Answer:
V = π ∫₀² (y² − 8y + 6√(2y)) dy
or
V = π ∫₀² (6x − 5x² + x³) dx
Step-by-step explanation:
y₁ = 0.5x²
y₂ = x
First, find the intersections of the curves.
0.5x² = x
x² = 2x
x² − 2x = 0
x (x − 2) = 0
x = 0 or x = 2
So the points of intersection are (0, 0) and (2, 2).
When we revolve this region about the line x = 3, we get a hollow shape that looks like an upside-down funnel, or a volcano.
One option is to use washer method to find the volume, by cutting a thin horizontal slice of thickness dy, inner radius 3−x₁ = 3−√(2y), and outer radius of 3−x₂ = 3−y.
V = ∫₀² π [(3−y)² − (3−√(2y))²] dy
V = ∫₀² π (9 − 6y + y² − 9 + 6√(2y) − 2y) dy
V = π ∫₀² (y² − 8y + 6√(2y)) dy
Another option is to use shell method to find the volume, by cutting a thin vertical slice of thickness dx, radius 3−x, and height y₂−y₁ = x−0.5x².
V = ∫₀² 2π (3 − x) (x − 0.5x²) dx
V = ∫₀² 2π (3x − 1.5x² − x² + 0.5x³) dx
V = ∫₀² 2π (3x − 2.5x² + 0.5x³) dx
V = π ∫₀² (6x − 5x² + x³) dx
The second option is arguably easier to evaluate, but either one will get you the same answer (V = 8π/3).
Find the volume of the cylinder
Volume:-
πr^2hπ(16)^2(17.5)π(256)(17.5)4480πmm^2train covers 20 km in one hour then how much distance will it cover in 1 min?
[tex]\sf\large\underline{Given:-}[/tex]
Speed of the train = 20km / 1hr.
[tex]\rightarrow[/tex] 1 hour = 60 minutes.
So, speed of the train = 20km/60min.
[tex]\sf\large\underline{To\: Find:-}[/tex]
[tex]\rightarrow[/tex]Distance covered by train in 1min.
[tex]\sf\large\underline{Solution:-}[/tex]
Let the distance covered by train in 1 min be [tex]\sf{x}[/tex] m.
So, if train covers 20 km in 60min then it covers [tex]\sf{x}[/tex] m in 1 min.
It can be written as,
[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}}[/tex] [tex]\sf{=\frac{x}{1}}[/tex](by cross multiplication)
[tex]\rightarrow[/tex][tex]\sf{20\: = \: 60x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}= x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{1}{3}= x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{0.33= x}[/tex](approx)
Therefore, distance covered by train in 1 min= 0.33km (approx).
_______________________________
Hope it helps you:)
Bobs store is making money selling products and he has $200 in his bank account. He saves $50 every week. How much money does bob have after 10 weeks.
W = Weeks
T = Total
Answer in equation
the rectangle below initially has dimensions of 10 inches and 14 inches as shown. after both dimensions have been increased by a length of x, the total area of the resulting rectangle is 320 square inches. algebraically determine the value of x.
The value of x determined algebraically given the total area of the rectangle is 1.5 inches
How to find area of a rectangleInitial dimensions:
Length = 14 inches
Width = 10 inches
New dimensions:
Length = 14 + x
Width = 10 + x
Area = 320 square inches
Area of a rectangle = Length × Width
320 = (14 + x) × (10 + x)
320 = 14x × 10x
320 = 140x²
x² = 320/140
x² = 2.28571428571428
x = √2.28571428571428
x = 1.511857892036908908858066144936720243
Approximately,
x = 1.5
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A student could run 2 miles. After extensive training, the student could run five times as far as she could before the training. How far can the student run now?
Answer:
10 miles
Step-by-step explanation:
He could run 2 miles.
Now he can run 5 times as far.
Now he can run 5 times 2 miles.
5 × 2 miles = 10 miles
QUESTION 20
Find the rate of interest required to achieve the conditions set forth.
A = $32,000
P = $8,000
t = 20 years
compounded annually
3.5265%
8%
5.6467%
7.1773%
The rate of interest required to achieve the conditions set forth is 7.1773%.
What is the interest rate?The interest rate is the rate at which the investment increases. The formula that can be used to determine interest rate is:
g = (FV / PV)^(1/N) - 1
Where:
FV = future value = $32,000PV = present value = $8000 n = number of years4^(1/20) - 1 = 7.1773%
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An arrow is shot vertically upward at a rate of 160 feet per second from ground level. Use the projectile formula
h
=
−
16
t
2
+
v
0
t
+
h
0
h
=
-
16
t
2
+
v
0
t
+
h
0
to determine when the height of the arrow will be 114 feet.
Answer:
0.772 seconds; 9.228 seconds
Step-by-step explanation:
The given projectile formula with the given numbers filled in is ...
[tex]\displaystyle h=-16t^2+v_0t+h_0\\\\114=-16t^2+160t[/tex]
We can "complete the square" to solve this for t, the times at which the height is 114 feet.
16(t² -10t) = -16(7.125) . . . . . rearrange, showing factor of 16
t² -10t +25 = -7.125 +25 . . . . divide by 16, add 25 to complete the square
t = 5 ±√17.875 ≈ 5 ± 4.228 . . . . take the square root, add 5
t ∈ {0.772, 9.228}
The arrow is 114 feet high after 0.772 seconds and again after 9.228 seconds.
Louisa is 5 feet 4 inches tall.
How tall is she in inches?
Answer: 64 inches
Step-by-step explanation:
Suppose you have a data set that includes the values 20, 30, and 50. If you add a fourth value to this data set, and after doing that the mean of the data set is 50, what was the value that you added? a. -10 c. 50 b. 40 d. 100 Please select the best answer from the choices provided A B C D
Answer:
D. 100
Step-by-step explanation:
Mean = Sum of all numbers divided by the count of all numbers
Mean = 50
Let say that the sum of all numbers = X
50 = X / 4
200 = X
X = (20+30+50) + The 4th Value
200 = 100 + 4th Value
The 4th Value = 100
What is the value of x?
Enter your answer in the box.
X =
Answer: x=20
Step-by-step explanation:
(6x-10)=(3x+50) (subtract both sides by 3x)
3x-10=50(add ten to both sides)
3x=60(divide both sides by 3)
x=20
John's employer increased his annual salary of $55,000 by $5,700. What percent was his raise, rounded to the nearest tenths place?
Answer:
3.64% (when rounded to the nearest hundredth)
Step-by-step explanation:
I'm assuming by 5700 you actually mean 57,000.
Calculate the percent change:
(57,000-55,000)/55,000 *100
(2000/55000)x100
0.036363x100
3.6363 rounded to the nearest hundredth is 3.64
Mindy has already saved $20 and plans to save $8 each month.Georgette has no money saved yet but plans to to save $5 each month.Will the girls ever have saved the same amount?
Answer:
no
Step-by-step explanation:
because mindy has already saved $20 and is putting $8 which is more than the amount georgette is putting (monthly) and plus georgette has no money saved so basically mindy will have more money saved
If the difference of 3 / 4 and 1 / 6 of a number is 7, find the number and also verify your answer.
The computation of the equation illustrates that the number will be 46.4.
How to solve the equation?Let the number be represented as x.
Therefore, the the difference of 3 / 4 and 1 / 6 of a number is 7 will be computed as follows:
(1/6 × x) - 3/4 = 7
0.167x = 7 + 3/4
0.167x = 7.75
x = 7.75/0.167
x = 46.4
Therefore, the number is 46.4.
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HELPPPPPPPP 50PTSSSSSS!!!!!!!!!
#1
Paved area:-
L(12)=205-7(12)=205-84=121mi#b
Let's see
205-7d=1567d=205-1567d=49d=7daysAnswer:
(a) 121 miles
(b) 7 days
Step-by-step explanation:
Given function:
[tex]\sf L(d)=205-7d[/tex]
Question (a)
When d = 12:
[tex]\sf \implies L(12)=205-7(12)[/tex]
[tex]\sf =205-84[/tex]
[tex]\sf =121 \ miles[/tex]
Therefore, the crew has 121 miles left to pave after 12 days.
Question (b)
When L(d) = 156
[tex]\sf \implies 156=205-7d[/tex]
[tex]\sf \implies 7d=205-156[/tex]
[tex]\sf \implies 7d=49[/tex]
[tex]\sf \implies d=\pm\sqrt{49}[/tex]
[tex]\sf \implies d=\pm7[/tex]
As distance is positive, [tex]\sf d=7[/tex] only
Therefore, the crew has been paving the the road for 7 days.
Calculus hw, need help asap with steps.
Answers are in bold
S1 = 1
S2 = 0.5
S3 = 0.6667
S4 = 0.625
S5 = 0.6333
=========================================================
Explanation:
Let [tex]f(n) = \frac{(-1)^{n+1}}{n!}[/tex]
The summation given to us represents the following
[tex]\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=\sum_{n=1}^{\infty} f(n)\\\\\\\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=f(1) + f(2)+f(3)+\ldots\\\\[/tex]
There are infinitely many terms to be added.
-------------------
The partial sums only care about adding a finite amount of terms.
The partial sum [tex]S_1[/tex] is the sum of the first term and nothing else. Technically it's not really a sum because it doesn't have any other thing to add to. So we simply say [tex]S_1 = f(1) = 1[/tex]
I'm skipping the steps to compute f(1) since you already have done so.
-------------------
The second partial sum is when things get a bit more interesting.
We add the first two terms.
[tex]S_2 = f(1)+f(2)\\\\S_2 = 1+(-\frac{1}{2})\\\\S_2 = \frac{1}{2}\\\\S_2 = 0.5\\\\\\[/tex]
The scratch work for computing f(2) is shown in the diagram below.
-------------------
We do the same type of steps for the third partial sum.
[tex]S_3 = f(1)+f(2)+f(3)\\\\S_3 = 1+(-\frac{1}{2})+\frac{1}{6}\\\\S_3 = \frac{2}{3}\\\\S_3 \approx 0.6667\\\\\\[/tex]
The scratch work for computing f(3) is shown in the diagram below.
-------------------
Now add the first four terms to get the fourth partial sum.
[tex]S_4 = f(1)+f(2)+f(3)+f(4)\\\\S_4 = 1+(-\frac{1}{2})+\frac{1}{6}-\frac{1}{24}\\\\S_4 = \frac{5}{8}\\\\S_4 \approx 0.625\\\\\\[/tex]
As before, the scratch work for f(4) is shown below.
I'm sure you can notice by now, but the partial sums are recursive. Each new partial sum builds upon what is already added up so far.
This means something like [tex]S_3 = S_2 + f(3)[/tex] and [tex]S_4 = S_3 + f(4)[/tex]
In general, [tex]S_{n+1} = S_{n} + f(n+1)[/tex] so you don't have to add up all the first n terms. Simply add the last term to the previous partial sum.
-------------------
Let's use that recursive trick to find [tex]S_5[/tex]
[tex]S_5 = [f(1)+f(2)+f(3)+f(4)]+f(5)\\\\S_5 = S_4 + f(5)\\\\S_5 = \frac{5}{8} + \frac{1}{120}\\\\S_5 = \frac{19}{30}\\\\S_5 \approx 0.6333[/tex]
The scratch work for f(5) is shown below.
Noah walked a family’s dog 5 times this past month and earned the same amount each time. To thank him, the family gave him an extra $6 at the end of the month. Noah earned $106 from dog walking.
1- This situation IS represented by the tape diagram.
2- This situation IS NOT represented by the tape diagram.
The situation IS NOT represented by the tape diagram.
How to represent the situationNumber of times Noah walked the dog = 5Amount earned each time = sExtra amount earned = $6Total amount earned = $106The situation can be represented by the equation:
s + s + s + s + s + 6 = 106
5s + 6 = 106
5s = 106 - 6
5s = 100
s = 100/5
s = 20
Therefore, the amount Noah earned each time he walked the dog is $20
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Evaluate the expression 21 ÷ 3 + 8 − 4. 19 17 15 11
Answer:
Your answer is D, 11
Step-by-step explanation:
PEMDAS, first you divide, 21/3 is 7
7+8 is 15
15 - 4 is 11
Hope this helps! :)
Answer:
[tex]\boxed{\sf{11}}[/tex]
Step-by-step explanation:
Solving this problem requires an order of operations.
PEMDAS stands for:
ParenthesisExponentsMultiplyDivideAddSubtract21÷3+8-4First, divide.
[tex]\sf{21\div3+8-4}[/tex]
[tex]\sf{21\div3=7}[/tex]
Then rewrite the problem.
[tex]\sf{7+8-4}[/tex]
Add.
[tex]\sf{7+8=15}[/tex]
Subtract.
[tex]\sf{15-4=\boxed{\sf{11}}[/tex]
11
Therefore, the correct answer is 11.
I hope this helps you! Let me know if my answer is wrong or not.
Diego is flying from Philadelphia to Barcelona. On the trip to Barcelona, the plane flies at a constant cruising
speed of 550 mph.
reaches its cruising speed, which is
On the trip home, Diego makes a chart of the plane's progress once
constant
Which is faster the cruising speed on the flight from Philadelphia to Barcelona, or the cruising speed on the flight home?
Hour
1
2
3
A
Miles
530
1060
1590
US
Choose 1 answer:
Со
The cruising speed on the flight from Philadelphia to Barcelona
The cruising speed on the flight home
Pro
Pro
© The two cruising speeds are the same.
The faster speed is the cruising speed on the flight from Philadelphia to Barcelona.
Which speed is faster?
Average speed is the total distance travelled per time. It is used to determine how fast an object is moving with respect to time.
Average speed = total distance / total time
Average speed on the flight back home = 530 / 1 = 530 mph
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Find the missing factor.
200 x ____ = 600
A) 2
B) 3
C) 4
D) 5
Answer:
B. 3
Step-by-step explanation:
we know 2x3 = 6 soo just add 2 zeros = 600
A school's principal wanted to give a special 'Good Luck' pencil for each student in the fifth grade. If there are 105 kids in the fifth grade, and there are 12 pencils in each box, how many boxes will he need to buy?
Answer:
9
Step-by-step explanation:
He would need to by 9 boxes. There might be some left over pencils.
Lily is 90 cm tall. If Anika is 3/5 of the height of Lily, and Sadaf is 4/3 of the height of Anika, how tall is Sadaf?
Can someone help me with this question?
Step-by-step explanation:
hope it helps, I have chegg and they seem to have more answers and a lot of topics. you can scan your books bar code and get end of chapter questions
A Goodyear Blimp is positioned at a height of 1,500 feet over the M&T
Bank Stadium to broadcast the Baltimore Ravens game. The blimp is
observed by a car of fans as they look upward at an angle of 22º.
Another car closer to the stadium can see the blimp if they look
upward at an angle of 65º.
DEOOV
כשע
Figure not
drawn to scale
1500 ft
65
22
x ft.
Determine x, the distance between the two cars.
The distance between two cars comes to be 4412.06 feet.
Find the attached diagram to visualize it better.
From the attached diagram
The Distance between two cars is x+y
The angle of elevation for the first car = 22 degrees
The angle of elevation for the second car = 65 degrees.
Height of the Goodyear blimp = 1500 feet
What is the tangent of an angle?The tangent of an angle is the ratio of the opposite side to the adjacent side of that angle.
So, tan 22° = 1500/x
So, x= 1500/tan 22°
x = 3712.63 feet
tan 65° = 1500/y
So, y = 1500/tan 65°
y = 699.46 feet
x+y = 4412.06 feet
So, the distance between two cars = 4412.06 feet
Therefore, the distance between two cars comes to be 4412.06 feet.
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For f(x) = 2x+1 and g(x) = y2 - 7, find (f+ g)(x).
Answer:
D
Step-by-step explanation:
When you look for (f+g)(x), we are in essence say that we're looking for f(x)+g(x)
=(2x+1)+(x^2-7). (substitute for f(x) and g(x))
=2x+1+x^2-7. (remove the brackets by substituting positive 1 into g(x))
=2x+x^2-6 (add like terms- in this case 1-7=6)
=x^2+2x-6 (rearrange the equation)
In the rectangular pyramid below, l=30, w=20, and h=28. What is the length of s?
Answer:
A=lw+l(w
2)2+h2+w(l
2)2+h2=30·20+30·(20
2)2+282+20·(30
2)2+282≈2127.25933
Your answer is 2127.259
I think it will help you
If "s" represents the slant height in the rectangular pyramid with dimensions l = 30, w = 20, and h = 28, then the length of "s" is approximately 29.75 units.
To find the length of "s" in the rectangular pyramid, we first need to understand the terminology used to describe the different dimensions of a pyramid.
In a rectangular pyramid, "l" usually represents the length of the base, "w" represents the width of the base, and "h" represents the height of the pyramid (the perpendicular distance from the base to the apex or top vertex of the pyramid).
However, there is no standard notation for the length of the slant height (s) in a rectangular pyramid. In this context, the term "s" could represent either the slant height or some other unknown dimension of the pyramid.
If "s" represents the slant height of the pyramid, we can use the Pythagorean theorem to find its value. The slant height, "s," is the hypotenuse of a right triangle formed by one of the triangular faces of the pyramid and the height and half the width of the base.
Using the given dimensions:
l = 30 (length of the base)
w = 20 (width of the base)
h = 28 (height of the pyramid)
Let's find the value of "s" using the Pythagorean theorem:
[tex]s^2 = h^2 + (w/2)^2\\s^2 = 28^2 + (20/2)^2\\s^2 = 28^2 + 10^2\\s^2 = 784 + 100\\s^2 = 884\\[/tex]
Now, take the square root of both sides to find the value of "s":
s ≈ √884
s ≈ 29.75 (rounded to two decimal places)
So, if "s" represents the slant height in the rectangular pyramid with dimensions l = 30, w = 20, and h = 28, then the length of "s" is approximately 29.75 units.
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There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete?
Answer:
85 dogs have signed up to compete
Step-by-step explanation:
its 85 small dogs because 49+36=85
To carpet a rectangular room, Erika must find the area of the floor. If the dimensions of the room are 9 yd by 15 yd, how much carpeting does she need?
Erika will need ______of carpeting?
Answer:
135 square yards
Step-by-step explanation:
9 yd * 15 yd = (9 * 15) yd^2 = 135 yd^2
Translate the sentence into an equation.
Eight times the sum of a number and 4 is 3.
Use the variable x for the unknown number.
Answer:
8(x+4)=3
Step-by-step explanation:
the answer is this!
DRAW a model of 1/2 ÷ 4 if i see a link im going to report
Answer:
1/8
Step-by-step explanation:
hi there im giving brainliest to the most accurate answer.