this is a calculus question.
The volume of a cube increases at a constant rate of 10 cm^3 per second. find the rate of change in its total surface area at the instant when its when its sides are 20 cm long.

Answers

Answer 1

Answer:

2 cm^2/sec

Step-by-step explanation:

side of cube ---- x cm

volume = x^3

d(volume)/dt = 3x^2 dx/dt

when c = 20, d(volume)/dt = 10 cm^3/sec

10 = 3(20^2) dx/dt

dx/dt = 10/1200 = 1/120 cm/sec

Surface area = SA = 6x^2

d(SA)/dt = 12x dx/dt

so when x = 20, as above

d(SA)/dt = 12(20)(1/120) cm^2/sec

= 2 cm^2/sec


Related Questions

Pls help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!please I’m begging u

Answers

Answer:

7. 36     8. 1     9. 21

Step-by-step explanation:

You plug in the variables in the equation.

7.[tex]5^{2} +-4^{2} = 41[/tex]

8. [tex](5-4)^{2} = 81[/tex]

9. [tex]5+4^{2} =21[/tex]

Answer:

See explanation

Step-by-step explanation:

1. 8^5 = 32768

2. a^6

3. 5^5*9^3 = 2278125

5. (-3)^5 = -243

6. (3/4)³ = 27/64

7. a² + b² = 5² + (-4)² = 25 + 16 = 41

8. (a + b)² = (5 + 4)² = 9² = 81

9. a + b² = 5 + 4² = 5 + 16 = 21

Determine the graph transformation....

Answers

Answer:

I think its b

Step-by-step explanation:

Please Help Will Mark as Brainlist

Answers

Answer:

Hey there!

We can write this equation: 2x+4x=180

6x=180

x=30

Hope this helps :)

The two angles are supplementary angles. When added together they equal 180 degrees.

2x + 4x = 180

Combine like terms:

6x = 180

Divide both sides by 6:

X = 180/6

X = 30

What's the perimeter of rectangle DEFG, shown? A) 17 B) 28 C) 40 D) 34

Answers

Answer:

[tex]\huge\boxed{Perimeter = 34\ units}[/tex]

Step-by-step explanation:

DE = 10 units

GF = 10 units

DG = 7 units

EF = 7 units

Perimeter of rectangle = Sum of all sides

P = DE + GF + DG + EF

P = 10 + 10 + 7 + 7

Perimeter = 34 units

Answer:

D) 34 units

Step-by-step explanation:

Coordinates:

D: (-5,4)

E: (5,4)

F: (5, -3)

G: (-5,-3)

Distance between points D and E = Distance between points F and G = 10

Distance between points E and F = Distance between points G and D = 7

Formula for perimeter of your rectangle:

2(x) + 2(y) =

2(10) + 2(7) =

20 + 14 = 34 units

That's your answer!

Hope that helps and maybe earns a brainliest!

Have a terrific day! >   <

                                   U

If the degree measures of the angles of a triangle are in the ratio 3 : 3 : 4, what is the degree measure of the largest angle of the triangle? (Sum of all three angles is 180)

Answers

x=3k

y=3k

z=4k

x+y+z=180

3k+3k+4k=180

10k=180

k=180/10

k= 18

z=4*18

z=72

answer: 72

Answer:72 degrees

Step-by-step explanation:

3:3:4 is the ratio of the angles of a triangle and we have been asked the degree measure of the largest angle.

First of all...add the three ratios

3+3+4=10

;Ratio 10=180 degrees(the sum of all the angles;ratios add up to the sum of all three angles)

10=180 how about ratio 3?

Cross multiply...3 times 180 over 10= 54 degrees

Both angles with ratio 3 are 54 degrees

180-108=72

The angle with ratio 4 has 72 degrees which makes it the largest angle

In which situation can a constant of proportionality be identified A. Allison earns $8 per hour for h hours and an $8 bonus for each cell phone plans she sells. B. Ben buys x cans of dog food for $1.25 each and uses a coupon $7 off his entire purchase. C. Claire orders b books online for $4.50 each plus shipping charges $0.30 for each book. D. John runs 3 miles per day for m days in a week and bicyles 20 miles/day the remaining days in the week.

Answers

Answer:

C

Step-by-step explanation:

C is the only situation in which there is a clear constant of proportionality and no offset (no initial value).  Claires rate is ($4.50 + $0.30)/book, or $4.80/book.

C is the answer. And i agree^^

PLease answer !!! Find constants $A$ and $B$ such that \[\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\] for all $x$ such that $x\neq -1$ and $x\neq 2$. Give your answer as the ordered pair $(A,B)$. and Find all values of $t$ such that $\lfloor t\rfloor = 2t + 3$. If you find more than one value, then list the values you find in increasing order, separated by commas.

Answers

Answer:

1. [tex](A,B) = (3,-2)[/tex]

2. The values of t are: -3, -1

Step-by-step explanation:

Given

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}[/tex]

[tex]|t| = 2t + 3[/tex]

Required

Solve for the unknown

Solving [tex]\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}[/tex]

Take LCM

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{(x - 2)(x-1)}[/tex]

Expand the denominator

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - 2x + x -2}[/tex]

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - x -2}[/tex]

Both denominators are equal; So, they can cancel out

[tex]x + 7 = A(x+1) + B(x-2)[/tex]

Expand the expression on the right hand side

[tex]x + 7 = Ax + A + Bx - 2B[/tex]

Collect and Group Like Terms

[tex]x + 7 = (Ax + Bx) + (A - 2B)[/tex]

[tex]x + 7 = (A + B)x + (A - 2B)[/tex]

By Direct comparison of the left hand side with the right hand side

[tex](A + B)x = x[/tex]

[tex]A - 2B = 7[/tex]

Divide both sides by x in [tex](A + B)x = x[/tex]

[tex]A + B = 1[/tex]

Make A the subject of formula

[tex]A = 1 - B[/tex]

Substitute 1 - B for A in [tex]A - 2B = 7[/tex]

[tex]1 - B - 2B = 7[/tex]

[tex]1 - 3B = 7[/tex]

Subtract 1 from both sides

[tex]1 - 1 - 3B = 7 - 1[/tex]

[tex]-3B = 6[/tex]

Divide both sides by -3

[tex]B = -2[/tex]

Substitute -2 for B in [tex]A = 1 - B[/tex]

[tex]A = 1 - (-2)[/tex]

[tex]A = 1 + 2[/tex]

[tex]A = 3[/tex]

Hence;

[tex](A,B) = (3,-2)[/tex]

Solving [tex]|t| = 2t + 3[/tex]

Because we're dealing with an absolute function; the possible expressions that can be derived from the above expression are;

[tex]t = 2t + 3[/tex]    and   [tex]-t = 2t + 3[/tex]

Solving [tex]t = 2t + 3[/tex]

Make t the subject of formula

[tex]t - 2t = 3[/tex]

[tex]-t = 3[/tex]

Multiply both sides by -1

[tex]t = -3[/tex]

Solving [tex]-t = 2t + 3[/tex]

Make t the subject of formula

[tex]-t - 2t = 3[/tex]

[tex]-3t = 3[/tex]

Divide both sides by -3

[tex]t = -1[/tex]

Hence, the values of t are: -3, -1

MIKE WAHOUSEKEYYYYYYYY

What is the expression in SIMPLEST radical form? (20)∧5/2

Answers

Answer:

The expression in the question can, and should, be written clearly as either  205(2)=8  or as  205(2)=2 . Relying on a left-to-right or right-to-left interpretation is not a good idea.

In cases of associative operators, like  a⋅b⋅c , the parenthesis or other grouping can be omitted because any reasonable interpretation will yield the same result. But this isn’t true of division, which is not associative, nor is it true of mixed operators at the “same level” of precedence, like multiplication/division.

The other answers which say the result is  8  may not be wrong, but they are missing the main issue in that this expression should not be used because of the ambiguity

Step-by-step explanation:

If you're good at angles of depression please help meeeeee and show full working out tyyyyyyyyyy

Answers

Answer:

  236.9 m

Step-by-step explanation:

Let x and y represent the distances to the near and far cars, respectively. You know from the definition of the tangent of an angle that ...

  tan(angle of depression) = building height/distance to car

  tan(10°39') = 150/x

  x = 150/tan(10°39')

and

  tan(8°15') = 150/y

  y = 150/tan(8°15')

The difference of these two distances is the distance between the cars:

  y - x = 150/tan(8°15') -150/tan(10°39')

__

The minutes of arc can be converted to fractional degrees:

  15' = 15'/(60'/1°) = (15/60)° = 0.25°

  39' = 39'/(60'/1°) = (39/60)° = (13/20)° = 0.65°

So, the distance of interest is ...

  distance between cars = (150 m)(1/tan(8.25°) -1/tan(10.65°)) ≈ 236.86 m

The cars are about 236.9 meters apart.

what they said is definitely right

Consider the function represented by the graph. What is the domain of this function?

Answers

Answer:

domain={8,7,6,5,4,3,2,1,0}

Answer:

[tex]\boxed{0 \leq x \leq R}[/tex]

Step-by-step explanation:

Well domain is the amount of x values on a graph,

so looking at the given graph we can tell the x values start at 0 and since it is a solid dot the x is greater than or equal to 0 then you can tell by the arrow that the line goes on forever.

0 ≤ x ≤ R

The R stands for all real numbers.

Hope this helps :)

Santiago is eight years younger than Juan is today. If, in four years, Santiago will be half Juan’s age, how old is Santiago today? a) 1 b) 2 c) 3 d) 4

Answers

Answer:

d) 4.

Step-by-step explanation:

Let Santiago be x years old today.

Then Juan is x + 8 years old.

In 4 years Santiago will be x + 4 years.

In 4 years Juan will be x + 12 years.

From the given information:

x + 4 = 0.5(x + 12)

x = 0.5x + 6 - 4

0.5x = 2

x = 2 / 0.5

x = 4.

Let S be Santiago’s age
Let J be Juan’s age.

Since Santiago is 8 yrs younger than Juan, we can write

Equation 1: S = J-8

In 4 yrs, Santiago age will be S + 4,
In 4 yrs, Juan’s age will be J + 4.

Given:
In 4 yrs, Santiago will be half of Juan’s age, so ..

Equation 2: S+4=(J+4)/2

We know the value of S from equation 1. Substitute S=J-8 in equation 2, we get

J -8 + 4=(J+4 )/2

J-4 = (J+4 )/2

2( J- 4) =J + 4
2J-8 =J + 4
2J-J =8+ 4
J = 12

Substitute J= 12 in equation 1
S= 12-8
S = 4

So, Santiago’s age is 4 yrs today.

John and Maria also want to put new tile in their living room. The floor measures 20 feet long by
20 feet wide. The tiles they want to purchase cost $2.25 each, and each tile covers exactly 1 square
foot of floor space. How much will they need to spend on tile? (Section 10.8) (1 point)

Answers

Answer:

$900

Step-by-step explanation:

First, find the area of the floor with the equation A = lw

A = lw

A = (20)(20)

A = 400 ft²

Since each tile covers 1 sq ft and the floor's area is 400 sq ft, they will need 400 tiles.

To calculate the total cost, multiply 400 by 2.25

400(2.25) = 900

= $900

900 dollars they will spend

Find an equation of the line with the slope m= 3 that passes through the point (2,2). Write the equation in the form Ax+By = C.

Answers

Answer:

[tex]y = 3x-4[/tex]

Step-by-step explanation:

We know that if we were to write an equation with the slope of 3, it would be [tex]y=kx[/tex], where k is the constant (in this case 3.)

So right now, we have [tex]y=3x[/tex].

However, this will not pass through the point (2,2). To do this, we need to add a y-intercept in which (2,2) will be crossed through.

If we have a y-intercept of -4, the points will be:

(0, -4)

(1, -1)

(2, 2)

So our final equation is [tex]y = 3x-4[/tex].

Hope this helped!

Answer: 3x-1y=4 in Ax+By=C form

Step-by-step explanation:

the intercept form is y=3x-4

subracting 3x from both sides would get  -3x+y=-4

distributing -(-3x+y=-4) would get 3x-y=4.

If f(x)=(2x^2)-1, find:
-f(3x-1)+2

Answers

Answer:

-f(3x - 1) + 2 = -18x² + 12x + 1

Step-by-step explanation:

Step 1: Find f(3x - 1)

f(3x - 1) = 2(3x - 1)² - 1

f(3x - 1) = 2(9x² - 6x + 1) - 1

f(3x - 1) = 18x² - 12x + 2 - 1

f(3x - 1) = 18x² - 12x + 1

Step 2: Plug in f(3x - 1)

-(18x² - 12x + 1) + 2

Step 3: Evaluate

-18x² + 12x - 1 + 2

-f(3x - 1) + 2 = -18x² + 12x + 1

-f(3x-1) + 2 = -18x2 + 12x+1


Ben deposited $2,700 in an account that pays 3.25% simple interest. He created a graph of his
account balance equation (A = Prt+P) with a slope of 8,775.

Answers

Step-by-step explanation:

His profit is 40%.

hope this helps

pls mark me brainliest

Answer:

40 percent i think

Step-by-step explanation:

hope its right

please put me brainlieeeeeeest

thxxx

Find the measure of the remote exterior angle. m∠x=(4n−18)°m∠y=(n+9)°m∠z=(151−5n)° A. 71 B. 16 C. 100 D. 46

Answers

Answer: A.71

Step-by-step explanation: 1.set up the equation

2. 4n-18+n+9=151-5n

3.combine like terms ->  5n-9=151-5n

4.solve for n

5.10n=160

n=16

now you have to plug 16 in for n in order to get the remote exterior angle.

151-5(16)

151-80

71°

The sum of any two interior angle is equal to the third exterior angle. The value of n will be 16°. Then the correct option is B.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The triangle having the interior angle x and y, and z is the exterior angle of triangle.

m∠x = (4n − 18)°, m∠y = (n + 9)°, and m∠z = (151 − 5n)°

Then the value of n will be

We know that the sum of any two interior angle is equal to the third exterior angle. Then we have

∠x + ∠y = ∠z

4n - 18 + n + 9 = 151 - 5n

10n = 160

n = 16°

Then the correct option is B.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ2

Michael just drank a cup of coffee to help him stay awake. The coffee had 110 milligrams of caffeine in it. If his body processes 5% of the caffeine every hour, how much will be left in 8 hours? A.74 B.72 C.56 D.73

Answers

Answer:C

Step-by-step explanation:

Answer C.56!

%5 of 110 is 5.5, 5.5 • 8= 54, 110-54= 56!


Select the equation of the line that passes through the point (5.7) and is perpendicular to the line x = 4.

Answers

The answer is y=7 because it makes more sense
The answer is y=7 because that’s the line that the point (5,7) is perpendicular to

What is the area of the figure? The figure is not drawn to scale.\ A. 27.36 cm2 B. 13.7 cm2 C. 9.1 cm2 D. 5.3 cm2

Answers

Answer:

B. 13.7 cm^2

Step-by-step explanation:

To find the height of any parallelogram, you must multiply the base x height.

The base is 1.9 cm. The height is 7.2 cm.

A = bh

A = (1.9)(7.2)

A = 13.68

13.7 is the closest answer we can get if we can round, but it really should be 13.68 cm^2.

Answer:

B. 13.7

Step-by-step explanation:

A = bh

A = 1.9*7.2

A = 13.68

(13.68 rounds up to 13.7)

solve the following problem (1+5^2)-16(1/2​)^3

Answers

Answer:

24

Step-by-step explanation:

Using PEMDAS, we know to solve exponents before everything else.

So:

[tex](1+5^2)-16(\frac{1}{2})^3 = (1+25) - 16(\frac{1}{8} )\\\\26 - 2\\24[/tex]

Hope this helped!

Answer:

24

Step-by-step explanation:

(1+5^2)-16(1/2​)^3

simplify

(1+25)-16(1/8)

simplify

26-2

simplify

24

Directions: Calculate the percent increase or decrease between the starting and ending
quantities below. Round your answer to one decimal place.
1. Start: 3
End: 10

Answers

Answer:233.333%

Step-by-step explanation:

1. 10-3=7 subtract end by start

2.7/3=2.333 divide difference by absolute value of start

32.333x100=233.333% multiply by 100 if negative its decreasing if positive it increasing

hoped this helped

233.333%. Njjjsjsksjsjsjsjsjsis

Express the product of 3x^2 - 4x +6 and x-2 in standard form.

Answers

Answer:

3x³ - 10x² + 14x - 12

Step-by-step explanation:

(3x² - 4x + 6) × (x - 2)

3x³ - 4x² + 6x - 6x² + 8x - 12

3x³ - 10x² + 14x - 12

Thus, the product of 3x² - 4x + 6 and x - 2 in standard form is 3x³ - 10x² + 14x - 12

the answer is 3x^3-10x^2+14x-12 hope this helps :)

Lara is x years old and her two best friends are (x-2) and (x+2). Write an expression for the square of Lara’s age and the product of ages of Lara’s best friends.

Please help with a detailed step by step thanks

Answers

Answer: x^2 + (x+2)(x-2)

Step-by-step explanation:

The caret ^ before the 2 indicates that the 2 is an exponent. It means "x squared"

If the keyboard doesn't allow exponents the caret is the thing to use.

The expression for the square of Lara’s age and the product of ages of Lara’s best friends is x² + (x-2)(x+2)

The first thing to do is to calculate the square of Lara's age and this will be:

= x × x = x²

The product of the ages of Lara’s best friends will be (x-2)(x+2).

Therefore, the expression that can be used to calculate the square of Lara’s age and the product of ages of Lara’s best friends is x² + (x-2)(x+2)

Read related link on:

https://brainly.com/question/16592251

4x = 2x + 2x + 5(x-x) does this have one solution, no solution or infinite solutions

Answers

Answer:

infinite solutions

Step-by-step explanation:

4x = 2x + 2x + 5(x-x)

Simplify

4x = 2x + 2x + 5*0

4x = 2x + 2x

4x = 4x

Divide by x

4 =4

This is always true so this has infinite solutions

Answer: Infinite solutions

PLEASE ANSWER ASAP The drama club is selling candles for a fundraiser. They spend $100 on the candles and sell them for $4.50 each. How many candles must they sell to make more than $125 profit? Let x represent the number of candles sold. Which inequality can you use to find x? 4.5x – 100 > 125 4.5x + 125 > 100 100 – 4.5x > 125 100 + 4.5x > 125

Answers

Answer: 4.5x-100 > 125

Step-by-step explanation: Each candle costs $4.50, which can be simplified to 4.5. To determine how much they will make from the candles, you want to multiply the cost of the candles (4.5) by how many candles are sold (x), and this is where the 4.5x comes from. We subtract 100, because that is how much they spent on the candles they are selling (profit means how much you make after expenses). Since they're trying to make MORE THAN $125 in profit, we use the > sign.

Answer:

So we know that they spend $100 on the candles. In order to make a $125 profit, they must sell $225 worth of candles. Each candle sells for $4.50, so: So we know that they spend $100 on the candles. In order to make a $125 profit, they must sell $225 worth of candles. Each candle sells for $4.50, so:

4.5x > 225 is the inequality for that. It just means $4.50 times the number of candles has to be more than the $225 we need. To simplify it, just divide both sided by 4.5:

x > 50

They have to sell more than 50 candles.

Someone pls help me in this plss
Im really confused in this

Answers

Answer:

Step-by-step explanation:

find LCM of the denominators= 77

so 66/77 - 63/77

3/77

hope this help you pls mark me as brainliest

working for division is on this question is

6/7 divide 9/11

so 6/7 *11/9

66/63 and then you can find its standard form and it cannot be do not

6/7 -9/11
LCM 77

66-63/77
3/77
Hope you’ll understand this method

How would I solve this question? y = -1 1/8 - 7/8x -4x + 9y = -22 x = ?, y = ?

Answers

Answer:

(1.222, -2.444)

Step-by-step explanation:

I hope you can understand the question now

(08.01) Two lines, A and B, are represented by the following equations: Line A: y = x − 1 Line B: y = −3x + 11 Which of the following options shows the solution to the system of equations and explains why? (3, 2), because the point does not lie on any axis (3, 2), because one of the lines passes through this point (3, 2), because the point lies between the two axes (3, 2), because both lines pass through this point

Answers

Answer:

the answer is D

Step-by-step explanation:

y=x-1

2=3-1

2=2

y=-3x+11

2=-3(3)+11

2=-9+11

2=2

Answer:

Step-by-step explanation:

If both lines pass through the point (3, 2), we automatically know that (3, 2) is the soution of the system of linear equations given here, AND that (3, 2) is a solution of equation A and equation B both.

Help, show work please.

Answers

Answer:

A

Step-by-step explanation:

A: 0^2+8=8

B: 1^2+8=9

C: 2^2+8=12

D: 3^2+8=17

as 8 is the smallest, A is the answer

7. Assume two people, Swanson and Suzie, are standing 35 feet apart and are watching a boat
race. At a given moment, Swanson approximates the angle formed by the lead boat, himself, and
Suzie to be 30°. Suzie approximates the angle formed by the lead boat, herself, and Swanson to be
130. How far is the boat from Swanson?
130°
30"
35 feet
Swanson
Suzie
Part I: What is the missing angle in this triangle? (1 point)
Part II: Use the law of sines to find the distance from Swanson to the boat. (2 points)

Answers

Answer:

78.4 ft

Step-by-step explanation:

Part I:

Missing angle = 180° - (130 + 30) (sum of angles in a triangle)

= 180° - 160°

Missing angle = 20°

Part II: distance (d) from Swanson to the boat

Law of Sines is given as:

[tex] \frac{a}{sin(A)} = \frac{b}{sin(B)} [/tex]

Where,

a = d

A = 130°

b = 35 ft

B = 20°

Plug in the values and solve for d

[tex] \frac{d}{sin(130)} = \frac{35}{sin(20)} [/tex]

Multiply both sides by sin(130) to make d the subject of the formula

[tex] \frac{d}{sin(130)}*sin(130) = \frac{35}{sin(20)}*sin(130) [/tex]

[tex] d = \frac{35*sin(130)}{sin(20)} [/tex]

[tex] d = 78.4 ft [/tex]

78.4 ft hope this helped good luck on the test or quiz or whatever it is good luck
Other Questions
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