Slope= 0 ; y-intercept=10 equation of the line
At a party, the punch bowl is hemispherical, with 2 foot radius and open at the top. The fruit punch weighs 66 pounds per cubic foot. At the beginning of the party the bowl is full to the brim. The rules for serving punch require each person to fill the ladle, raise it exactly 1 foot above the top of the owl (without spilling!), and then pour the punch into a cup at that level. After 10 minutes, 30 people have filled 30 cups, and the punch remaining in the bowl is 4 inches deep. Draw a picture of the situation, and then set up the integral for the work W involved in raising the punch until the punch remaining in the bowl has a depth of only 4 inches. Include all pertinent information in the integral, but do not evaluate the integral.
Answer:
W = ∫ [−2/3 to 0] 66π (2−y)(1−y²) dy = 2332π/27
Step-by-step explanation:
Vertical cross-section of bowl is a semi-circle of radius 1, centered at (0,0)
x² + y² = 1 (for y ≤ 0)
Bottom of bowl is at y = −1
Top of bowl is at y = 0
When punch is 4 inches deep, this 1/3 ft above bottom of bowl:
y = −1+1/3 = −2/3
So we integrate from y = −2/3 to y = 0
Radius of cross section at height of y is = x = √(1−y²)
Area of cross section at height y is πr²= πx² = π(1−y²)
Since each person is to lift ladle 2 feet above the top of the bowl, then distance = 2−y
W = Σ (density of punch * distance * volume of punch)
W = ∫ [−2/3 to 0] 66 * (2−y) * πr² dy
W = ∫ [−2/3 to 0] 66π (2−y)(1−y²) dy = 2332π/27
find the difference 4 1/3 - 2 2/3
Answer:
1 2/3
Step-by-step explanation:
convert to improper fraction:
13/3 - 8/3
then solve:
13/3 - 8/3 = 5/3
convert back to a mixed number (unless your not supposed to, if that is the case then "5/3" is your answer):
"1 2/3" is "5/3" as a mixed number.
so your answer (as a mixed number) is:
"1 2/3"
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answer:
By creating some crops that resist certain insects
Step-by-step explanation:
Answer:
Aww man i wasn't the earliest
Step-by-step explanation:
By creating some crops that resist certain insects
If there are 9 hippos, how many pumpkins do you need?
Answer:
9 go to the store rn.
Ben collects state quarters. He has 40 out of the 50 available quarters. What is 40 out of 50 as a percent?
Answer:
80%
Step-by-step explanation:
What is the total cost for x months?
Mac has 1/4 hour left of track practice and must be completed 8 laps around the track before he leaves which equation can be used to find how long has to complete each lap if mac runs at a constant pace?
A. X= 1/4 ÷ 8
B. X= 1/8 ÷ 1/8
C. X= 1/4 ÷ 1/8
D. X= 8 ÷ 1/4
Answer:
(a) [tex]Unit = \frac{1}{4}/8[/tex]
Step-by-step explanation:
Given
[tex]Time = \frac{1}{4}[/tex]
[tex]Lap = 8[/tex]
Required
Determine the time in each lap
The unit time in each lap is calculated by dividing the total time by the number of laps; i.e.;
[tex]Unit = \frac{Time}{Lap}[/tex]
Substitute values for Time and Lap
[tex]Unit = \frac{1}{4}/8[/tex]
State a, b, and the y-intercept then graph the function and describe the end behavior of the grpahs
9514 1404 393
Answer:
9. a = 3, b = 3, y-intercept = 3
10. a = 5, b = 0.6, y-intercept = 5
Step-by-step explanation:
The picture is fuzzy, but we think the given equations are ...
[tex]\text{9. }f(x)=3(3)^x\\ \text{10. }f(x)=5(0.6)^x[/tex]
You are comparing these to the form ...
[tex]f(x) = a(b)^x[/tex]
so the values of 'a' and 'b' should be readily identifiable. The y-intercept in each case is y = a.
The end behavior depends on whether b > 1 or not. Growth functions (b>1) go to 0 on the left and ∞ on the right. Decay functions (b<1) are the reverse.
__
9. a = 3, b = 3, y-intercept = 3
The end behaviors are (x, f(x)) ⇒ (-∞, 0), (∞, ∞).
__
10. a = 5, b = 0.6, y-intercept = 5
The end behaviors are (x, f(x)) ⇒ (-∞, ∞), (∞, 0).
A local restaurant offers pizza with a choice of toppings from this list: cheese, sausage, pepperoni, mushroom, green peppers, hot peppers, ham, pineapple, and anchovies. How many different 4-toppings pizzas can be made with these toppings?
Answer:
126
Step-by-step explanation:
The number of different 4-toppings pizzas can be made with given toppings is 70.
There are 8 different toppings of pizza are given.
What is a combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.
Here, n=8 and r=4
Now, 8C4
= [tex]\frac{8!}{4!(8-4)!} =\frac{8\times7\times6\times5\times4!}{(4\times3\times2\times1)4!}[/tex]
= (8×7×6×5)/(4×3×2×1)
= 7×2×5
= 70
Therefore, the number of different 4-toppings pizzas can be made with given toppings is 70.
To learn more about the permutation and combination visit:
https://brainly.com/question/28065038.
#SPJ5
Supposed that m=3 (x+2)
You’re five neighboring restaurants charge $9.95, $12.95, 8.50, 8.95, and $10.54 hamburger special. What is the mean price
Help i need asaaaaaap °∠°
Answer:
Cube 1 = 30 cubic
Cube 2 = 48 cubic
Cube 3 = 72 cubic
Step-by-step explanation:
Cube 1 = 5x2x3
Cube 2 = 6x2x4
Cube 3 = 8x3x3
Michael draws a scale model of a shed for his engineering class. It is made from a triangular prism on top of a rectangular prism. The volume of the shed is 966 cubic inches. The congruent sides of the triangle are 7.8 inches. A. What is the depth of the shed?
Please help with this question
Answer:
One book would cost $13.
Step-by-step explanation:
To solve this all you have to do is divide 65 by 5. Since 65 divided by 5 is 13, 13 is your answer. So one book would cost $13.
I hope this helps you.
150 copies will cost $15.00. How many copies can be made for $6.00?
Answer:
60 copies
Step-by-step explanation:
$15/150 = 0.1 each copy costs 1 cent
$6/$0.1 = 60 copies
Answer:
60 copies
Step-by-step explanation:
After using Unitary Method, We find that one copy costs 0.1 dollar. So divide 6.00 dollars by 0.1 and we find 60
For checking, we can multiply 60 by 0.1 and we get the same answer
Identify the constant term in this expression.
8x + 4y + xy + 1
Please help
The like terms are the terms that can be put
together. (9x) and (3x) are like terms because
they both have an x attached. (–5) and (3) are
like terms because they have nothing attached.
Which of the following could be the lengths of the sides for a triangle that is similar to the triangle shown?
Step-by-step explanation: {KILLA KWEEN} DAISAN NO BAKUDAN--/|BITES ZA DUSTO|\
Find each percent. 5 is what percent of 15?
Answer:
0.75
Step-by-step explanation:
this is what popped up in my calculator so i hope this helps you. :)
a = (5)
b = (3)
Work out 4a + b
Step-by-step explanation:
IF A=5, B=3
4*5+3=20+3
=23
THE ANSWER IS 23
find a, geometry help !
Answer:
the answer would be i think im right 7
Step-by-step explanation:
Convert the number 243FIVE to base ten
Step-by-step explanation:
ok that is the answer bro
It takes Emmanuel 20 minutes to walk to school. It takes Liah 80% as long to walk to school. How long does it take Liaqh to walk to school? Show your work, then put your answer in the text box.
Answer:
16 minutes
Step-by-step explanation:
80% of 20 is
80/100 * 20 = 16
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Change 6 1/8 from a mixed number to an improper fraction
Answer:
5 9/8
Step-by-step explanation:
4. Find the value of x. 140° 150° 130° to Da) 110 b) 90 O c) 130 O d) 120
Answer:
D
Step-by-step explanation:
The sum of angles of an hexagon is [tex]4\cdot 180[/tex]°.
What simple interest rate is needed for $1,000 to grow to $1,071.25 in 9 months? (Round to the nearest tenth of a percent, if necessary)
Answer:
9.6%
Step-by-step explanation:
Classify each polynomials degree
1) X^3+2x^2-8x+16
2) X^4+4
3) -x^4-5x^4+1
4) 3x^5+7x^4-9x
Answer:
1). 3
2) 4
3). 4
4). 5
hope it helps ☺️☺️
Answer the question and explain your answer. I will be marking brainiest! If you have the correct answer and explain why it’s correct, I will probably pick YOU as brainiest! :)
Answer:
A = 200.96 sq ft
Step-by-step explanation:
formula for area of a circle: A = π·r²
A = (3.14)·(8²)
A = 64·(3.14)
A = 200.96
3/4÷1/5 gffgdfdgfggdggdgdgdfgdgdgdgdgdgdgdgdfgdfgdgd ancer
Answer:
improper fraction- 15/4
Mixed number- 3 3/4
Decimal- 3.75
Step-by-step explanation:
use K.C.F (Keep Change Flip)
