solve all 4 please. ​

Answer:

At least 6 but are there answer choices or at least a picture of the mixture

~ Zachary

Using  cylindrical coordinates ∫∫∫ (r^3cos^2θ) dz dr dθ, where r ranges from 0 to 2, θ ranges from 0 to 2π, and z ranges from 0 to √(36r^2).

To evaluate the integral ∫∫∫ x^2 dV over the solid e, using cylindrical coordinates, we need to express the integral in terms of cylindrical coordinates and determine the appropriate bounds for the variables.

In cylindrical coordinates, the solid e can be defined as follows:

Radius: r ranges from 0 to 2 (from x^2 + y^2 = 4, taking the square root).

Angle: θ ranges from 0 to 2π (full revolution around the z-axis).

Height: z ranges from 0 to the height of the cone, which is determined by z^2 = 36x^2 + 36y^2.

To convert the integral, we need to express x^2 in terms of cylindrical coordinates:

x^2 = (rcosθ)^2 = r^2cos^2θ

The integral in cylindrical coordinates becomes:

∫∫∫ (r^2cos^2θ) r dz dr dθ

Now we can determine the bounds for the variables:

r ranges from 0 to 2.

θ ranges from 0 to 2π.

z ranges from 0 to the height of the cone, which can be determined by setting z^2 = 36r^2.

Substituting the bounds and integrating, we can evaluate the integral to find the desired result.

To know more about cylindrical coordinates refer here:

https://brainly.com/question/30394340

#SPJ11

Answer:

24

Step-by-step explanation:

\( {ba}^{2} = {bc}^{2} - {ac}^{2} \\ {ba}^{2} = {10 }^{2} - {8}^{2} \\ ba = \sqrt{100 - 64} \\ ba = \sqrt{36 } \\ ba = 6\)

Area of triangle = 1/2 × AC × BA

= 1/2 × 8 × 6

= 48/2

= 24 in²

25r(cos^2Ф-sin^2Ф)-6cosФ=0

The equation in rectangular coordinates is 25x2=25y2=6x, we need to write in cylindrical coordinates

The rectangular coordinate system consists of two real number lines that intersect at a right angle

In cylindrical coordinate, x=rcosФ

y=rsinФ

z=z

25(rcosФ)^2=25(rsinФ)^2=6rcosФ

25r^2cos^2Ф-25r^2sin^2Ф=6rcosФ

25r^2(cos^2Ф-sin^2Ф)=6rcosФ

25r(cos^2Ф-sin^2Ф)-6cosФ=0

25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required equation in cylindrical coordinates.

Therefore 25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required cylindrical equation

To learn more on rectangular system coordinates click here:https://brainly.com/question/21432890

#SPJ4

Answer:

8.4 Gallons

Step-by-step explanation:

15.54 divided by 1.85 is 8.4

Using the binomial probability principle, the probability of selecting two left-handed people at random is 0.0486.

In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment).

The binomial probability is nCx⋅px⋅(1−p)n−x if the likelihood of success on a given trial is p.

For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail.

A binomial probability distribution is another name for this distribution.

So, regarding a binomial distribution:

P(x = x) = nCx * p^x * q^(n-x)

Probability, p = 0.10

q = 1 - p = 1 - 0.10 = 0.90

and n = 4 trials.

Now, calculate as follows:
P(x = 2) = 4C2 × 0.10² × 0.90²

P(x = 2) = 6 × 0.01 × 0.81

P(x = 2) = 0.0486

Therefore, using the binomial probability principle, the probability of selecting two left-handed people at random is 0.0486.

Know more about binomial probability here:

https://brainly.com/question/9325204

#SPJ4

Correct question:
A small college has 800 students, 10%, percent of which are left-handed. Suppose they take an SRS of 444 students. Let X= equal the number of left-handed students in the sample.

What is the probability that exactly 2 of the 4 students are left-handed?

You may round your answer to the nearest hundredth.

Answer:

There is nothing wrong with the answer obtained

Step-by-step explanation:

Given the equation :

Y = mx + b

-2 = 3(4) + b

-2 = 12 + b

-14 = b

The correct calculation :

Y = mx + b

-2 = 3(4) + b

-2 = 12 + b

Subtract 12 from both sides

-2 - 12 = 12 + b - 12

-14 = b

Based on the details of the question given, the intercept, b is - 14 ;

Hence, there is nothing wrong with the answer

The probability of an outcome less than 5 in a discrete uniform distribution ranging from 2 to 9 inclusive is 37.5%.

In a discrete uniform distribution, each outcome has an equal probability of occurring. In this case, the range of possible outcomes is from 2 to 9 inclusive, which means there are a total of 8 possible outcomes (2, 3, 4, 5, 6, 7, 8, 9).

To calculate the probability of an outcome less than 5, we need to determine the number of outcomes that satisfy this condition. In this case, there are 4 outcomes (2, 3, 4) that are less than 5.

The probability is calculated by dividing the number of favorable outcomes (outcomes less than 5) by the total number of possible outcomes. So, the probability is 4/8, which simplifies to 1/2 or 0.5.

Therefore, the correct answer is B. 50.0%. The probability of an outcome less than 5 in this discrete uniform distribution is 50%, or equivalently, 0.5.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

Answer:

Explanation:

8.13×10¹⁴

Answer:

The equation of the line is y = \(-\frac{5}{6}\) x - 2

Step-by-step explanation:

The form of the linear function is y = m x + b, where

The rule of the slope is m =\(\frac{y2-y1}{x2-x1}\) , where

∵ The line passes through points (6, -7) and (-6, 3)

∴ x1 = 6 and y1 = -7

∴ x2 = -6 and y2 = 3

→ Substitute them in the rule of the slope above to find it

∵ m = \(\frac{3--7}{-6-6}\) = \(\frac{3+7}{-12}\) = \(\frac{10}{-12}\) = \(\frac{5}{-6}\)

∴ m = \(-\frac{5}{6}\)

→ Substitute it in the form of the equation above

∴ y = \(-\frac{5}{6}\) x + b

→ Substitute x and y in the equation by x1 and y1

∵ x1 = 6 and y1 = -7

∴ -7 = \(-\frac{5}{6}\) (6) + b

∴ -7 = -5 + b

→ Add 5 to both sides

∵ -7 + 5 = -5 + 5 + b

∴ -2 = b

→ Substitute the value of b in the equation

∴ y = \(-\frac{5}{6}\) x + -2

∴ y = \(-\frac{5}{6}\) x - 2

∴ The equation of the line is y = \(-\frac{5}{6}\) x - 2

Answer:

101

Step-by-step explanation:

101 X 8 = 808

Answer:

101

Step-by-step explanation:

The answer is one hundred and one (101)

#9) 180 - 116 = 64

(3x -13) + ( 2x +4 ) + 64 = 180

5x - 9 + 64 = 180

5x = 180 + 9 - 64

5x = 125

x = 25

#10) 3x - 13

= (3× 25) - 13 = 62

m< A = 62°

The minimum number of tiles will be 122 that Imane needs to cover the floor.

Multiply the area by the conversion ratio to convert a square foot measurement to a square inch measurement. Because one square foot equals 144 square inches, you may use the following easy formula to convert:

square inches = square feet × 144

The area in square inches is equal to the square feet multiplied by 144.

The floor she wants to cover has an area of 216 square feet.

The required area in square inches is :

216 × 144 = 31,104 sq in

Each tile covers an area of 256 square inches.

The minimum number of tiles = 31,104 sq in / 256 sq in

The minimum number of tiles = 121.5 ≈ 122

Thus, the minimum number of tiles will be 122 that Imane needs to cover the floor.

To learn more about the Conversion of Square Feet to Square Inches click here:

https://brainly.com/question/13880577

#SPJ1

In order to have an average speed of 6 miles per hour over the entirety of the trip, the man would need to travel 15 miles in the next 2 1/2 hours. This means that he would need to travel at a speed of 6 miles per hour for the remainder of the trip.

Answer:

$0.05/year

Step-by-step explanation:

Number of years:

2006 - 2004 = 2

From 2004 to 2006 it's 2 years.

Difference in prices:

$1.35 - $1.25 = $0.10

Average change of price per year:

$0.10 / 2 years = $0.05/year

92-√36 ×3√1000

92-√6^2 ×3√10^3

92-6×3×10√10

92-6×30√10

86×30√10

2580√10

There was $36 amount of money has Amy saved.

In mathematics, the Multiplication model performs Multiplying values on either side of the operator.

For example 4×2 = 8

The amount of money saved by Henry = $12

Since Amy has three times as much money as Henry.

The amount of money saved by Amy = $12 × 3

Apply the multiplication operation, and we get

The amount of money saved by Amy = $36

Hence, there was $36 amount of money has Amy saved.

Learn more about the Multiplication model here:

https://brainly.com/question/25573338

#SPJ9

The statement 'if you are balancing an object on its center of mass, there must be equal amounts of mass on both sides of the center of mass" is false.

A place at which the entire mass of a body or all the masses of a system of particles appears to be concentrated is defined as the center of mass of a body or system of particles.

We have statement:

If you are balancing an object on its center of mass, there must be equal amounts of mass on both sides of the center of mass.

As we know, center of a mass is an object balance point it doesn't need to have equal amounts of mass on both sides of the center of mass.

Thus, the statement 'if you are balancing an object on its center of mass, there must be equal amounts of mass on both sides of the center of mass" is false.

Learn more about the center of mass here:

https://brainly.com/question/8662931

#SPJ4

The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19

The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7

The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below

f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3

When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343

Then

f[g(x)] = - 64x³ - 336x² - 588x - 340

Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;

g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g

[f(x)] = -4x³ + 19

Therefore,

f[g(x)] = - 64x³ - 336x² - 588x - 340

g[f(x)] = -4x³ + 19

Learn more about the function at

https://brainly.com/question/32520165

#SPJ11

Compatible numbers are simply the approximated value of a number

Using the compatible numbers, the product of 2.4 and 0.18 is 0.5

The compatible numbers are given as:

The product is given as:

\(\mathbf{2.4 \times 0.18}\)

Replace 2.4 and 0.18 with their compatible numbers, 2.5 and 0.2, respectively

So, we have:

\(\mathbf{2.4 \times 0.18 =2.5 \times 0.2}\)

Calculate the product of 2.5 and 0.2

\(\mathbf{2.4 \times 0.18 =0.5}\)

Hence, the product of 2.4 and. 0.18 is 0.5.

Read more about compatible numbers at:

https://brainly.com/question/7068223

Answer:

(-8,-10)

Step-by-step explanation:

we have the two equations x-2y=12 and y=3x+14.

I'm going to assume this is a system of equations and we are looking for the solution.

we can use the substitution method as y is "defined".

x-2y= 12

substitute y = 3x + 14

x-2(3x+14)=12

distribute

x - 6x -28 = 12

combine like terms

-5x - 28 = 12

add 28 to both sides

-5x = 40

divide both sides by -5

x = -8

Now we plug in the value of x into one of the equations and solve for y

y = 3x + 14

x = -8

y = 3(-8) + 14

y = -24 + 14

y = 10

the solution is (-8,-10)

Answer:

112.5

Step-by-step explanation:

multiply 15 by 7.5

Using concept of geometric series, Assuming all conditions are perfect, and the environment is stable, the height of a potted plant on the 28th day, where the height of the plant h is 1cm on the first day and grows 6.5cm every day, with the growth rate r slowing by a third of its current rate every day is 37.75.

Given the question, height of plant on

day 1 = 1cm

day 2 = (1 + 6.5) cm

day 3 = \((1+6.5+ 6.5*\frac{1}{3})cm\)

...

day 28 =\((1+6.5+6.5*\frac{1}{3}^{2}...+6.5*\frac{1}{3}^{26})cm\)

A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.

\(a+ar+ar^2+ar^3+ar^4....ar^{n-1} = \frac{a(r^n-1)}{r-1}\)

Height of plant on day 28 =

\(=(1+6.5+6.5*\frac{1}{3}^{2}...+6.5*\frac{1}{3}^{26})cm\\\\=1+6.5(\frac{1}{3}^0+ \frac{1}{3}^1...+\frac{1}{3}^{26})\\\\=1+6.5(1-\frac{1}{3}^{27}) /(1-\frac{1}{3})\\ \\=37.75\)

Learn more about geometric series here

https://brainly.com/question/30264021

#SPJ4

Answer:

80

Step-by-step explanation:

You could multiply by 2 and then divide by 3

120*2 = 240

240/3 = 80

Or you could divide by 3 and then multiply by 2

120/3 = 40

40*2 = 80

Answer:

Step-by-step explanation:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

Answer:

The answer is 20s+10h=500

Step-by-step explanation:

The reason is because 20 times 20=400 and then 10 times 10= 100 then you add those together and get $500

The equation which we have created showing relationship between weights of both sides has a solution of y=1/2.

Given weight on one end is y+y+y+1+1+1 and weight on other end is y +y+ y+ y+2 where y is mystery weight.

We have to first form an equation.

If we see the figure we can notice that both sides are equal to other, it means the weight of both ends are equal to each other.

Equation is relationship between two or more variables expressed in equal to form. It is solved to find the value of variables. Equation of two variables look like ax+ by=c.

y+y+1+1+1=y+y+y+y+2

2y+3=4y+2

2y-4y=2-3

-2y=-1

y=1/2

Hence the solution of the equation a showing relationship between weights on both ends is y=1/2.

Learn more about equation at https://brainly.com/question/2972832

#SPJ4

Question is incomplete as it should include the given figure.