Let R be the region in the first quadrant bounded by the graphs of y =x^2 and y=2x, as shown in the figure above. The region R is the base of a solid. For the solid, each cross section
perpendicular to the y-axis is a square. What is the volume of the solid?
A) 0.404
B)0.533
С)1.333
D)2.667
Answers
Answer:
The area between the two functions is approximately 1.333 units.
Step-by-step explanation:
If I understand your question correctly, you're looking for the area surrounded by the the line y = 2x and the parabola y = x², (as shown in the attached image).
To do this, we just need to take the integral of y = x², and subtract that from the area under y = 2x, within that range.
First we need to find where they intersect:
2x = x²
2 = x
So they intersect at (2, 4) and (0, 0)
Now we simply need to take the integrals of each, subtracting the parabola from the line (as the parabola will have lower values in that range):
[tex]a = \int\limits^2_0 {2x} \, dx - \int\limits^2_0 {x^2} \, dx\\\\a = x^2\left \{ {{x=2} \atop {x=0}} \right - \frac{x^3}{3}\left \{ {{x=2} \atop {x=0}} \right\\\\a = (2^2 - 0^2) - (\frac{2^3}{3} - \frac{0^3}{3})\\\\a = 2^2 - \frac{2^3}{3}\\a = 4 - 8/3\\a \approx 1.333[/tex]
So the correct answer is C, the area between the two functions is 4/3 units.
The area between the two functions is approximately 1.333 units.
What will be the area?Area is defined as the region bounded by the sides on a plane. The areas of different shapes can be calculated by different formulas.
If I understand your question correctly, you're looking for the area surrounded by the line y = 2x and the parabola y = x², (as shown in the attached image).
To do this, we just need to take the integral of y = x², and subtract that from the area under y = 2x, within that range.
First we need to find where they intersect:
2x = x²
2 = x
So they intersect at (2, 4) and (0, 0)
Now we simply need to take the integrals of each, subtracting the parabola from the line (as the parabola will have lower values in that range):
[tex]a=\int\limits^2_0 {2x} \, dx -\int\limits^2_0 {x^2} \, dx[/tex]
[tex]a=(2^2-0^2)-(\dfrac{2^3}{3}-\dfrac{0^3}{3})[/tex]
[tex]a=4-\dfrac{8}{3}[/tex]
[tex]a=1.333[/tex]
Hence the area between the two functions is approximately 1.333 units.
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Related Questions
If the cost of electricity increases by 30% by what percentage one should reduce his spend in order that spends on electricity stays the same?
Answers
Answer:
That depend on how much you spend on electricity, and how much other spending you do.
For example: If your electric bill is 100 dollars, and it increases 30 percent to 130, that’s 30 extra dollars. If your electric bill is only 50 dollars, it will increase to 65, that’s an extra 15.
What percentage that increase is of your current spending will vary according to how much you spend. If you only spend 30 dollars, then you’ll need to cut all of it, or half of it to offset the increases I mentioned above. That’s a 100 percent or 50 percent reduction.
If you spend 1000 dollars, you’ll only need to cut spending by 3 percent to get that 30 dollars, or 1.5 percent to get the 15 dollars.
It all depends on your specific values, you can’t say “For every xx percent your electric bill increases, you need to cut spending by yy percent.”
for the consumption of X unit let u spends Y
for X - Y cost
for increased 30% means 13X/10 - 13Y/10 cost
extra money is 13Y/10 - Y = 3Y/10
note: hope this helps :)
thus (3Y/10)/ (13Y/10) *100 % = 300 / 13 = 23.07%.
5.9 divided by 35.4 equals?
Answers
5.9 divided by 35.4 is 0.16
Answer:
0.167 or 0.1666666666666
Step-by-step explanation:
5.9 ÷ 35.4 = 0.16666666666 (the 6 is unending)
if you round that:
0.167
The formula P=a+b+c gives perimeter P of triangle side lengths a,b,and c how much greater is perimeter when triangle measures 33yds 56yds and 65yds to a triangle that measures 26yds 49yds and 38yds
Answers
Answer:
41 yards greater is the perimeter of 1st triangular field than the perimeter of 2nd triangular field.
First we have to calculate the perimeter of 1st triangle.
Given:
a = 33 yards
b = 56 yards
c = 65 yards
Now we have to calculate the perimeter of 2nd triangle.
Given:
a = 26 yards
b = 49 yards
c = 38 yards
Now we have to calculate which triangle has greater perimeter and how much greater.
Therefore, 41 yards greater is the perimeter of 1st triangular field than the perimeter of 2nd triangular field.
Step-by-step explanation:
(154-113)
41 yards bigger
Answer:
41 yds
Step-by-step explanation:
33+56+65=154
26+49+38=113
154-113=41 yds
The Stock Market Nadia is a stockbroker. She earns 11% commission each week. Last week, she
sold $5,300 worth of stocks. How much did she make last week in commission? If she averages that
same amount each week, how much did she make in commission in 2011?
Last week, she made $
in commission.
Answers
Answer:
she made $583 commission last week
she made $30313
Step-by-step explanation:
5300 * .11=583
583 * 52 weeks =30316
3x3-5/5x6+19 i don’t know what I’m don’t wrong
Answers
Hi there!
For these two equations, we would be using PEMDAS...
[tex]3[/tex]·[tex]3=9-5=4[/tex]
[tex]5[/tex]·[tex]6=30+19=49[/tex]
Hope this helps!
What is-26000-(-9500)
Answers
Answer:
[tex]-16500[/tex]
Step-by-step explanation:
In order to find the answer to this question you need to use KCC (Keep, Change, Change) and solve.
[tex]-26000-(-9500)[/tex]
Use KCC
[tex]-26000 + 9500[/tex]
[tex]-26000+9500=-16500[/tex]
[tex]=-16500[/tex]
Hope this helps.
Answer:
-35500 hope this helps
Step-by-step explanation:
Renae drives a delivery can on the weekends
She had a total of 12 3/4 gallons of fuel Renae knows that ever gallon fbfuel she can travel 21 miles of she uses all her Fuel how many miles will she travel
Answers
Answer:
267 3/4 miles
just do 12 3/4*21
In 45 years will be 4 times older how old is she now
Answers
Answer and Step-by-step explanation:
The key for this has a current age and a future age. Sometimes these problems have more than one person or has a past age.
current age future age
x x+45
The future age is 4 times current age
x+45 = 4x
45 = 3x
15 = x
She is currently 15. 45 years from now she will be 60.
60 is 4 times her current age. So right now, she is 15.
#teamtrees #WAP (Water And Plant)
Answer:
11yrs (6months)
Step-by-step explanation:
11.5×4=45
Since .5 in years is 6 months
Question 6 of 10
What is the equivalent radical expression for the exponential expression
below?
151/2
O A √15²
B. 154
C. 15
D. 152
Answers
Answer:
√15
Step-by-step explanation:
Assuming that it is:
[tex]15^\frac{1}{2}[/tex]
Exponent rule for fractional exponents are:
[tex]x^\frac{a}{b}=\sqrt[b]{x^a}[/tex]
Apply rule:
[tex]15^\frac{1}{2}=\sqrt{15}[/tex]
Hope this helps!
Mia has 4 horses and 11 apples. She gives each horse the same number of
apples, and she uses as many apples as she can. How many apples does Mia
give each horse? How many apples are left?
» Complete the equation.
11 : 4 =
R
Answers
Answer:
She gives 2 apples to each horse, and there will be 3 apples left.
Step-by-step explanation:
We know that Mia has 4 horses and 11 apples
She gives each horse the same number of apples, such that she uses the maximum number of apples that she can.
If she has 4 horses and she gives the same amount to each horse (let's say that this amount is N apples to each horse)
Then she uses a total of 4*N apples.
Then if N = 1, she needs 4*1 = 4 apples.
if N = 2, she needs 4*2 = 8 apples.
if N = 3, she needs 4*3 = 12 apples.
But she has only 11 apples, so she can not give 3 apples to each horse.
Then the maximum number of apples that she can give to each horse is N = 2, 2 apples to each horse.
Now, we know that she has 11 apples in total, and she gives 2 to each of the 4 horses, then she gives:
4*2 = 8 apples.
The number of apples that are left are:
11 - 8 = 3
There are 3 apples left.
The difference of two times a number and the number is eight
Answers
Answer:
2n-5=8
Step-by-step explanation:
Find the volume of a cylinder with a diameter of 10 inches and a height that is three times the radius. Use 3.14 for pi and round your answer to the nearest hundredth. (Hint: You may only enter numerals, decimal points, and negative signs in the answer blank)
Answers
Answer:
Cylinder volume:
[tex]\pi {r}^{2} h = volume[/tex]
Hence: 3.14 × (5)^2 × 15V= 1178.1what is 100 divided by 52
Answers
1.92307692308
Hope this helps! :D
20% tip on a
$30 haircut.
Answers
the tip is 15$ im pretty sure
Question /
State the quadrant in which the terminal side of the given angle lies.
0 =
77
4.
А
II
B.
I
IV
Ос
Oo
III
Answers
Answer:
9y - 19 = 62
Step-by-step explanation:
thats not that answer i dont know what the answer is
Enter the solution to the problem x/2 = 4.5
Answers
Answer: 9
Step-by-step explanation:
do the opposite 2·4.5=9
x=9
check your work
9/2 or 9÷2=4.5
Answer:
x4
Step-by-step explanation:
what is equal to 45a-10b
Answers
Answer:
45b - 10a
Step-by-step explanation:
Answer:
5(9a-2b)
Step-by-step explanation:
This is a polynomial and you have to factor it.
GCF of 45a and 10b is 5
5(9a-2b)
Branliest would be Appreciated
The equation y =
12 represents a proportional relationship. What is the
constant of proportionality?
A. 12
B. X
C. 1
D. 0
Answers
Answer:
The constant of proportionality k = 12
Hence, option A is true.
Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get
y ∝ x
y = kx
Where 'k' is called the constant of proportionality.
In our case,
The given equation is
y = 12x
comparing with the equation y = kx, we can say
k = 12 which is the constant of proportionality.
Therefore, we conclude that:
The constant of proportionality k = 12
Hence, option A is true.
I need help 79 points
Answers
Answer:
can u explain this a little bit more i think ik the answer but im not sure #3 is well i think it is 120#4 is 164.85 #5 is 40 yea hope this helps :)
Step-by-step explanation:
Answer:
#3 = 120
#4 = 164.85
#5 = 40
#6= 240
Step-by-step explanation:
hope i helped!
5x +9 = 65 :solve
Please help me
Answers
Answer:
11 1/5
Step-by-step explanation:
subtract 9 from both sides
5x = 56
divide both sides by 5
x = 56/5
11 1/5
Answer:
11.2 because 65 - 9 = 56 and 56 divided by 5 is 11.2
that batch calls for 5 cups of flour and 4 teaspoons of vanilla if i use 6 teaspoons of vanilla how many cups will i need
Answers
? cups & 6 teaspoons
2.5 cups is half of 5
2 is half of 4
you increased the recipe by 1/2
so for 6 teaspoons you will need 7.5 or 7 1/2 cups of flour b/c 5 + 2.5 = 7.5
ANSWER: 7 1/2
What is the slope of the line that passes through the points (0,-8) and (12, 6)?
round to the one decimal place
Answers
Slope of line passing through (0, -8) and (12, 6) = (6-(-8))/(12-0) = 14/12 = 7/6
Pedro bought a movie ticket for $9.50 and popcom por $4.35. He has $8.75 left
over How much money did he have before he went to the movies?
Answers
Answer:
He had $22.60
Step-by-step explanation:
$9.50 + $4.35 = 13.85 + 8.75 = $22.60
You randomly choose a tile. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth.The probability of choosing an odd number and then a 20
Answers
Answer:
P odd number, then 20) = 1 /14
Step-by-step explanation:
P( odd number) = number of odd numbers/ total
number of odd numbers = 3
total = 7
P( odd number) = 3/7
We keep the tile so that there are only 6 tiles left
P (20) = number of 20/ total
= 1/6
We multiply the probabilities together
P odd number, then 20) = 3/7 * 1/6 = 3/42 = 1 /14
A school is purchasing graphing calculators for use in math classrooms. The graph shows a relationship between the number of graphing calculators purchased and the total cost.
The constant of proportionality is 120. True or false
If a graph is a straight line, it shows a proportional relationship. True or false
Any graph that passes through origin represents a proportional relationship. True or false.
A graph must be a straight line and go through the point (0,0) in order to represent a proportional relationship. True or false.
PLEASE HELP!!
Answers
Answer:
False; false; true
Step-by-step explanation:
Find the orthocenter of a triangle with vertices (−8, 11), (−3, 11), and (−3, −12).
The orthocenter of triangle is at ( , ).
Answers
Answer:
( -3, 11)
Step-by-step explanation:
find the equation of the line between points ( -8, 11) and (-3, 11)
y= mx +b , where m is slope snd b is y-intercept
m = (y2-y1)/ (x2-x1) = 11-11/ -8- -3 = 0/ -5 = 0 ( if slope is o is a horizontal line)
y = 0x + b and pick a point to find b
11 = 0*-8 + b so b= 11
y = 11 is the equation of the line between points ( -8, 11) and (-3, 11) and the equation of its perpendicular line is x=-3
the equation of the line between points (-3, 11) and ( -3, -12) is x= -3 and the perpendicular to it is y= 11
so we have a right triangle so the ortho center is at (-3, 11) where the vertex of the 90 degree angle is
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answers
Answer:
[tex]y=-10x+43[/tex]
Step-by-step explanation:
We need to put this line into slope-intercept form, which is [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the [tex]y[/tex]-intercept.
The slope is rise over run, how much the [tex]y[/tex] value changes for one [tex]x[/tex] value. This can be found with the equation: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points on the line. Plugging in the first two points:
[tex]m=\frac{3-13}{4-3}=-10/1=-10[/tex]
We know them that [tex]m=-10[/tex]. This gives us for now [tex]y=-10x+b[/tex].
Now, to solve for [tex]b[/tex], plug in any one of the points (I'll use (3,13)):
[tex]13=-10(3)+b[/tex]
[tex]13=-30+b[/tex]
[tex]b=43[/tex]
This gives us the equation [tex]y=-10x+43[/tex].
Draw a quadrilateral with one pair of parallel sides and two right angles. Explain why this figure is a trapezoid.
Answers
Answer:i cant draw on brainly
Step-by-step explanation:i cant draw
A line through the origin and (10,4) is showin in the standard (x,y) coordinate plane below. The acute angle between the line and the positive x-axis has measure θ.
Answers
Answer:
[tex]\cos\theta=\frac{10}{\sqrt{116}}[/tex]
Step-by-step explanation:
To solve this, we can imagine a line drawn directly down from the point (10,4) to the x-axis. This would make a right triangle with length 10 and height 4.
[tex]\cos\theta[/tex] is equal to the length of adjacent leg to the angle divided by the length of the hypotenuse of the triangle. From the picture, we can see the adjacent leg is 10.
We can use Pythagorean's Theorem to find the hypotenuse (let [tex]c[/tex] represent the length of the hypotenuse):
[tex]10^2+4^2=c^2[/tex]
[tex]100+16=c^2[/tex]
[tex]116=c^2[/tex]
[tex]c=\sqrt{116}[/tex]
Thus, we know the adjacent is 10, and the hypotenuse is [tex]\sqrt{116}[/tex]. This means [tex]\cos\theta=\frac{10}{\sqrt{116}}[/tex].
Hope this helps!
Which Heinz Ketchup offer is the better deal? (Assume the price stays proportional and the Ketchup is
Identical.) Show ALL work and labels, and make sure you include a "because." in your answer.
Deal A
38 oz for $2.98
Deal B
114 oz for $6.48