Oliver has a points card for a movie theater.
- He receives 65 rewards points just for signing up.
- He earns 9.5 points for each visit to the movie theater.
- He needs 141 points for a free movie ticket. Write and solve an equation which can be used to determine v, the number of visits Oliver must make to earn a free movie ticket. Answer Attempt 1 out of 2 Equation: □
Answer: v=□
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Use the Quadratic Formula to solve the equation x2−8x+61=0x=□ (Separate answers by a comma. Write answers as integers or reduced fractions.) If the answer is radical use sqrt(5) to denote 5 (use the correct radicand in the problem!) If the answer is complex use i to denote i.
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How could you correctly rewrite the equation 4(5+3)=2(22−6) using the distributive property?
20+12=44−12
As a town gets smaller, the population of its high school decreases by 7% each year. The senior class has 320 students now. In how many years will it have about 100 students? Write an equation. Then solve the equation. Write an equation to represent this situation. Let t be the number of years before the class will have 100 students.
□
(Type an equation using t as the variable. Use integers or decimals for any numbers in the equation.)
Solve the equation.
lnt=□ years the senior class will have about 100 students.
(Type an integer or decimal rounded to the nearest hundredth as needed.)
6. Two masses are tied to a rope on a pulley, as shown below.
a. When the system is released from this position, what is the acceleration of the 2.0-kg mass?
b. How long does it take for the 2.0−kg mass to fall to the floor?
Problem 6
Sothy plans to walk 10000 steps. He starts his walk at 8:00 AM. At 8:23 AM, his phone tells him that he has taken 2000 steps. If he continues at this rate, when will he reach 10000 steps?
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Does the equation below represent a relation, a function, both a relation and a function, or neither a relation nor a function?
y=9x2−9x+20
A. both a relation and a function
B. function only
C. relation only
D. neither a relation nor a function
Consider the curve given by the equation (2y+1)3−24x=−3.
(a) Show that dxdy=(2y+1)24. No response entered
(b) Write an equation for the line tangent to the curve at the point (−1,−2). No response entered
(c) Evaluate dx2d2y at the point (−1,−2). No response entered
(d) The point (61,0) is on the curve. Find the value of (y−1)′(0).
(3) 55∘F
Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through (8,−1) and perpendicular to the line whose equation is x−7y−9=0
A car has a velocity of 36m/s, and can accelerete at 22m/s2. How much time will it take for him to reach 81m/s ?
3.48 seconds
2.05 seconds
0.17 seconds
1.64 seconds
A company makes wax candles in the shape of a cylinder. Each candle has a radius of 3 Inches and a helght of 4 Inches. If the company used 3278.16 in 3 of wax, how many candles did it make? Use 3.14 for π, and do not round your answer.
candles
Question
A roclangular photograph that is 5 inches wide and 7 inches long is enlarged to produce a photograph is 12 inchos wide. If the enlarged photograph is in proportion to the original, what is the length, in inche the enlarged pholograph?
1235584
8
12
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A company uses paper cups shaped like cones for its water cooler. Each cup has a helght of 6 cm , and the base has a dlameter of 7 cm . How much water is needed to fill 200 cups? Use 3.14 for π, and do not round your answer.
cm3
01610.0 points
An outfielder throws a 1.73 kg baseball at a speed of 108m/s and an initial angle of 14.3∘. What is the kinetic energy of the ball at the highest point of its motion? Answer in units of J .
5. Which equation is linear? 4. xy=60
b. 3x−2y=52y−x2−3x+1 16. State whether each graph has line symmetry any lines of symmetry of points of symmetry.
a. point symmetry; (0,0)
coint symmetry; (−2,
b. (ine symertry; x=−2
a. line symmetry; y=1
Choose the correct answer :
(5 points)
1) A particular solution for the differential equation y(4)+y(3)=2+4ex is
(a) A+Bex
(b) A+Bx+Cx2+Dex
(c) Ax2+Bx2ex
(d) Ax2+Bex
e)NOTA
2) The solution for the I.V.P sin(t)y′′′+t−31y′′+ety=t3y(1)=0y′(1)=1y′′(1)=−1 is guaranteed on
a) (0,3)
b) (0,π)
c) (−∞,3)
d) (−∞,∞)
3) If a series solution is to be found for y′′−4xy′+4y=0,y(0)=2,y′(0)=3 then a2=
(a) -4
(b) 8
(c) -8
(d) 1
e)NOTA
4)Suppose the solution to the differential equation y′′+3y=0 is written as a power series y=∑n=0∞anxn What is the lower bound of the radius of convergence of this power series?
a) 0
b)1
c)2
d) 3
e) ∞
5) The general solution for y′′′+9y′=0 is :
a) c1+c2cost+c3sint
b) c1+c2t+c3e9t
c) c1+c2e3t+c3e−3t
d) c1+c2e3t+c3te3t
e)NOTA
false:
(5 points)
form of yp for y′′′−3y′+2y=xex is (Ax3+Bx2)ex
the roots of the indicial equation are −0.3,1.7 then the D.E. has two nearly independent solutions
W(f,g,h)=sint then the functions f,g,h are linearly dependent
er bound for the radius of convergence for the series 1 of (1−x3)y′′+4xy′+y=0,x0=3 is 2
=1 is a R.S.P for (x−1)2y′′+3y′+(x−1)y=0
ue or false:
(5 points)
- The form of yp for y′′′−3y′+2y=xex is (Ax3+Bx2)ex
- If the roots of the indicial equation are −0.3,1.7 then the D.E. has two linearly independent solutions
- If W(f,g,h)=sint then the functions f,g,h are linearly dependent
lower bound for the radius of convergence for the series lution of (1−x3)y′′+4xy′+y=0,x0=3 is 2
- x=1 is a R.S.P for (x−1)2y′′+3y′+(x−1)y=0
Q1) True or false:
(5 points) 1- The form of yp for y′′′−3y′+2y=xex is (Ax3+Bx2)ex
2- If the roots of the indicial equation are −0.3,1.7 then the D.E. has two linearly independent solutions 3- If W(f,g,h)=sint then the functions f,g,h are linearly dependent
4- The lower bound for the radius of convergence for the series solution of (1−x3)y′′+4xy′+y=0,x0=3 is 2 5- x=1 is a R.S.P for (x−1)2y′′+3y′+(x−1)y=0
8. Write the equation of the line in point slope form that contains P(3,−6) and is parallel to y=−4x+
A) y−3=41(x+6)
E) y+6=−4(x−3)
D) y−6=−4(x−3) 9. Write the equation of the line that contains P(−1,6) and is perpendicular to y=21x+2 ?
A) y=21x+213
B) y=2x+8
D) y=−21x+211
E) none of these Unit 2-Foundations of Geometry 10. Vertical angles are never
A) congruent
B) right angles
C) adjacent
D) supplementary
E) complementary 11. Are O,N, and P collinear? If so, name the line on which they lie.
A) Yes, they lie on the line NP
B) No, the three points are not collinear
C) Yes, the lie on the line MO
D) Yes, they lie on the line MP
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You have the following observations. Stock HJK will pay dividends $4 per share next year. The S\&P 500 index return averages 10% a year and the rate on Treasury bill is at 6\%. You have downloaded data from Bloomberg and estimated the beta of Stock HJK at 1.25.
A. What is the required rate of return?
B. What is the price of the stock if the amount of dividends stays at $4 per share forever?
6 A ladder leans against a brick wall. The foot of the ladder is 6 feet from the wall. The ladder reaches a height of 15 feer on the wall. Frod to the nearest degree, the angle the ladder makes with the wall. Round to the nearest whole number. Show all work for full credit.
□
kid's ride at Story Book Park has a diameter of 6 m and 8 boats around the outside. If the oats are numbered in order, how far is it directly from the 1st boat to the 4th boat? Round our answer to two decimal places. (4 marks)
PDF w/o expl 8. Slide \#8 10 pts possible A 790 N student stands in the middle of a frozen pond having a radius of 4.9 m . He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 3.5 kg physics textbook horizontally toward the north shore at a speed of 6.6m/s. The acceleration of gravity is 9.81m/s2.
How long does it take him to reach the south shore? Answer in units of s. Answer in units of s. Your response...
A) A farm has two cylindrical silos for storing grain as shown. Silo A Silo B How much greater is the volume, in cubic feet, of the larger silo than the smaller silo? Use 3.14 for pi. Show your work.
(3 points) The volume of Silo A is: ift t3. The volume of Silo B is ft3 The volume of Silo A is □ cubic feet larger than the volume of the Silo B.
33,912.020,347.2
: 6,782.4
27, 129.6
13,564.8
(MP) Model with Mathematics A box of pasta weighs 13.6 ounces. A recipe calls for 95.2 ounces of pasta. Write and solve an equation to find the number of boxes of pasta needed to make the recipe.
2. Line Segment AB has endpoints A(−10,4) and B(−6,2). What is the equation of the perpendicular bisector of AB. (Need to use midpoint formula, slope formula and point slope form to answer this question)
23.An RC circuit has an emf of 100 volts, a resistance of 5 ohms, a capacitance of 0.02 farad, and an initial charge on the capacitor of 5 coulombs. Find (a) an expression for the charge on the capacitor at any time t and (b) the current in the circuit at any time t .
1. Shantel studied for 20 minutes and is 41 done. How much longer will she study? 2. Damon has added 43 of the ingredients with 6 added. How many more does he need to finish?
Two docks are 2591 ft apart. From dock A, the bearing to a reef is 63∘22′, and from dock B, it's 333∘22′. Find the distance from dock A to the reef (round to nearest integer).