Find the volume of the solid that lies inside both the cylinder x 2 y 2 = 1 and the sphere x 2 y 2 z 2 = 16
The volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16 is 24.74 cubic units.
What is the volume of the solid?Find the volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16
From the sphere and cylinder, the cylindrical coordinate will be
[tex]z = \pm \sqrt{16 - r^2}[/tex]
And the radius of the cylinder is |r| < 1 and the 0 ≤ θ ≤ 2π.
Then the volume will be given as
[tex]\rm V = \int _0^{2\pi} \int _0^1 \int _{- \sqrt{16 - r^2}}^{\sqrt{16-r^2}} \left ( r \ dz \ dr \ d\theta \right ) \\\\\\V = 2\pi \int_0^1 \left ( 2r\sqrt{16-r^2} \right ) \ dr\\\\\\V = 4\pi \left [ -\dfrac{1}{3} (16 - r^2)^{3/2} \right ]\\\\\\V = \dfrac{4\pi}{3} \left ( 16^{3/2} - 15^{3/2} \right )\\\\\\V = 24.74[/tex]
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A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 4 cm and diameter of the base is 8 cm. Determine the volume of the toy. If the cube circumscribes the toy, then find the difference of the volumes of the cube and the toy. Also, find the total surface area of the toy.
Donno.. don't answer
Answer:
See below ~
Step-by-step explanation:
Things to Find
Volume of ToyDifference of Volumes in Cube and ToyTotal Surface of ToyVolume of Toy
Volume of Hemisphere + Volume (Cone)2/3πr³ + 1/3πr²h1/3πr² (2r + h)1/3 x 3.14 x 16 (8 + 4)1/3 x 50.24 x 1250.24 x 4200.96 cm³Volume of Circumscribing Cube
Edge length is same as diameterV = (8)³V = 512 cm³Difference in Volume
512 - 200.96311.04 cm³Slant height of cone
l² = 4² + 4²l² = 32l = 4√2 cm = 5.6 cmSurface Area of Toy
CSA (hemisphere) + CSA (Cone)2πr² + πrlπr (2r + l)3.14 x 4 (8 + 5.6)12.56 x 13.6170.8 cm²Find the value of 3√97.336
Answer:
3
√
97.336
Decimal Form:
29.59770261
Step-by-step explanation:
-2/5x - 1/2 + x = -40/11
Answer: x = 6.56
Step-by-step explanation: -0.4x - 0.5 + x = 3.63
-0.4x^2 - 0.5 = 3.63
-0.4x^2 = 4.13
0.63x = 4.13
x = 6.56
A baker made 326 cupcakes. Cupcakes are packed 4 per box
Answer:
The baker needs 82 boxes.
Step-by-step explanation:
326/4=81 r 2.
But, you have to fit in all the cupcakes, so you round ir up to 82.
A dog’s weight dropped to 62 kg after its weight decreased by 7%. What was the dog’s original weight?
Answer:
original weight= mass/weight
62kg/7
Step-by-step explanation:
8.85 original weight
A local baseball team is struggling this season, and many fans of the team believe it may be time to replace the head coach. To estimate support for firing the current head coach, a television news station provides a link on its website where fans of the team can respond to the question: "Do you feel the current head coach should be fired?” After 2,367 votes on the website, 79% of those who responded felt the coach should be fired. Which of these describes the type of bias in this survey and a likely direction of the bias in estimating overall support for firing the coach?
This is nonresponse bias. The result overestimates true support for firing the coach.
This is nonresponse bias. The result underestimates true support for firing the coach.
This is voluntary response bias. The result overestimates true support for firing the coach.
This is voluntary response bias. The result underestimates true support for firing the coach.
The statement third, “This is voluntary response bias. The result overestimates true support for firing the coach” is correct.
What is a survey?A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.
We have:
A local baseball team is struggling this season, and many fans of the team believe it may be time to replace the head coach.
Number of votes V(n) = 2367
After the value of V(n) 79% of those who responded felt the coach should be fired.
Based on the data given, we can say this is referred to as voluntary response bias. The outcome exaggerates the level of support for firing the coach.
Thus, the statement third “This is voluntary response bias. The result overestimates true support for firing the coach” is correct.
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Andrea is buying a $400000 house and wants to make a 20% down payment. What amount will her down payment be
Step-by-step explanation:
I always try to find the easiest way to solve this kind of questions.
The easiest percentage to calculate with is number 10.
first step , divide the whole amount of the money by ten.
as a result we get 40,000
second step, we were asked to calculate a20% so we will double the 10 percent
and the answer goes to 80,000.
Answer:
Step-by-step explanation: umm i think 6000000 i don't know it might be right because i guess you need to add
Jessie claims that if any number is doubled and then increased by 1, the result will be greater than 4.
Jessie’s claim is NOT true for all values of n.
enter a value of n for which Jessie’s claim is NOT true.
Answer:
n = 1
Step-by-step explanation:
1 x 2 = 2
2 + 1 = 3
3 < 4
hope this helps
Edna is fishing from a small boat. A fish swimming at the same depth as the hook at the end of her fishing line is 12 feet away from the hook. If Edna is 20 feet away from the fish, how far below Edna is the hook?
Answer:
16 feet
Step-by-step explanation:
The geometry of the problem can be modeled by a right triangle. The Pythagorean theorem tells us the relationship between the various distances.
EH² +HF² = EF²
EH² + 12² = 20²
EH² = 400 -144
EH = √256 = 16
The hook is 16 feet below Edna.
Answer:
8 feet
Step-by-step explanation:
The difference of a number,t, squared and 3 is at most 46
The inequality expression of the given word problem statement is;
t² - 3 ≤ 46
How to express inequality word problems?We are told that two numbers labelled t² and 3 have a difference that is at most 46.
Now, when we say at most, it means less than or equal to symbol.
Thus, the expression of the given statement is; t² - 3 ≤ 46
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what is the surface area of a rectangle polyhedron in square units?
Answer:
The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps.
can someone help me with this problem? Thank you!
Answer:
60
Step-by-step explanation:
AT = ½bh
AT = (6(20)) / 2
AT = 60
Answer:
The answer is 60
Step-by-step explanation:
^^
Happy to help :D
Monômios
[tex]2x^{3}+5x-3x^{2} +x-6+2x^{2}=[/tex]
There are 8 water bottles, and each bottle is 3/4 filled with water. If we pour all the water together, how many water bottles can be filled up?
Answer:
6
Step-by-step explanation:
8 * 3/4 = 24/4 = 6 WATER BOTTLES
which part of this graph shows a nonlinear relationship?
1. 4
2. 1
3. 3
4. 2
1.5 in
3.3 in
What's the area
Answer:
6.96
Step-by-step explanation:
2.9 x 1.5 = 4.35
3.3 - 1.5 = 1.8
1.8 x 2.9 = 5.22
5.22 divided by 2 = 2.61
4.35 + 2.61 = 6.96
Please help!!!
D is f(x)=500(x+30000)
Answer:
The correct answer is A
Step-by-step explanation:
The books sold are 30,000, so that is our total sale for January. His sales are decreasing by an average of 500 books per month, which means he is losing sales so it is a negative value, and we multiply that by x (number of months) since the question has not stated the number of months. Therefore, the equation would be f(x) = 30,000 - 500x
Hope this is of help!
Solve for x:
x =
Answers: 22.5 30 45
For 25 points-
Which graph represents the solution to the system of inequalities below?
5x-4y>4
x+y<2
SHOW YOUR WORK!
Answer:
Graph B
Step-by-step explanation:
Rearrange in the form y > mx + c :
5x - 4y > 44y < 5x - 4y < 5/4x - 12. x + y < 2
y < -x - 2Graph which shows this inequality is : Graph B
B. is the correct graph.
An official men's basketball has a diameter of 9.55 inches. The diameter of a woman's basketball is 9.23 inches. What is the difference in volumes?
A recent study found that the average length of caterpillars was 2.8 centimeters with a
standard deviation of 0.7 centimeters. what is the probability that a randomly selected caterpillar will have a
length longer than (greater than) 4.0 centimeters?
Using the normal distribution, it is found that there is a 0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 2.8, \sigma = 0.7[/tex].
The probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters is one subtracted by the p-value of Z when X = 4, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4 - 2.8}{0.7}[/tex]
Z = 1.71
Z = 1.71 has a p-value of 0.9564.
1 - 0.9564 = 0.0436.
0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
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Help me this pls as soon as possible this is due today!!!
Answer:
pls refer to given attachemnt
Need help. Will give 15 points.QSRT is a rectangle. Find the lengths of the following sides
Answer:
I don't know
Step-by-step explanation:
You didn't give a picture to see the rectangle.
Penny is planning a trip to egypt. she has mapped out the expected costs of some different components of her trip, and has compiled them below, including whether the cost is in us dollars ($) or egyptian pounds (£). item cost currency plane ticket 3,241.77 £ passport 65.00 $ tour guide 494.25 £ international phone card 41.38 $ hotel reservation 398.26 £ car rental 644.48 £ if the exchange rate of the us dollar to egyptian pound is 1:5.3841, how much has penny currently budgeted for her trip, in us dollars? round all currencies to two decimal places. a. $895.25 b. $993.95 c. $1,001.63 d. $1,468.01
The total amount that Penny has budgeted for her trip to Egypt is £5351.62.
What is the total amount budgeted for the trip?The exchange rate is the rate at which one currency is exchanged for another currency. The total amount that was budgeted by Penny is the sum of the different compoments that she compiled for the trip.
Cost of international phone card in Egyptian pound = 41.38 x 5.3841 =£222.79
Cost of passport in Egyptian pound = 65 x 5.3841 = £349.97
Total cost = 3,241.77 + £222.79 + 494.25 + £349.97+ 398.26 £ + 644.48 = £5351.62
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Which cone is similar to a right cone with a height of 3ft and a base with a diameter of 5ft
Please help i will give you 100 points
x = 50.5°
Explanation:In order to solve, get to know about the sine rule:
[tex]\bf Sine \ Rule = \dfrac{A}{sinA} = \dfrac{B}{sinB}= \dfrac{C}{sinC}[/tex]
Solve for BD:[tex]\sf \dfrac{BD}{sin(50)} = \dfrac{5.6}{sin(78)}[/tex]
[tex]\sf BD = \dfrac{5.6(sin(50))}{sin(78)}[/tex]
[tex]\sf BD = 4.385686657 \ cm[/tex]
Then find angle D = 180° - 78° = 102°
Solve for angle C[tex]\sf \dfrac{4.385686657}{sinC} = \dfrac{9.3}{sin(102)}[/tex]
[tex]\sf C = sin^{-1}(\dfrac{4.385686657sin(102)}{9.3} )[/tex]
[tex]\sf C = 27.37 ^{\circ \:}[/tex]
Total Sum of interior angles of a triangle is 180°[tex]\sf B + C + D = 180^\circ[/tex]
[tex]\sf x + 27.37^\circ + 102^\circ = 180^\circ[/tex]
[tex]\sf x = 180^\circ - 102^\circ - 27.37^\circ[/tex]
[tex]\sf x = 50.53^\circ[/tex]
[tex]\sf x = 50.5^\circ \ \ \ (rounded \ to \ nearest \ 3 \ significant \ figure)[/tex]
Answer:
x = 50.5° (3 sf)
Step-by-step explanation:
Sine Rule for side lengths
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Find BD:
[tex]\implies \sf \dfrac{BD}{\sin BAD}=\dfrac{AB}{\sin BDA}[/tex]
[tex]\implies \sf \dfrac{BD}{\sin 50^{\circ}}=\dfrac{5.6}{\sin 78^{\circ}}[/tex]
[tex]\implies \sf BD=\dfrac{5.6\:sin 50^{\circ}}{\sin 78^{\circ}}[/tex]
[tex]\implies \sf BD=4.385686657...cm[/tex]
Angles on a straight line sum to 180°
⇒ ∠ADB + ∠BDC = 180°
⇒ 78° + ∠BDC = 180°
⇒ ∠BDC = 102°
Sine Rule for angles
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Find ∠BCD:
[tex]\implies \sf \dfrac{\sin BCD}{BD}=\dfrac{\sin BDC}{BC}[/tex]
[tex]\implies \sf \dfrac{\sin BCD}{4.385...}=\dfrac{\sin 102^{\circ}}{9.3}[/tex]
[tex]\implies \sf BCD=\sin^{-1}\left(\dfrac{4.385...\sin 102^{\circ}}{9.3}\right)[/tex]
[tex]\implies \sf BCD=27.46935172...^{\circ}[/tex]
The interior angles of a triangle sum to 180°
⇒ ∠CBD + ∠BDC + ∠BCD = 180°
⇒ x + 102° + 27.469...° = 180°
⇒ x = 50.53064828...°
⇒ x = 50.5° (3 sf)
Math question 10 question PLSSS HELP
Answer:
A
Step-by-step explanation:
if it is at least -27 it will be greater than or equal to -27
What value of x makes this equation true? -90=-100+X
Answer:
-90=-100+x
-90+100=x
x=10
hence 10 is that value whose satisfy this equation
Step-by-step explanation:
what is the formula to finding the area of a trapizoid in sq cm
Answer:
½ (a + b) h
Step-by-step explanation: