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february 2020
23

Mathematics Questions and Answers February 23, 2020

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2. If x 2 is a zero of the polynomial function P(x) 11x 17x 6x3 2, find the sum of the other zeros of the polynomial.

If the tangent line to y f(x) at (7, 5) passes through the point (0, 4), find f(7) and f(7). f(7) f(7) Question Help Message inco

7. Assume c 0, find lim F 0 cx11

Solve the following equation for x. e5x13 x (Type an exact answer.)

a. Graph the function f(x) x4x3. b. Identify the point (a,f(a)) at which the function has a tangent line with zero slope. c. Confirm your answer to part (b) by making a table of slopes of secant lines to approximate the slope of the tangent line at this point.

Given the points A(2.0), B(7.13), C(1.6), D(4,5), E(2.2), and F (3242), find the position vector equal to the following vectors a. AB b. AC d. CO ABCD (Type exact answers, using radicals as needed.). b. AC00 (Type exact answers, using radicals as needed.) CEF00 (Type exact answers, using radicals as needed.) d.co00 (Type exact answers, using

fm the indicated operation. Write the result in standare 32i)(661) A. 306i B. 12 61 18 OC. 306i OD. 630i

Write the expression in the standard form a (5 3i) (57i) (53i)(57)(Simplify your answer) bi.

Solve the system with the addition method 7x 5y 33 10x 9y 49 Answer (x, y) ) Enter your answers as integers or as reduced fraction(s

Let f(x, y, z) xy z and x s, y st, and z st. (a) Calculate the primary derivatives dy af 4x32 2xy 2z (b) Calculate 8 2st as as 3st 3 35212 as I (c) Use the Chain Rule to compute of S 88

Multiply or divide the following rational expressions, as indicated, and simplify your answer. x 7x12 x 4 x3x18 x4

Construct a function that passes through the origin with a constant slope of 1, with removable discontinuities at x 6 and x 4. Enclose numerators and denominators in parentheses. For example, (a b)(1n). (x) sin (a) 00

Find fg, fg, fg, and fg and their domains. f(x) x x, g(x) x Find (fg)(x). Find the domain of (f g)(x). (Enter your answer using interval notation.). Find (f g)(x). Find the domain of (fg)(x). (Enter your answer using interval notation.) Find (fg)(x). Find the domain of (fg)(x). (Enter your answer using interval notation.) Find (4)(x). Find the

Follow the steps for graphing a rational function to graph the function P(x) 4 XXb XX 6 x36 A. P(x) (Type your answer in factored form. Do not simplify.) (x6)(x6) B. P(x) cannot be factored further. What is the domain of P(x) Select the correct choice below and, if necessary, fill in the answer box to complete you choice. OA. xx (Type an integer

Ben and Evan start from Listowel and drive along perpendicular roads. Ben drives at a speed of 45 kmh, and Evan travels at a speed of 40 kmh (ok, it was icy). If Evan begins one hour before Ben, at what rate are their cars separating three hours after Evan leaves olesworth Bowling E B Palmerston Norgan theatre

a. Sketch the given directed line segment. b. Write the vector in component form. c. Write the vector as the linear combination of the standard unit vectors i and j. d. Sketch the vector with its initial point at the origin. 9. Initial Point (2,0)..... Terminal Point (5, 5)

To offer scholarships to children of employees, a company invests 15,000 at the end of every three months in an annuity that pays 10 compounded quarterly. a. How much will the company have in scholarship funds at the end of ten years b. Find the interest. Click the icon to view some finance formulas. a. The company will have in scholarship funds.

f(x). Subsequently, we used that fact to compare the value of the integral with the value of an antiderivative obtained by using integration rules. Now, suppose on one hand f(x) is integrable but cannot be differentiated using the integration rules available. On the other hand, the integral can be evaluated numerically for any value of x. Many

Is the following matrix invertible Select the correct answer below Yes, the matrix is invertible. No the matrix is not invertible 435 3 4 332 44 3 4 2 5

1 Points Find all zeros of the polynomial. (Enter your answers as a commaseparated list. Enter all answers ind P(x) x 5x35x5x36 x

Find the intercepts of the function. a. f (x)x2x15 State the domain of the function. x3x2 a. y x4 b. y x10 x5 Determine if the function is even, odd or neither. a. f (x) f(x)1 b. yxx7 c. f(x) 3 XX b. y4x7x213x100 c. f (x)2x10 Determine the vertical asymptote(s). x35x7 a. y 23x28 x4x4x6 b. f(x). x32x5x6

3 A water tank, shown to the right, is shaped like an inverted cone with height 4 m and base radius 1 m. a. If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank Use 1000 kgm for the density of water and 9.8 ms for the acceleration due to gravity. b. Is it true that it takes half

For the spinner below, assume that the pointer can never lie on a border line. Find the following probabilities. (Enter the probabilities as fractions.) (a) P(D) (b) P(E) (c) P(F) D E F Need Help Read It Additional Materials Tech Guide Excel

a. Use the appropriate formula to find the value of the annuity. b. Find the interest. Periodic Deposit Rate Time 90 at the end of every six months 6.5 compounded semiannually 40 years Click the icon to view some finance formulas. xm a. The value of the annuity is W SO Formulas (Do not round until the final answer. Then round to the nearest

12. Set up but do not Evaluate Use sperical cordinates to set up the integral for the volumenof the solid bounded above by the sphere x y z 1 and below by the cone Z x y

Suppose that in 1623, a man bought a diamond for 29. Suppose that the man had instead put the 29 in the bank at 3 interest compounded continuously. What would that 29 have been worth in 2000 In 2000, the 29 would have been worth (Do not round until the final answer. Then round to the nearest dollar as needed.)

Let f(x)5x2 and g(x) x1. (fg)(x) help (formulas) (fg)(x) help (formulas) (fg)(x) help (formulas) (4) help (formulas) The domain of (fg)(x) is help (intervals) The domain of (fg)(x) is help (intervals) The domain of (fg)(x) is The domain of (4) is help (intervals) help (intervals)

TT Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume 0

Jenny and Jim are standing on a riverbank, at points A and B respectively. (See the figure below.) Jim is 160 meters from a house located across the river at point C. Suppose that angle A (angle BAC) is 41, and angle B (angle ABC) is 73. How far are Jenny and Jim standing from one another Round your answer to the nearest tenth of a meter. 41 73

Find the point (x, y) on the unit circle that corresponds to the real number t (x,y)( ST

Submit Answer 12.525 Points DETAILS PREVIOUS ANSWERS SCALCET8 3.8.017. MY NOTES PRACTICE When a cold drink is taken from a refrigerator, its temperature is 5C. After 25 minutes in a 20C room its temperature has increased to 10C. (Round your answers to two decimal places. (a) What is the temperature of the drink after 40 minutes C 12.15

For the exponential function f(x) 6(5)1, find f(6). f(6)24300000

9. Determine whether the points lie on a straight line. (a) A(2, 4, 2), B(3, 7, 2), C(1, 3, 3)

Question 4 Perform the indicated operation simplify. Express the answer as a complex number. (61)(51) Question Help Video M

X 5 5 5 5 5 Submit Answer 2. 1.04 Points DETAILS SCALCET9 2.XP.5.005. 02 Submissions Used For the function f, how would you remove the discontinuity In other words, how would you define f(4) in order for f to be continuous at 4 f(x) 22x8

4. The graph of a function g is shown on the xyplane on the interval (7,7. a. A table of selected values is given for a different function h, which has only one real zero. B h(x) 5 2 2 7 0 3 2 0 4 13 7 20

blem 11 Find matrices A, x, and b that express the below system of linear equations as a single matrix equation Ax b. 7x17x2 x3 6x4 2 2x4x28x3 5x4 2 3x1 2x2 4x3 7x4 1 7 7 1 6 x1 7 7 1 6 (A) A 2 4 8 5 x X2 b (B) A 2 4 8 5 3 2 4 7 3 2 4 X3 X1 7 7 1 6 7 7 1 6 (C) A 2 4 8 ,x b (D) A2 4 8 5 ,X X3 3 2 4 3 2 4 7 X4 108019810 X4

Analyze the polynomial function f(x) 7x7x7x21. Answer parts (a) through (h). (a) Determine the end behavior of the graph of the function. 1 3 The graph of f behaves like y 7x for large values of x. (b) Find the x and yintercepts of the graph of the function. The xintercept(s) isare (Simplify your answer. Type an integer or a fraction. Use a

In the process of finding the inverse of the following matrix, explain the indicated row operation. 3 3 6 100 1 3 10 0 10 1 3 5 0 0 1 Step 1 Switch row 1 and row 2. 1 3 10 0 1 0 Answer to Step 1 3 3 6 100 1 3 5 0 0 1 Step 2 Explain the row operation to change the answer from Step 1 to the result below. 1 3 10 0 1 0 Answer to Step 2 0 6 24 1 30 1

To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure (Figure 1). Suppose that the satellite has a mass of 1200 kg and a radius of 3.0 m, and that the rockets each add a mass of 250 kg. Part A What is the steady force required of each rocket if the satellite is to

Find the quotient and remainder using synthetic division. x4x3 x2x2 X2 quotient remainder

You are walking from home to the grocery store, which is 2 miles away. Twenty minutes later and halfway to the store, you realize that you forgot to bring money, so you turn around, return home, and then walk back to the store. A) Draw a graph that models your distance from home over time Assume that you are walking the same speed the entire trip.

Find the period and the amplitude. y 3 cos(4x) period amplitude 9 2 3 D

11 ft 23 ft Find the angle of elevation of the sun from the ground to the nearest degree. degrees

write down the first three terms of each of the following sequences. a) (4) (1) (up) 2) 3,8, r rezt W b) un (5n2), nezt b) (1, 1

7. The height of an object thrown from a cliff is modeled by h(t)4.913.6163, where is time in seconds, and h(t) is height in metres. a) What is the average velocity from time Os to time 1s A4 b) What is the instantaneous velocity of the object at 1 seconds

2. The cost, C, in dollars, of shipping a package that weighs w pounds can be modeled by the piecewise function given by 11 C(w) 0 10 a. How much does it cost to ship a package that weighs 1.5 pounds b. How much does it cost to ship a package that weighs 5 pounds c. How much more does it cost to ship a package that weighs 10 pounds than a package

X 12x Let f(x) and g(x) Express f(x)g(x) as a rational function. X7 12x f(x)g(x)for x (Use a comma to separate answers as needed.)

Find the area of the shaded region. Use 3.14. 26 m m r13 m 26 m

21. Find the center and radius for the circle (a) (x2)(y3) 16 (b) x(y3) 25 ..

Drag the choices above into the spaces below. A. D. B. Ay D E. AY Q F. Ay G G

213x x3 Let f(x) 25x2 x 3

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 9x 25y 15x 250y 543 0 O parabola O ellipse O circle O hyperbola Submit Answer

Systolic blood pressure levels above 120 mm Hg are considered to be high. For the 100 systolic blood pressure levels listed in the accompanying data set, the mean is 123.62000 mm Hg an standard deviation is 14.30602 mm Hg. Assume that a simple random sample has been selected. Use a 0.05 significance level to test the claim that the sample is from

(1 point) Use Stokes Theorem to find the circulation of F 4yi 5zj6xk around the triangle obtained by tracing out the (4,0,0) to (4, 0.6), to (4,3, 6) back to (4,0,0). Circulation F dr

Suppose that in a memory experiment the rate of memorizing is given by M(t) 0.006t 0.3t, where M(t) is the memory rate, in words per minute. How many words are memorized in the first 11 minutes words Round your answer to the nearest whole word

Factor the polynomial completely. Q(x)x256 Q(x) Find all its zeros. State the multiplicity of each zero. (Order your answers from smallest to largest real, followed by complex answers ordered smallest to largest real part, then smallest to largest imaginary par with multiplicity x X with multiplicity x with multiplicity x with multiplicity

K Consider the functions f(x)9x1 and g(x) 1 (a) Find f(g(x)). (b) Find g(f(x)). (x1). (c) Determine whether the functions f and g are inverses of each other. (Use a comma to separate answers as needed.) B. No values should be excluded from the domain. (b) What is g(f(x)) g(f(x))x (Simplify your answer.) Give any values of x that need to be

Find all values of x satisfying the following conditions. X5 x9 Y 223 and yY21 Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The value(s) of x for which yy2 1 isare (Type an integer or a simplified fraction. Use a comma to separate answers as needed. OB. y1 y21 for all values of x. There are

Suppose the charge q on a capacitor is given by q (2.95 C)et(0.220 s). (a) Find the value of q when t 0.0380 s. C (b) Find the value of t when q 1.12 C.

Solve the right triangle shown in the figure. A 0 B 69 C a b C 16 0 B C C b A

5. A table of selected values is given for a onetoone function, g. At x5,g has a vertical asymptote. I g(x) 5 undefined 2 14 0 11 3 1 6 0 a. What is the yintercept of g1 b. Write the equation for the horizont

Find two vectors parallel to v with three times the magnitude of v. V (9,3) Select the correct two vectors below. 9 3 A. 310 310 B. (9,3) C. 9 3,10 3 310 310 D. (27,9) E. (9,27) (27,9)

4. (2 points) Consider the curve (a helix) parametrized by r(t)(cost, sint, at) where a 0 is a positive constant. As a increases, does the curvature increa decrease, or stay the same Justify your answer by describing what happens to curve and interpreting the formula , where s K , where s s(t) is the reparametrizat dT ds of r such that r(s) 1.

If 30,000 cm of material is available to make a box with a square base and an open top, find the largest possible volume (in cm) of the box. cm

SHORT ANSWER. Show all work for full credit. 23) Find the total distance traveled by a particle on the xaxis with velocity given by v(x)3sin(2x) for the interval 0, 2.5 23)

Using a rock wall as one side and fencing for the other three sides, a rectangular patio will be constructed. Given that there are 172 feet of fencing available, determine the dimensions that would create the patio of maximum area and identify the maximum area. Enter only the maximum area. Do not include units in your answer.

Find the area of the largest rectangle that can be inscribed in the ellipse 1.

direction that is 165 counterclockwise from the x axis. Part A Find the x component of this vector. Express your answer in meters. View Available Hint(s) Hint 1. How to approach the problem Hint 2. Simplify expression for the horizontal component Tx Submit Request Answer

K f(x)4916x2 OA. OB. OC. D. 0 44

0 arithmetic geometric 2 Find the common difference or ratio. 12 Find the sum of the first 15 terms. 07.5 Need Help Read Submit Answer to low note DETAILE 005OLIC ANSWEDE LARPRECALCOMPR7.9.2007 MY

(d) Use a graphing utility to find the line of best fit. y 2.0357 x 1.3214 (Type integers or decimals rounded to four decimal places as needed.) (e) What is the correlation coefficient r (Type an integer or decimal rounded to three decimal places as needed.)

Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values of f. (Enter your answers as a commaseparated list. If an answer does not exist, enter DNE.) f(x)sin(x), 0 x absolute maximum value

Given the function defined by f(x)xx4x4 2. (a) (b) (c) Find the zeros of f. Write an equation of the line tangent to the graph of fat x1. The point (a,b) is on the graph of and the line tangent to the graph at (a,b) passes through the point (0,8) which is not on the graph of f. Find the values of a and b.

The campus of a college has plans to construct a rectangular parking lot on land bordered on one side by a highway. There are 680 ft of fencing available to fence the other three sides. Let x represent the length of each of the two parallel sides of fencing. (a) Express the length of the remaining side to be fenced in terms of x. (b) What are the

The sum of the interior angles of a polygon with n sides is given by the formula 180 (n 2). To solve for n, we set up the equation 180 x (n2) 2340 and solve for n. The correct answer is option C 15 sides.

2. (12 pts.) Test the following equation for symmetry. Show and label each symmetry test. Make sure that you state any types of symmetry that the graph of the equation exhibits. x3 2y83y4

Find a power series solution of the form y(x) o Cx of the given differential equation. 0 First compute y (x) x1 (Use cn for c,, in your answer) Then xy (x) y x2 100 (Use c0 for co, c1 for c, cn for c, and cnm1 for C1 in your answer) Requiring that the terms of this series for x2y y vanish gives Co C C Cn1 for n 2 The series solution

10 0 5 10 10 5 10 powered by desmos a) Find the vertical asymptote(s). Separate multiple answers with commas. Enter None if appropriate. b) Find the horizontal asymptote. Enter None if appropriate. y

Consider the function f(x) 100 (x 10) defined on 0, 10. (a) Compute the left Riemann sum L6. L6help (numbers) (b) Compute the right Riemann sum R6. R6help (numbers) (c) Compare the two values found in (a) and (b). The left Riemann sum is the right Riemann sum.

11 nv 0234 a) Identify the individual, variable, random variable X and the random variable in the context of this problem. The individual is a randomly selected college student The variable information collected from each individual is the percentage of 234 randomly selected college students that are lefthanded X The wording in context for the

Find the value of x. X x 3

2425 Find the magnitude of the resultant force and the angle it makes with the positive xaxis. 24. YA 20 lb 0 25. YA 200 N 45 300 N 60 30 X 0 X 16 lb

Condense the lefthand side into a single logarithm. Then solve the resulting equation for A. A log(x) log(y) 3 log(z) log(A) help (formulas)

where Friyj and S is the curved portion of the right circular cone given by x y 0, 0 x 1. Hide Transcribed Text (b) Calculate iint S(boldsymbol abla times boldsymbolF) cdot d boldsymbolS where and F xi yj S is the curved portion of the right circular cone given by NT

The graph of f(x) 5(x9)22 is a parabola that opens downward with its vertex at (x, y) and f(9) is the maximum value of f.

Find a vector function that represents the curve of intersection of the paraboloid z 3x5y2 and the cylinder y 6x2. Use the variable t for the parameter. Hint The answer prompts you to use x t. (1)(200

Match the exponential function with one of the graphs labeled I or II. Rx) 51 I 3 21 y 3 O The graph of f(x) 5 1 is graph I. O The graph of f(x) 5 1 is graph II. II 3 2 X X 1 2 3 3 2 1 1 2 3

Is there a value of n which makes y x a solution to the equation 3x dy dx y If so, what is the exact value Enter NA if there is no value for n. n

Find the equation of the line segment between Po(3, 1, 4), and P (0,5,2)

Find the rational number representation of the repeating decimal. 0.945

() The radius r of a sphere is expanding at a rate of 11 metres per minute. Determine the rate at which the volume is changing with respect to time when r 6m. The volume is changing at a rate of mmin.

The function f(x)3x is an exponential function with base Need Help Read It (2) f(0) F(2) , and f(6)

Find the equation of the slant asymptote of the rational function. f(x) 2x310x27x 24 2x25 The equation of the slant asymptote is y

Question 10 If 6000 dollars is invested in a bank account at an interest rate of 7 per cent per year, Find the amount in the bank after 6 years if interest is compounded annually Find the amount in the bank after 6 years if interest is compounded quarterly Find the amount in the bank after 6 years if interest is compounded monthly Finally, find

Consider a triangle ABC like the one below. Suppose that c 61, a 74, and C 38. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If no such triangle exists, enter No solution. If there is more than one solution, use the button

Use an inverse trigonometric function to write as a function of x. 0 9

Complete the table so that sin 0 is expressed in terms of the functions given across the top sin 0 cos 0 sin 0 tan 0 tan 01 tan 20 cot 0 1 cos 20 1 tan 20 1 cot 20 1 cot20 1 cot20 1cot 20 1 cot 20 sec 0 CSC 0 1 CSC 0

Simplify the following expression. 8 (9a 1810) 48(181819a183)31 Show your work here Hint To add an exponent (a), type exponent or press

10 10 5 5 Match each graph to the expression that transforms the black solid graph into the blue dashed graph. 5 0 5 10 5 5 1 0 5 10 10 f(x)2 f(x2) (x) ( x ) 5 5 10 5 10 5 0 5 10 5 10 10 5 10 5 0 5 10 5 5 5 10

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