Using the disk method, the volume would be
[tex]\displaystyle \pi \int_0^3 (\sqrt x)^2 \,\mathrm dx=\pi \int_0^3 x\,\mathrm dx=\frac\pi2 x^2\bigg|_0^3=\boxed{\frac{9\pi}2}[/tex]
That is, you split up the solid into disks of some small height ∆x, and each disk has radius at point x equal to the distance (√(x)) from the axis of revolution (the x-axis, y = 0) to the curve y = √(x). The volume of such a disk is then π (√(x))² ∆x. Take the sum of these volumes to get the total volume, then as the heights get smaller and smaller, replace ∆x with dx and the sum with the integral.
In this exercise we have to use the knowledge of the integral to calculate the volume of the disk that will correspond to:
[tex]V= \frac{9\pi }{2}[/tex]
That is, you split up the solid into disks of some small height ∆x, and each disk has radius at point x equal to the distance (√(x)) from the axis of revolution (the x-axis, y = 0) to the curve y = √(x). The volume of such a disk is then π (√(x))² ∆x. Take the sum of these volumes to get the total volume, then as the heights get smaller and smaller, replace ∆x with dx and the sum with the integral. Using the disk method, the volume would be:
[tex]\pi \int\limits^3_0 {(\sqrt{x})^2} \, dx = \pi \int\limits^3_0 {x} \, dx = \frac{\pi x^2}{2} = \frac{9 \pi }{2}[/tex]
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Find an explicit formula for the geometric sequence -40,-20,-10......
Note: the first term should be c(1).
c(n)= ?
Answer:
The explicit formula for the geometric sequence is [tex]c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}[/tex].
Step-by-step explanation:
By definition of geometric sequence, we should use the following expression:
[tex]c(n) = c_{1}\cdot r^{n-1}[/tex], [tex]n \ge 1[/tex] (1)
Where:
[tex]c_{1}[/tex] - First term.
[tex]r[/tex] - Geometric rate.
[tex]n[/tex] - Position of the element within the series.
If we know that [tex]c_{1} = -40[/tex] and [tex]r = \frac{1}{2}[/tex], then the explicit formula for the geometric sequence is:
[tex]c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}[/tex]
The explicit formula for the geometric sequence is [tex]c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}[/tex].
Deborah has $56 in her bank account currently. She earns $8 per hour at her job at the local ice cream shop. Micah has $32 in his bank account and earns $12 per hour at his job mowing lawns. How many hours do they need to work to have the same amount of money in their bank accounts?
Factorise: 6ax+2abx+3ay+by
Answer:
I think the question is not correct because it can't be factorize
Step-by-step explanation:
Solve the equation 17=5k-3
Answer:
4
Step-by-step explanation:
Simplifying
17 = 5k + -3
Reorder the terms:
17 = -3 + 5k
Solving
17 = -3 + 5k
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '-5k' to each side of the equation.
17 + -5k = -3 + 5k + -5k
Combine like terms: 5k + -5k = 0
17 + -5k = -3 + 0
17 + -5k = -3
Add '-17' to each side of the equation.
17 + -17 + -5k = -3 + -17
Combine like terms: 17 + -17 = 0
0 + -5k = -3 + -17
-5k = -3 + -17
Combine like terms: -3 + -17 = -20
-5k = -20
Divide each side by '-5'.
k = 4
Simplifying
k = 4
Your Assignment
AABC is translated 4 units to the left and 8 uzits up, then reflected across the y-axis. Answer the
questions to find the coordinates of A after the transformations.
B(2,9)
8
7
6
A(7,5)
C(1,3)
1
1
2
3
4
5
6
7
1. Give
rule for translating a point 4 units left and 8 units up.
Write your answer in the space below.
Answer:
this problem has this form, (x,y) (x-7)(y+5) and tells you that the X and Y coordinates are translated to X-7 and Y+5.
Step-by-step explanation:
The translated point A' of the triangle is given by A' ( -3 , 13 )
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.
Given data ,
Let the triangle be represented as ΔABC
Now , the coordinates of the triangle are
A ( 7 , 5 ) , B ( 2 , 9 ) and C ( 1 , 3 )
Now , the triangle is translated 4 units left and 8 units up
To translate the point A(7,5) 4 units to the left and 8 units up, we subtract 4 from the x-coordinate and add 8 to the y-coordinate:
A'(3,13)
To reflect this point across the y-axis, we change the sign of the x-coordinate:
A'(-3,13)
Hence , the translated point is A' ( -3 , 13 )
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i need help with this question asap!!I will give brainliest!!!please and thank you
Answer:
Step-by-step explanation:
(4,6) and (20,14) are points on the line.
slope of line = (14-6)/(20-4) = 8/16= 1/2
point-slope equation for line of slope 1/2 that passes through (6,4):
y-4 = (½)(x-6)
in slope-intercept form:
y = ½x + 1
y-intercept = 1
1. What type of association does this
graph have?
A:positive
B:negative
C:none
D:all of the above
Answer:
C
Step-by-step explanation:
The graph have negative type of association. the variables tend to increase as the other variable decreases.
What is the association of a graph?A positive association exists when one variable increases as the other variable increases. A negative association exists when one variable increases while the other variable decreases. If there is no relationship between the variables, the scatterplot points have no association.The association is linear when a straight line describes the relationship between the variables. The relationship is monotonic when it is described by a nonlinear function that is constantly increasing or decreasing. Other types of relationships could be nonlinear or non-monotonic.The appropriate statistical measures and tests of association are determined by the type of relationship.A bivariate normal density ellipse summarises the correlation between variables if the relationship is linear. The greater the correlation between the variables, the narrower the ellipse.To learn more about graph association refer :
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PLEASE HELP!! EXPLANATION TOO PLEASE THANK YOU
(CLICK IN FOR THE PICTURE OF QUESTION)
Answer:
x=57
Step-by-step explanation:
a triangle has a sum of 180 degrees
that angle 51 is vertical to the angle across it so it is 51
we do math now
180-72-51=57
I hope this helped :))
15. Geoff can mow an entire lawn of 450 square feet in 30 minutes. Assuming he mows at a constant rate, write the linear equation that represents the situation
Answer:
y=15x
Assuming he is mowing at a constant rate it would be 15 square feet per minute.
Step-by-step explanation:
PLEASE HELPPPP!!!! ITS ALMOST DUE
Answer:
1. The radius of the circle is 6cm. We know this because the radius measures from the center of a circle to the outer side. Since the radius is always half the diameter then half of 12cm is 6cm
2. The diameter is 14cm. We know this because diameter measures from one edge of a circle straight across to the other side. Also the radius is always half the diameter so 7cm*2=14cm
Greg went to the store. He bought 5 kilograms of purple beads, 1/2 of a kilogram of orange beads, and 2 kilograms of white beads. How much did he spend?
Answer:
Altogether, Greg spent $22.71.
Step-by-step explanation:
1) 5kg × $2.75 = $13.75
Purple beads: Spent $13.75
2) 1/2 kg = 1.5kg
1.5kg × $1.84 = $2.76
Orange beads: Spent $2.76
3) 2kg × $3.10 = $6.20
White beads: Spent $6.20
4) Add them all together.
$13.75 + $2.76 + $6.20 = $22.71
Hope this helps. :)
what is the exact value of X
Answer:
x=2
Step-by-step explanation:
hi so im gonna be honest im too lazy to write down how i found the answer but it should be x=2. hope it helps!
ps pls tell me if it was correct :)
Write the equation of the line that passes through the points (4, -8) and (-8, 1).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answer:
y = -3/4x -5
Step-by-step explanation:
(4, -8) and (-8, 1)
m = (y2-y1)/(x2-x1)
m= (1+8)/(-8-4)
m = (9)/(-12)
m = -3/4
y - y1 = m(x-x1)
y + 8 = -3/4(x -4)
y + 8 = -3/4x + 3
y = -3/4x -5
Answer:
y = -3/4x - 5
Step-by-step explanation:
Hope this helps!
Someoneeee helpppp !!1. Determine the area of the rectangle below.
Tam
m
15 m
Formula:
Plug in Values:
Area:
Answer:
Hope that answers your question
— 3х + 9y = — 21
— 3х +8y = -18
find the solution by system of equations
Answer:
x=-2,y=-3
Step-by-step explanation:
x=7+3x
-3x+8y=-18
-21-y=-18
x=7+3x
y=-3
x=7+3x
x=-2
y=-3
Answer:
x = -2
y = -3
Step-by-step explanation:
There are three methods for solving system of equations: elimination, substitution, and graphing. In this case elimination would be the best method since you have -3x for both equations. When solving by elimination, your goal is to eliminate one of the variables, in this case we will eliminate x. Subtract the bottom equation from the top (it is important to remember here that the negative will distribute to the entire equation).
-3х + 9y = -21
- (- 3х +8y = -18)
_____________
y = -3
Now plug this y-value in to either equation and solve for x
-3х + 9y = -21
-3х + 9(-3) = -21
-3x - 27 = -21
-3x = 6
x = -2
Check your answer by plugging both values in to the second equation
- 3х +8y = -18
- 3(-2) +8(-3) = -18
6 - 24 = -18
-18 = -18
factor the polynomial
Answer:
Step-by-step explanation:
[tex]6a^2-13ab-5b^2\\ \\ 6a^2+2ab-15ab-5b^2\\ \\ 2a(3a+b)-5b(3a+b)\\ \\ (2a-5b)(3a+b)[/tex]
4w-16 60
Simplify your answer as much as possible.
>
.
X Х
5
?
Answer:
w ≤ 19
Step-by-step explanation:
4w−16≤60
Add 16 to both sides.
4w−16+16≤60+16
4w≤76
Divide both sides by 4.
4w/4 ≤ 76/4
w≤19
Answer:
w<=19
Step-by-step explanation:
4w<=60+16
w<=76/4
What is g(-3) in the function g(x) = 4x2 + 3?
Ο Α. - 33
OB. 45
OC. 39
O D. -9
Answer:
39
Step-by-step explanation:
Last Monday, a parking lot had 80 cars. Of those 80 cars, 40% were silver, 20 were red, and the rest were white. What percent of the cars were white?
What percent of the cars were white?
solve 10r-5r+3r-8r plz
Answer:
0
Step-by-step explanation:
Combine like terms and everything cancels out
1) What is the product of (3x + 2) and (x - 7)?
2) What are the factors (multiplier) of 3x2 − 9x ?
Answer both of the questions
Answer:
1) [tex]3x^{2}[/tex]-19x-14
2) x=0, x=3
Step-by-step explanation:
1) (3x+2)(x-7)
Distribute the 3x to both x and -7, as well as the 2 to both x and - 7.
[tex]3x^{2}[/tex] - 21x + 2x -14
Combine like terms
[tex]3x^{2}[/tex] - 19x - 14
2)
In order to find the factors of x, set the expression equal to 0.
[tex]3x^{2}[/tex] - 9x = 0
Factor out the highest common multiple (3x)
3x(x-3) = 0
In order for x to satisfy the equality, you must either have a 0 in the parenthesis -> (x-3)=0 -> x =3
Or 3x = 0 -> x = 0
Hope this helps!
1. Find the value of x. in the below given diagram
Okay so I need to know what 1 + 1 =?
i know but yes i need to know it
Answer:
There are 1,035,779,173,390 different ways to answer 1+1
Step-by-step explanation:
I will give 4 examples
1. quentin trembley, the president on the negative 12 dollar bill.
2. d e s p a s i t o
3.(╭☞・◡・)╭☞ m0nkE bOnK
4. the cold heart of russian winter
at 3 weeks old, a corn is 4 inches tall and at 15 weeks it is 44 inches tall. calculate the rate of change.
Answer:
Im not a hundred percent sure if this is the right answer but im pretty sure it is 3.33333 repeated so the rate of change is 3 inches per week.
Step-by-step explanation:
I calculated the problem by subtracting the weeks from each other subtracting the amount of length corn has grown too. I found that the corn grew 40 inches in 12 weeks. So I divided the amount of weeks and the amount it has grown and it gave me 3.333333 repeated which makes the answer 3 inches per week. correct me if im wrong...
Hope this helps:)
If PQRS is a kite, find m angle Q
Answer:
Q = 35
Step-by-step explanation:
1. You add both (m)x values and y values making them equal to 180 creating a 2 step-equation: (7x+2) + (10x-31) making that 17x-33= 180
2. Now you have a 2 step-equation to solve: 17x-33 = 180-33=147
+-33 +-33
__________
17x = 147/17=21
/17 /17
3. From here with 21, knowing the kite must equal to 180, you add 21 to the other angle 124: 124+21=145
4. Seeing that you don't have a total of 180, you now subtract 145 from 180 in order to get the value of Q: 180-145= 35
Q= 35
Step-by-step explanation:
7x + 2 = 10x - 31
33 = 3x
x = 11
so, 7x + 2 = 7( 11 ) +2 = 79°
10x - 31 = 10( 11 ) - 31 = 79°
ΔP + ΔQ + ΔR + ΔS = 360°
79° + ΔQ + 79° + 124° = 360°
ΔQ + 282° = 360°
ΔQ = 360° - 282°
ΔQ = 78°
Find the solution of the system of equations.
−x−3y= −3
x−6y= −24
Answer:
(-6 , 3)
Step-by-step explanation:
-x-3y= -3
x-6y= -24
1. solve each eq so they make x=___
-x = -3 + 3y
x= 3 - 3y
and
x = -24 + 6y
2. set = to each other and solve for y
3 - 3y = -24 + 6y
27 = 9y
y = 3
3. plug the y value into one of the x=__ eq's and solve for x
x = 3 - 3y
x = 3 - 3(3)
x = 3 - 9
x = - 6
your solution is ( -6 , 3 )
I need help please this is due in like 20
Minutes i don’t understand this please !
Find the surface area of the cylinder
5 mm
2 mm
Answer:
1|3
Step-by-step explanation:
slo osma uetacunsecuescia
please help me with these last ones i need
Answer:
20 8 12 10
Step-by-step explanation:
Answer:
for 5. the answer is 15.
for 6. the answer is 8
Step-by-step explanation
hope this helped u again!!!!!!!!!!!!!!!!!!!!!!
Help quick pls
which figure is the image of figure 1 after reflection over the y-axis and a translation 3 units down?
The image of figure 1 after reflection over the y-axis and a translation 3 units down is figure B.
What is the reflection on y-axis?When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Coordinates of figure 1 are (-1, 1), (-1, 2), (-2, 2), (-3, 1), (-2, 4) and (-3, 4)
Reflection on y-axis, we get
(1, 1), (1, 2), (2, 2), (3, 1), (2, 4) and (3, 4)
Translation 3 units down
(1, 1-3), (1, 2-3), (2, 2-3), (3, 1-3), (2, 4-3) and (3, 4-3)
(1, -2), (1, -1), (2, -1), (3, -2), (2, 1) and (3, 1)
Figure B has following coordinate points, (1, -2), (1, -1), (2, -1), (3, -2), (2, 1) and (3, 1)
Therefore, the image of figure 1 after reflection over the y-axis and a translation 3 units down is figure B.
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