College Math - Others Questions

a Plot the following coordinates 7 7 5 7 7 5 5 5 What shape do the points make O a Square O b Diamond Oc Rectangle

Solve the system of equations by using the Substitution meth x OE y 0 4x 4y 560 y 5x 34 0

Find the slope and y intercept of the following equation 10x 2y 260 0 slope y intercept

For the equation x 10y 50 find the missing value in the following ordered pair 10

What valid inference can be made from the following proposition Take the truth value as specified All amusement parks are crowded places T Some crowded places are not amusement parks T All crowded places are amusement parks F No amusement parks are crowded places F All crowded places are amusement parks T

Find A Begin by finding A 1 and then evaluate its determinant Verify your result by finding A and then applying the formula A1 1 A A 0 1 1 A 9 1 9 1 9 6

Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution 5x1 X2 6x3 x4 7 x2 3x3 4x4 5 3x4 9 1 X1 2x1 5x 2x3 Xi 5X2 6x3 O The system has a unique solution because the determinant of the coefficient matrix is nonzero O The system has a unique solution because the determinant of the coefficient matrix is zero O The system does not have a unique solution because the determinant of the coefficient matrix is nonzero O The system does not have a unique solution because the determinant of the coefficient matrix is zero

Determine which property of determinants the equation illustrates 3 1 4 00 0 0 97 8 O If one row of a matrix is a multiple of another row then the determinant of the matrix is zero O If one row of a matrix consists entirely of zeros then the determinant of the matrix is zero If two columns of a matrix are interchanged then the determinant of the matrix changes sign O If a row of a matrix is multiplied by a scalar then the determinant of the matrix is multiplied by that scalar O none of these

Use either elementary row or column operations or cofactor expansion to find the determinant by hand Then use a software program or a graphing utility to verify your answer 0 1 10 1 1 90 1 9 10 5 1

A local carnival features a booth where a person guesses the participant s age Suppose that a 21 year old person has his ag guessed as 30 years a Compute the absolute error Simplify your answer completely AE Interpret the result The guesser estimates a person s age correctly this proportion of the time The guesser s estimate was off by this much relative to the participant s age This is the ratio of the guesser s estimate to the participant s age The guesser s estimate had this percent error The guesser s estimate was off by this many years b Compute the relative error Round to three decimal places Simplify your answer completely RE Interpret the result The guesser estimates a person s age correctly this proportion of the time The guesser s estimate was off by this much relative to the participant s age This is the ratio of the guesser s estimate to the participant s age The guesser s estimate had this percent error The guesser s estimate was off by this many years

nd IAI IBI AB and IABI Then verify that IA B AB 49 2 A 4 2 B 3 1 94 0 a A b B c AB d AB A

Let A and B be square matrices of order 3 such that A 6 and B 9 a Find ABI b Find 2A c Are A and B singular or nonsingular Explain O A and B are both singular because they both have nonzero determinants O A and B are both nonsingular because they both have nonzero determinants OA is singular but B is nonsingular because A B OB is singular but A is nonsingular because A BI d If A and B are nonsingular find A1 and B 1 If the inverse is undefined enter UNDEFINED A 1 B e Find AB 1

Find the value of k such that A is singular Enter your answers as a comma separated list 0 k 1 k 1 k 1 k O

Use a determinant to decide whether the matrix is singular or nonsingular 13 3 15 0 3 2 3 10 singular O nonsingular 7

Use the fact that CA C A to evaluate the determinant of the nx n matrix 6 9 A 2 15 12 15 STEP 1 Factor out the greatest common divisor 12 15 1 STEP 2 Find the determinant of the matrix found in Step 1 STEP 3 Find the determinant of the original matrix

Find AI IBI A B and IA B Then verify that A B A BI 1 30 A a b B c A B B 1 3 0 11

Solve v C n 1 s c for c If appropriate write only the positive root Assume all variables are nonzero

Solve P P 0 for p Assume the variable is nonzero P

A snack bag of potato chips is advertised as weighing 1 5 ounces Suppose a bag of potato chips is selected at random from snack pack and weighs 1 523 ounces a Compute the absolute error Simplify your answer completely AE Interpret the result The advertised weight is incorrect this proportion of the time This is the average weight of a single potato chip The advertised weight has this much percent error with the random sample s weight The advertised weight was this many ounces off of the random sample s weight The advertised weight was off by this much relative to the random sample s weight b Compute the relative error Round to three decimal places Simplify your answer completely RE Interpret the result The advertised weight is incorrect this proportion of the time This is the average weight of a single potato chip The advertised weight has this much percent error with the random sample s weight The advertised weight was this many ounces off of the random sample s weight The advertised weight was off by this much relative to the random sample s weight

Evaluate lim f x where f x X 5 4 5 5 4 Limit does not exist 0 6 x 25 x 2x 15 6 if x 5 if x 5

The sales of a math performance enhancing drug are given by S t when t 0 65 60 45 55 75 MY NOT 300t 1 where t is in years and S t is in millions of dollars What is the rate of change of sales in millions of dollars per yea t 5

If g s 8s 16s 4 s 8 12 5 5 33 2 S 08 s 8 s S 16 s S 32s3 2 32 5 8 O 12 s s O 16 s 4 s3 2 find g s

Evaluate lim f x where f x X 4 4 Limit does not exist 8 0 6 X 8 2 8 x 12x 36 if x 4 if x 4 if x 4

If f x O8 5 4 5 00 08 x39x 13 x 4 8 5 8 find f 1

If f x simplify X 1 2 2 h 1 h 1 1 2 2 h 1 4 h 1 4 h f 2 h f 2 h

Determine whether each statement is true or false J a The break even point occurs where the total revenue function is first equal to the total cost function OTrue False b If lim f x and lim f x both exist then lim f x also exists x a x a x a True False c If lim f x does not exist then lim f x does not exist x a x a True False d According to the law of demand p d x is an increasing function True False e If lim f x does not exist then lim f x does not exist x at x a True False

Let f x x kif x 3 kx 7 if x 3 For what value of k will f x be continuous everywhere 40 35 30 5 10

If x 49 5 x 12 and g x 2x 19 find the composition fog 4 63 O O O O O 68 74 59 67

Evaluate lim h 0 3 1m 1 1 2 3 3 2 3 h 3 h

Find an equation for the line tangent to the curve y 12 x 2x at x 9 Oy 7x 11 Oy 4x 18 Oy 7x 9 y 4x 11 Oy 9x 27

What is the domain of the function f x O 4 00 O 3 4 U 4 00 3 00 O 4 U 4 4 U 4 00 4 4 x 3 x 16

The demand and supply functions for Penn State ice hockey jerseys are p d x x 3x 39 P S x 2x 3 where x is the number of thousands of jerseys and p is the price in dollars Find the equilibrium price 11 16 14 7 9

Evaluate lim X 60 26 0000 81 0 8 0 60 60x9 62x8 16x 94 26x9

Consider the position function s t 16t2 92t representing the position of an object moving vertically along a line Sketch a graph of s with the secant line passing through 0 25 s 0 25 and 2 s 2 Determine the slope of the secant line and explain its relationship to the moving object A 120 22 0 25 Q Q 5 B 120 22 0 25 Type an integer or a decimal The slope of the secant line is msec What is the relationship of the slope to the moving object Q Q 57 OA The slope is the average velocity of the object over the interval 0 25 2 OB The slope is the instantaneous velocity when t 2 C The slope is the average velocity of the object over the interval 22 120 OD The slope is the maximum velocity of the object O C 120 22 0 25 EN Q Q G

Question 8 Construct a circuit that is equivalent to the given expression a xy yz 3 points

Solve Write a mixed numeral for the answer 6 6 Find the perimeter distance around of the polygon below Each side of the polygon has the same length side length 3 yd 7 A painter used 6 gallons of paint to paint the front of a house and another 65 gallons 9 to paint the back How much paint did he use in total 2 8 Mr Meredith is building a table The top will have a piece of marble 24 inches by 16 inches bordered by 22 inches of wood on all four sides Give the overall dimensions of 4 the table top 9 June wants to work for 14 hours at her part time job this week She has already 4 worked 5 hours How many more hours does she need to work 2 10 There were 25 3 yards of wire on a spool After a customer bought 27 yards of wire 8 from the spool how many yards were left 2 10

Ve are wanting to determine the resultant force and its angle for Point A for the system shown below Use the following information Point A is shown by the blue dot The forces are shown in black The blue lines are used to show direction The positive x direction is to the right and the positive y direction is up F 175 lb 1 F3 95 lb F4 45 lb 209 3 20P 30 F 75 lb

The total monthly revenue R x in dollars generated from sales of Math t shirts is related to the amount x spent on advertising by R x 2x 24x 30x 60 where x is in hundreds of dollars Compute the rate of change of revenue with respect to the amount of money spent on advertising R x Is monthly revenue increasing faster when the amount of money spent on advertising is 320 dollars or 400 dollars 320 dollars 400 dollars

Compute each of the following derivatives a 2x 8 b X dx 18 c 5 x 8 7 dx

Consider the function f x x4 4x 36x Determine the number of points on the graph of y f x that have a horizontal tangent line In other words determine the number of solutions to f x 0 Determine the values of x at which f x has a horizontal tangent line Enter your answer as a comma separated list of values The order of the values does not matter Enter DNE if f x does not have any horizontal tangent lines

If g s g s 4s 16s 6 s compute g s Hint Simplify g s by writing it as a sum of power functions before computing g s

If g s 8 s 5 S g s S 20 compute g s

Determine the equation of the line tangent to the curve y 3x X y at the point 2 7

Derivatives Course Packet on using the derivative to compute limits If f x 4x 15x 31 evaluate lim f 3 h f 3 h 0 h If an answer does not exist enter DNE Submit Answer

J If h z 6z8 3z5 5z 2 compute h z h z

Let f x x7 5 x4 7 Compute f x by first expanding f x and then differentiating term by term f x

If g s g s 2s 17s 8 s 1 compute g s Hint Simplify g s by writing it as a sum of power functions before computing g s

Compute each of the following derivatives a 10x dx b 4x3 4 dx 30 0 x dx

Let f x x7 2 2 x5 7 Compute f x by first expanding f x and then differentiating term by term f x

Your car has a 20 gallon gas tank and is full when you leave your house You are using gas at a constant rate and therefore the amount of gas in your car is a linear function of the time you are driving After traveling for two hours your car is half full Find the slope of the linear function Select one O a 5 O b 5 O c 5 2 O d 2 5