1, 1)

C. (0, 0)

D. (1, 1)

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4

What is the equation of the polar curve r = 2cos(?)?

A. A circle centered at the origin

B. A cardioid

C. A parabola

D. A line

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4

A ball is thrown into the air, and its height (in meters) above the ground at time t (in seconds) is given by h(t) = 4.9t^2 + 15t + 2. What is its initial velocity?

A. 4.9 m/s

B. 15 m/s

C. 2 m/s

D. 0 m/s

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4

What is the equation of a sphere with center (1, -2, 3) and radius 4?

A. (x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 4

B. (x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 16

C. (x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 4

D. (x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 16

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4

What is the dot product of two vectors a and b?

A. |a| × |b| × cos(?)

B. |a| × |b| × sin(?)

C. |a| + |b|

D. |a| - |b|

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4

If a plane is defined by the equation 2x - 3y + z = 7, what is the normal vector to the plane?

A. <2, -3, 1>

B. <3, 2, -1>

C. <1, 3, -2>

D. <-2, 3, -1>

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4

Which method is commonly used to solve separable differential equations?

A. Laplace transforms

B. Substitution

C. Separation of variables

D. Variation of parameters

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4

If a car's speed is decreasing over time, what can you conclude about its acceleration?

A. The acceleration is positive.

B. The acceleration is negative.

C. The acceleration is zero.

D. Nothing about the acceleration can be determined.

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4

What is the derivative of f(x) = 4x^3 - 2x^2 + 5x - 1 with respect to x?

A. 12x^2 - 4x + 5

B. 12x^2 - 4x - 5

C. 12x^2 - 2x + 5

D. 12x^2 - 2x - 5

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4

What is the integral of 1/(x^2 + 1) with respect to x?

A. arctan(x) + C

B. ln(x^2 + 1) + C

C. 2arctan(x) + C

D. (1/2)ln(x^2 + 1) + C

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4

What does the second derivative of a function represent?

A. The slope of the tangent line

B. The area under the curve

C. The concavity of the curve

D. The average rate of change

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4

Which test is used to determine the convergence or divergence of an infinite series involving alternating terms?

A. Integral Test

B. Comparison Test

C. Alternating Series Test

D. Divergence Test

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4

If the rate of change of a quantity is given by f'(t) and ?(0 to 4) f'(t) dt = 10, what can you conclude about the quantity at t = 4?

A. The quantity is 10 at t = 4.

B. The quantity is 0 at t = 4.

C. The quantity is increasing at t = 4.

D. Nothing about the quantity at t = 4 can be determined.

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4

What is the integral of 3x^2 with respect to x?

A. x^3 + C

B. x^2 + C

C. x^3/3 + C

D. 3x + C

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4

What is the derivative of the vector-valued function r(t) = <2t, t^2, 3t + 1> with respect to t?

A. <2, 2t, 3>

B. <2, 2t, 3t + 1>

C. <2t, 2t^2, 3>

D. <0, 0, 0>

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4

What is the limit of (sin x) / x as x approaches 0?

A. 1

B. 0

C. -1

D. Undefined

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4

What is the average value of the function f(x) = 2x^2 on the interval [1, 3]?

A. 4/3

B. 8/3

C. 16/3

D. 32/3

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4

What is the particular solution to the initial value problem dy/dx = 2x, y(0) = 1?

A. y = x^2 + 1

B. y = x^2

C. y = 2x + 1

D. y = 2x

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4

The definite integral ?(1 to 3) 2x dx is equal to:

A. 4

B. 8

C. 6

D. 10

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4

If f(x) = x^3 + 2x^2 - 5x + 1, what is f''(x)?

A. 3x^2 + 4x - 5

B. 6x + 4

C. 6x^2 + 4

D. 3x^2 + 4