A right triangle has legs of 33 inches and 44 inches
whose sides are changing. The short leg is increasing by 10 in/sec and the long leg is shrinking at 10 in/sec. What is the rate of change of the hypotenuse?

Answers

Answer 1

The rate of change of the hypotenuse is given as follows:

dh/dt = 2 in/sec.

What is the Pythagorean Theorem?

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The hypotenuse is then given as follows:

h² = x² + y².

For this problem, the hypotenuse has the value given as follows:

h² = 33² + 44²

h = square root(33² + 44²)

h = 55.

Applying implicit differentiation, the rate of change of the hypotenuse is obtained by the equation as follows:

h dh/dt = x dx/dt + y dy/dt.

Replacing the values, the rate of change is calculated as follows:

55dh/dt = 33 x 10 - 44 x 10

55dh/dt = -110

dh/dt = -110/55

dh/dt = 2 in/sec.

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Related Questions

The time required to complete a job varies inversely as the number of people working. It took 10 brick masons 300 hours to brick a new home. How long would it have taken 25 brick masons to complete the same job?

Answers

the 25 brick masons complete the same job in 120 hours.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

It took 10 brick masons 300 hours to brick a new home.

1 brick mason will take 300*10 =3000 hours

So 25 brick masons will take 3000/25 = 120 hours.

Hence the 25 brick masons complete the same job in 120 hours.

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Based on the table below after completing it for 30 u.s. dollars gets__British pounds

Answers

The value of 30 dollars in British pounds is 24.3

What is Unit of Measurement?

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

We have to convert the 30 us dollars to the British pounds

The value of one dollar in pounds is 0.81

Now let us calculate for 30 dollars

30×0.81

24.3 pounds

Hence, the value of 30 dollars in British pounds is 24.3

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Need assistance here looking REAL Answer and Solution please so i can understand. Please help math expert there.

Answers

The value of y'(2) is 135/16.

The correct option is A.

What is differentiation?

Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.

Given:

y = (x - 1/x)³

Differentiating the function with respect to x,

y' = 3x² +3/x⁴ - 3 - 3/x²

y'(2) = 12 + 3/16 - 3 -3/4

y'(2) = 135/16

Therefore, the value is 135/16.

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I need help
Grinding

Answers

Answer: 500

Step-by-step explanation:

25 x 20 = 500

Suppose the original quantity is $30 and the new quantity is $39. Estimate the percent change. Is this an example of a percent increase or a percent​ decrease?

Answers

Answer:

Step-by-step explanation:original quantity = $30

New quantity = $39

increase amount = 39-30 = 9

Percent change:

30 x = 9

x = 9/30

x = 0.3

0.3x 100 = 30%

Since the quantity grows, it's a percent increase.

A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Enter your answer, rounded to the nearest tenth, in the box.

Answers

If a large equilateral triangle pyramid stands in front of the city's cultural center. The time  it take the painter to paint 75% of the pyramid is 10.8 hours.

How to find the time?

The area of the base is:

(1/2) * 40 * 40

= 800 square feet

The area of one lateral face is:

(1/2) * 50 * 40

= 1000 square feet

So, the total area of all four lateral faces is:

4 * 1000

= 4000 square feet

The total surface area of the pyramid is:

800 + 4000 = 4800 square feet

To paint 75% of the pyramid, the painter needs to paint:

0.75 * 4800

= 3600 square feet

Time it will take them is:

3600 / 100 * 18

= 648 minutes or 10.8 hours

Therefore painter will take approximately 648 minutes, or 10 hours and 48 minutes, to paint 75% of the pyramid.

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Find the value of c. Round to the nearest tenth

Answers

The value of x is 16.2.

What are trigonometric identities?

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Perpendicular = 18

Base = x

Tan Ф = Perpendicular / Base

Tan 48 = 18 / x

1.11 = 18/x

Solve for x.

1.11 = 18/x

x = 18/1.11

x = 16.22

x = 16.2

Thus,

x is 16.2

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Which of the following is the result of rewriting the formula to solve for l

A.
B.
C.
D.

Answers

Step-by-step explanation:

Since we're solving for L, it has to equal L.

Which means C & D are the only options.

Only problem is... we don't have the original formula. Not sure if it was part of #1 or...

Let f(t) be the outside temperature (°F) t hours after 3 A.M. Explain the meaning of f(4) <ƒ(5).
The temperature at
than the temperature at

Answers

The temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M.

What is the temperature?

Temperature is a physical property of matter that measures the degree of hotness or coldness of an object. It is a scalar quantity that is expressed in units such as Celsius, Fahrenheit, or Kelvin.

The statement "f(4) < f(5)" means that the outside temperature 4 hours after 3 A.M. is less than the temperature 5 hours after 3 A.M. In other words, the temperature is rising over time and the value of f(t) increases as t increases. So, the temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M."f(4) < f(5)" means that the outside temperature 4 hours after 3 A.M. is less than the temperature 5 hours after 3 A.M. In other words, the temperature is rising over time and the value of f(t) increases as t increases. So, the temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M.

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Chee is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 4 points. What would be Chee's test score (out of 100) if she got 10 questions wrong? What would be her score if she got a questions wrong? Score with 10 questions wrong. score with x questions wrong

Answers

Answer:

i hope this help

Step-by-step explanation:

If each question is worth 4 points, then 100 questions would be worth 400 points.

If Chee got 10 questions wrong, she would have answered 100-10 = 90 questions correctly.

Her score would be 90 x 4 = 360 points out of 400 points.

As a percentage, her score would be 360/400 x 100 = 90%.

If Chee got x questions wrong, her score would be (100-x) x 4 points.

two negative integers have a sum of -17 and a product of 70 what are the integers?

Answers

Answer:

-10 and -7

Step-by-step explanation:

Notice that (-10) + (-7) = -17, and (-10)(-7) = 70, so these are the integers.

Answer:

-7 & -10

Step-by-step explanation:

-7 + -10 = -17

-7 x -10 = +70

A fair spinner contains the numbers 1, 2, 3, 4, and 5. For an experiment, the spinner will be spun 5 times. If Event A = the spinner lands on numbers all less than 3, what is an outcome of Event A?

Answers

Any sequence of five spins that consists only of numbers 1 and 2 would be an outcome of Event A.

What is an outcome of Event A?

From the question, we have the following parameters that can be used in our computation:

Event A = the spinner lands on numbers all less than 3

An outcome of Event A would be a sequence of five spins on the spinner that result in numbers all less than 3,

For example: 1, 2, 1, 2, 1.

See that each number in the above sequence is less than 3

Hence, the event A represents outcomes less than 3

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PLEASE HELP
I dont understand how to get the answer

Answers

For the given triangles ΔABC ≈ ΔXYZ, the length of the side AB is, 24

What is similarity of triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

One triangle, ΔABC

Another triangle , which is ΔXYZ

Triangle ΔABC and ΔXYZ similar,

So, we can say ΔABC ≈ ΔXYZ

And it is known that

for similar triangles, ratio of lengths of sides are equal for similar triangles

so, AB/BC = XY/ZY

⇒   X/18   =  16/12

⇒   X   =  24

Hence, the value of x is 24

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Select the correct answer. Let f(x) and g(x) be polynomials as shown below. Which of the following is true about f(x) and g(x)? A. f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial. B. f(x) and g(x) are closed under subtraction because when subtracted, the result will be a polynomial. C. f(x) and g(x) are closed under subtraction because when subtracted, the result will not be a polynomial. D. f(x) and g(x) are not closed under subtraction because when subtracted, the result will not be a polynomial.

Answers

f(x) and g(x) are closed under subtraction because when subtracted, the result is also a polynomial.

Option B is the correct answer.

What is a polynomial?

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

f(x) = a(0) + a(1)x + a(2)x² + ......... + a(n)[tex]x^n[/tex]

g(x) = b(0) + b(1)x + b(2)x² + .......... + b(n)[tex]x^n[/tex]

Now,

f(x) - g(x)

=  a(0) + a(1)x + a(2)x² + ......... + a(n)[tex]x^n[/tex] -  b(0) - b(1)x - b(2)x² - .......... - b(n)[tex]x^n[/tex]

= (a(0) - b(0)) + (a(1) - b(1))x + (a(2) - b(2))x² + ........... + (a(n) - b(n))[tex]x^n[/tex]

This is also a polynomial.

Thus,

f(x) and g(x) are closed under subtraction.

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10. La exigencia mínima para un cargamento de grava es que 85% de la grava pueda pasar a través de un colador de cierto tamaño. Al probar una carga de 6 yardas cúbicas se observó que solo un 65% cumple. ¿Cuánta grava de 90% se deberá agregar a las de 65% para que sea aceptable?

Answers

Se requiere agregar un volumen adicional de 24 yardas cúbicas para obtener una concentración de grava de 85 %.

¿Cuánta grava se debe agregar para mejorar concentración?

Este problema es un caso de aplicación de promedios ponderados, en donde se mezcla un volumen de un porcentaje menor de grava con otro volumen de un porcentaje mayor de grava para obtener una mezcla con un porcentaje deseado. Esta situación queda descrita en la siguiente ecuación:

(6 yd³) · 65 + x · 90 = (6 yd³ + x) · 85

Donde x es el volumen del cargamento de grava al 90 %, en yardas cúbicas. A continuación, procedemos a determinar el volumen requerido:

390 + 90 · x = 510 + 85 · x

5 · x = 120

x = 24 yd³

Observación

No aparecen problemas verificados en español sobre promedios ponderados. Se ha agregado un problema en inglés por defecto.

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What do you guys think the formula of a circle is?

Answers

Answer:

πr2

Step-by-step explanation:

The formula of a circle/finding its area is pi(r)^2

Answer: The formula for the area of a circle is π r squared

Fill in the blank with the value that makes the
number sentence true:
36 +27= 88 - O

Answers

The number 25 is the value at which the number sentence is true. An enumerated (numbered) list can be presented in sentence form in a variety of ways.

How should numbered sentences be written?

An enumerated (numbered) list can be presented in sentence form in a variety of ways. The number (not the number word) can be placed in parentheses in the following manner: I listed the following three causes: Here is my first justification, this is my second justification, and this is my third justification. A number sentence compares two numerical expressions and states their equivalence (or inequality).

Let the value be x

now 36 + 27 = 88 - x

36 + 27 = 88 - x

63 = 88 - x

x = 88 - 63

x = 25

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PLEASE HELP!!!
identify the lengths of KL and LW
Answers:
A- KL=2.4, LW=3.6
B- KL=6, LW=2.4
C- KL= 3.6, LW=2.4
D- KL=12, LW=18

Answers

Applying the angle bisector theorem, the lengths are:

A. KL = 2.4, LW = 3.6

What is the Angle Bisector Theorem?

The Angle Bisector Theorem states that in a triangle, the ratio of the length of a side to the length of another side is equal to the ratio of the length of the angle bisector of one of the angles to the angle bisector of the corresponding angle.

In other words, if two angles of a triangle have angle bisectors of lengths x and y, then x/y = a/b where a and b are the lengths of the sides of the triangle corresponding to the bisected angles.

Based on the angle bisector theorem, we have:

(6 - x)/(x) = 4/6

Cross multiply:

4x = 6(6 - x)

4x = 36 - 6x

4x + 6x = 36

10x = 36

x = 36/10

x = 3.6

LW = x = 3.6

KL = 6 - x = 6 - 3.6 = 2.4

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Mayra's brother is driving back from college to visit. His college is 330 miles away. After an hour of
driving, he still has 275 miles to go. If the roads are clear, he'll be able to keep up that pace for the
whole drive. Write a linear function to model how much further he'll have to go over time.

Answers

He has 5hrs  to drive and 275 miles to drive to cover to arrive at the university.

What is speed?

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

here, we have,

His college is 330 miles away.

After an hour of driving, he still has 275 miles to go.

If the roads are clear, he'll be able to keep up that pace for the whole drive.

If he drives 55 miles in 1 hr

he would drive 330 miles in

=6hrs.

his total travel time is 6 hr

He has 5hrs  to drive and 275 miles to drive.

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Why has she putten these parentheses? And the first number (xe2) goes from positive to negative ((-2)e2) and then back to positive (4)?

Answers

[tex]x=-2\hspace{5em}y=2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x^2 - y^3}{x^3 + y^2}\implies \cfrac{(-2)^2 - (2)^3}{(-2)^3 + (2)^2}\implies \cfrac{(-2)(-2)~~ - ~~(2)(2)(2)}{(-2)(-2)(-2)~~ + ~~(2)(2)} \\\\\\ \cfrac{(+4)~~ - ~~(+8)}{(-8)~~ + ~~(+4)}\implies \cfrac{4-8}{-8 + 4}\implies \cfrac{-4}{-4}\implies \text{\LARGE 1}[/tex]

for the sake of clarity, is better to parenthesize all, since plugging in the value for the variable, only includes the variable, no any exponents or signs in front.

that said, let's recall that minus * minus = plus, and that plus * plus = plus, however minus * plus = minus.

so you can think of it this way, if you have a negative value multiplied an "even times", it'll positivize, if you multiply it an "odd times", it'll go back to negative, so is not like it remains negative, it changed a few times and in the end negativized back.

selena erned $4,283.30 last month

Answers

The money left from last month's earnings is $1660.35.

What is Subtraction?

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

The process of subtraction can also be termed as finding difference.

In order to find the money left, we have to find the difference of earnings and expense.

Earnings = $4,283.30

Expense for bills = $4,283.30 × (3/5) = $2569.98

Expense for shirts = $19.99 × 2 = $39.98

Expense for sunglasses = $12.99

Total expense = $2569.98 + $39.98 + $12.99 = $2622.95

Money left = $4,283.30 - $2622.95 = $1660.35

Hence $1660.35 amount of money is left.

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The complete question is :

Selena earned $4,283.30 last month she used 3/5 of her earnings to pay her bills with the remaining money she bought two shirts $19.99 each and a pair of sunglasses for $12.99 how much money does Selena have left from last month's earnings?

CAN YALLL HELP ME (sorry bout the caps )

Answers

The answer is 2/3, because y2-y1/x2-x1 so we’ll get 6-4/ 3-0 which gives us 2/3

2,5 days to 80 hours​ ratio

Answers

The ratio of 2 days to 80 hours and 5 days to 80 hours is 1 day : 40 hours and 1 day : 16 hours respectively.

How to calculate ratio?

2, 5 days : 80 hours

So,

2 days : 80 hours

= 2/80

= 1/40

= 1 day : 40 hours

Also,

5 days : 80 hours

= 5/80

= 1/16

= 1 day : 16 hours

Hence, the ratio of days to hours is given by 1 day : 40 hours and 1 day : 16 hours respectively.

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What’s the domain of the function y =2 (2)x +2

Answers

Answer: X E R

Step-by-step explanation: y=2 x 2x+2

calculate the product

y=4x+2

The domain of a linear function is the set of all real numbers

x E R

11-12÷4+3(6-2)...anyone?​

Answers

Answer:

the answer is 20

Step-by-step explanation:

.........

Answer:

20

Step-by-step explanation:

Do it one step at a time using the correct order of operations.

11 - 12 ÷ 4 + 3(6 - 2) =

= 11 - 3 + 3 × 4

= 8 + 12

= 20

Part 1: For each compound figure,
a. Find the perimeter
b. Find the area
16 yd

32 yd
16 yd
8 yd

Answers

a. Perimeter = 72 yd

b. Area = 640 yd².

Calculate the area and perimeter for compound figure?

a. To find the perimeter of the compound figure, we need to add the lengths of all four sides together.

The perimeter is equal to 16 yd + 32 yd + 16 yd + 8 yd = 72 yd.

b. To find the area of the compound figure, we need to separate the figure into two separate shapes and find the area of each.

The figure can be separated into a 16 yd by 32 yd rectangle and a 8 yd by 16 yd rectangle.

The area of the 16 yd by 32 yd rectangle is 16 yd x 32 yd = 512 yd² and the area of the 8 yd by 16 yd rectangle is 8 yd x 16 yd = 128 yd². The total area is 512 yd² + 128 yd² = 640 yd².

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When you arrive at the family reunion, Uncle Mandla has already eaten 5 mini hot dogs. He continues to eat them at a rate of 4 hot dogs per minute. y = 4x + 5 models this situation. Make a graph of this situation

Answers

The graph of y = 4x + 5 that models this situation is added as an attachment

How to determine the graph of the situation

From the question, we have the following parameters that can be used in our computation:

Already eaten = 5 mini hot dogs

Rate = 4 hot dogs per minute

So, the equation is

y = 4x + 5

A linear equation is represented as

y = mx + c

Where

slope = m = 4

y-intercept = c = 5

See attachment for the graph

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A medium pizza at Big Time Pizza costs $6.80 plus $0.90 for each topping. The cost of a medium pizza at PizzaPizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a medium pizza from each restaurant in order for the pizzas to cost the same?

Answers

Step-by-step explanation:

At Big Time Pizza, you would need to add 5 toppings in order for the pizza to cost the same as a medium pizza from PizzaPizza, which would cost $9.50. At PizzaPizza, you would need to add 8 toppings in order for the pizza to cost the same as a medium pizza from Big Time Pizza, which would cost $9.50.

The product of one-fourth and the quantity of the sum of x and eight

Answers

Answer:

Step-by-step explanation:

Are you asking to have this sentence put into a mathematical expression?  If so, I think the answer is:

y = (1/4)(x + 8) = 1/4 x + 2

Sunday, Peeta earned $142.20 working at his fmaily's bakery. He earned $5.50 per hour plus $90.20 in tips.

Create an equation that can be used to determine the njmber of hours, h, Peeta worked on Sunday.

Answers

Peeta worked 9.41 hours on Sunday. The equation 5.5h + 90.2 = 142.2 can be used to determine the number of hours Peeta worked given his earnings.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let h be the number of hours that Peeta worked on Sunday. We know that he earned $5.50 per hour and $90.20 in tips. So, his total earnings can be represented as:

5.5h + 90.2 = 142.2

Solving for h:

5.5h = 142.2 - 90.2
5.5h = 52

h = 52 / 5.5
h = 9.41 hours

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