The bounded region in question is a triangle in the second quadrant. The line y = 2x + 6 has intercepts (0, 6) and (-3, 0), so revolving the triangle about the x-axis forms a cone with height 3 and whose circular base has radius 6. Its volume would then π/3 • 6² • 3 = 36π ≈ 113.1 units³.
But you're probably supposed to use calculus. Using the disk method, the integral for the volume is
[tex]\displaystyle V=\pi\int_{-3}^0 (2x+6)^2\,\mathrm dx[/tex]
[tex]\displaystyle V=\pi\int_{-3}^0(4x^2+24x+36)\,\mathrm dx[/tex]
[tex]V=\pi\left(\dfrac43x^3+12x^2+36x\right)\bigg|_{-3}^0=\boxed{36\pi}[/tex]
as expected.
Proportions 6. A certain salsa is made with 6 parts tomato and 2 parts bell pepper. How many cups of tomato should be combined with 1.5 cups bell pepper? Write a proportion, then solve.
Answer:
4.5 cups of tomatoes should be combined with 1.5 cups of bell peppers.
Step-by-step explanation:
Given that the salsa is made with 6 parts tomato and 2 parts bell pepper.
Let t be tomatoes and b be bell peppers
The proportion will be:
t:b
The ratio of tomatoes to bell pepper will be:
6:2
This ratio simplifies to 3:1
This means no matter how much more the tomatoes and peppers are, the simplified ratio will be same.
Now the bell peppers are 1.5 cups then the proportion will be:
[tex]t:b::t:b\\6:2::t:1.5\\\frac{6}{2} = \frac{t}{1.5}\\3 = \frac{t}{1.5}\\t = 1.5 * 3\\t =4.5[/tex]
Hence,
4.5 cups of tomatoes should be combined with 1.5 cups of bell peppers.
HELP PLEASE!! Two lines are drawn in the same plane.
Under what condition are the lines
perpendicular?
A two lines that never intersect
B. two lines that intersect and form right angles
C. two lines that intersect and form acute angles
D. two lines that intersect at more than one point
Answer:it is c or b
Step-by-step explanation:
The condition for the lines to be perpendicular will be two lines that intersect and form right angles. Then the correct option is B.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Two lines are drawn in the same plane.
If the two lines intersect then the angle between the line is 90 degrees.
The condition for the lines to be perpendicular will be two lines that intersect and form right angles.
Then the correct option is B.
The graph is given below.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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5.
3x3 + 2y2 - xy for x = 2 and y = 3
Answer:
21
Step-by-step explanation:
I need this ASAP and please show work
Answer:
B= 168
G=56
Step-by-step explanation:
3x+x= 224
4x=224
x=56
3x56=168
Suppose that Algeria has a workforce of 9,416,534, each of whom earns an average annual salary of (equivalent US dollars) $6,844. If the Algerian government wishes to raise $9 billion in tax revenue, approximately where should it set the income tax rate?
a.
9%
b.
14%
c.
18%
d.
26%
Answer:
its B on e2020
Step-by-step explanation:
14%
If the Algerian government wishes to raise $9 billion in tax revenue, income tax rate should be 14%.
What should the income tax rate be?
Income tax is a form of tax levied on the income of labor by the government. Income tax reduces the income earned by labor.
In order to determine the income tax rate, take the following steps:
Determine the total income of the workforce: 9,416,534 x $6,844 = 64.45 billion
Now, divide the desired tax revenue by the total income: (9 billion / 64.45 billion) x 100 = 14%
To learn more about taxes, please check: https://brainly.com/question/25311567
Find the value of X, then find AB and DC.
(opposite sides are congruent)
AB= 3x+8
DC= x+12
Answer:
X=2, AB=14, DC=14
Step-by-step explanation:
3x+8=x+12
Subtract x from both sides
2x+8=12
Subtract 8 from both sides
2x=4
Divide by 2 on the sides
Answer: x=2
Then replace the x's with (2) and multiply
3(2)+8 and (2)+12
Answer:
Both AB and DC are equal to 14.
Step-by-step explanation:
Help please! This has to do with the Pythagorean theorem.
2х + y = 4
у = 3х – 1
its 2 because 2plus is 2
Now I need thissss pls
What is the missing number?"
IN
OUT
1
2
2
3
3
4
4
5
5
6
7
f(x) = -6x - 7. Find f(-4)
Answer:
24-7 is the answer for u
Fill in the blank to find the y-intercept of-x+2y=10
Tricia has $37.25 in her account. Which shows the amount she will have left after she writes a check for $23.99?
A. $12.36
B. $12.74
C. $13.26
D. $13.74
The amount she will have left after writing a check for $23.99 is $13.26. The correct answer would be an option (C).
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
Tricia has $37.25 in her account, if she writes a check for $23.99, to find the amount left after that we need to subtract the check amount from her initial amount.
⇒ initial amount - check amount
⇒ $37.25 - $23.99
Apply the subtraction operations, and we get
⇒ $13.26
Therefore, the amount she will have left after writing a check for $23.99 is $13.26.
Learn more about Subtraction operations here:
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Brainliest if answer
Answer:
a. 3:4
b. 1:1.3
Student tickets cost $6.25 each at a local movie theater. Which proportion could be used to find the number of student tickets, t, that could be purchased with a $25 gift card?
Answer:
4
Step-by-step explanation:
bc I got jt right
what is √ − 3 ⋅ √ − 27 =
We are given the expression:
√-3 * √-27
__________________________________________________________
Explaining the concept:
We know that:
√ab = √a * √b
Using this concept, we will simplify the given expression and solve it
__________________________________________________________
Simplifying the expression:
√-3 * √-27
√(-1*3) * √[(-1)*(3)(3)(3)]
√-1 * √3 * √-1 * √3 * √3 * √3
(√-1 * √-1) * (√3 * √3 * √3 * √3)
(√-1)² * (√3)² * (√3)²
-1 * 3 * 3
-9
Hence, after simplifying the given expression, we get -9
How many solutions does the equation y=-7x+3 and y+7x=10 have
Answer:
Step-by-step explanation:
y=-7x+3
y+7x=3
y+7x=10
no solution.
What is the value of: | 18 |
a) 18
b) -18
c) -(-18)
Answer:
hey its a. the absolute value of any number is always positive.
Step-by-step explanation:
I started off with 430 Euros in an account, and I get an interest rate of 0.6% each year. How many Euros will be in my account after 15 years?
Find the slope of a line that passes through points (-2,1) and
(3,-5)
Answer:
-1.2
Step-by-step explanation:
Answer:
-6/5=M
Step-by-step explanation:
Chaston began making regular deposits of a certain amount of money each month, m, starting November 1st. The function F(m) = 25 m + 200 models the amount of money in his account after he started saving money. Assuming Chaston made no purchases from the account after November 1st, which of the following is NOT true?
A) Chaston made monthly deposits of 25 dollars per month
B) 2 months after he started saving Chaston would have $250 in his account
C) After 25 months of saving Chaston had $200 in his account
D) Chaston initially had $200 in his account before he began making regular monthly deposits
Answer:
c because 200 is the initial amount. He would have more than 200.
Need help Pronto! Will give braintliest.
Answer:
b
Step-by-step explanation:
please help me with this will give brainliest to best answer
Answer:
this may sound crazy but its A,B,C,D
Step-by-step explanation:
they not in the boundaries 0f 5 to 0 or -2 to 0
(x+0)(x-3)(x+0)(x+5)
Answer:
x^2 + 2x - 15
Step-by-step explanation:
(x-3)(x+5) = x^2 + 2x - 15
hope this helps, pls mark brainliest :D
Name the corresponding an
Answer:
what do you want to say?
Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Harrison Haulers Plant. Abel knows that absenteeism varies significantly between departments. For example, workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers. He orders a random sample of 10 workers from each of the six departments. Abel's sample is a
Answer:
disproportionate stratified sample
Step-by-step explanation:
Based on the given information we can say that Abel's sample is a disproportionate stratified sample. This is the case mainly because the department worker population ranges from 40 to 120 workers. This changing population makes the 10 workers that were chosen for the sample not proportionate to the entire population. Therefore, under different population sizes workers have different chances of getting selected for the study which ultimately creates different results.
Approximately 15% of Americans have a blood type of B. The local blood bank has 80 donors stop by on a given day (which can be considered a random sample from the population). What is the probability that between 15% and 20% of the donors on a given day have a blood type of B?
Answer: the probability that between 15% and 20% of the donors on a given day have a blood type of B is 0.3944
Step-by-step explanation:
Given that;
Binomial Distribution
n = 80
p = 0.15
q = 1 - p = 0.85
Mean = μ = np = 80 X 0.15 = 12
SD = σ = √(npq) = √(80 x 0.15 x 0.85) = -3.1937
Now; Assumptions in normal distribution to binomial distribution
- The sample size = n = 80 > 30 . Large sample
- np = 80 × 0.15 = 12 > 10
- nq = 80 × 0.85 = 68 > 10
so
80 × 0.15 = 12
80 × 0.20 = 16
To find P(12 < X < 16):
Z = (16 - 12) / 3.1937
= 4 / 3.1937
= 1.2525
Table of Area Under Standard Normal Curve gives area = 0.3944
Therefore the probability that between 15% and 20% of the donors on a given day have a blood type of B is 0.3944
Last month for work Mr. Wheelboogie traveled 5150 miles. This month that total increased to 7895 miles. What is the percent increase in Mr. Wheelboogie's mileage? Round to the nearest whole %
Answer:
53%
Step-by-step explanation:
use formula: (new value - original value) / original value and you will get .533 which rounds to 53%
PLEASE PLEASE PLEASE HELP!!!!!!!!!
Answer:
there will be 1 person = the winner at round 10, and at round 9 there will be 5 it goes down by fifteen every time
Step-by-step explanation:
Can I Get brainiest
A man flies a small airplane from Fargo to Bismarck, North Dakota- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1.2 hours. What is the planes speed in still air, and how fast is the wind blowing?
1) His plane speed equals ______ mph
2) The wind speed equals ______ mph
Answer:
1.) 120 mph
2.) 30 mph
Step-by-step explanation:
Given that a man flies a small airplane from Fargo to Bismarck, North Dakota- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1.2 hours. What is the planes speed in still air, and how fast is the wind blowing?
Let the wind speed = w
and the plane speed = p
From the first sentence,
P - w = 180/ 2
P - w = 90 ....... ( 1 )
From the second statement,
P + w = 180/1.2
P+ w = 150 ...... ( 2 )
Solve equation 1 and 2 simultaneously
P + w = 150
P - w = 90
Add the two equations
2P = 240
P = 120 mph
Substitute p in equation 1
W = 150 - 120
W = 30
Therefore, the wind speed is 30 mph and the plane speed is 120 mph
