Answers
Answer:
Step-by-step explanation:
I used calculus for this, as I'm not sure there's any other way to do it and to do it as easily. This is the volume of a solid found by using the disk method of rotation:
[tex]V=\pi\int\limits^a_b {[R(x)]^2-[r(x)]^2} \, dx[/tex]
where R(x) is the outer shell of the solid and r(x) is the space inbetween the solid and the axis of rotation. There is no space between the solid and the axis of rotation, so r(x) = 0. R(x) is the height of the solid which is 3. Therefore, f(x) = 3 and that's the function we put into the formula with the lower bound of 3 and the upper bound of 5:
[tex]V=\pi\int\limits^5_3 {3^2}-0^2 \, dx[/tex] and
[tex]V-\pi\int\limits^5_3 {9} \, dx[/tex] and integrating:
[tex]V=\pi(9x\left \} {{5} \atop 3}} \right.[/tex] and using the First Fundamental Theorem of Calculus:
V = π(9(5) - 9(3)) and
V = π(45 - 27) so
V = 18π units cubed or in decimal format,
V = 56.549 units cubed
Related Questions
The sides of a triangle are 3x+ 2, 6x, and 5x. Find the expression to represent the perimeter. To find the perimeter, we ADD the three sides
Answers
Answer:
3x+2+6x+5x
Step-by-step explanation:
perimeter of triangle = side 1 + side 2 + side 3
expression of the perimeter of triangle 3x+2+6x+5x
perimeter of traingle = 14x + 6
The expression 14x + 2 represents the perimeter of the triangle in terms of "x."
To find an expression that represents the perimeter of a triangle.
The perimeter is the sum of all three sides of the triangle. We have three sides with different lengths given by the expressions 3x + 2, 6x, and 5x. To find the expression representing the perimeter, we just need to add these three sides together.
Let's represent the sides as follows:
- The first side of the triangle is denoted as "a," which has a length of 3x + 2.
- The second side is denoted as "b," with a length of 6x.
- The third side is denoted as "c," having a length of 5x.
Now, let's find the expression for the perimeter, which we'll call "P." To do that, we add the three sides together:
P = a + b + c
Substitute the given expressions for the sides into the equation:
P = (3x + 2) + (6x) + (5x)
Now, let's simplify the expression by combining like terms (terms with the same variable "x"):
P = 3x + 2 + 6x + 5x
To further simplify, add the coefficients of the "x" terms:
P = (3 + 6 + 5)x + 2
Now, add the coefficients: 3 + 6 + 5 = 14, so the expression for the perimeter becomes:
P = 14x + 2
The expression 14x + 2 represents the perimeter of the triangle in terms of "x."
To know more about Perimeter here
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What is the standard deviation of the following data set rounded to the nearest tenth? 300,785,670,187,760,724
Answers
Answer:
S.D = 236.5
~~~~~~~~~~~~~~~~~~
300,
785,
670,
187,
760,
724
Answer:
300, 790, 670, 190, 760, 720
F(x)=-x^2+2mx+2m-3 with x<0
Answers
Answer:
m<√-3 OR m<√3i
Step-by-step explanation:
f(x)=x²+2m(x+1)-3
with x<0
b²-4ac<0
(2m)²-4(1×-3)<0
4m²+12<0
4m²<-12
m²<-12/4
m²<-3
m<√-3 OR m<√3i
Which expression is equivalent to (x^-6/x-2)^3
Answers
Answer:
= (6/x - 2)^3
A piece of fabric is 1/3 yard by 3 5/8 yards.
Irma solves 1/3*3 5/8 to find the area of the fabric in square yards.
Enter numbers to complete Irma's calculation for the area. (TTM)
Answers
Answer:
favricis 1/3 yard bt 3 5/8 yards wich it will be 64
Given the points (3, -1) and (-8, 0) find the slope.
Answers
Answer:
Step-by-step explanation:
(x₁ , y₁) = (3,-1) &(x₂,y₂) = (-8, 0)
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{0-[-1]}{-8-3}\\\\=\frac{0+1}{-11}\\\\=\frac{1}{-11}\\\\=\frac{-1}{11}[/tex]
Solve for x.
x - 42 = 98 – 9x
x = [?]
Answers
Answer:
x=14
Step-by-step explanation:
x - 42 = 98 – 9x
x+9x=98+42
10x=140
x=14
Answer:
[tex]x - 42 = 98 - 9x \\ x + 9x = 98 + 42 \\ 10x = 140 \\ x = 14 \\ thank \: you[/tex]
The local tennis club needed new tennis balls. To pay for all the new balls, each person in the club donated $12.45. The bill for the new balls came to a total of $510. The club had $50.25 left over and decided to put it towards their end of year Christmas party. How many people are members at the tennis club?
Answers
Answer:
45 people are members at the tennis club
Step-by-step explanation:
Let the number of people in the tennis club be denoted as "x".
Since each of them donated $12.45, then total donated = 12.45x
Since they had $50.25 left over after paying the cost of $510 for the ball, then;
12.45x - 510 = 50.25
12.45x = 510 + 50.25
12.45x = 560.25
x = 560.25/12.45
x = 45
the product of two consecutive terms of the Arithmetic sequence 5,8,11.....is 598.find the position of the term?
Answers
Answer:
Step-by-step explanation:
Common difference is 3.
Let x be a term in the sequence. The next term in the sequence is x+3.
x(x+3) = 598
x² + 3x - 598 = 0
x = [-3 ± √(3²-4⋅1(-598))]/[2⋅1] = [-3 ± 49]/2 = 23, -26
-26 is an extraneous solution, so x = 23.
The two terms are 23 and 26.
Please answer correctly and I will give brainliest and crown plus an extra 20 points
Answers
Answer:
30.28 yd²
Step-by-step explanation:
Area enclosed = area of trapezoid + area of semicircle
= ½(a + b)*h + ½(πr²)
Where,
a = 5 yd
b = 2 + 5 = 7 yd
h = 4 yd
r = ½(4) = 2 yd
Plug in the known values
Area enclosed = ½(5 + 7)*4 + ½(π*2²)
Area enclosed = ½(12)*4 + ½(π*4)
= 6*4 + π*2
= 24 + 2π
= 30.2831853
≈ 30.28 yd² (2 decimal places)
In the diagram below, what is the approximate length of the minor arc AB?
Answers
Answer:
The answer is "Option C"
Step-by-step explanation:
Given:
[tex]r= 30 \ cm\\\\\theta =60^{\circ}[/tex]
Using formula:
[tex]\frac{A}{\theta}=\frac{\pi r^2}{2\pi}\\\\\frac{A}{\theta}=\frac{\pi r^2}{2}\\\\A=\frac{r^2\times \theta}{2}[/tex]
A pancake recipe requires two and two thirds cups of milk to one cup of flour. If four and two thirds cups of milk is used, what quantity of flour will be needed, according to the recipe?
Answers
Answer:
There will need to be 2 and 1/3 cups of flour according to the recipe
Step-by-step explanation:
Given the recipe, we can say that for each 2 and 2/3s cups of milk, one cup of flour is used. We can write this as ( 2 + 2/3) cups of milk / (1) cup of flour.
We can also write 2 + 2/3 as 2*(3/3) + 2/3 = 6/3 + 2/3 = 8/3, making our ratio
(8/3) / 1
The ratio stays the same, no matter how many cups of milk or flour are used. Therefore, (8/3) /1 = (4 + 2/3) / cups of flour
Writing our final cups of flour as c, we can say
(8/3) / 1 = (4+2/3) / c
(4+2/3)/c = (12/3 + 2/3) /c = (14/3) /c
(8/3)/1 = (14/3) /c
anything divided by 1 is equal to itself
(8/3) = (14/3)/c
multiply both sides by c to make the variable not a denominator
(8/3) * c = 14/3
multiply both sides by 3 to remove the denominators
8 * c = 14
divide both sides by 8 to isolate the c
c = 14/8 = 7/3 = 6/3 + 1/3 = 2 + 1/3
There will need to be 2 and 1/3 cups of flour according to the recipe
Please help me I’m struggling
Answers
Answer:
1st box: 49
2nd box: 7
3rd box: 7
4th box: 2
5th box (above): 1
6th box (below): 3
7th box: 7
8th box: -12
9th box: -2
Which graph represents the function f (x) = 3 times 5 to the second power?
Answers
Please help me answer this question
Answers
Answer:
a, 14.13. b, 39.25
Step-by-step explanation:
so for a the diameter is 6 so the radius is 3. The equation for the area of the circle is πr2. So 3x3=9. then 9x3.14=28.26. But then we have to divide by two cause we are finding only the shaded area. 28.26/2=14.13.
A is 14.13
for b, its the same thing, so the radiu is 5 and 5x5=25. 25x3.14=78.5, and divide two, so 78.5/2=39.25.
B is 39.25
WARNING: I am not sure this is correct, so if this is wrong i'm sorry, i'm learning too :)
I don’t get number 5 someone help
Answers
Answer:
B
Step-by-step explanation:
We do 20 percent of 2500 which comes to 1500 and then you do plus 325 which gives you 2625
a)out of 300 students In a class 60% of the students took physics and 35 students took chemistry and 20% of the students did not take any of this subject. how many students take both the subject
Answers
Answer:
25 students take both subjects.
Step-by-step explanation:
Solve for 60% of 300 students:
60/100 = x/300
Cross multiply:
60 × 300 = 100 × x
18000 = 100x
Divide both sides by 100:
180 = x
Solve for 20% of 300 students:
20/100 = x/300
20 × 300 = 100 × x
6000 = 100x
60 = x
Solve for the percentage of students in chemistry:
x/100 = 35/300
x × 300 = 100 × 35
300x = 3500
x = 11.66666...7
x = about 11.7%
Find the difference in percentages:
100 - 60 - 20 - 11.7
8.3
8.3% take both subjects
Solve for 8.3% of students:
8.3/100 = x/300
8.3 × 300 = 100 × x
2490 = 100x
24.9
About 25 students
Check your work by adding all the students together (to get to 300):
25 + 60 + 180 + 35
300 students total
This is correct!
What graph below shows the solution for the linear inequality y ≥ -1/3x+1?
Answers
Answer:
b
Step-by-step explanation:
i just answered it
Answer:
D
I can suggest some insight how to analyze this type of problem...
1) the y intercept has to be 1... they all are so no help
2) the slope is negative, they all are so no help
3) the sign is ≥ so the "fill" goes up ... A or D
4) the ≥ means that the line has to be SOLID not a dash ONLY D left.
Step-by-step explanation:
This ellipse is centered at the
origin. Find its equation.
Vertices: (0,-6) and (0,6)
Foci: (0,-2) and (0,2)
y?
X^2/[?] + y^2/[?] =1
Answers
Answer:
Equation of Ellipse is [tex]\frac{x^{2} }{32} +\frac{y^{2} }{36} =1[/tex]
Step-by-step explanation:
Let's find the value for [tex]a^{2}[/tex] and [tex]b^{2}[/tex] to write the equation for vertical ellipse.
Here 'a' is the distance from center to one of the vertices.
"b" is the distance from center to one of the Co-vertices. We need to find this using formula [tex]a^{2} -b^{2} =c^{2}[/tex]
'c' is the distance between center to one of the Foci.
In this problem center is origin.
So, a =6(because distance between(0,0) and (0,6) is 6)
c= 2 (because distance between (0,0) and (0,2) is 2)
Plug in the known values into the formula [tex]a^{2} -b^{2} =c^{2}[/tex]
36-[tex]b^{2}[/tex]= 4
Subtract both sides 36
[tex]-b^{2}[/tex] = -32
Divide both sides by -1
[tex]b^{2}[/tex] =32
So, equation would be
[tex]\frac{x^{2} }{32} +\frac{y^{2} }{36} =1[/tex]
Addy is making two different recipies for the school bake sale. The brownie recipie calls for 2/3 cups of milk and the cut out cookie recipie calls for 3/4 cup of milk. How much total milk will Addy need to make both her recipies?
Answers
you just got to sum up the two fractions.
[tex]\frac{2}{3} +\frac{3}{4}[/tex] = [tex]\frac{8}{12} + \frac{9}{12}[/tex] = [tex]\frac{17}{12}[/tex]
she will need 17/12 cups of milk
hope it helps :)
Casey is kayaking on a lake. It took Casey 20 minutes to travel 0.4 miles. How many miles will he kayak in 2 hours?
Answers
Answer:
2.4 miles
Step-by-step explanation:
0.4 / 20 = 0.02
0.02 x 120
= 2.4
Someone please help me solve this
Answers
Answer:
Step-by-step explanation:
[tex]4[/tex] ± [tex]\frac{\sqrt{(-4)^{2} - 4(11) 8} }{2(11)}[/tex]
Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
|m^2+n^2|
Answers
Answer:
34
Step-by-step explanation:
We are here given a modulus expression and we need to find out the value when m = -5 and n = 3 .
Modulus :- It always gives positive value . For example ,
[tex]\rm\implies |-a| = a [/tex]
[tex]\rm\implies |a| = a [/tex]
The given modulus expression is :-
[tex]\rm\implies |m^2+ n^2| [/tex]
As the number inside the modulus operator are already squared therefore they will always give positive value for real numbers . Here we can omit the modulus .
[tex]\rm\implies m^2 + n^2 [/tex]
Plug in the given values ,
[tex]\rm\implies (-5)^2 + 3^2 [/tex]
Solve 5² and 3² and add them ,
[tex]\rm\implies 25 + 9 [/tex]
On adding ,
[tex]\rm\implies 34 [/tex]
Therefore ,
[tex]\rm\implies \boxed{\blue{\rm |m^2+n^2| = 34 }}[/tex]
Hence the required answer is 34 .
does this table represent a function? Why or why not?
X: 2 2 3 4 5
Y: 1 4 4 2 5
Please answer it ASAP
Answers
the diameter of a bicycle wheel is 71 cm. calculate the circumference of the wheel
Answers
Answer:
233.05
Step-by-step explanation:
take the diameter and divide it by 2, that will give you the radius. Take the radius and multiply it by 2 then by pi. That will give you the circumference. So for the this question it would be:
71 divided by 2 = 35.5cm
35.5 x 2 x pi = 233.05
SOMEONE HELP ME PLEASE
Answers
Answer:
what are the answer choicesss
Step-by-step explanation:
What is the solution to the linear equation?
x – StartFraction 2 Over 3 EndFraction x minus StartFraction one-half EndFraction equals StartFraction 1 Over 3 EndFraction plus StartFraction 5 Over 6 EndFraction x. = + x
x = –5
x = –negative StartFraction 1 Over 6 EndFraction
x = StartFraction 1 Over 6 EndFraction
x = 5
Central and Eastern Europe experienced ethnic tensions in the early 1900s primarily because
Answers
Answer:
Step-by-step explanation:
what is the best estimate for the value of 3/2
Answers
Answer:
[tex]1\frac{1}{2}[/tex] or 1.33%
Step-by-step explanation:
Please need help asap
Answers
Answer:
in which class you are if you are in 7 the ans will be -3.
find the original price if the price was 420 after a 10% discount
Answers
Answer:
466.67
Step-by-step explanation:
Let p be the original price
p - 10 % p = 420
p - .10p = 420
.9p = 420
Divide each side by .9
.9p/.9 = 420/.9
p =466.666666
Rounding to the nearest cent
p = 466.67
