Answers
[tex]V = 864\pi[/tex]
Step-by-step explanation:
Since one of the boundaries is y = 0, we need to find the roots of the function [tex]f(x)=-2x^2+6x+36[/tex]. Using the quadratic equation, we get
[tex]x = \dfrac{-6 \pm \sqrt{36 - (4)(-2)(36)}}{-4}= -3,\:6[/tex]
But since the region is also bounded by [tex]x = 0[/tex], that means that our limits of integration are from [tex]x=0[/tex] (instead of -3) to [tex]x=6[/tex].
Now let's find the volume using the cylindrical shells method. The volume of rotation of the region is given by
[tex]\displaystyle V = \int f(x)2\pi xdx[/tex]
[tex]\:\:\:\:\:\:\:= \displaystyle \int_0^6 (-2x^2+6x+36)(2 \pi x)dx[/tex]
[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \int_0^6 (-2x^3+6x^2+36x)dx[/tex]
[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \left(-\frac{1}{2}x^4+2x^3+18x^2 \right)_0^6[/tex]
[tex]\:\:\:\:\:\:\:= 864\pi [/tex]
Related Questions
Find the slope of the line that passes through the two points. -3,6 & -7,3
HELP!!!!
Answers
solve using
y - y1/x-x1
:)
Are the triangles similar ? If they are identify the similarity ratio.
Answers
Answer:
C
Step-by-step explanation:
The triangles are similar and the scale factor can be find out by computing 18/6=15/5=9/3=3
A chemical company makes two brands of antifreeze the first brand contains 65% pure antifreeze and the second brand contains 80% pure antifreeze in order to obtain 60 gallons of a mixture that contains 70% pure antifreeze how many gallons of each brand of antifreeze must be used
Answers
Answer:
30 gallons of each brand
Step-by-step explanation:
1 gallon of 60% + 1 gallon of 80% = 2 gallons 70% (60/2 = 30)
what graph shows the solution to the equation below log3(x+2)=1
Answers
Answer:
The solution to the equation log3(x+2)=1 is given by x=1
Step-by-step explanation:
We are given that
[tex]log_3(x+2)=1[/tex]
We have to find the graph which shows the solution to the equation log3(x+2)=1.
[tex]log_3(x+2)=1[/tex]
[tex]x+2=3^1[/tex]
Using the formula
[tex]lnx=y\implies x=e^y[/tex]
[tex]x+2=3[/tex]
[tex]x=3-2[/tex]
[tex]x=1[/tex]
Can someone help me with this? Thanks!
Answers
9514 1404 393
Answer:
x ∈ {5, 7}(5,7)Step-by-step explanation:
The graph shows the function value is zero for x=5 and x=7. These are the elements of the solution set.
x ∈ {5, 7}
__
The graph is below the x-axis between these points, so that is the region where f(x) < 0
5 < x < 7 . . . . . for f(x) < 0
In interval notation: (5, 7).
I need help with this question
Answers
9514 1404 393
Answer:
x = 22, y = 123
Step-by-step explanation:
The sum of angles in a triangle is 180°.
(2x +13)° +57° +3x° = 180°
5x +70 = 180 . . . . . . . . . . . . . collect terms, divde by °
5x = 110 . . . . . . . . . . . subtract 70
x = 22 . . . . . . . . divide by 5
__
Angles in a linear pair are supplementary.
y° + 57° = 180°
y = 123 . . . . . . . . divide by °, subtract 57
What complex number is represented by the expression 7i^5+9i^8
Answers
Answer:
[tex]9 + 7i[/tex]
Step-by-step explanation:
[tex]7i^5+9i^8[/tex]
[tex]i^5 = i\\ i^8 = 1[/tex]
consider this equation sin(theta) = -4 square root of 29/29 if theta is an angle in quadrant IV what is the value of cos (theta)
Answers
Answer:
[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]
Step-by-step explanation:
Given
[tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex] -- the correct expression
Required
[tex]\cos(\theta)[/tex]
We know that:
[tex]\sin^2(\theta) + \cos^2(\theta)= 1[/tex]
Make [tex]\cos^2(\theta)[/tex] the subject
[tex]\cos^2(\theta)= 1 - \sin^2(\theta)[/tex]
Substitute: [tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex]
[tex]\cos^2(\theta)= 1 - (-\frac{4}{\sqrt{29}})^2[/tex]
Evaluate all squares
[tex]\cos^2(\theta)= 1 - (\frac{16}{29})[/tex]
Take LCM
[tex]\cos^2(\theta)= \frac{29 - 16}{29}[/tex]
[tex]\cos^2(\theta)= \frac{13}{29}[/tex]
Take square roots of both sides
[tex]\cos(\theta)= \±\sqrt{\frac{13}{29}}[/tex]
cosine is positive in the 4th quadrant;
So:
[tex]\cos(\theta)= \sqrt{\frac{13}{29}}[/tex]
Split
[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}}[/tex]
Rationalize
[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}} * \frac{\sqrt{29}}{\sqrt{29}}[/tex]
[tex]\cos(\theta)= \frac{\sqrt{13*29}}{29}[/tex]
[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]
What is the smallest 6-digit- palindrome (a number that reads the same forward and backward) divisible by 99
Answers
Answer:
108801
Step-by-step explanation:
Palindrome as defined in the given question as a number which reads the same forward and backward. Examples are: 1001, 20202, 1331 etc.
Thus, to determine the smallest 6-digit palindrome divisible by 99 without a remainder, the digits should be in the form of abccba.
Therefore, the smallest 6-digit palindrome that can be divided by 99 is 108801.
So that,
108801 ÷ 99 = 1099
5. What is the value of x if the quadrilateral is a kite? B X+2 C С 13 A Xth12 D
Answers
Answer: just had this problem! X = 11
List the angles in order from the smallest to the largest.
Answers
Answer:
D. <S, <R, <T
Step-by-step explanation:
Recall: On a triangle, the bigger an angle measure the longer the side opposite it and vice versa.
In ∆RST,
The longest side, SR = 22, is opposite to <T
Therefore, <T is the biggest angle.
Medium side, ST = 21, is opposite to <R, therefore,
<R is the medium angle measure
The smallest angle measure <S is opposite to the shortest side, RT.
Angels I'm order form the smallest to largest will be:
<S, <R, <T
Find the value of x.
Answers
Answer:
x = 3
Step-by-step explanation:
A midsegment in a trapezoid is formed when one connects the midpoints of the two legs (non-parallel sides) in a trapezoid. The midsegment theorem states that the length of the midsegment is equal to the average of the two bases (that is the parallel sides).
One can apply the midsegment theorem here by stating the following;
[tex]\frac{(YZ)+(TM)}{2}=PW[/tex]
Substitute,
[tex]\frac{23+11x+2}{2}=29[/tex]
Simplify,
[tex]\frac{25+11x}{2}=29[/tex]
Inverse operations,
[tex]\frac{25+11x}{2}=29[/tex]
[tex]25+11x=58\\\\11x = 33\\\\x = 3[/tex]
can you help please I have no clue
Answers
Answer:
6, 15, 24, 33
Step-by-step explanation:
Basically, the number on top of the sigma represents the number of terms total in that sequence, and on the right you have the equation in which you can plug in whichever value that falls into what the top number says to find the output. In other words, just plug in 1 for k to find a1, 2 for k to find a2, etc.
Hope that helps!
Item 16
What is the area of the triangle in the coordinate plane?
36 units²
38 units²
66 units²
72 units²
Answers
Base is 8
Height is 9
9x8=72
72/2=36
36 units ^2
Find the volume of the box. The box shows the length is 6 feet, the width is 5 feet, and the height is 3 feet. The volume of the box is blank cubic feet. The solution is
Answers
Answer:
[tex]90[/tex] [tex]ft^3[/tex]
Step-by-step explanation:
----------------------------------------
The formula to find the volume of a rectangular prism is [tex]V=lwh[/tex]
Let's substitute the number for the length, width, and height now.
[tex]V=(6)(5)(3)[/tex]
[tex]V=(30)(3)[/tex]
[tex]V=90[/tex]
--------------------
Hope this is helpful.
what is the answer to 10% of 900
Answers
Answer:
90 cause 90 times 10 is 900 and 10% times 10 is 100%
Step-by-step explanation:
Answer: 90
Step-by-step explanation: 900 × .10 = 90
Mathematics I need help
Answers
Answer:
B
Step-by-step explanation:
Exclude C:
[tex] |x| [/tex]
is not curved
To shift right, minus inside the
[tex] |?| [/tex]
Thus
[tex] |x - 4| [/tex]
To shift up, add outside the
[tex] |?| [/tex]
Thus:
[tex] |x +4| + 2[/tex]
B
Brainliest please~
3x is 18 what value is x
Answers
Answer:
6
Step-by-step explanation:
We have the expression "3x is 18" and we want to find out x, so the easiest way is to isolate x. The way to do this is by dividing both 3x and 18 by 3, leaving us with 6. This means that our answer for x is 6. I hope this helped and please don't hesitate to reach out for clarification!
Answer:
6
Step-by-step explanation:
3x = 18
Divide both sides by 3
3x / 3 ( the 3s cancel out and we're left with x )
18/3 = 6
We get that x = 6
We can then plug in 6 to x in 3x = 18 to check if our answer is correct
3x = 18
Replace x with 6
3(6) = 18
3(6) = 18
18 = 18
This is true hence we can confirm that x = 6
Please help NO LINKS
Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by
y
=
x
2
,
y
=
0
, and
x
=
5
,
about the
y
-axis.
V
=
Answers
Answer:
[tex]\displaystyle V = \frac{625 \pi}{2}[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationGraphingCalculus
Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method: [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is volumeStep-by-step explanation:
Step 1: Define
y = x²
y = 0
x = 5
Step 2: Identify
Find other information from graph.
See Attachment.
Bounds of Integration: [0, 5]
Step 3: Find Volume
Substitute in variables [Shell Method]: [tex]\displaystyle V = 2\pi \int\limits^5_0 {x(x^2)} \, dx[/tex][Integrand] Multiply: [tex]\displaystyle V = 2\pi \int\limits^5_0 {x^3} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^5_0[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle V = 2\pi \bigg( \frac{625}{4} \bigg)[/tex]Multiply: [tex]\displaystyle V = \frac{625 \pi}{2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
Couch johnson needs to buy shirts for his soccer players. He finds a package of 2:shirts for 16.00. How much will it cost to buy 18 shirts?
Answers
Answer:
144
Step-by-step explanation:
We can write this as 2 shirts = 16.00 . Then, we can write this as a ratio, where
2 shirts / 16.00 = 18 shirts/ cost of 18 shirts as the cost for a pair of shirts remains the same, so the ratio will as well.
Therefore, writing the cost of 18 shirts as c, we have
2 shirts/16.00 = 18 shirts/c
multiply both sides by c to remove a denominator
2 shirts * c/16.00 = 18 shirts
multiply both sides by 16 to remove the other denominator
2 shirts * c = 18 shirts * 16
divide both sides by 2 shirts to isolate the c, as we want to figure that out
c = 18 shirts * 16/2 shirts
c=144
he parent function f(x) = x3 is represented by graph A. Graph A is transformed to get graph B and graph C. Write the functions represented by graph B and graph C.
Graph B represents the function g(x) =
.
Graph C represents the function h(x) =
.
Answers
Answer is graph b I believe
Graph b
help help HELP!! will give brainliest
If f(x) = x², g(x) = 5x, and h(x) = x + 4, find each value.
Find h[f(4)].
Answers
Answer:
[tex]h(f(4))=20[/tex]
Step-by-step explanation:
We are given the functions:
[tex]f(x)=x^2,\, g(x)=5x\text{, and } h(x)=x+4[/tex]
And we want to find
[tex]h(f(4))[/tex]
Find f(4) first:
[tex]f(4)=(4)^2=16[/tex]
Thus:
[tex]h(f(4))=h(16)[/tex]
Now, evaluate h(16):
[tex]h(16)=(16)+4=20[/tex]
Hence:
[tex]h(f(4))=20[/tex]
AXYZ is reflected across the line x = 3. What is the reflection image of X
Answers
Answer:
The answer should be (7, 5)
You paid $6.99 for a shirt that was 70% of what was the original price of the shirt?
Answers
Answer:
$23.3
Step-by-step explanation:
you can use ratios to solve this:
$6.99/x=0.30/0.100 then cross multiply to get 0.3x=6.99
So, 6.99 divided by 0.3 = 23.3
so the original price is $23.3
Jamal opens a savings account with a starting balance of $200 and plans to
deposit $75 each week after opening the account. His savings over time is
represented by the graph below. How would this graph change if Jamal
decided to deposit $100 each week instead?
Answers
the graph would steeper, meaning more savings over time
Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question.
A number line going from negative 9 to positive 1.
–3
0
2
Answers
Answer:
-5 it is
Step-by-step explanation:
The center of the circle is located (3'8), and the circle has a radius that is 5 units long. What is the general form of the equation for the circle
Answers
9514 1404 393
Answer:
x² +y² -6x -16y +48 = 0
Step-by-step explanation:
Given:
circle center: (3, 8)circle radius: 5Find:
general form equation for the circle
Solution;
The standard form equation for the circle is ...
(x -h)² +(y -k)² = r² . . . . . circle with radius r centered at (h, k)
(x -3)² +(y -8)² = 5²
Subtracting 25 and expanding this will give the general form.
x² -6x +9 +y² -16y +64 -25 = 0
x² +y² -6x -16y +48 = 0
_____
Additional comment
"General form" of an equation is usually the form f(x,y) = 0, where f(x, y) is written in "standard form," with terms in lexicographical order and decreasing degree.
What is the range of the given set of ordered pairs?
(9,-2) (4,3) ( 8, 10) (-4, 8)
Answers
Answer:
(-2,3,10,8)
Step-by-step explanation:
eg
(x,y)=(domain,range)
x components are domain and y components are range in the given set of ordered pairs
had
n=2
n²-n-2
n² – 5n+6
Answers
Answer:
0，0
Step-by-step explanation:
n=2，
[tex] {2}^{2} - 2 - 2 = 0 [/tex]
[tex] {2}^{2} - 5 \times 2 + 6 = 0[/tex]
NEED HELP ASAP!!
Which equations represent exponential growth?
Which equations represent exponential decay?
Drag the choices into the boxes to complete the table.
Exponential Growth:
Exponential Decay:
y = 1700(1.25)^t
y =240(1/2)^t
y = 4000(1.0825)^t
y = 1.5(10)^t
y = 12,000(0.72)^t
y = 8000(0.97)^t
Answers
Answer:
Growth: y = 1700(1.25)^t, y = 4000(1.0825)^t, y = 1.5(10)^t
Decay: y =240(1/2)^t, y = 12,000(0.72)^t, y = 8000(0.97)^t
Step-by-step explanation:
In an exponential equation, growth and decay are determined by the factor you are multiplying by exponentially. If it's under 1 you're basically exponentially dividing the initial value. Over 1 and you are increasing the value.