Sequences & Series Questions and Answers

Find the sum of the smallest four-digit positive integer and the greatest three-digit negative integer.

Add and subtract the following terms, if possible. 3√48-√√27 +3√75-√72 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 3√48-√27 +3√75-√72 = (Type an exact answer, using radicals as needed.) B. The radicals cannot be combined.

A rock weighing 32.0 g is placed in a graduated cylinder displacing the volume from 12.3 mL to 16.8 mL. What is density of the rock in g/cm3? density = __ g/cm³

Solve for u. 20=-5u/7 Simplify your answer as much as possible.

Which of the following is the correct way to express 0.0000321 in scientific notation? A. 32.1 x 106 B. 3.21 x 105 C. 3.21 x 10-5 D. 32.1 x 10-6

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. f(x) = 5(x 2 + 1)(x-6) ² 6, multiplicity 2, crosses x-axis 6, multiplicity 2, touches x-axis -1, multiplicity 1, crosses x-axis; 6, multiplicity 2, touches x-axis -1, multiplicity 1, touches x-axis; 6, multiplicity 2, crosses x-axis

Write an equation in slope-intercept form for the line with slope - and --5

What is the y-intercept of y = a cos(kx) + c? a) a+c b) a-c c) Not possible to find the y-int without the actual values of a, k and c d) c

Evaluate the following statement as true or false: In f(x) = sin(x) + c, if c < 0, the function f(x) = sin(x) moves down and if c > 0, f(x) = sin(x) moves up. a) True b) False

Calculate the volume of an object with dimensions measuring: 12 cm x 3 cm x 9 cm [?] cm³

A liquid that occupies a volume of 4.7 L has a mass of 5.1 kg. What is the density of the liquid in kg/L? density = [?] kg/L Round your answer to the tenths place. Density (kg/L)

A trigonometric function of the form f(x) = a sin(x) has a maximum at 4 and a minimum at-4. The function would be: a) f(x) = sin(x) + 4 b) J(x) = sin(4x) c) f(x) = 4 sin(x) d) f(x) = sin(x) - 4

The range for the function f(x) = -3 sin x is: a) Range:{y|0 ≤ y ≤ 3, y ≤ R} b) Range: {y-3 ≤ y ≤ 3, y ≤ R} c) Range: {y2 ≤ y ≤ 3, ye R} d) Range: {y-2≤ y ≤ 3, ye R}

Consider the graph of f(x) = 2 sin(x). How many x-intercepts are there in the interval 0 < x < 2π. a) 0 b) 2 c) 3 d) 4

Which of the following do we need to be concerned about when determining domain of a real-valued function? Partial Fractions Division by Zero Complex Numbers Irrational Numbers

The function f(x) = cos x is an example of: a) a horizontal compression b) a vertical stretch c) a horizontal stretch d) a vertical compression

This time, include both the coefficient and exponent. Express 0.00212 in scientific notation. [? ]×10¹²] Enter the coefficient in the green box and the

Insert < or > between the pair of integers to make the statement true. 0 4

Solve the absolute value inequality. |2x - 2| <6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is (Simplify your answer.) B. The solution set is Ø.

Convert 100.6 Kelvin to degrees C. °C = K -273 [?] °C

Find the average rate of change of f(x)=x²+2 over each of the following intervals. (a) From-1 to 1 (b) From 2 to 4 (c) From-1 to 2

The function f(x) = sin a can be transformed to a function equivalent to g(x): = cos a by a phase shift of: a) units to the left b) units to the right c) units to the right d) units to the left

In f(x) = cos kæ, if k is negative: a) the function is reflected about both the x and y axes b) the function is reflected in the x-axis c) the function's initial value is a minimum d) the function is reflected in the y-axis

A piece of copper has a volume of 5.00 cm3. The density of copper is 8.96 g/cm3. What is the mass of the copper piece? mass = [?] g

For the function f(x) = -2 cos (3x) -1, the period is: a) 2 b) 67 c) 1/10 d) -4/3

The volume of the granite as determined by water displacement is 9.35 mL. What is the volume of the granite in cm3? Remember: 1 mL = 1 cm3 volume = [?] cm³

Which function of the form f(x) = 3 sin(x) + c passes through the point: A(2,5) a) f(x) = 3 sin(x) +2 b) J(x) = sin(x) - Z c) f(x) = 3 sin(x) + 4 d) f(x) = 3 sin(x) + 5

Find the equation of the line that has y-intercept (0,-7) and slope-4. Write the equation in the form y = mx + b. y=-7x-4 y = -4x+7 y=-4x-7 y = 4x + 7 Oy=7x-4

The domain of the three basic trigonometric functions is Domain = {x|x € R}. This statement is: a) true only for the cosine function b) true for both the sine and cosine functions c) true for all three basic trigonometric functions d) true only for the sine function

Draw the given rotational angle on the x- y coordinate axis beginning at the positive x-axis. Show all rotation. Then find the EXACT SPECIAL ANGLE VALUE of each trigonometric function given below. Write your simplified and rationalized answers on the lines provided. DO NOT give decimal approximations. cot sec (-1320) cos 990°

Use the alternative form of the dot product to find u. v. ||u|| = 50, ||v|| = 50, and the angle between u and v is 5π/6.

The trigonometric functions have a period of 27 radians. This statement is: a) true for all three basic trigonometric functions b) true only for the cosine function c) true for both the sine and cosine functions d) true only for the sine function

The doubling period of a bacterial population is 10 minutes. At time 110 minutes, the bacterial population was 60000. What was the initial population at time t=0? Find the size of the bacterial population after 3 hours.

A 60-foot piece of siding is cut into three pieces so that the second piece is four times as long as the first piece and the third piece is five times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces. The length of the first piece of siding is long, the length of the second piece is long, and the length of the third piece is long.

A ferris wheel at an amusement park completes one revolution every 40 seconds. The cars can reach the maximum of 5 metres above the ground and a minimum of 1 metre above the ground. The height, h, in meters, above the ground can be modelled using a sinusodial function. What is the radius of the ferris wheel? a) 2 meters b) 4 meters c) 2.5 meters d) 5 meters

All asymptotes to the tangent function occur when: a) cos x = 1 b) sin x = 1 c) sin x = 0 d)

Find A in degrees.C = 110° a = 11 b=7 A = [?] degrees

Solve the absolute value inequality. |4x-2|<14

Find C in degrees. A = 29° b= 4 C = 10 C = [?] degrees

Find x if the mean of the given data is 7. x 12 3 4 3 85 11 X= = [?]

Use the Laplace Transformation to solve the IVP. dx/dt - x = e²t x(0) = 0

Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine, as in Example 4. sin(x)

Question 6. Continuous functions Consider the function f(x) = -2x, x < 0 0 < x < 1 x-1, x ≥ 1 (a) Sketch f. (b) At which points of its domain is the function continuous? (c) At which points of its domain is the function discontinuous? Appeal to the definition of continuity in justifying your answers.

Make a list of all possible rational zeros of f(x) = x5 2x² + 4x + 5. If the answer is not an integer, enter it as a fraction. If there are multiple zeros, separate the answers with commas (). Rational Zero Candidates:

Compute the value of the discriminant and give the number of real solutions of the quadratic equation. -4x²+7x-1=0

Solve the absolute value inequality. |x|<3 Rewrite the inequality without absolute value bars. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answers.) A. X< B. X< or x> C. <x<

Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line. 2x+4> 10 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer using interval notation.) B. The solution set is Ø.

Solve the absolute value inequality. |3x-9| > 15 Rewrite the inequality without absolute value bars. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answers.) A. 3x-9> __ B. 3x-9< __ or 3x-9>__ C. __<3x-9< __

If nominal rate of interest is 4% per annum and interest is compounded quarterly, then find the effective rate of interest.

Use the given conditions to find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas. cos u = -4/5, π/2<u<π sin 2u = ________ cos 2u =________