Use cavalieri's Principle to calculate the exact of an oblique cylinder with a radius of 10 meters and a height of 11 meters.

Answers

Answer 1

Am I to assume this is for volume? The volume formula for a cylinder...oblique or not...is V = 1/3pi r^2 h. Cavalieri's principle tells us that the formulas for both are the same. So V = 1/3*pi*100*11 and V = 366.67 pi

Answer 2

Answer: Volume of cylinder is 1152.38 m³.

Step-by-step explanation:

Since we have given that

Radius of cylinder = 10 m

Height of cylinder = 11 m

Using Cavalieri's principle , volume of an oblique cylinder is equal to volume of cone.

So, Volume of an oblique cylinder is given by

[tex]V=\frac{1}{3}\pi r^2h\\\\V=\frac{1}{3}\frac{22}{7}\times 10\times 10\times 11\\\\V=1152.38\ m^3[/tex]

Hence, Volume of cylinder is 1152.38 m³.

Related Questions

A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day

Answers

(1073 + 1108 + x) / 3 = 1000
(2181 + x) / 3 = 1000 ....multiply both sides by 3
2181 + x = 1000 * 3
2181 + x = 3000
x = 3000 - 2181
x = 819 <== they would need to earn $ 819 on Sunday

WILL GIVE BRAINLIEST ANSWER!!
Help, please!
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 16°23'. When the boat stops, the angle of depression is 49°29' . The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

Answers

check the picture below.

now, bear in mind that, there are 60minutes in 1 degree, so 23' is just 23/60 degrees or about 0.38 degrees.

and 29' is just 29/60 degrees or about 0.48 degrees.

so 16°23' is about 16.38°, and 49°29' is about 49.48°

[tex]\bf tan(16.38^o)=\cfrac{200}{a+b}\implies a+b=\cfrac{200}{tan(16.38^o)} \\\\\\ \boxed{b=\cfrac{200}{tan(16.38^o)}-a} \\\\\\ tan(49.48^o)=\cfrac{200}{b}\implies \boxed{b=\cfrac{200}{tan(49.48^o)}}\\\\ -------------------------------\\\\ \cfrac{200}{tan(49.48^o)}=\cfrac{200}{tan(16.38^o)}-a\\\\\\a=\cfrac{200}{tan(16.38^o)}-\cfrac{200}{tan(49.48^o)}[/tex]

make sure your calculator is in Degree mode.

The distance covered by the boat is [tex]\boxed{489.67{\text{ feet}}}.[/tex]

Further explanation:

The Pythagorean formula can be expressed as,

[tex]\boxed{{H^2} = {P^2} + {B^2}}.[/tex]

Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.

The formula for tan of angle a can be expressed as

[tex]\boxed{\tan a = \frac{P}{B}}[/tex]

Explanation:

The perpendicular AB. The length of AB is [tex]200{\text{ feet}}.[/tex]

The angle of depression is [tex]\angle ACB = {14^ \circ }52'.[/tex]

One degree has 60 minutes.

[tex]{1^ \circ } = 60'[/tex]

[tex]\begin{aligned}\angle ACB &= 49 + \frac{{29}}{{60}}\\&= 49 + 0.48\\&= 49.48\\\end{aligned}[/tex]

The angle ADB is [tex]\angle ADB = {16^ \circ }23'.[/tex]

[tex]\begin{aligned}\angle ADB&= {16^ \circ }23' \\&= 16 + \frac{{23}}{{60}}\\&= {16.38^ \circ }\\\end{aligned}[/tex]

In triangle ABC.

[tex]\begin{aligned}\tan\left( {{{49.48}^\circ }} \right)&=\frac{{200}}{{BC}}\\1.13&= \frac{{200}}{{BC}}\\BC &= \frac{{200}}{{1.13}}\\BC &= 177{\text{ feet}}\\\end{aligned}[/tex]

In triangle ABD.

[tex]\begin{aligned}\tan \left( {{{16.38}^ \circ }} \right)&= \frac{{200}}{{BD}}\\0.30&= \frac{{200}}{{BD}}\\BD&= \frac{{200}}{{0.30}}\\BD &= 666.67{\text{ feet}}\\\end{aligned}[/tex]

The distance boat can travel can be obtained as follows,

[tex]\begin{aligned}DC& = BD - BC\\&= 666.67 - 177\\&= 489.67{\text{ feet}}\\\end{aligned}[/tex]

The distance covered by the boat is [tex]\boxed{489.67{\text{ feet}}}.[/tex]

Kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: perpendicular, person watching boat, top, lighthouse, angle of depression, angle of elevation, 200 feet tall, travel, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions.

Which of the following is true when probability answer is written in the form of a fraction

Answers

The subject area of probability is actually expressed as a fraction or percentage because it represents a part of a whole. In lay man's term, probability is the scientific study of chance, likeliness and odds of an event happening. For example, you want to find the odds of getting a heads in a toss of the coin. You know that there are 2 possible results: head and tails. So, the probability of getting a head is 1/2 or 50%. Since it is a part of a whole, the probability in fraction should never be an improper fraction. This is the type of fraction in which the numerator is greater than the denominator. This is impossible as a probability because it will never exceed 1.

In probability, a fraction does not need to be simplified but converting to a percentage or decimal can aid in interpretation, with percentages being fractions with a denominator of 100. (First option)

When a probability answer is written in the form of a fraction, it is important to know how to handle the result. Simplifying the fraction is not generally required, especially in Probability Topics, where the focus is on understanding the probability itself rather than the arithmetic of fractions.

However, converting the probability to a percentage is a common practice that can help with interpretation. This is done by writing the value of the percent as a fraction with a denominator of 100 and then simplifying it if possible.

Converting a fraction to a decimal is another common step, which involves dividing the numerator by the denominator. It's also important to note that for rounding answers to probability problems, the convention is to round to four decimal places.

Find the number of permutations of the first 10 letters of the alphabet taking 2 letters at a time.

Answers

This is the concept of permutations, the number of times the first 10 letters of the alphabet taking 2 letters at a time will be:
10P2
=90
Therefore there are more than 90 ways in which the letters can take 2 letters at a time.

Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?

Answers

The first inequality is
(2/3)x - 3 ≥ y
or
y ≤ (2/3)x - 3 (1)

The second inequality is
y + (2/3)x < 4
or
y < 4 - (2/3)x (2)

A graph of the two inequalities indicates the solution as a shaded region in the figure below.

Answer? Multiple choice?

Answers

Given fraction is
[tex]f(x) = \frac{x^2 + 4x + 3}{x^2 - 9} [/tex]

As we know fraction is not defined where denominator is equal to zero.

So let's find where denominator is zero.

[tex]x^2 - 9 = 0[/tex]

We can factorize it as [tex]a^2 - b^2 = (a+b)(a - b)[/tex]

So we can write given equation as

[tex](x+3)(x-3) = 0[/tex]

So x = 3 or x = -3.

So function is undefined at x = 3 and x = -3.

So option 3 is correct.

Plz help!

What is the constant of variation for the quadratic variation?

A. 5

B. 10

C. 15

D. 25

Answers

dy/dx=25, 35, 45, 55

d2y/dx2=10,10,10 (this constant just proves that it is a quadratic relation)

Now we can set up a system of equations for ax^2+bx+c

16a+4b+c=80, 9a+3b+c=45, 4a+2b+c=20 getting differences

7a+b=35, 5a+b=25 and again

2a=10, a=5, making 7a+b=35 become:

7(5)+b-35, b=0, making 4a+2b+c=20 become:

4(5)+2(0)+c=20, c=0 so

y=5x^2

So the constant of variation for this quadratic is 5.

the correct answer to the problem is A or 5

Stanfing in your tree house 50ft off the ground you look down at a 60 degree angle how many feet from the base of the tree is the frisbee

Answers

multiply 50 x tan(60) = 86.6 feet.

round your answer as needed

the volume of a gas varies inversely as the pressure upon it. if the volume of the gas is 160 cubic centimeters at a pressure of 108 centimeters find the volume when the pressure is 87 centimeters

Answers

It was stated in the problem that a given volume of a is inversely proportional with the pressure of the system. It means that the as the volume increases, the pressure would decrease and as the volume decreases, the pressure would increase. We would express it as:

V α 1/P

To change it to an equality, we introduce a proportionality constant, k. We do as follows:

V = k/P

So, to determine what is asked, we need to first calculate for the value of k.

V = k/P
At V = 160 m^3 P = 108 cmHg
160 = k / (108)
k = 17280

Thus, at P = 87 cmHg
V = 17280 / 87
V = 198.62 m^3

in the system shown below, what are the coordinates of the solution that lies in quadrant I? x^2-y^2=25, x+y=25

Answers

The given equations in this item are,
x² - y² =25
and
x + y = 25

It can be deduced that the first equation is a difference of two squares and can be factored out as that one shown below.
(x - y)(x + y) = 25

From the second equation, x+y = 25. Substituting this to the equation above,
(x-y)(25) = 25
Hence, x - y = 1

The system of linear equations is,
x + y = 25
x - y = 1
Adding the equations together,
2x = 26
x = 13

The value of y is 12.

Since both x and y are positive values then, this solution lies in the first quadrant.

ANSWER: (13,12)

Find the equation of the circle that has a diameter with endpoints located at (7, 3) and (7, –5).

Answers

Final answer:

The equation of the circle with a diameter between (7, 3) and (7, -5) is (x - 7)² + (y + 1)² = 2².

Explanation:

To find the equation of the circle, we first need to find its center. The center of a circle is the midpoint of its diameter. To find the midpoint of (7, 3) and (7, -5), we can add the x-coordinates and divide by 2 to get 7. For the y-coordinates, we add -5 and 3 and divide by 2 to get -1. So, the center of the circle is (7, -1).

The radius of the circle is half the length of the diameter. The distance between the center of the circle and one of the endpoints of the diameter (7, 3) is the radius. Using the distance formula, the radius is √((7-7)² + (3+1)²) = 2.

Now, we can use the center and radius to write the equation of the circle, which is (x - 7)² + (y + 1)² = 2².

Learn more about Equation of a Circle here:

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The length of the shadow of a flagpole was found to be 72 feet. the shadow of a 3 foot picket fence in line with the flagpole was 4 feet. what is the height of the flagpole?

Answers

We can solve this problem by simply using ratio and proportion. Let us call the height of the flagpole to be X. Therefore the ratio and proportion would be:

3 ft is to 4 ft and X ft is to 72 ft

3 / 4 = X / 72

X = (3 / 4) * 72

X = 54 ft

The height of the flagpole is 54 ft.

helpppppppppppppppppppppppppppp

Answers

Finding the area of one triangle:

h^2 + 3^2 = 6^2
x^2 = 27
x=sqrt(27)
x=3*sqrt(3)

0.5*x*6=9*sqrt(3)

Then multiplying by 7 for all 7 sides,

9*sqrt(3)*7

63*sqrt(3)

Final simplification: 109.12, D

Hope this helps.

What are the exact solutions of x2 − 3x − 1 = 0?
Select one:

a. x = the quantity of 3 plus or minus the square root of 5 all over 2 Incorrect

b. x = the quantity of negative 3 plus or minus the square root of 5 all over 2

c. x = the quantity of 3 plus or minus the square root of 13 all over 2

d. x = the quantity of negative 3 plus or minus the square root of 13 all over 2

Answers

Option C is the answer!

Hi, the quadratic formula is: [tex]\boxed{X= \dfrac{-b \pm \sqrt{b ^{2}-4ac } }{2a}}[/tex]

Values: a = 1; b = - 3; c = -1
Solving:

[tex]X ^{2}-3X-1=0[/tex]

[tex]X= \dfrac{-(-3) \pm \sqrt{(-3) ^{2}-4(1)(-1) } }{2(1)}[/tex]

[tex]X= \dfrac{3 \pm \sqrt{9+4} }{2}[/tex]

[tex]X= \dfrac{3 \pm \sqrt{13} }{2}\ ===\ \textgreater \ \ Answer:\ \boxed{ \textbf{Option\ {C.}}}[/tex]

GOOD LUCK...!!!

monique deposited 1800 at the beginning of each quarter for 6 years into an ira. given an interest rate of 6% compounded quarterly find the value

Answers

Use the formula of the future value of annuity due because the amount of 1800 is deposited at the (beginning) of each quarter
The formula is
Fv=pmt [((1+r/k)^(kn)-1)÷(r/k)]×(1+r/k)
Fv future value?
PMT amount deposited 1800
R interest rate 0.06
K compounded quarterly 4
N time 6years
Fv=1,800×((((1+0.06÷4)^(4×6)
−1)÷(0.06÷4))×(1+0.06÷4))
=52,313.44....answer

The table shows the ages and weights of babies at a hospital.

What is the correlation between age and weight as shown in the table?

A.) none

B.) positive

C.) negative

D.) constant

Answers

Answer:

Option (b) is correct.

The correlation between age and weight shown in the table is positive.

Step-by-step explanation:

Given: The table shows the ages and weights of babies at a hospital.

We have to determine the correlation between age and weight as shown in the table.

We first Plot these points to obtain the graph as show in attachment below.

Since, Using correlation calculator , we find the correlation as 0.83113

Which is positive

Thus, The correlation between age and weight shown in the table is positive.

As age increases the weight increase.Hence, positive.

The correlation between age and weight as shown in the table is positive, This is further explained below, Option B is correct

What is correlation?

Correlation is simply a relationship that exists between events or objects, A relationship between mathematical variables that are subject to variation.

In conclusion, Therefore we look at the table to decipher the correlation between age and weight.

Answers

The minimum value for f(x) is pretty straight-forward. -5+2=-3

We can tell by looking at the graph of g(x) that its minimum is -2

By symmetry the table shows a minimum of 3

So f(x) has the smallest minimum.

Answer:

Step-by-step explanation:

We are given three functions and we have to find which one has the smallest minimum.

I function is

[tex]f(x) = -5sin(2x-\pi) +2[/tex]

Since sine varies from -1 to 1, we get this function has a minimum when sine takes value 1.

Minimum of f(x) =1(-5)+2 =-3

II function is

a graph of parabola with minimum at x=3 and y =-2

III function is shown in tabular form.

From the table we find that minimum is x=1 y=3

Tabulating we have

f(x) (3pi/4, -3)

g(x) (3,-2)

h(x) (1,3)

Smallest is for f(x) with least value of -3

a plane intersects a prism parallel to the base of the prism. the cross section is a polygon with eight sides. The base of the prism had how many sides

Answers

eight sides, hope this helps!

The answer is eight sides.

2 Questions~
Evaluate the expression.

38+16⋅12÷2−(30⋅2)

Simplify this expression.

5 + 10 ÷ 5

3

7

10

15

Answers

answer is 3 hope this helps

Your answer would be a.

Answer: 3

hope this helps! :)

~Izzie

8% of x is equal to 48

Answers

48 / 0.08 = 600

answer

8% of 600 is equal to 48

divide 48 by 8%

48/0.08 = 600

check

600*0.08 = 48

x=600

What type of transformation can be defined as turning a figure about a fixed point with no change to the size or shape of the figure?

Answers

The type of transformation that turns a figure without changing the size or the shape of the figure is called a ROTATION. An example is given in the diagram below. The triangle has been rotated 90° about the origin

tristen is a saleman whose base pay plus commissions amounted to $59,238 last year. if his base pay was $31,050 and he made $97,200 is sales last year what was his rate of commission?

Answers

subtract base pay from what he made

59238-31050 = 28188

so he made 28188 in commissions

now divide that by 97200

28188/97200 = 0.29

so he makes 29% commision

(04.01 LC)

Which of the sets of ordered pairs represents a function?

A = {(2, −2), (5, −5), (−2, 2), (−5, 5)}
B = {(4, 2), (4, −2), (9, 3), (9, −3)}

Only A
Only B
Both A and B
Neither A nor B

Answers

Answer:

Only A

Step-by-step explanation:

Let's remember the definition of a function:

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

In A, each input has exactly one output so it's a function.

But in B, the inputs 4 and 9 have two different outputs, it can't represent a function.

The answer is only A.

1,226 days late to answer this question but that will not stop me!

The answer is... drumroll please ... Only A :]

The course for the frog hopping race is 59 inches long. Max's frog has jumped 2 feet and 3 inches. How much further does Max's frog need to jump in order to reach the finish line?

Answers

2ft is equal to 24 inches+3 is equal to 27 inches travelled total.
To find what is left subtract 59-27=32 inches left, which is equivalent to 2 ft 8 inches

To find the remaining distance Max's frog needs to jump in the race, convert the initial jump to inches, and subtract it from the total race length.

The frog hopping race's course is 59 inches long. Max's frog has jumped 2 feet and 3 inches. To find out how much further Max's frog needs to jump to reach the finish line, convert 2 feet and 3 inches to inches and subtract it from 59 inches.

The conversion is: 2 feet x 12 inches = 24 inches. Adding 24 + 3 inches gives 27 inches. Subtract 27 inches from 59 inches to find the remaining distance Max's frog needs to jump.

The distance Max's frog still needs to jump is 32 inches.

What is the length of CF? look at image attached

Answers

If two chords intersect each other inside a circle, the products of their segments are equal.

СF * DF = BF * EF
СF * 14 = 7 * 17
14СF = 119
СF = 119/14
СF = 8.5

PLEASE HELP!! Use the following image↓

Answers

I assume it is negative three fourths (c) because when you graph that line, it is the closest line that meets the needs of the points.

Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by seven.

Answers

check the picture below.

you simply come "clockwise" to get the negative angle.

and to get the positive angle, simply go around 2π and then add π/7 to it.

12.38 in expanded form

Answers

12.38 in expanded form is write like:-

10 + 2 + .3 + .08 = 12.38

To write a number in expanded form just means to write the number in a layout and when you add it up it will become the number you needed to write in expanded form.

So, 12.38 written in expanded form is:- 10 + 2 + .3 + 0.8

Hope this helps. Please make me brainliest

10+2+0.3+0.08 because you split each number into tens, ones, tenths, and hundredths.

Find the measure of each interior angle and each exterior angle of the following regular polygons. Show your work

Answers

[tex]\bf \textit{sum of all interior angles of a regular polygon}\\\\ n\theta =180(n-2)\qquad \begin{cases} n=\textit{number of sides}\\ \theta =\textit{interior angle} \end{cases}\\\\ -------------------------------\\\\ \textit{sum of all exterior angles of a regular polygon}\\\\ n\theta =360\qquad \begin{cases} n=\textit{number of sides}\\ \theta =\textit{interior angle} \end{cases}[/tex]

now, with that in mind... let's take a peek at .. hmmm say c) dodecagon
now, a Dodecagon has 12 sides.... let's check the angles then

[tex]\bf n\theta =180(n-2)\qquad n=12\implies 12\theta =180(12-2) \\\\\\ 12\theta =180\cdot 10\implies 12\theta =180\implies \theta =\cfrac{1800}{12} \\\\\\ \theta =150^o\impliedby \textit{interior angle of a Dodecagon}\\\\ -------------------------------\\\\ n\theta =360\qquad n=12\implies 12\theta =360\implies \theta =\cfrac{360}{12} \\\\\\ \theta =30^o\impliedby \textit{exterior angle of a Dodecagon}[/tex]

so... hmm now for a) a decagon is 10 sides, b) pentagon is 5 sides, d) and e) pretty much you can tell how many sides on those already.

Answer:

Step-by-step explanation:

As we know for a regular polygon sum of all interior angles is represented by n A = 180 (n-2)

and sum of all exterior angles is represented by n A' = 360°

Here n represents number of sides of the polygon.

Now we will go for each options given.

(A) Decagon : (Having 10 sides)

(1) 8A = 180 ( 8-2 )

8A = 180 × 6

A = [tex]\frac{1080}{8}[/tex] = 160° ( interior angle )

(2) n A' = 360°

8 A' = 360°

A = 45° ( exterior angle )

(B) Pentagon ( having 5 sides )

(1) 5A = 180 ( 5-2 )

5A = 180 × 3 = 540

A = 108° ( interior angle )

(2) 5A' = 360

A' = 72° (exterior angle )

(C) Dodecagon : ( having 12 sides )

(1) 12A = 180 (12-2)

12 A = 180 × 10 = 1800

A = 150° ( interior angle )

(2) 12 A' = 360

A' = 30° ( exterior angle )

(D) 16-gon ( having 16 sides )

(1) 16 A = 180 ( 16 - 2 )

16A = 180 × 14

16 A = 1520

A = 157.5° ( interior angle )

(2) 16 A' = 360

A' = 22.5°

(E) 25-gon ( having 25 sides )

(1) 25 A = 180 ( 25-2)

25A = 180 (23)

A = 165.6° ( interior angle )

(2) 25A' = 360

A = 14.4° ( exterior angle)

Choose the graph below that correctly represents the equation 15x − 5y = 30.

will give brainiest to best answer!!

PLEASE HELP!!!

Answers

You didn't give us a picture but I'll help you as best as I can.

First, convert the equation into the form y=mx+b:
15x-5y=30
-5y=-15x+30

Divide both sides by -5.
y=-3x-6

Below is a graph of that equation:

Final answer:

To choose the correct graph that represents the equation 15x - 5y = 30, isolate y, find the slope and y-intercept, and compare to the given graphs.

Explanation:

In order to choose the correct graph that represents the equation 15x - 5y = 30, we need to solve the equation for y.

First, let's isolate y by subtracting 15x from both sides of the equation:

15x - 5y - 15x = 30 - 15x

-5y = -15x + 30

Next, divide both sides of the equation by -5 to find the value of y:

-5y/-5 = (-15x + 30)/-5

y = 3x - 6

Now that we have the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can determine the graph that represents the equation. The slope of the equation is 3, which means that for every 1 unit increase in x, y increases by 3 units. The y-intercept is -6, which means that the graph intersects the y-axis at the point (0, -6).

Based on this information, we can determine that the graph that correctly represents the equation 15x - 5y = 30 is the one where the slope is 3 and it intersects the y-axis at (0, -6).

Learn more about Choosing the correct graph for an equation here:

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