express using algebra A inscreased by 15%
Answer:
A(1.15)
Step-by-step explanation:
Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. y
Answer:
[tex]Volume = \frac{384}{7}\pi[/tex]
Step-by-step explanation:
Given (Missing Information):
[tex]y = x^\frac{3}{2}[/tex]; [tex]y = 8[/tex]; [tex]x=0[/tex]
Required
Determine the volume
Using Shell Method:
[tex]V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy[/tex]
First solve for a and b.
[tex]y = x^\frac{3}{2}[/tex] and [tex]y = 8[/tex]
Substitute 8 for y
[tex]8 = x^\frac{3}{2}[/tex]
Take 2/3 root of both sides
[tex]8^\frac{2}{3} = x^{\frac{3}{2}*\frac{2}{3}}[/tex]
[tex]8^\frac{2}{3} = x[/tex]
[tex]2^{3*\frac{2}{3}} = x[/tex]
[tex]2^2 = x[/tex]
[tex]4 =x[/tex]
[tex]x = 4[/tex]
This implies that:
[tex]a = 4[/tex]
For [tex]x=0[/tex]
This implies that:
[tex]b=0[/tex]
So, we have:
[tex]V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy[/tex]
[tex]V = 2\pi \int\limits^4_0 {p(y)h(y)} \, dy[/tex]
The volume of the solid becomes:
[tex]V = 2\pi \int\limits^4_0 {x(8 - x^{\frac{3}{2}}}) \, dx[/tex]
Open bracket
[tex]V = 2\pi \int\limits^4_0 {8x - x.x^{\frac{3}{2}}} \, dx[/tex]
[tex]V = 2\pi \int\limits^4_0 {8x - x^{\frac{2+3}{2}}} \, dx[/tex]
[tex]V = 2\pi \int\limits^4_0 {8x - x^{\frac{5}{2}}} \, dx[/tex]
Integrate
[tex]V = 2\pi * [{\frac{8x^2}{2} - \frac{x^{1+\frac{5}{2}}}{1+\frac{5}{2}}]\vert^4_0[/tex]
[tex]V = 2\pi * [{4x^2 - \frac{x^{\frac{2+5}{2}}}{\frac{2+5}{2}}]\vert^4_0[/tex]
[tex]V = 2\pi * [{4x^2 - \frac{x^{\frac{7}{2}}}{\frac{7}{2}}]\vert^4_0[/tex]
[tex]V = 2\pi * [{4x^2 - \frac{2}{7}x^{\frac{7}{2}}]\vert^4_0[/tex]
Substitute 4 and 0 for x
[tex]V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [{4*0^2 - \frac{2}{7}*0^{\frac{7}{2}}])[/tex]
[tex]V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [0])[/tex]
[tex]V = 2\pi * [{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}][/tex]
[tex]V = 2\pi * [{64 - \frac{2}{7}*2^2^{*\frac{7}{2}}][/tex]
[tex]V = 2\pi * [{64 - \frac{2}{7}*2^7][/tex]
[tex]V = 2\pi * [{64 - \frac{2}{7}*128][/tex]
[tex]V = 2\pi * [{64 - \frac{2*128}{7}][/tex]
[tex]V = 2\pi * [{64 - \frac{256}{7}][/tex]
Take LCM
[tex]V = 2\pi * [\frac{64*7-256}{7}][/tex]
[tex]V = 2\pi * [\frac{448-256}{7}][/tex]
[tex]V = 2\pi * [\frac{192}{7}][/tex]
[tex]V = [\frac{2\pi * 192}{7}][/tex]
[tex]V = \frac{\pi * 384}{7}[/tex]
[tex]V = \frac{384}{7}\pi[/tex]
Hence, the required volume is:
[tex]Volume = \frac{384}{7}\pi[/tex]
The volume of the solid of revolution generated by revolving the plane region about the y-axis is [tex]\frac{10240\pi}{3}[/tex] cubic units.
How to calculate the volume of a solid of revolution by shell method
Let be [tex]f(x) = x^{5/2}[/tex] and [tex]g(x) = 32[/tex], whose point of intersection is [tex](x,y) = (4, 32)[/tex]. Solid of revolution generated by revolving the plane region about the y-axis is defined by the following formula:
[tex]V = 2\pi\int\limits^{32}_0 {y\cdot g(y)} \, dy[/tex] (1)
If we know that [tex]g(y) = y^{2/5}[/tex], then the volume of the solid of revolution is:
[tex]V = 2\pi\int\limits^{32}_{0} {y^{7/5}} \, dy[/tex]
[tex]V = 2\pi\cdot \left(\frac{5}{12}\cdot y^{12/5}\right)\left|_{0}^{32}[/tex]
[tex]V = \frac{5\pi}{6} \cdot y^{12/5}|\limit_{0}^{32}[/tex]
[tex]V = \frac{5\pi}{6}\cdot 32^{12/5}[/tex]
[tex]V = \frac{10240\pi}{3}[/tex]
The volume of the solid of revolution generated by revolving the plane region about the y-axis is [tex]\frac{10240\pi}{3}[/tex] cubic units. [tex]\blacksquare[/tex]
Remark
The statement is incomplete. Complete form is shown below:
Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. [tex]y = x^{5/2}[/tex], [tex]y = 32[/tex], [tex]x = 0[/tex].
To learn more on solids of revolution, we kindly invite to check this verified question: https://brainly.com/question/338504
please help mee with this thing
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PLS SHOW THE WORK!!!!!!!!
Now im not 100% sure, but this is what i got (for number one).
y=2x−1
Swap sides so that all variable terms are on the left hand side.
2x−1=y
Add 1 to both sides.
2x=y+1
Divide both sides by 2.
2x/2 = y+1/2
Dividing by 2 undoes the multiplication by 2.
So therefore, X = Y+1/2.
(i couldnt explain that very well im sorry, i dont know the 2nd answer im very bad at these)
Answer:
I need 1 Brainliest before I can become Virtuoso
Step-by-step explanation:
How do you solve the following word problem
A small radio transmitter broadcasts in a 49 mile radius. If you drive along a straight line from a city 67 miles north of the transmitter to a second city 63 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
I must give the answer in miles and am unclear as to what equations to use and need details on what equations to use to get to the correct answer.
thanks for any help.
M
Answer:
Step-by-step explanation:
Let the transmitter be located at (0,0)
The equation for its effective coverage area will be a circle centered at (0,0) with a radius of 49.
So....the equation is
[tex]x^2 + y^2 = 49^2[/tex]
[tex]x^2 + y^2 = 2401[/tex]
Let the point 67 miles north of the transmitter be (0, 67)
Let the point 63 miles east of the transmitter be (63, 0)
The line connecting these (the line of travel) will have a slope of
[67 - 0] / [ 0 - 63] = -67/63
The equation of this line will be: y = (-67/63)x + 67
The signal will be received between the points:
(21.681, 43.942) and (45.192, 18.938)
The distance between these points is
[tex]\sqrt{[ ( 45.192 - 21.681)^2 + ( 43.942 - 18.938)^2 ] } = 34.322 miles[/tex] (1)
The distance between (0, 63) and (67, 0)
[tex]\sqrt{[ ( 63)^2 + ( 67)^2 ] }=91.97miles[/tex] (2)
So....you will receive the signal using (1)/ (2)
(34.322 / 91.97) x 100 ≈ 37% of the drive
What is the answer
5+7+9+8=
Answer:
29
Step-by-step explanation:
5 more than the product of 12 and 8 as a numerical expression.
Answer:
(12x8) + 5
Step-by-step explanation:
The product of 12 and 8 would be multiplication, so you can represent that as
(12x8) or 12x8
"5 more" simply means addition
So if you were to put all that together as a numerical expression it would be
(12x8) + 5
Hope this helps!
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9514 1404 393
Answer:
x = 19
Step-by-step explanation:
Corresponding sides are proportional.
full length/right segment = 36/20 = (x+5+30)/30
Multiplying by 30 gives ...
54 = x +35
19 = x . . . . . . . subtract 35
Which function rule represents the data in the table below ?
y = 4 + 5 x
y = 3 + 6x
y= 5 + 4x
y = 6 + 3x
Please help me with this thank you!
Answer:
y = -x + 1
Step-by-step explanation:
y=mx+b
m:slope= rise/run, the line goes down 1 and over 1 so it would be -1/1 which is -1
b:y-intercept: the line crosses the y-axis at 1
plug in m=-1 and b=1 into y=mx+b
y=-1x+1
y=-x+1
PLEASE HELP AND VERY FAST
Answer:
B
Step-by-step explanation:
I am so sorry if that is incorrect
HELP ME NOW ASAPPP UnU
Answer:
56.757 and if u divide it : 676.75
Step-by-step explanation:
uwu
When Brandon went bowling, it cost $4.95 per game, plus a one-time fee to rent the shoes. Brandon played 5 games and paid $32. Write and solve a linear equation to find the cost to rent the shoes. Enter just the equation in slope-intercept form on this question.
Use the equation from the previous question to find the cost of renting the shoes.
Answer:
$7.25.
Step-by-step explanation:
Given that, when Brandon went bowling, it cost $ 4.95 per game, plus a one-time fee to rent the shoes, and knowing that Brandon played 5 games and paid $ 32, to find the cost to rent the shoes the following equation must be performed :
4.95 x 5 + X = 32
24.75 + X = 32
X = 32 - 24.75
X = 7.25
Thus, the cost of renting the shoes was $ 7.25.
Which point is a reflection of (-3,-3) across the y-axis?
(-3, 3)
(3, 3)
0 (-3,-3)
o
(3,-3)
The point which is a reflection of (-3,-3) across the y-axis is, (3, - 3)
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
We have to given that;
The point is,
⇒ (- 3, - 3)
Now, We know that;
The rule of reflection after across the y - axis is,
⇒ (x, y) = (- x, y)
Thus, The point which is a reflection of (-3,-3) across the y-axis is,
⇒ (x, y) = (- x, y)
⇒ (-3, -3) = (- (-3), -3)
= (3, - 3)
Learn more about the coordinate visit:
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HELP ME PLEASEEE ASAPPP
WILL MARK BRAINLIEST!!!
DUE SOON!!
Explain the need for businesses to use forecasting models and evaluate the use of Time Series Analysis as one of these models
Answer:
They can be used to develop alternate models with different factors.
Step-by-step explanation:
Factor each expression:
27+12
12+36
16+20
2x+8
30+12x
42x+49
Here are the ingredients needed to make 8 pancakes
250ml milk
140 g flour
5 g butter
a) Simon makes 4 pancakes.
Answer: To make 4 pancakes, Simon will need 125 ml milk, 70 grams flour, and 2.5 grams of butter.
Step-by-step explanation:
If that is the recipe to make 8 pancakes, and Simon has 4 pancakes, then Simon needs to cut the recipe in half. So we can multiply each ingredient by 1/2.
250 x 1/2 = 125.
140 x 1/2 = 70.
5 x 1/2 = 2.5
In conclusion, to make 4 pancakes, Simon will need 125 ml milk, 70 grams of flour, and 2.5 grams of butter.
At a gourmet coffee shop. 3 pounds of dark-roast coffee beans cost $56 and 7 pounds of the same coffee cost $112. On the grid below, graph a line that shows how the cost of these coffee
beans varies proportionally with the number of pounds purchased. Use your graph to identify the unit rate for these coffee beans.
PLEASE ITS DUE IN A HOUR
Answer:
In the question, it says that this is a proportional relationship.
A proportional relationship is something like:
y = k*x
So when we have x = 0, we also need to have y = 0.
For the case in the question, this does not happen, so i guess that the actual question is:
"At a gourmet coffee shop. 3.5 pounds of dark-roast coffee beans cost $56 and 7 pounds of the same coffee cost $112."
We can define:
x = amount of coffee
y = price of that coffee
Now we have two pairs:
$56 to get 3.5lb
$112 to get 7lb
Then we have two points:
(3.5lb, $56)
(7lb, $112)
We can draw these two points and then connect them with a line, this line will represent the proportional relationship.
Now we need to look at the value 1 in the x-axis, then draw a vertical line
At the point where this vertical line intersects the graph, we draw a horizontal line, and the value of y is the value at which this horizontal line intersects the y-axis.
(you can see a rough sketch of this in the image below)
The solution is 1lb of coffee costs $16.
put a digit in the gap, such that the answer is a whole number 10x + 11 = 144
Answer:
13.3 or 13
Step-by-step explanation:
10x+11=144
10x=144-11
10x=133
x=133/10
x=13.3
x-1/x^2 - x - 20 Give the equivalent numerator if the denominator is (X - 5)(x + 4)(x + 3)
x^2 + 2x + 3
x^2 + 2x - 3
x^2-3
Answer:
[tex]x^2+2x-3[/tex]
Step-by-step explanation:
Note that [tex]x^2-x-20=(x-5)(x+4)[/tex], so, if the denominator is [tex](x-5)(x+4)(x+3)[/tex], we need to multiply the numerator by [tex](x+3)[/tex]. And [tex](x-1)(x+3)=x^2+2x-3[/tex].
2. 7 2/6 + 1/12 = M
A.7 3/18
B.7/18
C.7 2/12
D.7 5/12
3. 1 6/10 + 1 4/5 = ?
A. 2 10/15
B. 2 10/50
C. 3 4/10
D. 3 10/10
4. 5/8 + 1/2 = Z
A. 9/8
B. 6/8
C. 1
D. 1 5/8
5. 2/12 + 2/4 = R *
A. 4/16
B. 8/16
C. 4/12
D. 8/12
Answer:
2 a 3 d 4 c 5 b
Step-by-step explanation:
let x represent one number and let y represent the other number. use the given conditions to write a system of equations. solve the system and find the numbers. three times a first number decreased by a second number is 22. the first number increased by twice the second number is 12.
9514 1404 393
Answer:
(x, y) = (8, 2)
Step-by-step explanation:
The relevant equations are ...
3x -y = 22
x +2y = 12
__
We can eliminate y by adding twice the first equation to the second.
2(3x -y) +(x +2y) = 2(22) +(12)
7x = 56
x = 8
Substituting into the first equation gives ...
3(8) -y = 22
y = 24 -22 = 2
The first number is 8; the second number is 2.
Middle school students were asked how they got to school each morning. There were 375 students who said they rode the bus. This number represents 60 percent of the school enrollment. How many students are enrolled?
Answer:
give me 1 second to answer with the correct answer
Evaluate 7y - 2
when y = 9
Answer:
The answer is 61.
Step-by-step explanation:
7(9)-2
63-2
61
Answer:61
7*(9)-2
63-2
61
Hope it's useful
what type of number is -
[tex] \sqrt{16} [/tex]
Answer:
perfect square / rational
4
Step-by-step explanation:
Answer:
root of 16. or 4
Step-by-step explanation:
what is the answer of this question?
Answer:
Its B.
Step-by-step explanation:
Because [tex]11^{2}[/tex] + [tex]12^{2}[/tex] does not equal [tex]15^{2}[/tex]
121 + 144 [tex]\neq[/tex] 225
265 [tex]\neq[/tex] 225
how would I do linear expression
Answer:
Linear expression is linear equations
Step-by-step explanation:
D
Angles that have the same
_________________
are called
__________________
angles.
Answer:
Can’t trust anyone these days fake is becoming the new trend.
When 2/3 tons of coal cost $13.50, what will in ton cost?
Answer:
20.25
Step-by-step explanation:
Divide 13.50 by 2 and then multiply by 3.
