Tutors Answer Your Questions about Quadratic Equations (FREE)
Question 1006202: A can of soda at 82°F is placed in a refrigerator that maintains a constant temperature of 39°F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by
T(t) = 39 + 43e^−0.058t.
(a) Find the temperature, to the nearest degree, of the soda 10 minutes after it is placed in the refrigerator.
=°F
(b) When, to the nearest minute, will the temperature of the soda be 43°F?
=min
Click here to see answer by Boreal(15235)   |
Question 1006197: In a city with a population of 70,000 people, the number of people P(t) exposed to a rumor in t hours is given by the function
P(t) = 70,000(1 − e^−0.0009t).(Round your answers to the nearest hour.)
(a) Find the number of hours until 10% of the population have heard the rumor.
(b) Find the number of hours until 90% of the population have heard the rumor.
Click here to see answer by josmiceli(19441)  |
Question 1006210: Solve the given problem related to population growth.
The number of bacteria N(t)present in a culture at time t hours is given by
N(t) = 1200(2)^t.
Find the number of bacteria when
t = 0 hours and t = 5 hours.
(a) t = 0 hours
=Bacteria
(b) t = 5 hours
=Bacteria
Click here to see answer by josmiceli(19441) |
Question 1006212: Sodium-24 is a radioactive isotope of sodium that is used to study circulatory dysfunction. Assuming that 4 micrograms of sodium-24 are injected into a person, the amount A in micrograms remaining in that person after t hours is given by the equation A = 4e^−0.046t.
(b) What amount of sodium-24 remains after 8 hours? (Round your answer to two decimal places.)
=µg
(c) What is the half-life of sodium-24? (Round your answer to two decimal places.)
=h
(d) In how many hours will the amount of sodium-24 be 1 microgram? (Round your answer to two decimal places.)
=h
Click here to see answer by josgarithmetic(39617) |
Question 1006203: Compare the intensity of an earthquake that measures 6.0 on the Richter scale to the intensity of an earthquake that measures 4.0 on the Richter scale by finding the ratio of the larger intensity to the smaller intensity.
to 1
Click here to see answer by Theo(13342)  |
Question 1006254: Solve the given problem related to compound interest.
Find the balance if $6500 is invested at an annual interest rate of 6.5%, compounded annually, after the following number of years. (Round your answers to the nearest cent.)
(a) 5 years
$
(b) 12 years
$
Click here to see answer by rfer(16322) |
Question 1006251: The percent l(x)of the original intensity of light striking the surface of a lake that is available x feet below the surface of the lake is given by the equation
l(x) = 100e^−0.95x.
(a) What percentage of the light, to the nearest tenth of a percent, is available 4 feet below the surface of the lake?
%
(b) At what depth, to the nearest hundredth of a foot, is the intensity of the light one-half the intensity at the surface?
ft
Click here to see answer by Boreal(15235) |
Question 1006256: A function that can be written in the form
y = ax^b
is said to be a power function. Some data sets can best be modeled by a power function. On a TI-83/84 calculator, the PwrReg instruction is used to produce a power regression function for a set of data. Find the power regression function for the following data. (Round your numerical values to five decimal places.)
x 1 2 3 4 5 6
y 2.4 5.4 9.7 14.4 19.8 26.0
Click here to see answer by MathLover1(20849)  |
Question 1006172: The most significant time to be aware of the UV index on a sunny day is modelled by the function f(x)=-0.08(x-13)^2+9 where x is the time of day on a 24 hour clock and f(x) represents the uv index.Whats is the UV index at 2 pm? when will the UV index be 7?
Click here to see answer by josmiceli(19441) |
Question 1006255: Find the exponential regression function for the data. State the coefficient of determination r^2. (Round your numerical values to five decimal places.)
{(10, 7), (12, 6.8), (14, 14.9), (16, 16.2), (18, 49.9), (19, 20.3)}
y(x) =
r^2 =
Click here to see answer by Boreal(15235) |
Question 1006439: An escalaster in a department store is made to carry people a vertical distance of 24 feet between floors. How long is the escalator if it makes an angle of 45 with the ground? The escalator is how many feet long
Click here to see answer by ikleyn(52780)  |
Question 1006201: Solve the given problem related to compound interest.
Find the balance if $6500 is invested at an annual interest rate of 6.5%, compounded annually, after the following number of years. (Round your answers to the nearest cent.)
(a) 5 years
$
(b) 12 years
$
Click here to see answer by lwsshak3(11628) |
Question 1006546: Use completing the square to write the following equations in vertex form. State the vertex and whether the parabola has a maximum or minimum value. (4 marks each)
y=x2−10x+3
y=−x2+12x+2
y=4m2+32m+33
The height, h metres, of a flare as a function of time, t seconds, since the flare was fired from a boat, can be modeled by the function: (5 marks)
h=−5.25(t−4)2+86
What was its height when it was fired?
What was the maximum height of the flare?
What was the time when the flare reached its maximum height?
How many seconds after it was fired did the flare hit the water?
The path of a soccer ball can be given by the quadratic function :
h=29.4t−4.9t2, where t is the time in seconds and h, is the height in metres.
Put the function in vertex form and state the maximum height reached by the ball.
How many seconds did it take to reach this height?
A police officer is investigating a crime which occurred in a rectangular field next to a building. He wants to seal the three sides of the area around the scene with 300 m of yellow police tape. What is the maximum area that he can enclose and what are the dimensions of this area? (Hint: Draw a picture and introduce a variable x for the width…think about an expression for the length in terms of x) (6 marks)
A parabola passes through the point (3, 5) on its way to the vertex at (7, 11). Determine the equation in vertex form that represents this parabola. (3 marks)
Click here to see answer by josgarithmetic(39617) |
Question 1006526: Remember to include a LET statement to define your variable and a concluding statement.
The sum of an integer and five times its square is 174. Find the integer. (5 marks)
A right triangle has a height 8 cm more than twice the length of the base. If the area of the triangle is 96 cm2, what are the dimensions of the triangle. (6 marks)
A baseball is hit from a height of 0.8 m. After "t" seconds, its height "h", in metres, is given by the equation h=−5t2+20t+0.8. How long does the ball stay at least 15 m above the ground? (5 marks)
An art dealer advises that, for the best display of a painting, the area of the frame should be (15) the area of the painting. Determine the best width of the frame for a painting 20-cm by 20-cm, if the width is to be the same on all sides. Round your answer to the nearest tenth. (6 marks)
A rectangular flower bed is to be created so that the length is 3 m more than the width. If the length of the diagonal of the flower bed is 15 m, determine the length and the width. (5 marks)
Click here to see answer by ikleyn(52780) |
Question 1006584: Jim can row his boat upstream at four kilometers per hour, and downstream at six kilometers per hour. He rowed upstream a certain distance and then rowed back downstream to his starting point in one hour. How far did he row upstream?
Click here to see answer by Boreal(15235) |
Question 1006597: Given g(x) = 1/(4(x-5)^2 -1). For what value of x is function g undefined?
My attempt: I take this to mean "for what value of x does the denominator = 0." Assuming that's correct, I set the denominator equal to 0. I get a quadratic equation. I plug the coefficients into the quadratic formula, but I do NOT get the correct answer, which is supposed to equal 4 and 1/2.
I think I'm not doing the order of operations right in converting the denominator into the quadratic formula.
I won't belabor you with all my different attempts. Could someone show me how the math should go? The other answer choices are 5 and 1/4, 5, and 1. I did get to 5 and 1/4, but I do think that's wrong mathematically.
Thank you.
Click here to see answer by jim_thompson5910(35256) |
Question 1006597: Given g(x) = 1/(4(x-5)^2 -1). For what value of x is function g undefined?
My attempt: I take this to mean "for what value of x does the denominator = 0." Assuming that's correct, I set the denominator equal to 0. I get a quadratic equation. I plug the coefficients into the quadratic formula, but I do NOT get the correct answer, which is supposed to equal 4 and 1/2.
I think I'm not doing the order of operations right in converting the denominator into the quadratic formula.
I won't belabor you with all my different attempts. Could someone show me how the math should go? The other answer choices are 5 and 1/4, 5, and 1. I did get to 5 and 1/4, but I do think that's wrong mathematically.
Thank you.
Click here to see answer by josgarithmetic(39617) |
Question 1006789: Tee-jay has a photo that measures 10cm by 15cm. He want to fix it to a mat, so that there is a border of uniform width around the photo. the mat and photo will have an area of 500cm2. What should the width of the mat be?
Steps and Answer?
Click here to see answer by josgarithmetic(39617) |
Question 1006861: Hi. I am facing problem in this word problem. It is quadratic equation.
In may 1994 Mr Chauhan changed 1140 Indian Rupees into German Marks when the rate of exchange was x rupees =1 Mark.
(a) write down an expression in terms of x , for the number of Marks he received
In july, Mr Chuhan again changed 1140 rupees into Marks. The rate of exchange was then (x+1) rupees=1 Mark
(b) write down an expression in term of x, for the number of Marks he received this time,
(c)Given that he received 3 Marks less in July than he did in May, form an equasion in x and show that it reduces to x^2 +x-380=0
(d) Solve this equation to find the rate of exchange in May 1994.
Thank you for reading my question. Please reply.
Click here to see answer by Theo(13342) |
Question 1006211: Find the exponential regression function for the data. State the coefficient of determination r^2. (Round your numerical values to five decimal places.)
{(10, 7), (12, 6.8), (14, 14.9), (16, 16.2), (18, 49.9), (19, 20.3)}
y(x)=
r^2=
Click here to see answer by Fombitz(32388)  |
Question 1006930: A slingshot is used to launch a marble vertically into the air with a velocity of 90 meters per second, from a starting height of 1.5 meters. The height of the marble can be modeled by the function  where h(t) is the height in meters and t is the time in seconds after the slingshot is fired.
a.) What is the maximum height the marble will read? Round to the nearest meter.
b.) How long will the marble stay in the air before returning tot he ground? Round to the nearest second.
Thanks in advance!
Click here to see answer by Alan3354(69443)  |
Question 1007151: The following function models the average typing speed S, in words per minute, for a student who has been typing for t months.
S(t) = 5 + 29 ln(t + 1), 0 ≤ t ≤ 9
Use S to determine how long it takes the student to achieve an average typing speed of 65 words per minute. Round to the nearest tenth of a month.
months
Click here to see answer by josmiceli(19441) |
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