A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 6t, where t represents time in minutes and p represents how far the paint is spreading.

The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2.

Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points)

Part B: How large is the area of spilled paint after 8 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Answers

Answer 1

p(t)=6t

A(p)=πp^2, since p(t)=6t

A(t)=π(p(t))^2

A(t)=π(6t)^2

A(t)=36πt^2, so when t=8 and approximating π≈3.14

A(8)≈36(3.14)(8^2)

A(8)≈36(3.14)64

A(8)≈7234.56 u^2

Answer 2

Answer:

r(t) = 3t ; where t represents the time in minutes and r represents how far the paint is spreading.

A(r) = πr²

Part A:

A[r(t)] = π (3t)² = 3.14 * 9t² = 28.26t²

Part B:

r(10) = 3(10) = 30

A(r) = 3.14 * 30² = 3.14 * 900 = 2,826 square unit

Step-by-step explanation:

Related Questions

A triangle has one side that measures x, and the other two sides each measure 4 inches less than x. The perimeter is 19 inches.

What is the measure of x?

Answers

perimeter of a triangle = all 3 sides added together

x + (x - 4) + (x - 4) = 19
3x - 8 = 19
3x = 19 + 8
3x = 27
x = 27/3
x = 9 <==

Answer: Simplified version of the answer above: (x = 9) is the correct answer.

Step-by-step explanation:

Part A: Solve −np − 90 < 30 for n. Show your work. (4 points) Part B: Solve 5m − 3h = 45 for h. Show your work. (6 points)

Answers

Hello there!

Part A: Solve for n; -n*p - 90 < 30
Add 90 to both sides.
-n*p < 120
Divide both sides by p.
-n < 120/p
Divide both sides by -1.
n [tex] \geq [/tex] 120/-p is your answer for part A.

Part B: Solve for h; 5m - 3h = 45
Subtract 5m from both sides.
-3h = -5m + 45
Divide both sides by -3.
h = (-5m + 45)/-3 is your answer for part B.

I hope this helps!

A bag contains nickels, quarters and pennies. If a handful of coins brings in five nickels, 3 quarters, and nine pennies, how much money is expected to be in the bag if 90 coins are in the bag?

Answers

The expected amount of money in the bag if 90 coins are in the bag is [tex]$\$5.78$[/tex].

We need to determine the total value of the coins in the bag based on the given handful and then extrapolate that to the total number of coins in the bag.

First, let's calculate the value of the coins in the handful:

The value of five nickels is [tex]$5 \times 5$[/tex] cents = 25 cents.

The value of three quarters is [tex]$3 \times 25$[/tex] cents = 75 cents.

The value of nine pennies is [tex]$9 \times 1$[/tex] cent = 9 cents.

Adding these values together gives us the total value of the handful:

[tex]\[25 + 75 + 9 = 109 \text{ cents}\][/tex]

Next, we need to find out the ratio of each type of coin in the handful. We have a total of [tex]$5 + 3 + 9 = 17$[/tex] coins in the handful.

The ratios for each type of coin are as follows:

Nickels: [tex]$\frac{5}{17}$[/tex]

Quarters: [tex]$\frac{3}{17}$[/tex]

Pennies: [tex]$\frac{9}{17}$[/tex]

Now, let's calculate the expected number of each type of coin in the bag, given that there are 90 coins in total:

Expected nickels: [tex]$90 \times \frac{5}{17}$[/tex]

Expected quarters: [tex]$90 \times \frac{3}{17}$[/tex]

Expected pennies: [tex]$90 \times \frac{9}{17}$[/tex]

Using these ratios, we can calculate the expected number of each coin type:

Expected nickels: [tex]$90 \times \frac{5}{17} \approx 26.47$[/tex], but since we can't have a fraction of a coin, we'll consider 26 nickels.

Expected quarters: [tex]$90 \times \frac{3}{17} \approx 15.88$[/tex], rounding to 16 quarters.

Expected pennies: [tex]$90 \times \frac{9}{17} \approx 47.65$[/tex], rounding to 48 pennies.

Finally calculate the total expected value in the bag by multiplying the number of each type of coin by its value:

Value of expected nickels: [tex]$26 \times 5$[/tex] cents = 130 cents

Value of expected quarters: [tex]$16 \times 25$[/tex] cents = 400 cents

Value of expected pennies: [tex]$48 \times 1$[/tex] cent = 48 cents

Adding these values together gives us the total expected value in the bag:

[tex]\[130 + 400 + 48 = 578 \text{ cents}\][/tex]

To convert the total value from cents to dollars, we divide by 100:

[tex]\[578 \text{ cents} \div 100 = \$5.78\][/tex]

Solve the following system of equations by substitution. 3x + 2y = -12 x = 2 A. (2, -9) B. (-2, -3) C. (3, 2) D. (2, 3)

Answers

Plugging it in, we get (3)(2)+2y=-12 and 6+2y=-12. Subtracting 6 from both sides, we get -18=2y and dividing by 2 we get y=-9 to get (2, -9) since x is first in the pair

Last year, Raul estimated that he would need 480 night lights, but he sold 420 night lights. This year, he bought 425 night lights and only sold 375. Which set of statements about the percent errors for the two years is true

Answers

The percent error for this year was lower. Raul estimated better this year is your answer.
Hope it helped <3

Answer:

The answer is C in edg.

Write a word phrase for the algebraic expression 3x+10

Answers

Hello there!

Jenny wants to park in an airport parking lot. The parking lot costs x amount of money per hour, plus an additional parking fee of $10. Jenny stays in the parking lot for 3 hours.

This causes our equation to be 3x (3 hours) + 10 (additional parking fee).

I hope this helps!

Jared flipped a fair coin 50 times. He expected half of his tosses to land on heads, but he only got heads 15 times. If he increased the number of times he flipped the coin to 500, he should expect the number of heads to be-

Answers

150 but this wouldnt be how many times it happens because it is all based of off chance and possibility

Maybe its 150, i think

the age of two groups of yoga students are shown in the following dot plot

Answers

Since the mean absolute deviation (MAD) is lower for group P, this means that group P has less variability compared to group Q.

The answer is choice A.

Which expression shows a sum of three terms?

3x
3 + x
x3
x + 3 + x

Answers

the sum of 3 terms..." sum " means add

x + 3 + x <==

The correct answer is: [D]: " x + 3 + x" .
___________________________________________________
The three (3) terms are: "x" , "3" , and "x" .
___________________________________________________
Answer choice [A]: "3x" ; only has one term.
___________________________________________________
Answer choice [B]: "x + 3 " ; only has two terms: "x" and "3" .
___________________________________________________
Answer choice [C]: "x³ " ; only has one term.
___________________________________________________

how many solutions does the equation 4y+7=5+2+4y have?
A. one
B. two
C. None
D. infinitely many

Answers

4y + 7 = 5 + 2 + 4y...simplify
4y + 7 = 7 + 4y

same line....infinite solutions

BEST ANSWER GETS BRAINLIEST
The following data show the height, in inches, of 11 different garden gnomes:

2 9 1 23 3 7 10 2 10 9 7

After removing the outlier, what does the mean absolute deviation of this data set represent?

A, On average, the height of a garden gnome varies 3.2 inches from the mean of 7 inches.
B, On average, the height of a garden gnome varies 3.6 inches from the mean of 6 inches.
C, On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.
D, On average, the height of a garden gnome varies 3.6 inches from the mean of 7 inches.

Answers

In doing experiments, it is sometime inevitable to commit errors. This is reflected on the set of data points that you have. When you notice that there is an absolute unique point that is very different from the rest, that is the outlier. In this data set, the outlier is 23. You remove the outlier from the data set so as not to significantly affect your results.

The average or mean, therefore, is

μ = Σx/N = (2+9+1+3+7+10+2+10+9+7)/10
μ = 6

The equation for the mean absolute deviation is

MAD = ∑|x-μ|/N
MAD = [|2-6|+|9-6|+|1-6|+|3-6|+|7-6|+|10-6|+|2-6|+|10-6|+|9-6|+|7-6|]/10
MAD = 3.2

Therefore, the answer is C.

Use a calculator to evaluate 8 · cos30° rounded to four decimal places.

Answers

Cos(30) • 8 = 6.9282-0323

Answer:

The value of 8 cos 30° rounded to four decimal places = 6.9282

Step-by-step explanation:

Here we need to find the value of 8 cos 30° rounded to four decimal places.

Using the calculator to find the value

8 cos 30° = 6.9282032302755

Rounding the number to four decimal places, we will get

8 cos 30° = 6.9282

The value of 8 cos 30° rounded to four decimal places = 6.9282

What value does 4 represent in the number 487.009

Answers

400 is the answer :)

The answer to this question is 400

What is the value of x in this equation: 4x + 5 = 3x + 4? Solve the equation using the algebra tiles. x =

Answers

Answer:

Solution of the equation 4x + 5 = 3x + 4 is:

x= -1

Step-by-step explanation:

We are given a equation:

4x + 5 = 3x + 4

We have to solve the equation for x

4x+5=3x+4

subtracting both sides by 4

4x+5-4=3x+4-4

4x+1=3x

subtracting both sides by 4x

4x|+1-4x=3x-4x

1= -x

⇒ x= -1

Hence, solution of the equation 4x + 5 = 3x + 4 is:

x= -1

find the solution of the system of equations 2x-4y=32 2x-8y=48

Answers

2x-4y=32
2x-8y=48
--------------subtract
4y = - 16
y = -4

2x-4y=32
2x- 4(-4)=32
2x + 16 = 32
2x = 16
x = 8

answer
(8, -4)

2x - 4y = 32
2x - 8y = 48

Multiple equation 2 by -1 so the 'x' variables will cancel.
-1(2x - 4y = 32)
-2x + 4y = - 32
2x - 8y = 48
-------------------- add
- 4y = 16 divide both sides by -4
y = -4
Plug -4 back into either equation and solve for y.
2x - 4y = 32
2x -4(-4) = 32
2x + 16 = 32 subtract 16 from both sides
2x = 16 divide both sides by 2
x = 8
(8, -4)

Each of the four outside walls of the large wooden box shown above is to be covered with waterproof plastic that comes in 3-foot-wide rolls. The plastic does not overlap. What is the total length, in feet, of plastic, needed to cover the four walls?

A) 21 ft
B) 42 ft
C) 63 ft
D) 84 ft
E) 126 ft

Explain too, thanks.

Answers

we need the lateral aera
that will be
LA=2H(L+W)

H=6
L=12
W=9
LA=2(6)(12+9)
LA=12(21)
LA=252

so we need 252 square feet
it comes in 3ft width so
3ft times ?=252
divide both sides by 3ft
?=84

we need 84ft of that wrap

D is answer

The equation x = 6 represents a vertical line. True or false

Answers

True, as for any line [tex]x=a[/tex]

the answer is true because you need to find similar coordinates to make it vertical

find the volume of the shaded solid. Round your answer to 2 decimal places if necessary. Use pi=3.14 when necessary. cylinder with these 6ft, 18ft, 30 ft.

Answers

Ok so what we have is a large cylinder with a hollow cylindrical tube running thru the center. The volume of the shaded region should be the volume of the entire large cylinder (C) minus the volume of the small cylindrical tube (c): C - c
The volume of any cylinder is the area of the top circle (pi×r^2) times the height (h) of the cylinder, where r=radius of the circle. So: h×pi×r^2
The heights are the same for C and c, so we can call that h in both, which = 30ft. Now C's radius (R) = 1/2 of diameter, which is 18ft. So R = 9ft
c's radius (r) is 1/2 of its diameter, which is 6ft. So r = 3ft. Now we can set it up:
C - c = (h×pi×R^2) - (h×pi×r^2)
*since the h and pi in both formulae are multiplied by the other variable, we can factor that out:
h×pi(R^2) - h×pi(r^2) = h×pi(R^2-r^2)
h×pi = 30ft.×3.14 = 94.2ft. -->
94.2ft(9ft^2-3ft^2) = 94.2ft(81-9ft^2)
= 94.2ft(72ft^2) = 6782.4 ft.^3

F^(-1) when f(x)=2x-7/3

Answers

y=2x-7/3
x=2y-7/3
x+7/3=2y-7/3+7/3
(x+7/3)/2=2y/2
(x+7/3)/2= f^-1(x)

when multiplying two or more fractions, you should?

Answers

you should multiply 2 at a time and not try to do them at the same time also if the fraction numbers a high you can cross simplify the numbers so multiplying them won't be as hard. so, for example, 8/12*16/36*50/100 you can simplify 8/12 to 2/3 16/36 to 4/9 50/100 to 1/2 then you can multiply 2/3*4/9 and then 8/27*1/2 to equal 8/54 and you can still simplify 8/54 to 4/27

For his craft project, James bought 10 pieces of ribbon that were each 2.1 feet long. How many total yards of ribbon did James buy?

Answers

2.1 (ribbon length) * 10 (ribbon #) = 21

There is 1 yard in 3 feet. Divide by 3 to convert.

21 / 3 = 7

Therefore he brought 7 yards of ribbon.

James buy 7 yard of ribbon

What is unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

James= 10 pieces of ribbon

Each of length= 2.1 feet

So, length of 10 ribbons

=2.1*10

=21 feet

Now, 1 yard= 3 feet

So, 21 feet= 21/3= 7 yard

Learn more about unitary method here:

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PLZZZ HELP WILL GIVE BRAINLIESTTTT

Answers

10 is the missing number.

Simplify (−34.67)0.
−34.67
−1
0
1

Answers

Im pretty sure that it's 0

Answer:

The answer is 1.

Im sorry I forgot the step by step explanation, but I had this in a quuiz a while ago and the answer is 1.

Solve for x: the quantity of x plus 4 all over 2 = 7.

x = 3
x = 5
x = 6
x = 10

Answers

the actual answer is 10 , 10 plus 4 is 14 and 14 divided by 2 equals 7 so the answer is 10
i hope this helped

Which number is equivalent to the fraction 18/5

Answers

(18/5)(2/2)=36/10=3.6

18/5 = 36/10
Multiply two to both numerator and denominator and the answer would be 36/10 and when simplified 18/5.

A store had 235 MP3 players in the month of January. Every month ,30% of the MP3 players were sold and 50 new MP3 players were stocked in the store. Witch recursive best represents the number of MP3 players in the store f(n) after n months?

Answers

f(n)=235-(235*.3^n)+50n is your equation where * is multiplication and ^ it to the power to.

What's the area of a circle with a radius of 5?

Answers

First, multiply the radius by itself. 5x5=25. Then multiply by pi, or 3.14. 25x3.14=78.5. The area of the circle is 78.5units^2. Hope this helps! ;)

area=pi times radius²
given that the radius=5 units
area=pi 5²=25pi

area=25pi square units
if we use pi=3.14 aprox then
area=78.5 square units

To take a taxi, it costs $3 plus an additional $2.00 per mile traveled. You spent exactly $ 20 on a taxi, which includes the $1 tip you left. How many miles did you travel

Answers

Without a tip, the price is $19.
19=3+2x
16=2x
x=8
Answer: 8 miles

What is the range of y=sec x

Answers

y≤-1, y≥1 is the range of y=sec x

The values where cos(x) is equal to 0 are excluded from the domain of the function y=sec(x)=1cos(x), or the values 2+n for all integers n. The function's range is either y<=1 or y>=1.

What is domain?

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

here, we have,

we know that "secant function" mean:

Its root is the Latin verb secare, which means "to cut." Any line that intersects a circle twice is referred to as a secant line, and you can conceive of this line as slicing the circle in half. The distance from the origin to the point where the tangent line intersects the x-axis is the secant function.

now, the identity of the sec is:

1/cos(x) = sec(x) Cot (x) = 1/Tan (x)

To know more about domain visit:-

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Write an algebraic expression for 15 decreased by twice a number

Answers

The expression would be:
15-2x

Hope this helps!
-Benjamin

15- (y2) should get you the answer... Hopefully.

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