Find the volume of the ellipsoid x^2 + y^2 + 9 z^2 = 64 using cylindrical Coordinates. (Calculus 3)

Answer:

m∠1 = 41°

m∠2 = 139°

Step-by-step explanation:

Set variables:

  1. ∠1 = x

  2. ∠2 = y

Make first equation:

It says "m∠2 is 16 more than 3 times m∠1."

So let's convert that into an equation:

y = 16° + 3x

Now, by looking at the photo, we can tell that its a straight line, which is equal to 180°

Derived from that, we can get m∠1 + m∠2 = 180°, which in other "words" is x + y = 180°.

Great, now we have our 2 equations, and we just have to solve.

Equations:

  1. y = 16° + 3x

  2. x + y = 180°

Let's substitute what we have for y into the second equation:

x + (16° + 3x) = 180°

Solve:

(We can take out parentheses because it's a "+" sign)

Combine like terms:

4x + 16° = 180°

Subtract 16° from both sides

4x = 164°

Isolate x by dividing both sides by 4

x = 41°

Substitute:

Now that we have x = 41°, we can substitute that in for the equation - "y = 16° + 3x"

New Equation:

y = 16° + 3(41°)

Solve:

Multiply 3 and 41°, which is 123°

y = 16° + 123°

Simplify:

y = 139°

Reminder:

m∠1 = x

m∠2 = y

Therefore,

m∠1 = 41°

&

m∠2 = 139°

Hopefully this helps!

(If you want, please mark me brainliest tomorrow)

Answer:

Basically, a straight line is equal to 180 degrees. If angle 2 is 16 more than 3 times angle 1, we get the equation of y = 16 + 3x. Put them together and you get x + 16 + 3x = 180. Then you just solve, and get x = 41. Then you put x in for the other equation and get y = 139.

Answer:

The sum of the sequence is 40.

Step-by-step explanation:

The given sequence is an arithmetic sequence with a common difference of 3. To find the value of n for the number 14 in the sequence, we can use the explicit formula for an arithmetic sequence:

a_n = a_1 + (n-1)d

where a_n is the nth term of the sequence, a_1 is the first term, d is the common difference, and n is the term number.

Substituting the given values, we get:

14 = 2 + (n-1)3

Simplifying the equation, we get:

12 = 3n - 3

15 = 3n

n = 5

Therefore, the number 14 appears as the 5th term in the sequence.

To find the sum of the sequence, we can use the arithmetic sum formula:

S_n = (n/2)(a_1 + a_n)

where S_n is the sum of the first n terms of the sequence.

Substituting the given values, we get:

S_5 = (5/2)(2 + 14)

S_5 = 40

Therefore, the sum of the sequence is 40.

Step-by-step explanation:

the difference is 3 a is is first term which is 2

the formula is sn= a+(n-1)d

2+(n-1)3

2+(3n-3)

The correct inequality that represents the statement "One half of a number decreased by 3 is at most -5" is option C) x ≤ -4.

What is an inequality?

Let's start by defining a variable for the number we are trying to find. Let's call it "x".

"One half of a number" can be represented as (1/2)x.

"Decreased by 3" means we need to subtract 3 from (1/2)x. So, "one half of a number decreased by 3" can be represented as:

(1/2)x - 3

Now, the problem says that this expression is "at most -5". "At most" means that the expression can be equal to -5 or any number less than -5. We can represent this as:

(1/2)x - 3 ≤ -5

To simplify this inequality, let's add 3 to both sides:

(1/2)x ≤ -2

Multiplying both sides by 2 (to eliminate the fraction) gives:

x ≤ -4

Therefore, the correct inequality that represents the statement "One half of a number decreased by 3 is at most -5" is option C) x ≤ -4.

To know more about inequality, visit:

https://brainly.com/question/30228778

#SPJ1

Answer:

Step-by-step explanation:

Question 1:

Answer:

[tex]C:25\frac{1}{3}[/tex]

Step-by-step explanation:

To find the number of pounds of milk chocolate sold, you have to multiply the amount of pounds of white chocolate sold by 4.

[tex](6+\frac{1}{3}) *4\\\\(6*\frac{3}{3}+\frac{1}{3})*4\\\\(\frac{18}{3} +\frac{1}{3} )*4\\\\\frac{19}{3} *4\\\\\frac{76}{3} \\\\25\frac{1}{3}[/tex]

Question 2:

Answer:

C: 19

Step-by-step explanation:

To find how many more pounds of milk chocolate were sold we subtract the white chocolate sold from the milk chocolate sold

[tex]25+\frac{1}{3} - 6+\frac{1}{3}\\\\25*\frac{3}{3}+\frac{1}{3}-6*\frac{3}{3}+\frac{1}{3}\\\\\frac{76}{3}-\frac{19}{3}\\\\\frac{57}{3}\\\\19[/tex]

Step-by-step explanation:

so you can do it in this way

No. The function is nonlinear and its slope is not constant.

A linear function can be written in this form, y = a + bx.

In this function, b is the slope of the line. The slope describes the constant unit of change in x, the independent variable, that will result in a change in y by the amount of b.

The slope can be determined as the change in y/change in x or rise/run.

In a nonlinear function, the slope does not produce a constant unit of change in that results in a change in y by the amount of b.

Thus, while a linear function shows a straight line when graphed, a nonlinear function shows a curve.

Learn more about linear and nonlinear functions at https://brainly.com/question/1418397.

#SPJ1

Step-by-step explanation:

The density of gold is given as 5×2^2 grams/cm³, which means that one cubic centimeter of gold has a mass of 5×2^2 grams.

To find the mass of 8 × 25 cm³ of gold, we need to first find the total volume of gold:

Total volume = 8 × 25 cm³ = 200 cm³

Now we can use the density of gold to find the mass:

Mass = Density × Volume

Mass = (5×2^2 grams/cm³) × 200 cm³

Mass = 5 × 4 × 200 grams

Mass = 4000 grams

Therefore, the mass of 8 × 25 cm³ of gold is 4000 grams.

Answer:

I have graphed it and attached it in the explanation part.

Step-by-step explanation:

y ≥ 3x - 2 is the red line.

y ≥ 1 is the blue line.

The height of the box must be at least 2.9111 feet.

The volume of the cylinder is given by the formula V = πr²h, where r is the radius of the cylinder and h is its height.

Since the width of the cylinder is 3 feet, the radius is 1.5 feet.

The volume of the oil is 15 gallons, which is equivalent to 0.2 cubic feet. We know that this volume of oil takes up 75% of the space between the cylinder and the box, so the total space between the cylinder and the box is 0.2 / 0.75 = 0.2667 cubic feet.

Since the cylinder fits perfectly inside the box, the volume of the box is equal to the volume of the cylinder plus the space between the cylinder and the box. Therefore, we have:

Volume of box = Volume of cylinder + Volume of oil

Volume of box  = πr²h + 0.2667

Substituting the values we have:

Volume of box = π(1.5)²h + 0.2667

Volume of box = 7.0686h + 0.2667

To find the height of the box, we need to isolate h. We know that the volume of the box must be greater than or equal to the volume of the cylinder, so we can set up the inequality:

Volume of box  ≥ Volume of cylinder

πr²h + 0.2667 ≥ πr²(3)

h + 0.0889 ≥ 3

h ≥ 2.9111

Therefore, the height of the box must be at least 2.9111 feet.

To know more about radius, visit:

https://brainly.com/question/13449316

#SPJ1

Answer:

[tex]V=(3.14)(2.25)^2(3)[/tex]

Step-by-step explanation:

In order to find the volume of a cylinder you have to use the formula [tex]V=\pi r^2h[/tex]

For [tex]\pi[/tex], we plug in 3.14 (because that is what the question asks for)

To find the radius (r), we take half of the diameter

[tex]4.5/2[/tex]

For h, we plug in the height of the mold

When we plug all of these in, we get

[tex]V=(3.14)(2.25)^2(3)[/tex]

I think the answers 3048_&8_9_)_)_

The statement "cos 0° = 1, because the angles are complements" is true.

Answer: 9.84*10^6

Step-by-step explanation: Multiply 2.46 by 4

If the federal reserve sets the reserve rate to %4, the resulting money multiplier is 25.

The link between the quantity of reserves kept by banks and the amount of money that may be generated through the practise of fractional reserve banking is known as the "money multiplier" in economics and finance. Under a system known as fractional reserve banking, banks are only obligated to maintain a portion of their deposits as reserves and are free to lend the remainder to borrowers.

The reserve ratio, or the percentage of deposits that banks must retain in reserves, is used to compute the money multiplier.

The money multiplier is determined using the formula:

Money multiplier = 1 / reserve ratio

Given the reserve ratio is 4% = 0.04.

Thus,

Money multiplier = 1 / 0.04 = 25

Hence, if the federal reserve sets the reserve rate to %4, the resulting money multiplier is 25.

Learn more about money multiplier here:

https://brainly.com/question/14986591

#SPJ1

The two numbers that multiply to 2 but add to -5 are -1 and -2.

The two numbers that multiply to 2 and add to -5 are -1 and -2.

To see why, you can use the factoring method:

Find two numbers whose product is 2 (possible pairs are 1 and 2, or -1 and -2).

Check if their sum is -5.

If you use 1 and 2, the sum is 3, so they don't work.

If you use -1 and -2, the sum is -3-2 = -5, so they work.

Therefore, -1 and -2 are the two numbers that multiply to 2 and add to -5.

Learn more about  prime number at https://brainly.com/question/145452

#SPJ1

Answer: You're answer is 3

or exactly 3.464.

[tex]\sqrt{100}[/tex]Answer:

10

Step-by-step explanation:

You have to reverse the square root [tex]3\sqrt{12}[/tex]

what perfect square makes 3? 9.

what is [tex]\sqrt{9} \sqrt{12}[/tex]

[tex]\sqrt{108}[/tex]

what is the perfect square between 108? 100 and 121.

what is the different between them?

108-100=8

121-108=13

obviously, 8 is closer than 13, so now find the square root of the closer perfect square.

[tex]\sqrt{100}[/tex]=10

Answer: option B.

Step-by-step explanation:

We can use the formula for the margin of error of a confidence interval for a proportion:

Margin of error = zsqrt(p(1-p)/n)

where z is the critical value from the standard normal distribution for the desired confidence level (98% in this case), p is the estimated proportion (0.60), and n is the sample size.

We are given that the margin of error should be 0.07. Setting this equal to the above expression, we have:

0.07 = zsqrt(0.60(1-0.60)/n)

We need to solve for n. To do this, we first need to find the appropriate value of z for a 98% confidence level. Using a standard normal distribution table or calculator, we can find that z = 2.33.

Substituting this into the above equation and solving for n, we have:

0.07 = 2.33sqrt(0.60(1-0.60)/n)

Squaring both sides and solving for n, we get:

n = (2.33^2)(0.60(1-0.60))/(0.07^2) ≈ 265

Therefore, the sample size needed to construct a 98% confidence interval with a margin of error of 0.07 is approximately 265.

So the correct answer is option B.

Value of m and b of the straight line in the graph is 0 and 2 respectively.

In mathematics, slope refers to the steepness or inclination of a line, and is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. It is often represented by the letter m. The slope of a line can be positive, negative, zero, or undefined.

Let us assume that the equation of line be y=mx+b.

where m is the slope

and b is the intercept

The line in the graph is parallel to x axis

so, slope is 0

m=0

the line passes through(0,2)

Putting the value in the equation, we get

b=2

Hence, the equation of line be y=2

Therefore, value of m=0 and b=2.

to know more about coordinate, visit:

https://brainly.com/question/16634867

#SPJ1

The complete question is:

The graph is showing the equation of straight line y=mx+b, find the value of m and b.

Image is attached below:

Answer:

Step-by-step explanation:

Value of x :-

Therefore, the value of x is 23.

________________________

Hope this helps!

The line of tangency at the point (–6, 3) is x = -6. So, the correct option is (b).

What is tangent?

In geometry, the tangent is a trigonometric function that relates to the angles and sides of a right triangle. Specifically, the tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the adjacent side.

To find the line of tangency to a circle at a given point, we need to first find the slope of the radius that passes through that point, and then take the negative reciprocal of that slope to get the slope of the tangent line.

Given the circle equation: (x + 2)² + (y - 3)²  = 16, we can see that its center is at the point (-2, 3) and its radius is 4.

To find the slope of the radius passing through the point (-6, 3), we can use the point-slope formula:

(y - y1) = m(x - x1)

where m is the slope of the radius, and (x1, y1) is the center of the circle (-2, 3). Plugging in the values, we get:

(y - 3) = m(x + 2)

Substituting the point (-6, 3) into the equation, we get:

(3 - 3) = m((-6) + 2)

0 = -4m

m = 0

So the slope of the radius is 0. To find the slope of the tangent line, we take the negative reciprocal of the slope of the radius:

slope of tangent line = -1/0 = undefined

Since the slope of the tangent line is undefined, it must be a vertical line passing through the point (-6, 3). Thus, the line of tangency at the point (-6, 3) is the vertical line x = -6.

To learn more about tangent, visit the link:

https://brainly.com/question/31186629

#SPJ1

The x-coordinate (or t-coordinate) of the vertex is 1.5 seconds and represents the time at which the rocket reaches its maximum height. The y-coordinate (or h-coordinate) of the vertex is 334 feet and represents the maximum height reached by the rocket.

A function is a mathematical relationship that describes how one quantity (the output or dependent variable) depends on one or more other quantities (the inputs or independent variables).

A function can be thought of as a machine that takes in input values, applies a set of rules or operations to them, and produces an output value. The input values can be any set of numbers or other objects that the function is defined for, and the output values can be any set of numbers or objects that the function can produce.

To find the x-coordinate (or t-coordinate) of the vertex, we can use the formula:

x = -b / (2a)

where a is the coefficient of the squared term, b is the coefficient of the linear term, and x represents the time at which the rocket reaches its maximum height. The equation of the parabolic function that models the height of the rocket is:

h = at² + bt + c

where h is the height of the rocket at time t.

We can use the coordinates of the points on the parabola to find the values of a, b, and c:

(0, 260): 260 = a(0)² + b(0) + c, so c = 260

(2, 324): 324 = a(2)² + b(2) + 260, so 4a + 2b = 64

(6.5, 0): 0 = a(6.5)² + b(6.5) + 260, so 42.25a + 6.5b = -260

We can solve this system of equations to find the values of a and b:

4a + 2b = 64

42.25a + 6.5b = -260

Multiplying the first equation by 3.25 and subtracting from the second equation, we get:

42.25a + 6.5b - 13a - 6.5b = -260 - 208

29.25a = -468

a = -16

Substituting a = -16 into the first equation, we get:

4(-16) + 2b = 64

b = 48

Therefore, the equation of the parabolic function is:

h = -16t² + 48t + 260

The x-coordinate (or t-coordinate) of the vertex is:

t = -b / (2a) = -48 / (2(-16)) = 1.5

The x-coordinate (or t-coordinate) of the vertex is 1.5 seconds and represents the time at which the rocket reaches its maximum height.

To find the y-coordinate (or h-coordinate) of the vertex, we can substitute t = 1.5 into the equation of the parabolic function:

h = -16(1.5)² + 48(1.5) + 260 = 334

Therefore, the y-coordinate (or h-coordinate) of the vertex is 334 feet and represents the maximum height reached by the rocket.

To know more about coefficient visit:

https://brainly.com/question/30220934

#SPJ1

The complete question is:

Answer:4x^2-4x-1

Step-by-step explanation:

Answer:

−x2−6x+8

Step-by-step explanation:

1,Rearrange terms

2.Distribute

3.Add the numbers

4.combine like terms

hope this helps i lfet some steps for you!!!<3333

The greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³ is 3s²t², and the factored expression is 3s²t²(2st² + 4s² - 5t).

The greatest positive integer that divides two or more numbers without leaving a residual is known as the greatest common factor (GCF). In other words, the greatest number that is a factor of both (or all) of the specified numbers is chosen.

To identify the greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³, we need to look for the largest expression that divides evenly into each term.

First, we can factor out the greatest common factor of the coefficients, which is 3: 3(2s³t⁴ + 4s⁴t² - 5s²t³)

Next, we can look for the greatest common factor of the variables. We can see that s²t² divides into each term: 3s²t²(2st² + 4s² - 5t)

Therefore, the greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³ is 3s²t², and the factored expression is 3s²t²(2st² + 4s² - 5t).

To know more about factored expression, visit

brainly.com/question/19386208

#SPJ1

Answer:

Zoe started with 7.917 meters of cloth.

Step-by-step explanation:

If each pillowcase uses 5/8m of cloth and Zoe made 12 pillowcases, then the total amount of cloth used is:

(5/8) x 12 = 15/2 or 7.5 meters

If Zoe has 5/12m of cloth left, then the total amount of cloth she started with is:

7.5 + 5/12 = 90/12 + 5/12 = 95/12 or 7.917 meters

Therefore, Zoe started with 7.917 meters of cloth.

Answer:

B

Step-by-step explanation:

Answer:

its either D or C but I think its D

Step-by-step explanation:

Answer:

50 pages are filled with stamps.

Step-by-step explanation:

If 50% of the album is empty, then 50% of the album is filled with stamps.

So, the total number of stamps that the album holds is 500, and half of that (50%) is filled with stamps, which is:

500 * 50% = 250 stamps

Each page holds 5 stamps, so the number of pages filled with stamps is:

250 stamps / 5 stamps per page = 50 pages

Therefore, 50 pages are filled with stamps