Math Questions

Given the sets of system linear of differential equation; 2x"+6x'+y" + 3y' = 12e ^-t x'+2x + y' = 0 (a) Determine x(t) by using Elimination Method. (b) Determine y(t). (c) Check number of arbitrary constant and determine the final solutions.

Shannon is paid a monthly salary of $1025.02. The regular workweek is 35 hours. (a) What is Shannon's hourly rate of pay? (b) What is Shannon's gross pay if she worked 7(3/4) hours overtime during the month at time- and-a-half regular pay? A) The hourly rate of pay is $------ (b) The gross pay is $----

Subtract the following polynomials. Simplify your answer. (2x² + 2x + 3) - (-4+ 2x – 2x² – 3x³) Provide your answer below:

You owe $190 on your credit card. The minimum payment is $20.00 and the interest rate on the credit card is 1.8%. What is the interest charged?

What is the simplest form of 3√2 + 5√2 ? (Do NOT approximate your answer) 30 16 8√2 None of the choices are correct. 30√2

A piece of wire 19 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Round your answers to two decimal places.) (a) How much wire (in meters) should be used for the square in order to maximize the total area? (b) How much wire (in meters) should be used for the square in order to minimize the total area?

Antonio wants to invest $7600 in a savings account that pays 7.9% simple interest. How long will it take for this investment to double in value? Round your answer to the nearest tenth.

Fred and Wilma purchase a new home for $180,000. The value of the home increases by 4% every 2 years. Determine the value of the home after 23 years. After 23 years, the home is worth $ Round your answer to the nearest cent.

Match the volume of the pyramid to the volume of the prism with the same height and base area.

Given 2 exponential functions, discuss all their features (Domain, range, increasing/decreasing, the equation of the asymptote, the x- and y-intercepts, their steepness) and highlight all the similarities and differences between them

Let an 2 + (-3)(n-1) a) To find a3, which variable in the equation should we substitute 3 in? b) If a7 = -16, which part in the equation an = 2 + (-3)(n-1) is -16? Which part is 7? c) Find a10 d) If an = -40, find n.

Find the first 5 terms of the following sequence: an = 2an-2+ an-1 for n > 2; a₁ = 1, a₂ = 2 Answers:

Find the first 5 terms of the following sequence: a = (-1)n 2n Answers:

Find the first 5 terms of the following sequence: an=n!(-1)n Answers:

Let an = 2 + (-3) (n − 1) Find a10.

Use the notation for sequences to translate the following to mathematical equations. "The nth term of the sequence is 78." Use fx to type math equations or insert a image of your hand written equation.

On average the number of drum sets sold in Texas each year is equivalent to five times the average number sold yearly in Montana. If, on average, there are 46,625 drum sets sold each year in Texas, how many are sold in Montana?

Solve the system of equations. a+8n=22 a+3n=10

Write this number in standard form. Four thousand nine hundred ninety-nine

A function that converts dress sizes in the United States to those in Europe is given by D = f(x) = 2x + 24 where is the size in the United States. a. Find the European dress size that corresponds to a U.S. dress size of = 10. b. Find the function that converts European dress size to U.S. dress size. x = ƒ-¹(D) = c. Use part b. to find the U.S. dress size that corresponds to a Europen dress size 62.

Determine all important features, and sketch a complete graph of ƒ(x)=(5x–10)/(x²+8x-20)

3) A fan of trigonometry is building a right triangular pool in his backyard. The hypotenuse of the right triangle is 30 feet long and the height of the right triangle is 24 feet long. If the fan of trigonometry wants to purchase a pool cover, how many square feet of material should he purchase?

In 1970, 11% of people in a certain region completed four years of college, 40% of them were women. In 1990, 19% of people in the same region completed four years of college: 53% of them were women Complete parts (a) through (c) below. In each part below, a person is selected at random from the region (a) Given that a person completed four years of college in 1970, what is the probability that the person was a woman? The probability is (b) What is the probability that a woman finished four years of college in 1990? The probability is (c) What is the probability that a person was not a male college graduate in 1990? The probability is

At the beginning of an experiment, a scientist has 244 grams of radioactive goo. After 105 minutes, her sample has decayed to 7.625 grams. What is the half-life of the goo in minutes? Find a formula for G(t)G(t), the amount of goo remaining at time tt. G(t)=G(t)= How many grams of goo will remain after 2 minutes? You may enter the exact value or round to 2 decimal places.

In many cases the Law of Sines works perfectly well and returns the correct missing values in a non-right triangle. However, in some cases the Law of Sines returns two possible measurements. Statement of the Law of Sines. Helpful Hint: Draw a unit circle and think about the range of arcsin. Also, recall that the trigonometric functions in iMathAS use radians as the default, so you may need to change units. Consider the diagram below, and assume that mZB= 61, AB= 4.25 cm, and AC = 3.9 cm. 3.9 cm a. Using the Law of Sines, determine the value of mLC. You should notice that there are actually neo possible values-list both of them (separated by a comma). b. If we assume the diagram is to scale, which value of mLC makes more sense? Enter the appropriate value. mLC= c. Using your answer to part (b), determine the length of BC. BC= cm

An asymptote is a line that the the graph of a function will get closer and closer to, but never reach. a) True b) False

Graph the equation. Let x= -3, -2, -1, 0, 1, 2, and 3. y=2x+2 x y -3

A bacterial population doubles every 4 months. If there were originally 2000 cells in the sample, how many will there be in 2 months? a) 512 000 b) 2828 c) 2519 d) 8000

Write the complex number in rectangular form. 6 cis 135° 6√3 + 3i√3 -3√2+ 3i√2 6√2 - 3i√2 3√2 - 3i√2

State the equation of the rational function if the vertical asymptote is x=5, the horizontal asymptote is y=2, and the x-intercept is -(1/2) a) f(x) = 4x-1/2x-5 b) f(x)=2x+1/2x-10 c) f(x)=2x+1/2/x-5 d) f(x) = 2x+1/x-5

Graph the equation y = -5|x|. Let x = -3, -2, 1, 0, 1, 2, and 3. Find the following y -values. Then choose the correct graph of the equation to the right. X y -3 -15 -2

Use the critical value method to solve the rational inequality. Write the solution set in interval notation. x-9/x+8 ≥5

Solve the equation. Check your solution(s). 3x³/4 - 14 = 67 a)x = 9x = 3(81) ³/4 b)x = 81 c)no real solution d)x = ±81

The slope of the tangent to the curve f(x) =2^x at x =1 is approximately (to three decimal places): a) 1 b) 0.347 c) 0.693 d) 1.388

In a village there is a farmer, carpenter, and a tailor, who provide the three essential services: food, shelter, and clothing. Suppose the farmer himself consumes 40% of the food he produces, and gives 40% to the carpenter, and 20% to the tailor. Thirty percent of the carpenter's production is consumed by himself, 40% by the farmer, and 30% by the carpenter. Fifty percent of the tailor's production is used by himself, 30% by the farmer, and 20% by the tailor. What 'prices' should the providers get if the equilibrium condition of a closed economy is to be satisfied, and if the lowest-price is $720?

If Solution A has a pH of 5.0 and Solution B has a pH of 3.0, which statement below is true? a) Solution A is twice as acidic b) Solution B is 100 times more acidic c) Solution B is twice as acidic d) Solution A is 100 times more acidic

Evaluating the cosine of a sum of two angles can be done using cos(A + B) = ? a) sin(A) sin(B) – cos(A) cos(B) b) None of these c) cos(A) cos(B) + sin(A) sin(B) d) cos(A) cos(B) – sin(A) sin(B)

Solve the equation. Check your solution(s). √6x+1=x-9 a) X = 4 b) x = 4 and x = 20 c) x = 20 d) x = -4 and x = -20

The profits for a company can be modeled by the logarithmic function P(t) = (3/2)log(2t + 1) With P in thousands of dollars and tin years. What is the average increase in profit from year 2 to 3? a) 219 dollars/year b) 0.23 dollars/year c) 4.39 dollars/year d) 4386 dollars/year

Solve 3 cos²(x) + 5 cos(x) - 2 = 0 for the interval 0≤x≤ 2π a) 1.231 and 5.052 b) 1.231 c) 1.231, 2.356, 2.759 and 5.052 d) 5.052

Since the relationship sin²(x) + cos²(x) = 1 is correct, it stands to reason that sec²(x) + csc²(x) = 1 must also be correct. This statement is: a) True for all values of x b) Never true c) True for the interval 0 ≤ x ≤ 2π d) Not true only for the interval 0 ≤ x ≤ 2π

Find the area and perimeter of the figure below. Do not forget units. Arc AB is a semicircle (half of a circle, ABC is a right triangle, AB = 16 yards, BC = 12 yards and AC = 20 yards. Area = Perimeter =

Solve the equation. 2/3x+1/5x-1/4=4/5x The solution is x = (Type an integer or a simplified fraction.)

How much more intense is an earthquake of magnitude 3.6 than an earthquake of magnitude 1.8? a) 63 times more intense b) twice as intense c) 100 times more intense d) 1.8 times more intense

We are now going to work with Conditional Probability with Percentages. We will use the information from question 1. This time you will take the number of men divided by the total group. Next we will take that percentage of men who prefer chocolate chip cookies which is 5.67% and divide it by the percentage of men. Show your work.

Which statement is TRUE for the graph of the logarithmic function f(x) = log₂x: a) There is a horizontal asymptote b) The graph only exists above the x-axis c) The graph only exists to the right of the y-axis d) There is no restriction on the domain

Find the point that is symmetric to the point (0, -3) with respect to the x-axis, the y-axis, and the origin The point symmetric to (0, -3) with respect to the x-axis is (Type an ordered pair.) The point symmetric to (0, -3) with respect to the y-axis is (Type an ordered pair.) The point symmetric to (0, -3) with respect to the origin is (Type an ordered pair.)

Express as a single logarithm and simplify; log₃6+log₃1.5 a) 0 b) 1 c) 2 d) log₃7.5

Write an exponential function y= abˣ whose graph passes through (1, 3) and (3, 75). a y = 0.6(x⁵) b y = 5(0.6ˣ) c y = 0.6(36ˣ) d y = 0.6(5ˣ)

Simplify the expression. 4³√2+³√2 a 10 b 5³√2 c 5⁶√2 d 5³√4