# Pre- Calculus

21,537 results, page 12

### Pre Calculus

A motorboat travels 48 miles down a river in the same time it takes to travel 32 miles up the river. If the rate of the current is 4 miles per hour that is the rate of the boat still water?

### Pre-Calculus

A.Verify the identity. B.Determine if the identity is true for the given value of x. Explain. Sec(x) / tan(x) = tan(x) / [tan(x) – cos(x)],x = π I already solved A and I believe it's true; however, I need help with B.

### pre calculus

if the cost to to produce 100 cups of coffee is 11.02, while the cost to produce 400 cups is 401.12, what is the linear cost function?

### pre calculus

A bag contains 4 blue marbles, 2 black marbles, and 3 red marbles. If a marble is randomly drawn from the bag, what is probability that it is not black? 1/2 2/9 5/9 7/9 14/19

### Pre-Calculus

Find the inverse function for the function f(x)=2^(x)+1/2^(x)-1 You will need to use some properties of logarithmic functions to find the inverse of this particular function.

### Pre Calculus

interest 7%; investment $2000, compounded monthly - how much after 10 years. I am very close on this one but must be missing an important step: A(t) = 2,000(1 + .07/12)^(10)(12) A(10) = 2,000(1.0058)^120 A(10) = 2,000(2.0017 = 4003.4 However the answer is actual $4220.29 What ...

### Pre Calculus

mx3-nx2+5x-1 is divided by x-2 the remainder is -39. When divided by x-1 the remainder is 3. What are the values of m and n. Didn't know how to do the superscript for mx3

### Pre Calculus

How are the factors of a polynomial related to the x-intercepts of a polynomial? How do you find the x-intercepts given the factors?

### Pre Calculus 12

Solving problems that involve logarithms the sound at a rock concert decreases by 10% for every 5m travvelled. how far does it take for a volume of 2000 decibels to decrease to 20 decibels? i don't know what to do for this one the growth decay formula i got is A = P(X)^t/n I ...

### Pre Calculus

A contractor is to fence off a rectangular field along a straight river, the side along the river requiring no fence. What is the least amount of fencing needed to fence of 30,000 meters squared?

### Pre-calculus

You are given a 12"x18" piece of construction paper. You are to cut a square out of each corner in order to create a 3-dimensional open-top box. What size squares would you need to cut in order to maximize the volume of the box?

### Pre-Calc

Can you show me how to find the rectangular equation of r=2costheta + 3 sin theta All I need is an example to work off I was absent today from Pre-Calc and I have homework to do and no explanation with them-Please help with this one Thank you

### Pre-Calculus

Define the inverse secant function by restricting the domain of the secant function to the intervals (0, pi/2) and (pi/2, pi), and sketch the inverse function’s graph.

### pre calculus

A triangular parcel of land has borders of lengths 55 meters, 85 meters, and 100 meters. Find the area of the parcel of land.

### Pre-Calculus

A certain sum of money is invested in a business. in each year this investment earns 1 1/2 times as much as in the preceding year. If the investment earned a total of $29,250.00 in four years, how much did it earn in the fourth year?

### Pre Calculus

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 69 grams, how much will remain after 75 years? a. 1.5848 grams b. 61.5289 grams c. 0.0000 grams d. 1.0426 grams e. 17.2500 grams

### pre calculus

can you check my work? find two sets of parametric equations for the given rectangular equation x+y^2=4 x=-y^2+4 y=-t^2 x=-t^2+4 x=-t^3 y=-t^3+4 Find a polar equation of an ellipse with its focus at the pole an eccentricity of e=1/4 and directrix at y=4. answer: √(x^2 + y^2...

### Pre-calculus

A square of size x inches is cut out of each corner of an 8in by 12in piece of cardboard, and the sides are folded up to form an open-topped box. Determine the dimensions of the cut-out squares that will produce the box of maximum volume.

### Pre-Calculus

Which is the best example of the use of parametric equations? A. Measuring weight on the moon. B. Finding the position of a person in a city. C. Determining the position of a satellite during a specific time of day. D. Finding the right parameters to use for a construction ...

### Pre calculus

Find the domain of the function. f(x) = -2x + 4 A. (-∞, 0) u(0, ∞) B. (-∞, ∞) C. [-4, ∞) D. (0, ∞)

### Pre calculus

Find the domain of the function. f(x) = -2x + 4 A. (-∞, 0) u(0, ∞) B. (-∞, ∞) C. [-4, ∞) D. (0, ∞)

### Pre-Calculus

Operations with Functions write the function below as either a sum/difference/product/quotient of 2 r more functions a. h(x) = x^2+3x+9 How Would I do this? My teacher just did this f(x) = x^2 g(x) 3x+9 ^I don't really understand h(x)=(x+5)(x-3) how would I do this one? If h(x...

### Pre-Calculus

Solve 0 = 3x^2 + 5x -1 by completing the square. Express your answer as exact roots. 3(x^2 + 5/3 + 25/36) = -1 (x+ 5/6)^2 = 37/36 sq root( x + 5/6)^2 = sq root (37/36) x + 5/6 = +- sq root 37/6 x = -5/6 +- square root 37 /6 <--- (Sorry for the work being so messy! It'd be ...

### Pre-Calculus

The function f(x)= x^4 is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of f. Restrict it to be non-negative to meet the 1-1 requirement.

### pre-calculus

I posted a problem earlier and made a mistake the question is what is the domain and range of f(x)= log subscript 3 (1-x)? Sorry! The answer is the same. The domain and range will be the same as if it were log base 40.

### Pre Calculus

Newton's law of cooling T(t)= Tm + (To-Tm)e^-kt, k >0\ Evaluate T(0). Simplify and explain the result I'm very confused on how to do this, i think i will be able to explain the result but if you could help me simplify this that would be great, Thank you very much.

### Pre-Calculus

A.Verify the identity. B.Determine if the identity is true for the given value of x. Explain. [cot(x) – 1] / [cot(x) + 1] = [1 – tan(x)] / [1 + tan(x)], x = π/4 I solved A and I believe it's true; however, I need help with B.

### Pre Calculus

Let $\bold{w} = \begin{pmatrix} 2 \\ -1 \end{pmatrix}$. There exists a $2 \times 2$ matrix $\bold{P}$ such that \[\text{proj}_{\bold{w}} \bold{v} = \bold{P} \bold{v}\] for all 2-dimensional vectors $\bold{v}$. Find $\bold{P}$.

### Pre-calculus

1)Which term best describes the linear programming situation represented by x+y=2 why is the answer infeasible? 2)Describe the linear programming situation for this system of inequalities. x < 1 y > 0 3x + y < 5 why is the answer unbounded?

### pre calculus

How many gallons of gas is in a cylindrical tank (that is laying on it’s side, the circular bases are vertical, the diameter of the bases are 5 feet, the length of the tank is 8 feet, the gas is at a 2 ft level)?

### Pre-Calculus

The exponential function y(x)=Ce^ax satisfies the conditions y(0)=6 and y(1)=7. (a) Find the constants C and a. Enter the exact value of a. (b) Find y(2). Enter the exact answer. Simplify the answer so it does not contain any logarithms.

### pre calculus

Which is worth more after 5 years, an investment of $1000 at 5% interest compounded semi - annually(twice a year). or an investment of $1000 at 5% interest compounded continuously?

### pre-calculus

suppose a triangle has two sides of lengths a and b. if the angle between these sides varies, what is the maximum possible area that the triangle can attain? what can you say about the minimum possible area?

### pre calculus

Candy and Tim share a paper route. It takes Candy 70 min to deliver all the papers, and it takes Tim 80 min. How long does it take the two when they work together?

### Pre-Calculus

A town has a population which is growing linearly. In 1970 its population was 36,000 while in 1985 its population was 63,000. Find a formula for its population P(t), where t=0 corresponds to the year 1970.

### pre-algebra

I am actually in 6th grade but I really want to learn more about pre algebra. I was given a task to solve the question of y=9x+3*7 and i don't get what to do. Should I graph? Or solve for y?

### Pre Calculus

Find all $2 \times 2$ matrices $\bold{A}$ that have the property that for any $2 \times 2$ matrix $\bold{B}$, \[\bold{A} \bold{B} = \bold{B} \bold{A}.\]

### Calculus

What is the use of Calculus? How is it use in jobs? What jobs use Calculus? Calculus is used in engineering, economics, any physical science, and in business (e.g., actuary studies and statistics).

### Pre-Calculus

Can someone please help me with this problem? De Moivre’s theorem states, “If z = r(cos u + i sin u), then zn = rn(cos nu + i sin nu).” • Verify de Moivre’s theorem for n = 2. a. Provide a correct proof that includes written justification for each step.

### Pre calculus

Dternine the unknown side and angles of each triangle give both solutions. In Abc. Angle C is 31 degrees. a is 5.6 cm and c is 3.9 cm. solve this triangle and give both solutions along with all the steps. tanks

### Pre Calculus

The electricity in your house is alternating current because the current varies sinusoidally with time. The frequency of sinusoid is 60 cycles per second. Suppose at Time = 0 seconds the current is at its max of 5 amperes. Write an equation expressing current in terms of time

### pre calculus

A farmer will be adding a rectangular corral to his barn. He has 600 feet of fencing. The part of the barn that is attached to the corral is 150 feet long. Write a function for the area of the corral, A(x) and include the domain Find the answers for both 'x' and 's'

### Pre-Calculus

The angle θ is in the second quadrant and tan θ = -3/5. Point P is on the terminal arm of angle θ/ Which is a possible coordinate for P? A) (-5,√29) B) (-3,√29) C) (-10,6) D) (-6,10) I drew the triangle, and aren't the coordinates supposed to be (-5...

### pre-calculus

suppose a triangle has two sides of lengths a and b. if the angle between these sides varies, what is the maximum possible area that the triangle can attain? what can you say about the minimum possible area? could you explain by detail

### pre-calculus

solve the equation 1. In x + In (x+12) =2 x= ? or either there is no solution 2. solve the exponential equation 9^x=6 What is the exact answer? 3. Use transformations to indentify the graph of the function. Then determine its domain, range, and horizontal asymptote. f(x)=2^-x+...

### Pre-Calculus

An open box is to be made from a piece of cardboard 11 in by 17 in, by cutting out a square of length x from each corner and turning up the sides. Express the volume V of the box as a function of the length x of the side of the square cur from each corner.

### math: pre-calculus

The Department of Commerce estimated that there were 53 million internet users in the country in 1999 and 90 million in 2002. Find an exponential function that the models the number of Internet users in year x, with x=0 corresponding to 1999.

### Pre-Calculus

Given that x is an integer, state the relation represented by absolute value y = x/2 and 0 is less than or equal to x which is less than or equal to 2 by listing a set of ordered pairs. Then state whether the relation is a function. Write yes or no. Please help--no clue what ...

### pre-calculus

I'm trying to describe how the graph is related to the parent function. The parent function is x^3 and the problem is: y=-(0.8x)^3 I know its a reflection over the x-axis, but what is the formula for how much it expands or shrinks? Like on another problem it's y=|x| and y= |0....

### pre-calculus

Callaway golf Company has determined that the marginal cost C of manufacturing x Big Bertha Golf clubs may be expressed by the quadratic function: C(x) = 4.9^2 - 617.4x + 19,600 How many clubs should be produced to minimize marginal cost?

### Honors Pre Calculus

Verify the trigonometric identity:￼ ￼(1+sin x)/ (1-sinx)=￼(1+sin x)/[cos x] Hint: [cos x] means the absolute value of cos x

### Honors Pre Calculus

Verify the trigonometric identity:￼ ￼(1+sin x)/ (1-sinx)^2=￼(1+sin x)/[cos x] Hint: [cos x] means the absolute value of cos x

### Pre-calculus

How do you write an equation of a translated line given the equation of the original line and both the translated and original lines on a graph?? Thanks in advance!!

### Pre-calculus

How do you write an equation of a translated line given the equation of the original line and both the translated and original lines on a graph?? Thanks in advance!!

### pre-calculus

the path of a ball is given by y=-.05+3x^2+3x+5, where y is the height (in feet) of the ball and x is the horizontal distance (in feet) from where the ball was thrown. Find the maximum height of the ball.

### Pre Calculus

Prove that the equation is an identity. sec x/(sec x -tan x)=sec^2 x +sec x tan x

### Pre-Calculus

If h(x)=x^3, what is the difference between h(x) reflected about the x-axis and h(x) reflected about the y-axis?

### Pre-calculus

prove the identity sin2x-sin2y/sin2x+sin2y=tan(x-y)/tan(x+y)

### Pre-Calculus

The median salary for male workers for the years 1975-2006 can be modeled by the function thousand dollars, where x is the number of years from 1970. Find the minimum on the graph of this function between x = 10 and x =30 and interpret it.(Use the window [10, 30] by [40, 45...

### Pre-Calculus

If a manufacturer has fixed costs of $ 300 , a cost per item for production of $ 60 , and expects to sell at least 100 items, how should he set the selling price to guarantee breaking even? I set up the cost function by writing 300 + 60x, but I don't know what to do next...

### Pre-Calculus

Find the slope of the tangent line to the curve √(1x+2y) + √(1xy) = 8.24 at the point (2,8)? I know you have to use implicit differentiation, but the radicals keep making me mess up algebraically. Is the changing the radicals to exponents the fastest way? please ...

### Pre calculus

When “superballs” sprang upon the scene in the 1960’s, kids across the United States were amazed that these hard rubber balls could bounce to 90% of the height from which they were dropped. If a superball is dropped from a height of 2 m, how far does it travel by the ...

### education

I'm doing a power point on pre-k classroom. I need help finding a classroom arragment picture. Like how the room needs to be set up before a pre-k room open. I hope this makes sense.

### Pre-Vet

I am doing a research paper for my pre vet class but I cant think of a subject to do it on. I would like to use a subject in wildlife veterinary and it needs to be about a medical topic or carreer. Any suggestions?

### pre-calculus

Move point (3,50 degrees) according to the following symmetries (keep positive) a. symmetrical to the origin b. symmetrical to theta=0 degrees c. symmetrical to theta= 90 degrees

### pre calculus

find 2 solutions of tan θ=.6524 in both degrees and radians. I know the answer are 33.12 degrees/.578 radians and 213.12 degrees/3.72 radians, but how do you find this? Thanks!!!!

### Pre-Calculus

Consider a class with 10 sophomores, 8 juniors, and 6 seniors. Two students are selected at random. 1) What is the probability of selecting 1 junior and 1 senior. 2) Find the odds of selecting two students who are not seniors. How do I set these up to solve?? Any help is ...

### pre-calculus

At a selling price of $ 54 , a lamp company breaks even on total sales of $ 3564 . If the company's overhead is $ 396 , find the marginal production cost per lamp and find the profit on sales of 145 lamps.

### Pre-calculus

Hello, Consider a geometric sequence with t3= 18 and t7= 1458. Are there one or two values for the common ratio? How does this affect the sequence (I got one, but the way this question mentions 2 ratios, I get the feeling there are 2 values.) My work: 1458 = 18r^4 81 = r^4 3 = r

### Pre-Calculus

Two cities are due north of each other. One city has a latitude of 32¢ª45'12" and the second city has a latitude of 51¢ª12'45". Assuming that the earth is a sphere with a radius of 4000 miles, how far apart are the two cities?

### Pre calculus

ramp needs an angle of elevation no greater than 4.8. the business has 8 ft to build the ramp. the ramp must rise 6 inches above the ground. can a ramp be built in this space? if a ramp can be built what is the minimum horizontal distance possible? please show work. i'm ...

### Pre-Calculus

Rational Functions does the following function have a hole or a vertical asymptote or both? how do you know? find the y-value at that point. y=x^2+7x+12/x^2+8x+15 I factored this out to y = (x+3)(x+4)/(x+5)(x+3) The x+3's cancelled out. I don't get the whole verticle and ...

### Pre calculus

Log base 10(log base 8 8)=x

### Pre-K lesson plan

I am a pre-k summer school teacher, and the theme for this week is "my neighbors." Can you suggest any lesson plans or art and craft activities that connects to the "my neighbor" theme.... or do you know a particular website that could help me.... thanks alot

### Pre-Calculus/Trigonometry

For the sequence an = 4n + 5: find: the first five terms: find the sum of the first 25 terms: is it a arithmetic sequence? If so how can you tell, if not, why not?

### pre-calculus

Hi I have this question regarding ellipses. the equation is.. x^2/25 + y^2/169= 1 it asks for major and minor axis (i got 10 and 26) x-intercept y-intercept ((5,0)(0,13)) foci (-12,0) points of intersection with line y= 1-2x graph graph the equation of the ellipses after it is...

### Pre-Calculus-Trig

Two trains depart simultaneously from the same station. The angle between the two tracks on which they leave is 120 degrees. One train travels at an average speed of 45 mph and the other at 70 mph. How far apart are the trains after three hours?

### Pre-Calculus

Could someone help me with this-we learned this today in school but I'm not getting it now that I'm home with my homework-I have lots of these to do can someone help with this one and then maybe it'll click-thank you Find (sqrt3/2 -1/2i)^4 by using DeMoivre's Theorem I have to...

### Pre-Vet

I'm doing a report on shark and ray behavior for my pre-vet class and I have been trying to get some good information on tonic immobility. There is not much about it on the internet so any information would be helpful.

### Pre Calculus

1. Find all rational zeros of the polynomial. Then determine any irrational zeros, and factor the polynomial completely. 3x^4-11x^3+5x^2+3x 2. Find the polynomial with leading coefficient 1 that has a degree of 4, a zero of multiplicity 2 at x=1 and a zero at x=2+i

### Pre-Calculus

Use a graphing calculator to write a polynomial function to model this set of data {(5,2) (7,5) (8,6) (10,4) (11, -1) (12 -3) (15,5) (16,9)} A) f(x) = 2x3 + 2.70x2 + 0.09x - 65.21 B) f(x) = 2x3 - 0.09x - 65.21 C) f(x) = 0.09x3 - 2.70x2 + 24.63x - 65.21 D) f(x) = x4 - 5.7x3 + 2...

### Pre-Calculus

At 34 degrees north latitude, the longest day of the year has 14.273 hours of daylight, and the shortest day 9.726 hours. If the equinox falls on march 21(day 80), model the hours of the daylight by day?

### Pre-Calculus

Determine the derivative at the point (2,−43) on the curve given by f(x)=7−7x−9x^2. I know that the answer is -43, but I was wondering if it was just a coincidence that the derivative at the point (2,−43) is -43, or is there a reason why -43 is the same...

### Pre-Calculus

Hi! I need help with this math homework question: If you had a triangle that has the vertices (-2, 1), (0, -5), and (1. 2) and you had to shift that triangle 5 units left and 4 units down, how would you find the vertices of the shifted triangle?

### Pre-Calculus

Can you create another pair of six-sided dice (different from the standard dice) that produces the exact same probabilities of the sums two through twelve appearing? The only rule is that the numbers on each face must be positive integers. I've been attempting this problem in ...

### Pre-Calculus

If the sum of two numbers is 1 and the sum of the cubes of the numbers is 3, what is the sum of the squares of the numbers?

### Pre Calculus

The following table shows the rate of water flow (in L/min) through a dam. t (min) 1 5 9 13 17 21 25 V'(t) (L/min) 6 6 2 2 3 6 2 Approximate the total volume of water that passed through the dam from t=1 to t=25 using Simpson's rule, with n=6.

### Pre-calculus

I am having difficulty with two problems: 1) Evaluate (1+i)^12 by using DeMoivre's Theorem. Express the result in rectangular form. So far I have: r=sqrt(1)^2+(1)^2 which simplified is sqrt2. Don't know how to proceed. 2) Write the polar equation theta = 45 degrees in ...

### Pre Calculus

The burial cloth of an Egyptian mummy is estimated to contain 56% of the carbon-14 it contained originally. How long ago was the mummy buried? (the half-life of carbon-14 is 5730). Please round the answer to the nearest tenth. I have figured that: m(t) = Moe(-ln2/5730) is a ...

### Pre Calculus

please help me with this problem? I have the answer but I need to know how to do it. Write the slope intercept form the equations of the lines through the given point parallel to the given line and (B) perpendicular to given line. point slope ((7,-2) m= 1/2

### Pre-Calculus-Trig

A pole tilts 12 degrees from the vertical, away from the sun, casts a 34 foot long shadow on level ground. The angle of elevation from the end of the shadow to the top of the pole is 64 degrees. How long is the pole?

### Pre-calculus

a triangular shelf is to be placed in a curio cabinet whose sides meet at an angle of 105 degrees. If the edges of the shelf along the sides measures 56 centimeters and 65 centimeters, how long is the outside edge of the shelf? Round to the nearest tenth. Thanks for any help--...

### pre-calculus

solve the following logarithmic equation. be sure to reject any value of x that is not in the domain of the original logarithmic expression. give the exact answer. then, use the calculator to obtain a decimal appromiation, correct to two decimal places, for the solution. In x=...

### pre calculus

The diameter of the wheels on your car (including the tires) is 25 inches. You are going to drive 218 miles today. Each of your wheels is going to turn by an angle of how many degrees? Hint: A mile has 5280 feet, a foot has 12 inches, and the circumference of a circle with a ...

### Math

darry and nay eat dinner at a restaurant with 6% sales tax. They leave an 18% tip on the pre tax amount of the bill. If they paid a total of 37.20, what was their pre tax bill?

### Pre-Calculus

Solve by using the substitution method 1.x=-3y+4 and 3x+9y=12 3(-3y+4)+9y=12 -9y+12+9y12 0=0 x=-3(0)+4 x=4 Would there be infinite solutions or would it be (0,4)? 2. x=3y-1 and 2x-6y=-2 2x-6y=-2 2(3y-1)-6y=-2 6y-2-6y=-2 0=0 x=3y-1 x=3(0)-1 x=-1 Would there be infinite ...

### pre calculus

Use the remainder theorem to find the remainder when f(x) is divided by x -2. Then use the factor theorem to determine whether x -2 is a factor of f(x) f(x) = 2x^5 + 6x^4 - x^2 - 7x - 12

### Pre-calculus

Verify the identity (Left side to right side). {(cosu-cosv)/(cosu+cosv)}=-tan1/2(u+v)tan1/2(u-v)

### Pre calculus

How do I solve this exponent problem? I understand the exponent rules, but I getting 1 but 1 is not the answer! I don't want anyone to solve the problem for me, I want to learn how to solve this type of problem. Thank you! Solve the equation: -8=-3-6 (3sqrtx^2) Thanks again!