Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region y=4x^2, y=x^2 + 3
Answers
Answer:
Step-by-step explanation:
integrate with respect to x
Area is symmetric so will be twice the integral from zero to 1
( I cannot seem to figure out how to make the lower limit negative in this editor)
[tex]A = 2\int\limits^1_0 {(x^2 + 3) - 4x^2} \, dx[/tex])
[tex]A = 2\int\limits^1_0 {-3x^2 + 3} \, dx[/tex]
[tex]A = 6\int\limits^1_0 {-x^2 + 1} \, dx[/tex]
A = 6(-⅓x³ + x)[tex]\left \| {{x=1} \atop {x=0}} \right.[/tex]
A = 6((-⅓(1)³ + (1)) - (-⅓(0)³ + (0)))
A = 6(⅔)
A = 4 units²
Related Questions
Twice a number is 46 less than 4 times the number. Find the number.
Answers
Answer:
23
Step-by-step explanation:
let the number be n then twice the number is 2n and 4 times the number is 4n
Then
2n = 4n - 46 ( subtract 4n from both sides )
- 2n = - 46 ( divide both sides by - 2 )
n = 23
The number is 23
Answer:
34.5
Step-by-step explanation:
23 x 2 = 46 less than 4 times = 11.5
46 - 11.5 = 34.5
It was in -5 degrees Celsius Copenhagen and -10 degrees Celsius in Oslo. Which city was
colder?
Answers
Answer:
Oslo
Step-by-step explanation:
The farther the number from zero at the right hand side, the colder.
So its Oslo
I hope this helps!
An auto insurance company classifies each motorist as "high risk" if the motorist has had at least one moving violation during the past calendar year and "low risk" if the motorist has had no violations during the past calendar year. According to the company's data, a high-risk motorist has a 50% chance of remaining in the high-risk category the next year and a 50% chance of moving to the low-risk category. A low-risk motorist has a 90% chance of moving to the high-risk category the next year and a 10% chance of remaining in the low-risk category. In the long term, what percentage of motorists fall in each category? (Round your answers to two decimal places.)
high-risk category %
low-risk category %
Answers
The percentage of motorists falling in each category, in the long term, are as follows:
High-risk category = 70%
Low-risk category = 30%
Data and Calculations:
Risk Profile Categories of Motorists
High Risk Low Risk
Probability of remaining
in the same category 50% 10%
Probability of moving to another
category 50% 90%
Probability a motorist falling in the high-risk category = (50% x 50%) + (50% x 90%)
= 25% + 45%
= 70%
Probability a motorist falling in the low-risk category = (50% x 50%) + (50% x 10%)
= 25% + 5%
= 30%
Thus, the probability of a motorist falling in the high-risk category is 70%, while the probability of a motorist falling in the low-risk category is 30%.
Learn more about probability here: https://brainly.com/question/24756209
A person of 600 newtons
gets on an elevator which
lifts him 6 meters in
10 seconds. How much
power was used?
Answers
Answer:
360J/s
Step-by-step explanation:
power=work done/ time
power=600×6/10
=3600/10
=360
Tyler is saving to buy a new videogame system. For every $15 he earns mowing lawns, he saves $9. On Saturday, Tyler earned $105 mowing lawns. How much money did he save?
Answers
Answer:
$63
Step-by-step explanation:
First, we find the percentage that he saves:
9 is 3/5 of 15 which is 60%, 9 is 60% of 15 which means he save 60% of the money that he earns so,
60% of 105 = 63
This means he saved $65 from the money he earned.
Hope this helps!
PLS HELP PLEASSSSS IM SERIOUSLY CRYING RN
Answers
[tex]x = 23[/tex]
Step-by-step explanation:
First, we need to write the equations in their standard form, i.e., all the variables and their coefficients are to be placed on the left hand side and the plain numbers on the right hand side. The first equation is already in its standard form:
[tex]2x + 5y = 35\;\;\;\;\;(1)[/tex]
but we need to rewrite the 2nd one. So the standard form of the 2nd equation can be written as
[tex]x + 15y = -10\;\;\;\;\;(2)[/tex]
Now that the equations are in their standard forms, the next step that we need to do is to eliminate one of the variables, namely the y. To do that, we need to multiply either one of the equations so that when we add them together, the y-variable gets eliminated. Note if we multiply Eqn(1) by -3, we'll get -15y on one equation and a +15y on the other equation so that when they are added together, they cancel out. So if we do that, we get
[tex]-6x - 15y = -105\;\;\;\;\;(3)[/tex]
Adding Eqn(3) to Eqn(2), we get
[tex]-5x = -115[/tex]
or
[tex]x = \dfrac{-115}{-5} = 23[/tex]
pls help quick
plssss
plssssss
Answers
The third year would be 20.
At Pathmark, 4 pounds of pork chops cost $12.60 and 5 pounds of ground beef cost $10.25. Find the total cost of 11 pounds of pork chops and 12 pounds of ground beef.
Answers
Answer:
Let pork chops and ground beef be x and y respectively.
4x = $12.60
x = $3.15
11x = $34.65
5y = $10.25
y = $2.05
12y = $24.60
11x + 12y = $34.65 + $24.60
= $59.25
Multiply and fill in the blanks
a) 5pq(p2+ q2+pq)
b) -7pr (pq – qr - rq)
c) (4x-3y) (5x-4a)
with explanation pls !
Answers
The solution to the simplification of the algebraic expressions are;
A) 5p³q + 5pq³ + 5p²q
B) 14pqr² - 7p²qr
C) 20x² - 15xy - 16ax + 12ay
A) We have the expression;
5pq(p² + q² + pq)
Multiplying out using the concept of distributive property, we have;
(5pq × p²) + (5pq × q²) + (5pq × pq)
>> 5p³q + 5pq³ + 5p²q
B) We have the expression;
-7pr(pq – qr - rq)
Multiplying out using the concept of distributive property, we have;
-7p²qr + 7pqr² + 7pqr²
>> 14pqr² - 7p²qr
C) (4x - 3y)(5x - 4a)
By quadratic expansion, we have;
(4x * 5x) - (3y * 5x) - (4x * 4a) + (4a * 3y)
>> 20x² - 15xy - 16ax + 12ay
Read more about simplification of algebra at; https://brainly.com/question/4344214
Help me out please???
Answers
Answer:
5
Step-by-step explanation:
The interquartile range is Q3-Q1.
in this problem, Q3=7 and Q1=2
PLS HELP FAST!!
During a snowstorm, Lucy tracked the amount of snow on the ground. When the storm began, there were 4 inches of snow on the ground. For the first 2 hours of the storm, snow fell at a constant rate of 3 inches per hour. The storm then stopped for 5 hours and then started again at a constant rate of 1 inch per hour for the next 7 hours. Make a graph showing the inches of snow on the ground over time using the data that Lucy collected.
Answers
Hope this helped
You buy candy bars at 85 cents each plus one newspaper for 60 cents. You can spend no more than $4. How many candy bars can you buy? answer
Answers
Answer:
4
Step-by-step explanation:
Well first you want to take 0.60 from the total amount which is $4 leaving you with $3.40
then you want to divide the remaining amount of money by the cost of a candy bar ($0.85)
So you do 3.40/0.85 which is equal to 4
Given the following acceleration function of an object moving along a line, find the position function with the given initial velocity and position.
a(t) = -24; v(0) = 17, s(0) = 0
s(t) =
Answers
Answer:
Position function is [tex]s(t)=-12t^2[/tex]
Step-by-step explanation:
Given [tex]a(t)=-24[/tex], since velocity is the antiderivative of acceleration, then [tex]v(t)=-24t[/tex].
Also, since position is the antiderivative of velocity, then [tex]s(t)=-12t^2[/tex].
A company tests two new products to make sure they last for more than a year. Product 1 had 950 out of 1,000 test items last for more than a year. Product 2 had 150 out of 200 last for more than a year. If you had to choose one of these two products to use for more than a year, which one is more likely to last? Explain your reasoning
30 POINTS GIVE GOOD ANSWER
Answers
Answer:
product one; it has a higher success rate
Step-by-step explanation:
to find out which has a higher rate of success we can find out their percentage of success
we can divide their success amounts by test amounts
950 / 1000 = 95/100 = 95%
150/200 = 75/100 = 75%
product 1 has a higher success rate
The product is more likely to last is mathematically given as
Product 1
What product is more likely to last?
Question Parameter(s):
Product 1 had 950 out of 1,000 test
Product 2 had 150 out of 200 test
Generally, the equation for the percentage success is mathematically given as
Product 1 950 / 1000 = 95/100 x 100 = 95%
Product 2 150/200 = 75/100 x 100 = 75%
In conclusion, the product is more likely to last is
Product 1
Read more about Trade
https://brainly.com/question/15115779
21 cans of tomato paste of the same size have weight of 7300 grams. What is the weight of 5 cans.
Answers
Answer:
answer is 347.6
Step-by-step explanation:
21/7300= 347.6
How does the number 7 in 777.77 in the tenths place compare to 7 in the hundredths place
Answers
Answer:
0.7 is 7/10 Example out of ten cookies 7 are chocolate chip
0.07 is 7/100 Example out of 100 cookies 7 are chocolate chip
Hope This Helps!!!
Ron wants to make money painting portraits of people at the local mall. The mall
charges Ron $22.00 a day for Ron to set up his materials to sell his portraits. He
charges $15.50 a portrait, but it costs him $3.25 in materials to make that portrait.
If x represents the number of portraits that Ron sells at the mall, which of the
following expressions would represent Ron's profit (how much money Ron will walk
away with at the end of the day)? (There is more than one answer)
12. 25x – 22.00
15.50x – 22.00
0-22.00 + 15.50x – 3.25x
15.50x
3. 25x – 22.00
22.00x – 3.25x
15.50
Answers
Answer:
A and CStep-by-step explanation:
With the amount x of portraits the daily balance is:
- $22.00+ $15.50x- $3.25xThe total is:
15.50x - 3.25x - 22.00 ⇒ 12.25x - 22.00Correct choices are A and C
With the amount x of portraits the daily balance is:
- $22.00
+ $15.50x
- $3.25x
The total is:15.50x - 3.25x - 22.00 ⇒ 12.25x - 22.00
Correct choices are A and CPlease look for the question in the picture.
Answers
Answer:
I beleive the missing value is -3
Step-by-step explanation:
if you plug -3 into the pink box it will give you the result of -5
(anyone is free to correct me)
) f(x) = 4x + 5, g(x) = 2/x;
Find (g • f)(3).
Answers
[tex]\text{Given that,}\\\\f(x) = 4x+5,~~~g(x) = \dfrac 2x\\\\\\f(3) = 4(3) +5 = 12 +5 = 17\\\\\\(g\circ f)(3)=g(f(3))=g(17)=\dfrac 2{17}[/tex]
Answer:
The answer is 2/17
Step-by-step explanation: Can I get brainliest again my answer was deletedee
(4 − 3)(−3 + 6) − (2 − )
simplify
show all work
Answers
Answer:
(4 − 3)(−3 + 6) − (2 )
1(3)-2
3-2
1
Hope This Helps!!!
The function g(x) undergoes a vertical stretch of 2, a horizontal shift to the right 3 units, and a vertical shift up 1 to become f(x). Which equation describes f(x).
F(x) = 2|x + 3|- 1
F(x) = 2|x - 3| + 1
F(x) = 2|x - 3| + 1
F(x) = 2|x- 3| - 1
Answers
Answer:
NONE OF THE OPTIONS GIVEN
Step-by-step explanation:
F(x) = 2|x - 3| + 1 is close, but vertical bars in stead of parentheses completely changes the curve shape
I believe it should be f(x) = 2(x - 3) + 1
if g(x) = x
here are some plots to compare the possibilities. I've shifted the vertical of each to separate the blue and green lines slightly. If they were both true "1" values the lines would be colinear for x>3.
The red line has a slope of 1, stretching by a factor of 3 means the slope is now 3. The absolute value signs from the answer options makes f(x) have a sharp V shape whereas the parentheses creates a single line for all values of x as does g(x) = x.
Ten minus three tenths of n
Answers
Answer:
[tex]10 - \frac{3}{10} n[/tex]
Step-by-step explanation:
hope that is right and hope it helps
Based on the above chart, which service profession would you choose to enter into if you wanted to ensure that you would have the larg
increase in wages and job availability?
Chart 4. Numeric change in wage and salary employment, service-
providing industry divisions, 1996-2006
A Information
B Financial activities
C Education and health services
D Professional and Business services
Answers
Answer:
Education and health services
Step-by-step explanation:
It has had the most increase over the years, so it will most likely keep increasing and let you get more wages and job opportunities.
What is the value of (-5)2?
Answers
Answer:
-10
Step-by-step explanation:
when a number Inside of parentheses is close to another number (like being near a fireplace trying to say warm) it means to multiply :3 !
Example: (3)2=6 6(6)=36
in our case it is (-5)2 So was ist -5 x 2? -10
hope this helped!
for some extra practice to check your knowledge, what is (-3+-2)2 ?
I need help solving this problem
Solve for X
Answers
Answer:
x = -7
Step-by-step explanation:
The 2 horizontal lines are parallel as given ion the problem.
The x + 97 angle is congruent to the right angle.
x + 97 = 90
x = -7
a prisms base has a perimeter of 12cm and a height of 2 cm. the area of the base was 5cm. what is the surface area of the prism.
Answers
==============================================================
Explanation:
For any prism, there are two congruent bases opposite one another. In other words, the bases are identical polygons with the same area. Each base is 5 square cm. So far, that accounts for 5+5 = 10 square cm of surface area. Let A = 10 as we'll use it later.
The perimeter is 12 cm and the height is 2 cm. It turns out that the lateral surface area is found by multiplying the two items. This is because the perimeter is made up of the lengths of the sides of the base, which when multiplied by the height, will give the area of each rectangular side panel.
So the lateral surface area is 12*2 = 24 sq cm. Let B = 24.
Overall, the total surface area is A+B = 10+24 = 34 square cm
pls help it is math for 7th grade.
Answers
Answer:
36.8 *36 8/10 of 36 4/5
Step-by-step explanation:
2/5x(-1/2)= -2/10
37+(-2/10)=36.8
The formula for finding the perimeter of a rectangle is P = 2L + 2W. If a rectangle has a perimeter of 68 inches and the length is 14 inches longer than its width, find the width.
Enter a number answer only.
Answers
Answer:
Width = 10 inches
Step-by-step explanation:
Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.
We can establish the following values to help us solve for the width of a rectangle:
Perimeter (P) = 68 inches
Length (L) = 14 + W inches
Width (W) = unknown
Solve for the Width (W)P = 2(L + W) ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.
Divide both sides by 2:
[tex]\displaystyle\mathsf{\frac{P}{2}\:=\:\frac{2(L\:+\:W)}{2}}[/tex]
[tex]\displaystyle\mathsf{\frac{P}{2}\:=L\:+\:W}[/tex]
Substitute the value of the Perimeter and the length (L) into the formula:
[tex]\displaystyle\mathsf{\frac{68}{2}\:=14\:+W\:+\:W}[/tex]
Combine like terms on the right-hand side, and simplify the left-hand side of the equation:
[tex]\displaystyle\mathsf{34\:=14\:+2W}[/tex]
Subtract 14 from both sides:
34 - 14 = 14 - 14 + 2W
20 = 2W
Divide both sides by 2 to solve for the width (W):
[tex]\displaystyle\mathsf{\frac{20}{2}\:=\:\frac{2W}{2}}[/tex]
W = 10 inches
Therefore, the width of the rectangle is 10 inches.
Double-check:Verify whether the derived value for the width is correct:
P = 2L + 2W
68 = 2(14 + 10) + 2(10)
68 = 2(34) + 20
68 = 48 + 20
68 = 68 (True statement).
Thus, the length of the rectangle is 34 inches, and the width is 10 inches.
Find the perimeter of a rectangle whose width is 30cm and diagonal 50cm.
Answers
Answer:
P=140cm
Step-by-step explanation:
P=2(l+w)
d=w2+l2
Solving forP
P=2w+2d2﹣w2=2·30+2·502﹣302=140cm
Hope This Kind of Helps
Answer: 140cm
P=2(l+w)
P=2w+2d2﹣w2=2·30+2·502﹣302=140cm
Can someone help with this math problem?
Answers
Answer:
Hope it will help you a lot.