42 results

input - what goes into a function

A 12 feet ladder leans against the side of a house. The bottom of the ladder is 9 feet from the side

A 12 feet ladder leans against the side of a house. The bottom of the ladder is 9 feet from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth.
We have a right triangle, where 12 is the hypotenuse. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=9&hypinput=12&pl=Solve+Missing+Side']Using our right triangle calculator[/URL], we get:
side = [B]7.9[/B]

A 13 ft. ladder is leaning against a building 12 ft. up from the ground. How far is the base of the

A 13 ft. ladder is leaning against a building 12 ft. up from the ground. How far is the base of the ladder from the building?
This is a classic 5-12-13 pythagorean triple, where the hypotenuse is 13, and the 2 sides are 5 and 12. The building and the ground form a right triangle.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=12&hypinput=13&pl=Solve+Missing+Side']You can see the proof here[/URL]...

A 13ft ladder leans against the side of a house. The bottom of the ladder is 10ft from the side of t

A 13ft ladder leans against the side of a house. The bottom of the ladder is 10ft from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth.
We have a right triangle. Hypotenuse = 13, one leg = 10.
We use our [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=10&hypinput=13&pl=Solve+Missing+Side']Pythagorean theorem Calculator to solve for the other leg[/URL]:
s = [B]8.3066[/B]

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of t

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of the two poles, what is the minimum length of cord you would need?
The difference between the 70 foot and 50 foot pole is:
70 - 50 = 20 foot height difference.
So we have a right triangle, with a height of 20, base of 30. We want to know the hypotenuse.
Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=20&side2input=30&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator to solve for hypotenuse[/URL], we get:
hypotenuse = [B]36.06 feet[/B]

A 74 inch rake is Leaning against a wall. The top of the rake hits the wall 70 inches above the grou

A 74 inch rake is Leaning against a wall. The top of the rake hits the wall 70 inches above the ground. How far is the bottom of the rake from the base of the wall?
We have a right triangle.
Hypotenuse is the rake length fo 74 inches. One of the legs is 70. We [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=70&hypinput=74&pl=Solve+Missing+Side']use our right triangle calculator to solve for the other leg[/URL]:
[B]24 inches[/B]

A computer screen has a diagonal dimension of 19 inches and a width of 15 inches. Approximately what

A computer screen has a diagonal dimension of 19 inches and a width of 15 inches. Approximately what is the height of the screen?
We have a right triangle, with hypotenuse of 19, and width of 15.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=15&hypinput=19&pl=Solve+Missing+Side']Using our right triangle calculator, we get [/URL][B]height = 11.662[/B]

A helicopter rose vertically 300 m and then flew west 400 m how far was the helicopter from it’s sta

A helicopter rose vertically 300 m and then flew west 400 m how far was the helicopter from it’s starting point?
The distance forms a right triangle. We want the distance of the hypotenuse.
Using our [URL='http://www.mathcelebrity.com/pythag.php?side1input=300&side2input=400&hypinput=&pl=Solve+Missing+Side']right triangle calculator[/URL], we get a distance of [B]500[/B].
We also could use a shortcut on this problem. If you divide 300 and 400 by 100, you get 3 and 4. Since we want the hypotenuse, you get the famous 3-4-5 triangle ratio. So the answer is 5 * 100 = 500.

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall,

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall, how high up the wall does the ladder reach?
We have a right triangle, where the ladder is the hypotenuse, and we want the measurement of one leg.
Set up the pythagorean theorem with these given items using our P[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=7&hypinput=25&pl=Solve+Missing+Side']ythagorean Theorem Calculator[/URL].
We get Side 1 = [B]24 feet.[/B]

A ladder is 25 ft long. The ladder needs to reach to a window that is 24 ft above the ground. How fa

A ladder is 25 ft long. The ladder needs to reach to a window that is 24 ft above the ground. How far away from the building should the bottom of the ladder be placed?
We have a right triangle, where the ladder is the hypotenuse, and the window side is one side.
Using our right triangle and the [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=24&hypinput=25&pl=Solve+Missing+Side']pythagorean theorem calculator[/URL], we get a length of [B]7 ft [/B]for the ladder bottom from the wall.

A ladder rests 2.5 m from the base of a house. If the ladder is 4 m long, how far up the side of the

A ladder rests 2.5 m from the base of a house. If the ladder is 4 m long, how far up the side of the house will the ladder reach?
We have a right triangle with the hypotenuse as 4, the one leg as 2.5 We want to solve for the other leg length. We use our [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=2.5&hypinput=4&pl=Solve+Missing+Side']right triangle solver[/URL] to get [B]3.122[/B]

A young dad, who was a star football player in college, set up a miniature football field for his fi

A young dad, who was a star football player in college, set up a miniature football field for his five-year-old young daughter, who was already displaying an unusual talent for place-kicking. At each end of the mini-field, he set up goal posts so she could practice kicking extra points and field goals. He was very careful to ensure the goalposts were each straight up and down and that the crossbars were level. On each set, the crossbar was six feet long, and a string from the top of each goalpost to the midpoint between them on the ground measured five feet. How tall were the goalposts? How do you know this to be true?
The center of each crossbar is 3 feet from each goalpost. We get this by taking half of 6, since midpoint means halfway.
Imagine a third post midway between the two goal posts. It has the same height as the two goalposts.
From the center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=3&hypinput=5&pl=Solve+Missing+Side']Using the Pythagorean Theorem[/URL], the other leg -- the height of each post -- is 4 feet.

An interior designer charges $100 to visit a site, plus $55 to design each room. Identify a function

An interior designer charges $100 to visit a site, plus $55 to design each room. Identify a function that represents the total amount he charges for designing a certain number of rooms. What is the value of the function for an input of 6, and what does it represent?
[U]Set up the cost function C(r) where r is the number of room to design:[/U]
C(r) = Cost per room * r + Site Visit Fee
C(r) = 55r + 100
[U]Now, the problem asks for an input of 6, which is [I]the number of rooms[/I]. So we want C(6) which is the [I]cost to design 6 rooms[/I]:[/U]
C(6) = 55(6) + 100
C(6) = 330 + 100
C(6) = [B]430[/B]

Black-Scholes

Free Black-Scholes Calculator - Calculates the call or put option value of a stock based on inputs related to the option using Black Scholes method.

Body Mass Index (BMI)

Free Body Mass Index (BMI) Calculator - Solves for the popular health measurement of Body Mass Index or Weight using inches and pounds input or meters and kilos input.

Also calculates the estimated surface area of the body using the Mosteller Formula

Also calculates the estimated surface area of the body using the Mosteller Formula

Cevian Triangle Relations

Free Cevian Triangle Relations Calculator - Given a triangle with a cevian, this will solve for the cevian or segments or sides based on inputs

Earnings Before Interest and Taxes (EBIT) and Net Income

Free Earnings Before Interest and Taxes (EBIT) and Net Income Calculator - Given inputs of sales, fixed costs, variable costs, depreciation, and taxes, this will determine EBIT and Net Income and Profit Margin

For g(x) = 4-5x, determine the input for x when the output of g(x) is -6

For g(x) = 4-5x, determine the input for x when the output of g(x) is -6
We want to know when:
4 - 5x = 6
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=4-5x%3D6&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]-0.4 or -2/5[/B]

Gigi’s family left their house and drove 14 miles south to a gas station and then 48 miles east to a

Gigi’s family left their house and drove 14 miles south to a gas station and then 48 miles east to a water park. How much shorter would their trip to the water park have been if they hadn’t stopped at the gas station and had driven along the diagonal path instead?
[IMG]https://mathcelebrity.com/community/data/attachments/0/pythag-diagonal.jpg[/IMG]
Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=14&side2input=48&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator[/URL], we see the diagonal route would be:
50 miles
The original trip distance was:
Original Trip Distance = 14 + 48
Original Trip Distance = 62 miles
Diagonal Trip was 50 miles, so the difference is:
Difference = Original Trip Distance - Diagonal Distance
Difference = 62 - 50
Difference = [B]12 miles[/B]

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.
[IMG]http://www.mathcelebrity.com/images/math_problem_library_129.png[/IMG]
If AB = 6 and AD = 8, by the Pythagorean theorem, we have BD = 10 from our [URL='http://www.mathcelebrity.com/pythag.php?side1input=6&side2input=8&hypinput=&pl=Solve+Missing+Side']Pythagorean Theorem[/URL] Calculator
Using that, we have another right triangle which we can use the [URL='http://www.mathcelebrity.com/pythag.php?side1input=10&side2input=24&hypinput=&pl=Solve+Missing+Side']pythagorean theorem[/URL] calculator to get [B]FD = 26[/B]

if the input is 3 and the output is 13

if the input is 3 and the output is 13
We write this as:
[B]f(3) = 13[/B]

Income Elasticity of Demand

Free Income Elasticity of Demand Calculator - Calculates the income elasticity of demand using demand changes and income changes. Inputs are demand 1 and demand 0 and income 1 and income 0.

Input Table

Free Input Table Calculator - Given an input table with input and output values, this will determine the operator and rule used to populate the missing values.

Kinematic Equations

Free Kinematic Equations Calculator - Given the 5 inputs of the 4 kinematic equations, this will solve any of the equations it can based on your inputs for the kinematics.

Kites

Free Kites Calculator - This calculates perimeter and/or area of a kite given certain inputs such as short and long side, short and long diagonal, or angle between short and long side

Leilani can read 20 pages in 2 minutes. if she can maintain this page, how many pages can she read i

Leilani can read 20 pages in 2 minutes. if she can maintain this page, how many pages can she read in an hour?
We know that 1 hour is 60 minutes.
Let p be the number of pages Leilani can read in 1 hour (60 minutes)
The read rate is constant, so we can build a proportion.
20 pages /2 minutes = p/60
We can cross multiply:
Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2
[SIZE=5][B]Solving for Numerator 2 we get:[/B][/SIZE]
Numerator 2 = Numerator 1 * Denominator 2/Denominator 1
[SIZE=5][B]Evaluating and simplifying using your input values we get:[/B][/SIZE]
p = 20 * 60/ 2
p = 1200/2
p = [B]600[/B]

Linear Congruential Generator

Free Linear Congruential Generator Calculator - Using the linear congruential generator algorithm, this generates a list of random numbers based on your inputs

Littles Law

Free Littles Law Calculator - Given two out of the three inputs for Littles Law, Throughput (TH), Cycle Time (CT, and WIP, this solves for the third item.

Octagon

Free Octagon Calculator - Calculate side, area, and perimeter of an octagon based on inputs

output is 3 times the input x

output is 3 times the input x
Let output be y. We have:
[B]y = 3x[/B]

Polygons

Free Polygons Calculator - Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon.
This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.

Profit Equation

Free Profit Equation Calculator - Using the Profit Equation with inputs (Revenue-Cost-Profit-Tax), this determines the relevant output including gross proft, gross profit margin, net profit, and net profit margin.

Rhombus

Free Rhombus Calculator - Given inputs of a rhombus, this calculates the following:

Perimeter of a Rhombus

Area of a Rhombus

Side of a Rhombus

Perimeter of a Rhombus

Area of a Rhombus

Side of a Rhombus

Right Triangles

Free Right Triangles Calculator - This solves for all the pieces of a right triangle based on given inputs using items like the sin ratio, cosine ratio, tangent ratio, and the Pythagorean Theorem as well as the inradius.

Running from the top of a flagpole to a hook in the ground there is a rope that is 9 meters long. If

Running from the top of a flagpole to a hook in the ground there is a rope that is 9 meters long. If the hook is 4 meters from the base of the flagpole, how tall is the flagpole?
We have a right triangle, with hypotenuse of 9 and side of 4.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=4&hypinput=9&pl=Solve+Missing+Side']Using our Pythagorean Theorem calculator[/URL], we get a flagpole height of [B]8.063[/B].

Sam leaves school to go home. He walks 10 blocks North and then 8 blocks west. How far is John from

Sam leaves school to go home. He walks 10 blocks North and then 8 blocks west. How far is John from the school?
Sam walked at a right angle. His distance from home to school is the hypotenuse.
Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=8&side2input=10&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator[/URL], we get:
[B]12.806 blocks[/B]

Sectoral Balance

Free Sectoral Balance Calculator - Solves for any of the 6 inputs in the Sectoral Balance equation by Wynne Godley

Sine Wave

Free Sine Wave Calculator - Solves for any of the 3 items of the Sine Wave: Peak Value, Average Value, and RMS value given 1 input.

The distance between consecutive bases is 90 feet. An outfielder catches the ball on the third base

The distance between consecutive bases is 90 feet. An outfielder catches the ball on the third base line about 40 feet behind third base. How far would the outfielder have to throw the ball to first base?
We have a right triangle. From home base to third base is 90 feet. We add another 40 feet to the outfielder behind third base to get: 90 + 40 = 130
The distance from home to first is 90 feet.
Our hypotenuse is the distance from the outfielder to first base.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=130&side2input=90&hypinput=&pl=Solve+Missing+Side']Using our Pythagorean theorem calculator[/URL], we get:
d = [B]158.11 feet[/B]

the output is double the input

the output is double the input
Double means multiply by 2. So this means a function with input of x and output of y such that:
[B]y = 2x[/B]

Trapezoids

Free Trapezoids Calculator - This calculator determines the following items for a trapezoid based on given inputs:

* Area of trapezoid

* Perimeter of a Trapezoid

* Area of trapezoid

* Perimeter of a Trapezoid

Triangle KLM has vertices at . k(-2,-2), l(10,-2), m(4,4) What type of triangle is KLM?

Triangle KLM has vertices at . k(-2,-2), l(10,-2), m(4,4) What type of triangle is KLM?
[URL='https://www.mathcelebrity.com/slope.php?xone=-2&yone=-2&slope=+2%2F5&xtwo=10&ytwo=-2&pl=You+entered+2+points']Side 1: KL[/URL] = 12
[URL='https://www.mathcelebrity.com/slope.php?xone=10&yone=-2&slope=+2%2F5&xtwo=4&ytwo=4&pl=You+entered+2+points']Side 2: LM[/URL] = 8.4853
[URL='https://www.mathcelebrity.com/slope.php?xone=-2&yone=2&slope=+2%2F5&xtwo=4&ytwo=4&pl=You+entered+2+points']Side 3: KM[/URL] = 6.3246
Then, we want to find the type of triangle. Using our [URL='https://www.mathcelebrity.com/tribasic.php?side1input=12&side2input=8.4853&side3input=6.3246&angle1input=&angle2input=&angle3input=&pl=Solve+Triangle']triangle solver with our 3 sides[/URL], we get:
[B]Obtuse, Scalene[/B]

Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM)

Free Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM) Calculator - Calculates the Weighted Average Cost of Capital (WACC) and also calculates the return on equity if not given using the Capital Asset Pricing Model (CAPM) using debt and other inputs such as Beta and risk free rate.