The Volume of the given solid using polar coordinate is:[tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
V= [tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
What is Volume of Solid in polar coordinates?
To find the volume in polar coordinates bounded above by a surface z=f(r,θ) over a region on the xy-plane, use a double integral in polar coordinates.
Consider the cylinder,[tex]x^{2}+y^{2} =1[/tex] and the ellipsoid, [tex]4x^{2}+ 4y^{2} + z^{2} =64[/tex]
In polar coordinates, we know that
[tex]x^{2}+y^{2} =r^{2}[/tex]
So, the ellipsoid gives
[tex]4{(x^{2}+ y^{2)} + z^{2} =64[/tex]
4([tex]r^{2}[/tex]) + [tex]z^{2}[/tex] = 64
[tex]z^{2}[/tex] = 64- 4([tex]r^{2}[/tex])
z=± [tex]\sqrt{64-4r^{2} }[/tex]
So, the volume of the solid is given by:
V= [tex]\int\limits^{2\pi}_ 0 \int\limits^1_0{} \, [\sqrt{64-4r^{2} }- (-\sqrt{64-4r^{2} })] r dr d\theta[/tex]
= [tex]2\int\limits^{2\pi}_ 0 \int\limits^1_0 \, r\sqrt{64-4r^{2} } r dr d\theta[/tex]
To solve the integral take, [tex]64-4r^{2}[/tex] = t
dt= -8rdr
rdr = [tex]\frac{-1}{8} dt[/tex]
So, the integral [tex]\int\ r\sqrt{64-4r^{2} } rdr[/tex] become
=[tex]\int\ \sqrt{t } \frac{-1}{8} dt[/tex]
= [tex]\frac{-1}{12} t^{3/2}[/tex]
=[tex]\frac{-1}{12} (64-4r^{2}) ^{3/2}[/tex]
so on applying the limit, the volume becomes
V= [tex]2\int\limits^{2\pi}_ {0} \int\limits^1_0{} \, \frac{-1}{12} (64-4r^{2}) ^{3/2} d\theta[/tex]
=[tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(64-4(1)^{2}) ^{3/2} \; -(64-4(2)^{0}) ^{3/2} ] d\theta[/tex]
V = [tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
Since, further the integral isn't having any term of [tex]\theta[/tex].
we will end here.
The Volume of the given solid using polar coordinate is:[tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
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30. The average of a list of 4 numbers is 92.0. A new list
of 4 numbers has the same first 3 numbers as the
original list, but the fourth number in the original list
is 40, and the fourth number in the new list is 48. What
is the average of this new list of numbers?
F. 81.0
G. 92.0
H. 94.0
J. 94.4
K. 96.6
Answer:
H. 94.0
Explanation:
The original list: [tex]a _1[/tex] [tex]a _2[/tex] [tex]a _3[/tex] [tex]40[/tex]
The new list: [tex]a_1[/tex] [tex]a_2[/tex] [tex]a_3[/tex] [tex]48[/tex]
[tex]\frac{a_1+a_2+a_3+40}{4} =92[/tex]
[tex]a_1+a_2+a_3=92[/tex] × [tex]4-40=328[/tex]
[tex]\frac{a_1+a_2+a_3+48}{4} =\frac{328+48}{4} =94[/tex]
if someone in 2022 is now 89, how old were they in 1971?
Answer:38
Step-by-step explanation:
they were born in 1933 and 1971 minus 1933 is 38.
What is the slope of the line passing through the points (4, 5) and (0, -7)? Show all your work.
Answer:
slope = 3
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 5 ) and (x₂, y₂ ) = (0, - 7 )
m = [tex]\frac{-7-5}{0-4}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3
rise over run
you can also use the y2-y1/x2-x1 but these numbers where small enough where graphing can help visually
A circle with some chord, where a diameter of a circle intersects the
midpoint of that chord. Prove: The diameter is perpendicular to the chord.
Answer:
Step-by-step explanation:
Answer:
This is a theorem that says "if a diameter of a circle bisects a chord, then it is perpendicular."
Step-by-step explanation:
How are the two functions f(x) = 0. 7(6)x and g(x) = 0. 7(6)–x related to each other? g(x) is the reflection of f(x) over the x-axis. G(x) is the reflection of f(x) over the y-axis. G(x) is the reflection of f(x) over both axes. G(x) and f(x) will appear to be the same function.
Evaluate what is the answer to
3.4
+
5.14
pleasee help me! One circle has a circumference of 12 cm. Another circle has a circumference of 32 cm. What is the ratio of the radius of the smaller circle to the radius of the larger circle? 3:8 8:3 1:3 3:1
Answer:
A: 3;8
Step-by-step explanation:
12/2 = 6
32/2 = 16
6/2 = 3
16/2 = 8
3:8
PLESSE HELP IM FAILING MATH RN
5) Find the x-intercept and the y-intercept of the equation: 8x - y = -24.
Answer:
First we have to turn it into slope intercept form which is y = mx + b.
we need to isolate y. To do this, we have to subtract 8x from both sides to get
-y = -8x - 24
-25 is the y intercept and -8 is the slope.
Step-by-step explanation:
answer the question then, I will award you with a answer to your question!
Answers: 585, 587, and 593
Basically everything except 599
==============================================================
Why?
Those answers in bold are closer to 590 than they are to 580 or 600. When rounding to the nearest ten (not tenth) we look at the units digit. If it is 5 or larger, then we bump the tens digit up by 1 and replace the units digit with a 0.
This explains why 585 and 587 round to 590
The number 599 rounds to 600 for similar reasoning, but we cross it off the list since we want 590.
The number 593 rounds to 590 because the 3 in the units digit isn't 5 or larger. So we just replace the 3 with 0 and keep everything else as is.
A right circular cone is intersected by a plane that passes through the cone's
vertex and is perpendicular to its base, as in the picture below. What is
produced from this intersection?
A. A single line
B. A pair of intersecting lines
C. A point
D. A pair of parallel lines
When a circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base, a pair of intersecting lines is formed.
How to know what is formed from a line intersecting a cone?The right circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base.
This means the intersecting line forms a right angle with the base of the right circular cone.
Therefore, what is produced from this interaction is a pair of intersecting lines. The intersecting lines also have a point.
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Which of the following points on the number line would be the plotted point for √5
Answer:
Point C
Step-by-step explanation:
The correct answer would be about 2.2 so C is the closest.
Help me pls answer pls I’m pls
Graph the following features:
Slope = -3
Y-intercept = 5
Answer:
y=-3x+5
Step-by-step explanation:
Work out ( 7x10^5) divide ( 2x10^2)
Answer:
The value of the division of \frac{7\times 10^{5} }{2\times 10^{2} }
2×10
2
7×10
5
is 3.5\times 10^{3}3.5×10
3
.
Step-by-step explanation:
Given:
\frac{7\times 10^{5} }{2\times 10^{2} }
2×10
2
7×10
5
To Find:
The value of the division of \frac{7\times 10^{5} }{2\times 10^{2} }
2×10
2
7×10
5
.
Solution
As given- \frac{7\times 10^{5} }{2\times 10^{2} }
2×10
2
7×10
5
.
\frac{7\times 10^{5} }{2\times 10^{2} } = 3.5\times 10^{5-2}
2×10
2
7×10
5
=3.5×10
5−2
= 3.5\times 10^{3}=3.5×10
3
Thus, the value of the division of \frac{7\times 10^{5} }{2\times 10^{2} }
2×10
2
7×10
5
is 3.5\times 10^{3}3.5×10
3
.
Step-by-step explanation:
Hope it helps.
A microscope shows you an image of an object that is 80 times the object's actual size. So the scale factor of the enlargement is 80. An insect has a body length of 9 millimeters. What is the body length of the insect under the microscope?
Answer:
80
Step-by-step explanation:
2) Find the surface area of the cube. You should have at least 2 steps shown
Answer: 294 square millimeters
Step-by-step explanation:
Each side of the cube is 7 mm.
First, find the area of one face. The formula for the area of a square is [tex]s^2[/tex]. 7 mm squared is 49 square millimeters.
A cube has 6 faces, so multiply the area of one face by 6. 49*6 = 294 square millimeters
(128 ÷ 32) ÷ -4?
tysm for de help :D
Answer:
-1
Step-by-step explanation:
(128 ÷ 32) ÷ -4?
Alright, first things first lets think about PEMDAS.
Parenthesis first so 128/32 is 4!
4/-4 is going to be -1!
Your answer will be -1
Hope this helps!
does someone mind helping me with this question? Thank you!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: a = \pi {r}^{2} [/tex]
where, r = d/2 = 6/2 = 3 ft[tex]\qquad \sf \dashrightarrow \: a = 3.14 \times {3}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: a = 3.14 \times 9[/tex]
[tex]\qquad \sf \dashrightarrow \: a = 13.26 \: \: ft {}^{2} [/tex]
Answer: 28.26
Step-by-step explanation:
D = 6
R = 3
3.14 x 3 x 3 = 28.26
Abag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).
a. 9 b. 4/3 c. 1/4 d. 3/4
Answer:
A: 9
Step-by-step explanation:
if p is red and green
Answer:
--------------------------HeyA-------------------------
GiveN :
Total no.of marbles : 12Total no.of red marbles : 8 Total no.of blue marbles : 3Total no.of green marbles : 1To FinD :
P ( not blue )SolvinG :
- First step is to find out P( blue )
P ( blue ) = 3 / 12 = 1/4- Now , find out P ( not blue )
P ( not blue ) = 1 - 1/4 = 3/4- Option D [ 3/4 ] is the right option.
--------------------HappY LearninG <3 --------------
The fabric store is having a sale the price of every item in the store has been reduced 30% which equation show the proportional relationship between the regular price of an item at the fabric store and its sale price, s?
Find the sum (pre calc)
[tex]\text{It is a geometric series.}\\\\\text{First term,}~ a = 2\\\\\text{Common ratio,}~ r = \dfrac{-\tfrac 43}2 = -\dfrac 46 = -\dfrac 23\\\\\text{Sum of an infinite geometric series,}\\\\S_{\infty} = \dfrac{a}{1-r}\\\\\\~~~~~=\dfrac{2}{1-\left(- \dfrac 23 \right)}\\\\\\~~~~~=\dfrac{2}{1+ \dfrac 23}\\\\\\~~~~~=\dfrac{2}{\tfrac 53}\\\\\\~~~~~=\dfrac{6}{5}\\\\[/tex]
[tex]\text{The answer is}~ \dfrac 65[/tex]
Solve. 3(a – 5) – 6 = –15
Answer:
a=6
Step-by-step explanation:
distribute:
3a-15-6=-15
combine like terms:
3a-21=-15
add 21 to each side:
3a=6
divide by 3:
a=2
whats the answer to 3x1/2
Answer:
1.5
Step-by-step explanation:
3×1/2
3×1/2=
3/1×1/2
3/2= 1.5
Question 5 (1 point)
(07.07)
Find the product of (x + 3). (1 point)
o a
x2 + 6x + 9
x2 - 6x + 9
Ос
x2-9
d
x2 + 9
Answer:
a) x² + 6x + 9
Step-by-step explanation:
When we square something, we multiply it by itself:
⇒ (x + 3)² = (x + 3)(x + 3)
Using the FOIL method: (a + b)(c + d) = ac + ad + bc + bd
⇒ (x + 3)(x + 3) = x² + 3x + 3x + 9
= x² + 6x + 9
a.
[tex]\huge{{x}^{2} + 6x + 9}[/tex]
Step-by-step explanation:
Using Binomial Theorem:
[tex]\boxed{{(a+b)} ^n= \sum_{k=0}^{n}\binom{n}{k} a^{n-k}b^{k}}[/tex]
.
.
.
[tex](a+b) ^2 =a^{2} + 2ab +b^{2} [/tex]
The answer seems to be [tex]x^{2} + 6x + 9[/tex]...
The diameter of the circle above is 86 cm. What is the circumference of the circle? (Use = 3.14.)
A. 135.02 cm
B. 5,805.86 cm
C. 11,611.72 cm
D. 270.04 cm
Answer:
D
Step-by-step explanation:
Circumference = pi × diameter
pls solve and show steps!
Answer:
? Not a solution
Step-by-step explanation:
Lindsey bought supplies for a class project and brought the receipt to school. The 6 items cost:
$5.00$3.00$8.00$5.00$4.00$5.00
What was the mode of the prices of the items?
Answer:
$5
Step-by-step explanation:
$5 appeared more in the prices
Answer:
5 dollars
Step-by-step explanation:
cuz I just know
The members of the Math Club need to elect a president and a vice president. They determine that there are a total of 272 ways that they can fill the positions with two different members. How many people are in the Math Club
Answer:
544
Step-by-step explanation:
EASY JUST MULTIPLY!!!
multiply your total of ways to fill the position, by how many members!
so... 272 x 2 = 544 hopes this helps!!
Is there any bias in the survey question? Explain.
What do you think would help students pay more attention in class?
SOMEONE PLEASE HELP!!!
Answer:
yes
Step-by-step explanation:
because everyone has a different method that works for them.
but then again it uses the pronoun you which means its asking for your opinion its not phrased
what would help študents pay more attention in class
so yes and no
