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What is the correct answer?

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

Correct Answer :

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


Related Questions

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4

Which technique of integration is used to evaluate the integral of a product of two functions, often when integration by parts is required?

A. Trigonometric substitution

B. Integration by substitution

C. Integration by partial fractions

D. Integration by u-substitution

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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 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 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

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

A. 4

B. 8

C. 6

D. 10

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4

Which test can be used to determine the convergence of a series when its terms are all positive?

A. Alternating Series Test

B. Ratio Test

C. Integral Test

D. Comparison Test

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4

If a point has polar coordinates (r, ?), what are its Cartesian coordinates?

A. x = rcos(?), y = rsin(?)

B. x = r?, y = r?

C. x = cos(?), y = sin(?)

D. x = rsin(?), y = rcos(?)

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4

What is the distance between the points A(2, -1, 3) and B(4, 3, -2)?

A. v42

B. v30

C. v29

D. v35

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4

Which trigonometric substitution is commonly used to integrate rational functions involving v(a^2 - x^2)?

A. u = sin(x)

B. u = cos(x)

C. u = sec(x)

D. u = tan(x)

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4

If f(x) = sin(x), what is f'(x)?

A. cos(x)

B. -cos(x)

C. sin(x)

D. -sin(x)

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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

If a particle's position at time t is given by r(t) = <3t, t^2, 2t - 1>, what is its velocity vector v(t)?

A. v(t) = <3, 2t, 2>

B. v(t) = <3t, t^2, 2t - 1>

C. v(t) = <3t^2, 2t, 2>

D. v(t) = <2, 2t, 2t - 1>

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4

What is the general solution to the differential equation dy/dx = 3x^2?

A. y = x^3 + C

B. y = 3x + C

C. y = x^3/3 + C

D. y = 3x^3 + C

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4

What is the unit vector in the direction of vector v = <4, -3>?

A. <1, 1>

B. <2, -1.5>

C. <4/5, -3/5>

D. <0, 0>

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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

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

The area between the curve y = x^2 and the x-axis from x = 0 to x = 2 is equal to:

A. 2

B. 4

C. 8/3

D. 16/3

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4

What is a vector?

A. A point in space

B. A scalar quantity

C. A quantity with magnitude and direction

D. A constant value

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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

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 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 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

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 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

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 cost C(x) of producing x units of a product is given by C(x) = 3x^2 + 2x + 7. What is the marginal cost when x = 5?

A. 47

B. 37

C. 27

D. 17

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4

Which of the following limits does not exist?

A. lim (x -> 0) (1/x)

B. lim (x -> 2) (x^2 - 4)/(x - 2)

C. lim (x -> 1) (x^2 - 1)/(x - 1)

D. lim (x -> 3) (1/x^2)

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4

What are the parametric equations for a circle of radius r centered at the origin in polar coordinates?

A. x = rcos(?), y = rsin(?)

B. x = rcos(t), y = rsin(t)

C. x = r?, y = r?

D. x = cos(?), y = sin(?)

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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 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