Two legs of a right triangle are each 70 cm. If one leg grows at the rate of 5cm/min and the oth
shrinks at the rate of 5 cm/min.
A)how fast is the hypotenuse of the triangle changing 2 minutes later?

Answers

Answer 1

The rate of change of the hypotenuse after 2 minutes is 0.505 cm/min

Let L be the length of one leg and D be the length of  the other leg of the right triangle and y its hypotenuse

Since it is a right angled triangle, we have that, using Pythagoras' theorem

y² = L² + D²

Since the length of sides are the same, L = D = 70 cm.

So, y² = L² + D²

y² = 70² + 70²

y² = 2(70²)

y = 70√2

y = 98.99 cm

Also, one side increases at a rate of 5 cm/min and the other side decreases at a rate of 5 cm/min.

The increase in length of one side after 2 min is 5cm/min × 2 min = 10 cm.

So, it new length is L' = 70 + 10 = 80 cm

The decrease in length of the other side after 2 min is -5cm/min × 2 min = -10 cm.

So, it new length is D' = 70 + (-10 cm) = 60 cm

So, the new hypotenuse length is y' = √(L'² + D'²)

= √(80² + 60²)

= √(6400 + 3600)

= √10000

= 100 cm

Now, the change in length of the hypotenuse side in 2 minutes is Δy = 100 cm - 98.99 cm = 1.01 cm

So, rate of change of the hypotenuse after 2 minutes is 1.01 cm/2 min = 0.505 cm/min

The rate of change of the hypotenuse after 2 minutes is 0.505 cm/min

Learn more about rate of change here:

https://brainly.com/question/18721795


Related Questions

Help! Please! Help! Please!

Answers

Step-by-step explanation:

a midsegment is the line segment connecting the midpoints of two sides of a triangle. Since a triangle has three sides, each triangle has three midsegments (that create the midsegment triangle). A triangle midsegment is parallel to the third side of the triangle and is half of the length of the third side (due to similar triangles and their constant scaling factors, when one side of the similar triangle is half of the sys of the original triangle, then all its sides are half of their original counterparts).

the 3 sides of the main triangle are

2x + 5

3x - 1

5x

the perimeter of the main triangle is the sum of these :

2x + 5 + 3x - 1 + 5x = 10x + 4

since the sides of the midsegment triangle are all exactly half the length of the sides of the main triangle, also the perimeter of the midsegment triangle is half of the perimeter of the original triangle :

(10x + 4) / 2 = 5x + 2

What is the distance between (-8, -1) and (-4, -9)?​

Answers

Answer:

The distance formula between two points is

D=√([tex]x_{2} \\[/tex] -[tex]x_{1\\}[/tex])^2 + ([tex]y_{2}[/tex]-[tex]y_{1}[/tex])^2

Whereas

d is distance

So in this case

(-8, -1)

(-4, -9)

x2 is -4

x1 is -8

y2 is -9

y1 is -1

Now we plug them in

d= √(-4 + 8)^2 + (-9+1)^2

Now solve

it’s about

8.94427

A recipe for cooking a turkey states to allow 20 minutes for each pound of turkey and to add 5 minutes per pound if the turkey is stuffed. Our turkey weighs 16 pounds and will be stuffed. To have dinner at two o'clock in the afternoon, what time does the turkey need to go in the oven? Allow 1/2 hour for cooling and carving. Explain your answers and your thinking.​

Answers

Answer:

6:30 A.M

Step-by-step explanation:

That's if you wanted it right at 2 after cooling for 30mins

write a equation of the line that goes through the points (-2,-4) (0,6)

Answers

Answer:

323563

Step-by-step explanation:

Hello there!

To find the slope, we use the following formula:

m=[tex]\frac{y2-y1}{x2-x1}[/tex]

m=[tex]\frac{6-(-4)}{0-2} \\\frac{6+4}{-2} \\\frac{10}{-2} \\-5[/tex]

So the slope is -5.

Hope this helps!

~Just a cheerful gal

#CarryOnLearning

[tex]SilentNature[/tex]

Ahhhhhh please help me!!

Answers

Answer: chrome

Step-by-step explanation:

new tab then search it up

how do i simplify these expressions?
. 3x x 4y
. 2p x 3q x 5r

Answers

Answer:

[tex] \\• \tt \: 3x \times 4y[/tex]

[tex] \\ \tt = 12xy[/tex]

[tex] \\ \tt • \: 2p \times 3q \times 5r[/tex]

[tex] \\ \tt = 30pqr[/tex]

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 4 and 3 - I.

f(x)=

Answers

Answer:

f(x) =  x³ - 6x² + 5x + 12

Step-by-step explanation:

Given polynomial function f(x) with:

a = 1, r₁ = 4, r₂ = 3, r₃ = -1

With the least degree it is:

f(x) = 1*(x - 4)(x - 3)(x - (-1)) =         (x² - 7x + 12)(x + 1) =          x³ - 6x² + 5x + 12

plz help will mark as brainliest​

Answers

Answer:

Side AB and side BC

Step-by-step explanation:

Hope it helps

Express the following equation in standard form y=5x-3

Answers

Answer:

5x - y = 3

Step-by-step explanation:

Standard form of a linear equation is expressed as Ax + By = C

In order to express the given equation in this form, we need to isolate the constant.  We can achieve this by subtracting 5x from both sides:

y = 5x - 3

y - 5x = -3

If possible, we want A to be positive, so we can multiply both sides by -1:

-1(y - 5x) = -1(-3)

-y + 5x = 3 or 5x - y = 3

Use the remainder theorem to find P(-3) for P(x) = 2x² + 4x²+4.
Specifically, give the quotient and the remainder for the associated division and the value of P(-3).
Quotient= ?
Remainder= ?
P(-3) = ?

Answers

Answer:

P ( 3 ) = 16

the remainder is  

P ( a )

(2^4x+4)÷(2^x+1)
60 POINTS
BRANLIEST IF RIGHT

Answers

Answer:

[tex]\frac{2^4^x + 4}{2^x + 1}[/tex]

The file includes the input of your equation, comment if the equation you input is a mistake.

Answer:

2 ^ 3(x+1)

Step-by-step explanation:

Assuming  2^(4x+4) / 2 ^(x+1)

when bases are equal and exponents are in division it becomes subtraction

=> 2 ^ (4x + 4 - (x + 1) )

=> 2 ^ (4x + 4 -x - 1)

=> 2 ^ (3x + 3)

=> 2 ^ 3(x+1)

=> [tex]2^{3(x+1)}[/tex]

HOW MUCH IT’S ( 4/2 - 1/2 ) + 3/4 I need the answer because I’m stay in test

Answers

Answer:

= 7.25

Conversion a mixed number 4 3/

4

to a improper fraction: 4 3/4 = 4 3/

4

= 4 · 4 + 3/

4

= 16 + 3/

4

= 19/

4

To find a new numerator:

a) Multiply the whole number 4 by the denominator 4. Whole number 4 equally 4 * 4/

4

= 16/

4

b) Add the answer from previous step 16 to the numerator 3. New numerator is 16 + 3 = 19

c) Write a previous answer (new numerator 19) over the denominator 4.

Four and three quarters is nineteen quarters

Conversion a mixed number 2 1/

2

to a improper fraction: 2 1/2 = 2 1/

2

= 2 · 2 + 1/

2

= 4 + 1/

2

= 5/

2

To find a new numerator:

a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/

2

= 4/

2

b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5

c) Write a previous answer (new numerator 5) over the denominator 2.

Two and one half is five halfs

Add: 19/

4

+ 5/

2

= 19/

4

+ 5 · 2/

2 · 2

= 19/

4

+ 10/

4

= 19 + 10/

4

= 29/

4

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(4, 2) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 2 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - nineteen quarters plus five halfs = twenty-nine quarters.

Step-by-step explanation:

Answer:

you can write it in exact form which is 9/4 or decimal form which is 2.25 or mixed number form 2 1/4

Step-by-step explanation:

In ⊙V, QT ≅ RS. If UV = 4 cm, then VW = _______ cm.

Answers

Answer:

VW = 4 cm

Step-by-step explanation:

Congruent chords are equidistant from the centre , so

VW = UV = 4 cm

what is 5x5? please help

Answers

Answer:

25

Step-by-step explanation:

That's a simple question.

Step-by-step explanation:

Just do it like 5 plus 5 (five times)

5+5+5+5+5=25

PLS HELP ASAP ILL GIVE BRAINLKEST THANKS PLS ANSWER

Answers

Answer:

4

Step-by-step explanation:

I think if not sorry

Diana made 143 treats for her visit to the nursing home. There are 37 patients and she wants each person to get the same number of treats. How many more treats will she need to make in order for each patient to receive 4 treats?

Answers

D, she needs to make 5 more treats.

Answer:

D) 5 more treats

Step-by-step explanation:

Number of required treats:

37*4 = 148

Remaining number of treats:

148 - 143 = 5

Correct choice is D

Someone help, this is kinda boring...
I'll give brainliest if someone gives me the correct answer

Answers

Answer:

Step-by-step explanation:

[tex]a+b =1\dfrac{3}{5} + (-2)\\\\=\dfrac{8}{5}-\dfrac{2*5}{1*5}\\\\=\dfrac{8-10}{5}\\\\\\=\dfrac{-2}{5}\\\\\\2-c = 2-[-7] = 2+7 = 9\\\\\\dfrac{- I a + b I}{2-c}=\dfrac{\dfrac{-2}{5}}{9}\\\\=\dfrac{-2}{5}*\dfrac{1}{9}\\\\=\dfrac{-2}{45}\\\\[/tex]

Help Me WHAT is 2 + 2

Answers

Answer:

4

Step-by-step explanation:

Answer:

= 4

2 + 2 = 4

Step-by-step explanation:

yw :-)

please solve y. y/4-16=-14 and also have a bless day

Answers

Answer:

y=8

Step-by-step explanation:

Multiply both sides of the equation by 4.

y−64=−56

Add 64 to both sides.

y=−56+64

Add −56 and 64 to get 8.

y = 8

and have a good day as well

What is six times a number in algebraic expression

Answers

Answer:

6(x)

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

x represents a number, it is also called a variable.

If there is 2 of x, it would be represented like this: 2x

If there is 1 of x, it would be represented like this: x

Using the appropriate Algebraic identity evaluate the following:(3p -q) (3p +q)​

Answers

Step-by-step explanation:

expand and multiply the terms

What is Integration ?

Answers

Answer:

Integration is the act of bringing together smaller components into a single system that functions as one. These links usually are established between the components of the process and control layer of each system to promote the free flow of data across systems.

Answer:

Integration is the action or process of integrating.

Step-by-step explanation:

PLEASE HELP ME!!
Find the domain, in interval notation too.

Answers

I sadly do not have an answer to this problem but,  have a great explanation for a similar problem. (I really am sorry that I don't have the answer, in a bit of a time constraint)

Step-by-step explanation:

Example (graph found below):

The domain of a function f(x) is the set of values of x for which f(x) has a defined value.



In the graph we can see that we have two asymptotes: one vertical and one slant asymptote.



The slant asymptote does not affect the domain,  but the vertical asymptote at x = 0 implies that f(x) does not have a defined value at x = 0.

Then, x = 0 is not part of the domain of f(x). All the real numbers different from 0 are part of the domain.



Then, we can write the domain as x ≠ 0 or, in interval notation, as (-∞,0) ∪ (0,∞).



Answer: the domain is all the real numbers different from 0.



NOTE:

If we want to know the range of the function, we have to look at the values that f(x) can take for the domain for which it is defined.

In this case, we can see that there is no limitation for the values f(x) can take: f(x) can take all real numbers, so the range is all real numbers.

Answer:

[tex]D = (-\infty, -1) \ \cup \ (-1, 2) \ \cup \ (2, \infty)[/tex]

Step-by-step explanation:

This function is rational function that's meaning that is of the form:

[tex]\frac{1}{x}[/tex]

So you have to take care when [tex]x[/tex] is equal to 0 because the function is undefine in that number (is represented with an asymptote and means that go to positive or negative infinity).

In the given graph there are 2 asymptotes in -1 and 2 so you have to avoid this two points in the notations by intervals. You can achieve this using the parenthesis indicating that you don't take the value in account.

Someone could help me with problem 3-75 (b) please

Answers

Answer:

a. is correct

b. not correct

c. not correct

d. is correct

Step-by-step explanation:

3-75:

a) 3x + 7 = x - 1

Subtract 7 on both sides to get 3x = x - 8, then subtract x from 3x to get 2x = -8, finally divide 2 on both sides to get x = -4. (Answer is yes)

b) -2x - 4 = -4x + 3

Add 4 on both sides to get -2x = -4x + 7, then add 4x to -2x to get 2x = 7, finally divide 2 on both sides to get x = 7/2. (Answer is no)

c) -3x + 5 + 5x - 1 = 0

Add 1 on both sides to get -3x + 5 + 5x = 1, then subtract 5 on both sides to get -3x + 5x = -4, next combine -3x and 5x together to get 2x = -4, finally divide 2 on both sides to get x = -2. (Answer is no)

d) -(x - 1) = 4x - 5 - 3x

Combine 4x and -3x together to get

-(x - 1) = x - 5, then add (x - 1) and (x - 5) together to get 2x - 6, next do 2x - 6 = 0 and solve for x, by adding 6 on both sides to get 2x = 6, and finally dividing 2 on both sides to get x = 3. (Answer is yes)

Explanation:

I did the whole 3-75 section for you, but I didn't really understand 3-76, and my brain was already hurting by the time I got to section 3-77, sorry.

Hope this helps though, I did my best :)

Which quadrilateral has the highest order of rotational symmetry?

Answers

Answer:

it should be C

Step-by-step explanation:

hope this is helpful


Simplify: 4x(x^2 – 3x + 1)

A)4x^3 - 7x^2 +5
B)4x^2 – 12x^2 + 4
C) 4x^3 - 12x^2 + 4x
D)4x^2 - 12x + 1

Answers

Answer:

its c

Step-by-step explanation:

4x*x^2= 4x^3

-3x*4x =-12x^2

1*4x = 4x

= 4x^3 -12x^2 + 4x

RE
Which graph represents the function f(x) = -X2 + 5?
N
10-
8-
6
2
o
-10 -56-4
ca
M
4
6
8
10
X
do ou

Answers

Answer:

I can't interpret the data the way it is presented.  Are there two columns?  I'll assume "-x2" is really "-x^2."

I've attached a plot of the function.  Check to see which of your points fall on the line.

Step-by-step explanation:

y = -x^2 + 5

What is the height of the flagpole?

Answers

Right angle: a^2 + b^2 = c^2
c = longest side which is 26
a = 10
Now plug it in to find b
10^2 + b^2 = 26^2
100 + b^2 = 676
b^2 = 576
b = squareroot of 576 = 24

Solution: 24

Helpppppppppp please​

Answers

Answer:

20 million

Step-by-step explanation:

Answer:

C twenty million

Step-by-step explanation:

Round the 2 populations to the nearest million.

The population of California is about 38 million.

The population of Texas is about 20 million.

The difference is 18 million.

The closest choice is 20 million.

Answer: C twenty million

how to find the vertex of a parabola in standard form

Answers

Step-by-step explanation:

TO find the vertex, you need to find the x− and y− coordinates.

The formula for the axis of symmetry and the x-coordinate of the vertex is:

x = -b over 2a

To find the y-coordinate the vertex, substitute the value for x into the equation and solve for y

y=a(-b over 2a) squared + b(-b over 2a) + c

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