Please Help I’m failing geometry and I need to pass this

The volume of the region bounded by the coordinate planes, the plane xy=6, and the cylinder y^2+z^2=36 is 108π cubic units.

To find the volume of the region bounded by the coordinate planes, the plane xy=6, and the cylinder y^2+z^2=36, we can use a triple integral to calculate the volume.

Let's set up the integral based on the given region:

The coordinate planes bound the region, so we can set the limits of integration as follows:

For x: From 0 to ∞

For y: From 0 to 6/x (derived from the equation xy=6)

For z: From -√(36-y^2) to √(36-y^2) (derived from the equation y^2+z^2=36)

The volume integral setup is as follows:

V = ∫∫∫ R dV

V = ∫[0, ∞] ∫[0, 6/x] ∫[-√(36-y^2), √(36-y^2)] dz dy dx

Now, we evaluate the integral:

V = ∫[0, ∞] ∫[0, 6/x] [√(36-y^2) - (-√(36-y^2))] dy dx

V = ∫[0, ∞] ∫[0, 6/x] 2√(36-y^2) dy dx

To simplify the integration, we can change the order of integration:

V = ∫[0, 6] ∫[0, 6/y] 2√(36-y^2) dx dy

Now, let's integrate with respect to x:

V = ∫[0, 6] [2x√(36-y^2)] from 0 to 6/y dy

V = ∫[0, 6] (12√(36-y^2)) dy

To further simplify the integration, we can make a substitution y = 6sinθ:

dy = 6cosθ dθ

When y = 0, θ = 0

When y = 6, θ = π/2

V = ∫[0, π/2] (12√(36-(6sinθ)^2)) 6cosθ dθ

V = 72 ∫[0, π/2] (√(36-36sin^2θ)) cosθ dθ

V = 72 ∫[0, π/2] (6cosθ) cosθ dθ

V = 432 ∫[0, π/2] (cos^2θ) dθ

Using the trigonometric identity cos^2θ = (1 + cos2θ)/2, we have:

V = 432 ∫[0, π/2] [(1 + cos2θ)/2] dθ

V = 432/2 ∫[0, π/2] (1 + cos2θ) dθ

V = 216 [θ + (1/2)sin2θ] from 0 to π/2

V = 216 [(π/2) + (1/2)sin(2π/2) - (0 + (1/2)sin(2*0))]

V = 216 (π/2 + 0 - 0)

V = 108π

Therefore, the volume of the region bounded by the coordinate planes, the plane xy=6, and the cylinder y^2+z^2=36 is 108π cubic units.

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Answer:

6 and 7

Step-by-step explanation:

Pythagorean theorem,      

          \(\sf hypotenuse^2 = leg_1^2 + leg_2^2\)      

                             = 2² + 6²

                            = 4 + 36

                            = 40

   hypotenuse     = √40

40 is between the perfect squares 36 and 49.

So, √40 will be between √36 and √49.

⇒ √40 will be between 6 and 7.

According to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

Odds and probability are two different concepts.

Calculating odds involves dividing the probability of an event by the probability that it won't happen.

Probability is the study of random events in mathematics, and it can be classified into four main categories: axiomatic, classical, empirical, and subjective.

So, we must determine the likelihood that a standard normal random variable will occur with a probability between 0.3 and 3.2.

First, a standard normal random variable with a mean and standard deviation is introduced.

We must determine the likelihood that a standard normal random variable will fall within the range of 0.3 and 3.2.

The likelihood therefore should be:

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using z's typical value:

P(0.3<z<3.2)=0.9993−0.6179

Simplify as follows:

P(0.3<z<3.2)=0.3814

Therefore, according to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

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SAS

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Answer: 180°

Step-by-step explanation:

If given the bearing from B to A, the bearing from A to B can be found using interior angles. Subtract the bearing of B to A from 180° to find the missing interior angle, then use the fact that angles in a full turn add to 360° to find the bearing of A to B.

Answer:

x = -2

Step-by-step explanation:

y + 2x = -1

y = 1/2 x + 4​

y + 2x= -1

(1/2x + 4) + 2x = -1

1/2x + 2x + 4 = -1

5/2x + 4 = -1

5/2x = -5

x = -2

Answer:

x = -2

Step-by-step explanation:

First, we need to represent y in terms of x by using the first equation. If we do this we will get the following...

y + 2x = -1

y = -1 - 2x

Now we substitute the "y" in the second equation with an equal value in terms of "x" that we got in the last equation, and we will get the follolowing equation...

\(y = \frac{1}{2} x + 4\\- 1 - 2x = \frac{1}{2} x + 4\\-2 -4x = x + 8\\-4x - x = 8 + 2\\- 5x = 10\\5x = -10\\x = 10 /5\\x = 2\)

The number of quarters that Alexa has is 13 and the number of dimes she has is 5.

The first step is to determine the system of equation using the information in the question:

0.1d + 0.25q = 4.75 equation 1

d - q = 2 equation 2

Where:

The elimination method would be used to determine the required values:

Multiply equation 2 by 0.1

0.1d - 0.1q = 0.2 equation 3

Subtract equation 3 from equation 1

0.35q = 4.55

Divide both sides of the equation by 0.15

q = 4.55 / 0.35

q = 13

Substitute for q in equation 2

d - 13 = 2

d = 13 + 2

d = 15

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(A) bb and ss are not mutually exclusive because P(B∩S)=5/78.

Given total students = 78
students in band = 35
students in sports = 32
students not in band Or sports = 16
total students in band, in sports, not in both = 35 + 32 + 16 = 83
the students which are in both band and sports = 83 - 78 = 5


We know that,
P(B) = probability of selecting a student which in band
P(S) = probability of selecting a student which in sports
P(B∩S) = P(B) * P(S)
P(B∩S) = 5/78

So there are 5 students who are both in the band and in a sports team. The events can occur at the same time, they are not mutually exclusive.
So (A) is the right answer bb and ss can not be mutually exclusive since P(B∩S)=5/78

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The full question is :

A high school science teacher has 78 students. Of those students, 35 are in the band and 32 are on a sports team. There are 16 students who are not in the band or on a sports team. One student from the 78 students will be selected at random. Let event bb represent the event of selecting a student in the band, and let event ss represent the event of selecting a student on a sports team. Are bb and ss mutually exclusive events?
A) No, because P(B∩S)=5/78
B) No, because P(B∩S)=48/78
C) No, because P(B∩S)=62/78
D) Yes, because P(B∩S)=5/78
E) Yes, because P(B∩S)=62/78

"Centripetal is the word used to describe a vector that always points toward the centre of a circular path."

The centripetal acceleration vector is an acceleration in the radial direction that is directed towards the centre of the circular line of motion. It runs perpendicular to the linear motion, or v.

The direction of the velocity shift for a ball travelling around a curve is in the direction of the curve's centre. Centripetal acceleration is the acceleration that is directed towards the centre of a curved or circular route.

Any force that changes the path of motion towards the centre of a circular motion is known as a centripetal force. The portion of the force that produces the centripetal force is the part that is perpendicular to the velocity.

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Boundary value analysis is a testing technique used to identify defects or issues at the boundaries or limits of input values. True, in boundary value analysis both valid and invalid inputs are tested to verify potential issues.

Boundary value analysis is a testing technique used to identify defects or issues at the boundaries or limits of input values. The main idea is to test inputs that are just above, just below, and exactly at the specified boundaries or limits. This helps in uncovering potential issues that may arise due to boundary conditions.

Valid inputs are those that fall within the acceptable range of values, while invalid inputs are those that fall outside the acceptable range of values. Both valid and invalid inputs are tested during boundary value analysis to ensure thorough testing of the system under test. By testing valid inputs, we can verify if the system handles inputs within the acceptable range correctly. By testing invalid inputs, we can identify any issues or defects that may arise when inputs fall outside the acceptable range.

Therefore, in boundary value analysis, both valid and invalid inputs are tested to verify potential issues or defects in the system

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Answer:

150, 108, 90 , 12

Step-by-step explanation:

Angle in France:

= Fraction occupied by France x 360 degrees

= 25/60 x 360

= 150

Angle in Spain:

= 18/60 x 360

= 108

Angle in Greece:

= 15/60 x 360

= 90

Angle in OTHER:

= 2/60 x 360

= 12

Answer:

72

Step-by-step explanation:

C = pi* d

pi= 3 (given in the problem)

d=24(the diameter is given in the picture)

C= 3*24 = 72

The volume of a cylinder with a height of 9 cm and a radius of 3 cm in terms of π is 81π cm³

Volume of cylinder = πr²h

where,

So,

Volume of cylinder = πr²h

= π × 3² × 9

= π × 9 × 9

= 81π cm³

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Answer:

Step-by-step explanation:

If Madison purchased 2 more frozen dinners than cans of soup, then we have the equation

If each can of soup has 500 mg, each dinner is 700 mg, and she bought 7400 mg of sodium total, we can come up with the equation

Replacing the d in  with s + 2, we get the equation

Using the distributive formula, we get

Simplifying this equation gives

6000/1200 = 5

so s = 5

if d = s + 2, d must equal 7

So Madison ordered 5 cans of soup and 7 frozen dinners.

Correct me if im wrong smiley

Answer:

D

Step-by-step explanation:

You can tell it's a right angle by the box drawn

Answer:

D. The number will be less than 1 because when adding the exponents,

11 + (-14) = -3, and a number in scientific notation with a negative exponent is less than 1.

Step-by-step explanation:

The question lacks appropriate option. Find the options below;

A. The value will be greater than 1 because 4.296 x 10^11 is a very large number and multiplication always increases the size of a number.

B. The value will be greater than 1 because 4 x 2 = 8 and 8 is larger than 1.

C. The value will be less than 1 because (4.296 x 10^11) x (1.8614 x 10^-14) will be a negative number. All negative numbers are less than one.

D. The number will be less than 1 because when adding the exponents,

11 + (-14) = 3, and a number in scientific notation with a negative exponent is less than 1.

Given the expression \((4.296*10^{11})(1.8614*10^{-14})\), to expand the expression we will apply some of the law of indices below. If a, b and m are integers

\(a^m*a^n = a^{a+m}\)

\(= (4.296*10^{11})(1.8614*10^{-14})\\\\= (4.296*1.8614)(10^{11}*10^{-14}) \\\\= 7.9965744 * 10^{11}*10^{-14}\\sum \ up \ the\ power\ of\ the \ exponents\\\\= 7.9965744 *10^{11-14}\\\\= 7.9965744 *10^{-3}\\\)

= 0.0079965744

Based on the result, it can be seen that the resulting value is less than 1 due to the negative power of its exponent (i.e -3). Any scientific notation having a negative exponent always returns a value that is less than 1.

Answer:

The number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1.

Step-by-step explanation:

Took the quiz (:

1 cup of milk is used with 3/4 cup of water

Explanation:

milk : water

1/3 : 1/4

x12 to get rid of fractions:

12/3 : 12/4

= 4/3

which means 4 cups of milk are used with 3 cups of water

÷4:

1 cup of milk is used with 3/4 cup of water.

Answer: I calculated the value after 5 years to be 5,734.40 or 5,734

Step-by-step explanation:

Answer:

1. -3/1

2.negative

3.$18

Step-by-step explanation:

since the graph is going down, it is negative, and look at the ending points on the x and y-axis. 18/6 is 3. so the slop is -3 :)

Answer:

1. -3

2. negative

3. $18

Step-by-step explanation:

1. slope is rise/run so...

-3/1=-3

2. because run was a change of 3 DOWN the y axis we and run is a change of 1 to the right on x axis we have a negative slope. -3

3. she borrowed $18. Vertical intercept means the point where our line crosses the vertical axis. (Vertical axis is Y axis.)

The value of the missing number and the 6th term is 3750

The formula for determining the nth term of a geometric sequence with a common ratio greater than one is expressed as;

Tn = ar^n-1

From the information given, the first term(a) is 6 and we are to find the 5th term, thus, n is 5

Let's substitute into the formula

T5 = 6 × 5^5-1

T5= 6× 5^4

Find the value

T5 = 6 × 625

T5 = 3750

Thus, the value of the missing number and the 6th term is 3750

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Hey there!

\(3x+6*4x-1\)

Let's add parenthesis to 6 and 4 and remove the multiplication sign.

\(3x+(6)(4)x-1\)

This equals:

\(3x+24x+-1\)

Now we have to combine the like terms.

\(3x+24x+-1\)

Separate with parenthesis.

\((3x+24x)+(-1)\\Equals\\27x+-1(ANSWER)\)

\(-TestedHyperr\)

write question correctly

Answer:

= 15/20 + 1 10/20 + 4 4/20

= 5 29/20

= 6 9/20

Exact Form:

\(\frac{3}{4}\)

Decimal Form:

6.45

Mixed Number Form:

6\(\frac{9}{12}\)

Answer:

12 and 3

Step-by-step explanation:

3 * 4 = 12

12 + 3 = 15

Answer:

1.) Time in minutes

2.) Distance in feet.

Step-by-step explanation:

What is the independent quantity?

Independent quantity are the domain. In this question since the rate is 400 feet per minute, this can be refer to slope.

The independent quantity is therefore the time in minutes.

What is the dependent quantity?

Dependent quantity depends on independent quantity. Since time is the independent quantity, distance in feet will be the dependent quantity.

1. I based my decision on allocating points to maximize my own score, while also considering the potential benefits of contributing to the group fund.

2. The best outcome for me would be allocating the minimum points required to the GIVE account, while putting the majority in the KEEP account. This would ensure I receive the most points for myself.

3. The best outcome for the group would be if both participants maximized their contributions to the GIVE account. This would create the largest group fund, resulting in the most redistributed points and highest average score.

4. There are parallels with risk management strategies. Individuals may act in their own self-interest, but a larger group benefit could be achieved if more participants contributed to "group" risk management strategies like vaccination, safety protocols, insurance policies, etc. However, some individuals may free ride on others' contributions while benefiting from the overall results. Incentivizing group participation can help align individual and group interests.