The following curves bound an area: y = 2x + 1, y = -3, and x = 3. Set up the integral to find the VOLUME if this area is revolved about the line x = 3. DO NOT EVALUATE.
Answers
First note the intersections of each pair of lines.
x = 3 ⇒ y = 2•3 + 1 = 7 ⇒ (3, 7)
y = -3 ⇒ -3 = 2x + 1 ⇒ x = -2 ⇒ (-2, -3)
y = -3 and x = 3 ⇒ (3, -3)
Using the disk method, we consider disks with thickness ∆y and radius equal to the horizontal distance between the line y = 2x + 1 (or x = (y - 1)/2) and the axis of revolution, x = 3. Each disk will then contribute a volume of
∆V = π (radius)² (thickness) = π/4 (y - 1)² ∆y
As we let ∆y go to zero and let the number of disks go to infinity, the total volume of the resulting cone will be given by the integral
[tex]\displaystyle \frac\pi4 \int_{-3}^7 (y-1)^2 \, dy[/tex]
Related Questions
what is the exponent of 24?
Answers
Answer:
576
Step-by-step explanation:
24 squared which means 24 multiplied by itself(24)
I hope my answer is okay
Is the eye color of a student in class classified as a qualities or quantitive variable
Answers
Answer:
Qualities variable, because eye color is something you observe from a study on someone. Eye color cannot be observed very well from a quantitive variable, because quantitive variables record height, weight, and other statistics other than eye color.
Tia's tent is in the form of a triangular prism as shown below.
If Tia plans to waterproof the tent, excluding the base, what
is the area in which she will waterproof?
(round to the nearest hundredth)
Answers
Answer: 279.43
Step-by-step explanation:
The area of the tent that she will need to waterproof is 279.43 feet².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Given a tent in the form of a triangular prism as given.
We have to find the surface area of the tent excluding the base.
There are 2 triangular faces and 2 rectangular faces.
Area of the prism that needs to waterproof = area of 2 rectangles + area of 2 triangles
Area of rectangles = 2 × 14 × 8 = 2 × 112 feet² = 224 feet²
Height of the triangular face = √(8² - 4²) = √48
Area of 2 triangles = 2 × 1/2 × 8 × (√48) = 8√48 feet²
Area needed to be waterproofed = 224 feet² + 8√48 feet² = 279.43 feet²
Hence the area of the tent is 279.43 feet².
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53. (a) if the symbol [tex]\lbrack\rbrack[/tex] denotes the greatest integer function defined in example 10 , evaluate
(i) [tex]\lim _{x\rightarrow-2^+}\lbrack x\rbrack[/tex]
(ii) [tex]\lim _{x\rightarrow-2}\lbrack x\rbrack[/tex]
(iii) [tex]\lim _{x\rightarrow-2.4}\lbrack x\rbrack[/tex]
Answers
If x is between two consecutive integers such that n ≤ x < n + 1, then the greatest integer function [x] maps x to the largest integer smaller than x so that [x] = n.
(i) If x is approaching -2 from above, that means x > -2. As x gets closer to -2, we essentially have -2 < x < -1, so that [x] will approach
[tex]\displaystyle \lim_{x\to-2^+} [x] = \boxed{-2}[/tex]
(ii) However, if x is approaching -2 from below, then x < -2, so that [x] = -3. In other words
[tex]\displaystyle \lim_{x\to-2^-} [x] = -3 \neq -2[/tex]
Because the one-sided limits do not match, the two-sided limit
[tex]\displaystyle \lim_{x\to-2} [x] ~~\boxed{\text{does not exist}}[/tex]
(iii) -2.4 lies between -3 and -2, so
[tex]\displaystyle \lim_{x\to-2.4} [x] = \boxed{-3}[/tex]
Juanita has 2 rolls of film with 36 exposures and 3 rolls of film with 24 exposures. How many photos can she take with this film? She can take ____ pictures
Answers
Answer:
65 pictures because 24+36+3+2
A sociologist wishes to test . the sociologist takes a sample of size 100 and calculates a standardized test statistic of -2.34. to calculate a p-value for the test in excel, the sociologist should use:
Answers
Answer:
One-sample Z-test
Step-by-step explanation:
As the sample size is greater than 30, assuming the data is a simple random sample, and that the data has a normal distribution, the sociologist should conduct a one-sample z-test to calculate the p-value.
Find the arc length of the subtending arc for an angle of 35 degrees on a circle of radius 10.
Answers
Step-by-step explanation:
arc length = radius × central angle in radian
= 10 × (35 × π/180)^c
= 10 × ( 7π/36)
= 70π/36
= 70/36 × 22/7
= 55/9
= 6.111cm
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and
i hope my ans is helpful
Answer:
formula for length of an arc = 0 / 360 × 2ūr
Given , 0 = 35 , ū = 22/7 ,r =10
therefore; 35/360 × 2 x 22/7 ×10
= 6.111 or 55 /9
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A packed box that is being shipped will be weighed in order to calculate the correct postage needed. The total weight of a packed box will be the combined weight of the empty box and the product that is placed in the box. Jasmine is currently packing medium-sized boxes. Before packing her first box, Jasmine measured the weight of the empty medium-sized box to be 0.88 pounds. After packing the box, Jasmine measured the total weight of the box to be 7.24 pounds.
Complete the following equation so that it can be used to find the weight, w, of the product inside the first box that Jasmine packed, and then find the weight of the product.
0.88 pounds + w pounds = 7.24 pounds
The weight of the product inside the first box is
pounds ____?
Answers
Answer: 6.36lb
Step-by-step explanation:
Step-by-step explanation:
Total Weight of the package = weight of product + weight of box
Weight of empty box =0.88lb
Total weight of the box is =7.24lb
Let Weight of product inside box=w
Let wet of empty box =y
Total weight = F
Then,
F=y+w
Since F=7.24lb. y=0.88
Then, w=F-y
w=7.24-0.88
w=6.36lb
The weight of the product is 6.36lb
hope this helps :)
#3. estimate the perimeter and area of the figure to the nearest whole number
Answers
Answer:
Perimeter = 29 unitsArea = 37 square unitsStep-by-step explanation:
Perimeter
1 + 2(3) + 6 + 8 + √(5² + 6²)15 + 6 + √6121 + 8 (nearest whole number)29 unitsArea
2 x 2 + 3 x 6 + 1/2 x 5 x 64 + 18 + 1537 square unitsA helicopter is flying over a straight highway between
two exits, A and B. The angle of depression from the
helicopter to exits A and B are 28° and 45°,
respectively. If the exits are 4 miles apart, find the
height of the helicopter
Answers
Answer:
about 1.3885 miles ≈ 7331 ft
Step-by-step explanation:
The height of the helicopter can be found using the tangent relation, which we know relates the sides and angles of a right triangle by ...
Tan = Opposite/Adjacent
__
setupWith reference to the attached diagram, the above relation can be used to find the lengths of AC and BC, which we know total 4 miles.
tan(28°) = h/AC ⇒ AC = h/tan(28°) = h·tan(90° -28°) = h·tan(62°)
tan(45°) = h/BC ⇒ BC = h/tan(45°) = h·tan(90° -45°) = h·tan(45°)
The total distance between A and B is then ...
AB = AC +BC
4 = h·tan(62°) +h·tan(45°) = h(tan(62°) +tan(45°))
solutionDividing by the coefficient of h, we have the value of h:
h = 4/(tan(62°) +tan(45°)) = 4/(1.88073 +1) ≈ 1.38854 . . . . miles
In feet, that is ...
(1.38854 mi)(5280 ft/mi) = 7331 ft
The height of the helicopter is 1.38854 miles, or 7331 feet.
1 point
11
y
Find x and y.
DO
30°
x=11√2 y = 22
x = 22 y=11√/3
x = √√√3 y = 11
Answers
Answer:
x = 22, y = 11√3
Step-by-step explanation:
Here,
x is the Hypotenuse side
y is the adjacent side.
11 is the opposite side.
Formula : -
sin θ = Opposite side / Hypotenuse side
Here,
θ = 30
Note : -
The value of sin 30 = 1 / 2
1 / 2 = 11 / x
Cross multiply,
x * 1 = 2 * 11
x = 22
By Pythagoras theorem,
11² + y² = x²
11² + y² = 22²
y² = 22² - 11²
22² = 11² x 2²
11² = 11² x 1²
y² = 11² ( 2² - 1 )
y² = 11² x ( 4 - 1 )
y² = 11² x 3
Square root on both sides,
y = 11√3
Kent multiplies both sides of the equation below by an expression. k startfraction 12 over k endfraction = 8 then he moves all the terms to one side of the equal sign in the resulting equation. which equation must he solve now?
Answers
The resulting equation that Kent has when he moves all the terms to one side of the equal sign is k² - 8k + 12 = 0
What is quadratic equation?A quadratic function is a function that usually has a single variable and it is raised to the power of 2. An example is x² + 10x + 25 = 0
Given this equation: k + 12/k = 8
If both sides are multiplied by k, the equation becomes: k² + 12 = 8k
If all the terms are moved to one side of the equal sign: k² - 8k + 12 = 0
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Answer:
d
Step-by-step explanation:
edge
SOMEONE PLEASE HELP ME
Answers
Answer:
A= 77/2 or 38.5 cm^2 and p= 29.5 cm
Step-by-step explanation: Remember the formula for area and perimeter for a triangle A=1/2bh and P= a+b+c. So the equations would look like A=1/2 x 11 x 7 and P= 11 + 11 + 7.5 and that'll result in A= 77/2 or 38.5 cm^2 and p=29.5 cm.
please please answer (-2)(-4)(-1)(-7)(1) = and explain
Answers
Answer:
56
Step-by-step explanation:
(-2)(-4)(-1)(-7)(1) =
(8)(-1)(-7)(1) =
(-8)(-7)(1) =
(56)(1) = 56
hope this helps
have a good day
find the zeros f(x)=x^2+4x-12
Answers
Answer:
Step-by-step explanation:
f(x)=x2−4x−
12Set x2−4x−
12 equal to 0.x2−4x−
12
=
0
Solve for
x
.
x
=
6
,
−
2
Which of the following functions is represented in the graph shown?
f(x) = −2cos(2x) + 1
f(x) = −4cos(2x) − 1
f(x) = −2cos(x) − 1
f(x) = −4cos(x) + 1
Answers
Answer:
[tex]f(x)=-2\cos(2x)+1[/tex]
Step-by-step explanation:
Recall the general cosine equation
Function: [tex]f(x)=a\cos(bx+c)+d[/tex]Amplitude: [tex]|a|[/tex]Period: [tex]\frac{2\pi}{|b|}[/tex]Vertical Shift: [tex]-\frac{c}{b}[/tex]Midline: [tex]y=d[/tex]Identify amplitude
[tex]\text{Amplitude}=\frac{\text{Max-Min}}{2}=\frac{3-(-1)}{2}=\frac{4}{2}=2[/tex]
Identify period and solve for b
[tex]\frac{3\pi}{2}-\frac{\pi}{2}=\pi\\ \\\frac{2\pi}{|b|}=\pi\\ \\2\pi=b\pi\\\\2=b[/tex]
Identify midline
[tex]y=d=1[/tex]
Final Equation
[tex]f(x)=-2\cos(2x)+1[/tex]
Also, the reason why [tex]a=-2[/tex] is because a cosine function starts at its maximum, but since it starts at its minimum, the value of [tex]a[/tex] must be negative and causes the wave to flip about the midline.
Find two positive consecutive odd integers such that the square of the large integer is one less than twice the square of the smaller integer.
Answers
Step-by-step explanation:
x, x+2 are the two positive consecutive of integers (x + 2, because the minimum distance between 2 odd numbers is always 2, as there can never be 2 odd numbers directly following each other; and neither can even numbers, by the way).
(x+2)² = 2×x² - 1
x² + 4x + 4 = 2x² - 1
0 = x² - 4x - 5
we can solve this by factoring.
that means we need to find a and b so that
(x - a)(x - b) = x² - 4x - 5 = 0
and x = a and x = b are the 2 solutions of the quadratic equation.
x² - ax - bx + ab = x² - 4x - 5 = 0
x² - (a+b)x + ab = x² - 4x - 5 = 0
a+b = 4
ab = -5
that means that either a or b has to be 5 and the other -1.
so, the result is
(x - 5)(x + 1) = 0
x = 5
or
x = -1
are the possible solutions.
since we are only looking for positive integers, x = -1 is not a valid solution.
and only x = 5 remains as valid solution.
therefore, the 2 positive consecutive odd integers are
5, 7
The phythagorean spiral is a spiral composed of right angles triangle. Using the information provided on the spiral calculate p
Answers
The right angle triangle has an angle that is 90° while the other angles makes up 90° too.
What is a right angle triangle?Your information is incomplete. Therefore, an overview of right angle triangle will be given. It should be noted that a right angle triangle simply means a triangle that has aright angle which is 90°.
The hypothenuse is the longest side in a right angle triangle which is the side facing the 90°.
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I’m confused on where you got the numbers from. Did you get them from the amount of full squares each shape takes up?
Answers
A square simply means a shape that has four equal sides and four equal angles.
How to illustrate the square?Your information is incomplete. Therefore, an overview of a square will be given.
A square is a quadrilateral. It's also a rectangle that has two equal length adjacent sides. The four angles are equal to 90° each and are congruent to each other.
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What is 1/4 of 12? I can’t figure it out.
Answers
Answer:
3
Step-by-step explanation:
1/4 of 12 means (1/4) x 12
=> (1/4)x12
=> 12/4
=> 3
Answer: Heyaa! ~
Your Answer would be 3!
Step-by-step explanation:
We can write 1/4 of 12 as 1/4 × 12
To multiply fractions, follow the given steps:
Multiply the numerators.
Multiply the denominators.
Reduce the resultant fraction to its lowest terms.
Now,
1/4 × 12 = (1 × 12) / 4 = 12/4 = 3
Meaning the answer is.. 1/4 of 12 = 3
Hopefully this helps you!
What is 10% of 695,000
Answers
Answer:
69500
Step-by-step explanation:
[tex]\frac{695000}{x}=\frac{100\%}{10\%}\\\frac{x}{695000}=\frac{10}{100}\\\Rightarrow x=69500[/tex]
In circle H with m/GHJ = 82 and GH = 12 units, find the length of arc GJ.
Round to the nearest hundredth.
H
Answers
The length of the arc GJ is 17.17 units if the in circle H with m/GHJ = 82 and GH = 12 units.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have angle GHJ = 82 units
Length of GH = 12 units
We know:
s = 2πr(θ/360)
s = (2π)12(82/360)
s = 17.17 units
Thus, the length of the arc GJ is 17.17 units if the in circle H with m/GHJ = 82 and GH = 12 units.
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6% of a length is 390m what is the original length
Answers
Explanation:
Picture
The original Length is, 6500 m.
What is the Length?Length is the term used for identifying the size of an object or distance from one point to the other.
Given that 6% of a length is 390 m
Let original length be a
Therefore, 6% of a = 390
a*6/100 = 390
a = 390*100/6
a = 6500
Hence, The original Length is, 6500 m.
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Can you help me with this
Answers
Answer:
Step-by-step explanation:
3x + 8 = 4x + 4
-x + 8 = 4
x = 4
answer is A
Pls answer I’ll mark brainly
Answers
Answer:
52 miles
Step-by-step explanation:
since 1 unit is 26 miles and the distance from Daytona beach to Orlando on the map is 2 units just multiply 26 by 2 to get 52 miles
1 unit = 26
So multiply 2 times 26
Simplify:
2r + 7 + 11r + 3
Answers
Answer:
13r+10
Step-by-step explanation:
1. Combine Like Terms
(2r+11r)+(7+3)
13r+10
Answer:
13r+10
Step-by-step explanation:
2r+7+11r+3
collect like terms
2r+11r+7+3
13r+10
Can somebody please help me?
Answers
Answer:
1 23/36
Step-by-step explanation:
hope this helped
You roll a 6-sided die.
What is P(greater than 4 or factor of 5)?
Answers
Answer:
P(greater than 4 or factor of 5) = 1/3
Step-by-step explanation:
→ let A be the set {the numbers greater than 4}
then A : {5 , 6}
p(A) = 2/6
→ let B be the set {the factors of 5}
then B : {1 , 5}
p(B) = 2/6
P(greater than 4 or factor of 5) = p(A∪B)
Formula =================
p(A∪B) = p(A) + p(B) - p(A∩B)
………………………………………………
A∩B : {5}
then
cardA∩B = 1
Then
p(A∩B) = 1/6
Finally :
p(A∪B) = p(A) + p(B) - p(A∩B)
= 2/6 + 2/6 - 1/6
= 3/6
= 1/3
What is the Slope-Intercept form of the equation of a line that passes through the point (5,-3) and is parallel to the line y = 2x +3?
Answers
Answer:
123456098765432112345678900000000000000000000000987654444443221111111111122222233333333333334444444444455555555555556666666666666667777777777888888888889999999000
Step-by-step explanation:
In City Park, the playground takes up 3/8 of the area. The soccer field area is 1/3 of the playground area. The product 13×38 can be used to find the area of the soccer field. Which is the area of the soccer field?
Answers
The area of the city park will be equal to 3952 square units.
What is the area?The Area is defined as the space occupied by the two-dimensional geometry in a plane.
We have the following information:-
In City Park, the playground takes up 3/8 of the area:-
[tex]\rm PGA=\dfrac{3}{8}\times CP[/tex]
The soccer field area is 1/3 of the playground area.
[tex]\rm SF=\dfrac{1}{3}\times PGA[/tex]
The product 13×38 can be used to find the area of the soccer field
SF= 13 x 38=494 square units
Noe the PGA will be:-
PGA =3 x SF
PGA= 3 x494=1482 square unit
Now the area of the city park will be calculated as:-
[tex]\rm CP=\dfrac{8}{3}\times PGA\\\\\\CP=\dfrac{8}{3}\times 1482[/tex]
CP=3952 square unit
Hence the area of the city park will be equal to 3952 square units.
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