What is the volume of the cylinder below?

Answer:

Step-by-step explanation:

From the given information:

We can see that:

[tex]x + 2y + 3z = 0 --- (1) \\ \\ 2x + 4y + 6z = 0 --- (2)[/tex]

From equation (1), if we multiply it by 2, we will get what we have in equation (2).

It implies that,

x + 2y + 3z = 0    ⇔   2x + 4y + 6z = 0

And, W satisfies the equation x + 2y + 3z = 0

i.e.

W = {(x,y,z) ∈ R³║x+2y+3z = 0}

Now, to determine the distance through the plane W and point is;

[tex]y = [1 \ 1 \ 1]^T[/tex]

Here, the normal vector [tex]n = [1\ 2\ 3]^T[/tex] is related to the plane x + 2y + 3z = 0

Suppose θ is the angle between the plane W and the point [tex]y = [1 \ 1 \ 1]^T[/tex], then the distance is can be expressed as:

[tex]||y|cos \theta| = \dfrac{n*y}{|n|}[/tex]

[tex]||y|cos \theta| = \dfrac{[1 \ 2\ 3 ]^T [1 \ 1 \ 1] ^T}{\sqrt{1^2+2^2+3^2}}[/tex]

[tex]||y|cos \theta| = \dfrac{[1+ 2+ 3 ]}{\sqrt{1+4+9}}[/tex]

[tex]||y|cos \theta| = \dfrac{6}{\sqrt{14}}[/tex]

[tex]||y|cos \theta| = 3\sqrt{\dfrac{2}{7}}[/tex]

Answer:

5

Step-by-step explanation:

the only point in the chart, which has x=0 as coordinate, is the point up there at y=5.

and that is automatically the result. there is not anything else to it.

Answer:

Following are the complete solution to the given question:

Step-by-step explanation:

The two main elements are geometry. One of them is analyzing the form of something. The second element is distance thinking. Four dominant sides are united into the triangle. Its sides can be of any height, however, the biggest side can be even more than and equal to a sum of the other two sides. Also, there are two concentric angles in a triangular, with the overall amount of three angles being 180 °.

Answer:

The best way to create a linked list using PublListNode and Publication classes is ensuring that:

d. The PublListNode class contains the Publication class.

Step-by-step explanation:

A linked list contains a set of address-connected nodes (elements).  The first node is called a header address, while the last node is called a null address. A linked list can be a single list (linear list), double list, multiple linked list, or circular linked list.  The PublListNode is a type of multiple linked list.  It forms a linked list of different publications using an inheritance tree.

Answer:

Point estimate = 76.4

Margin of Error = 2.680

Step-by-step explanation:

Given that distribution is approximately normal;

The point estimate = sample mean, xbar = 76.4

The margin of error = Zcritical * s/√n

Tcritical at 95%, df = 42 - 1 = 41

Tcritical(0.05, 41) = 2.0195

Margin of Error = 2.0195 * (8.6/√42)

Margin of Error = 2.0195 * 1.327

Margin of Error = 2.67989

Margin of Error = 2.680

It looks like the equation reads

2yy' = exp(x - y ²)

(where exp(blah) = e ^(blah))

This DE is separable:

2y dy/dx = exp(x) exp(-y ²)

==>   2y exp(y ²) dy = exp(x) dx

Integrating both sides gives

exp(y ²) = exp(x) + C

The initial condition tells you that y = -2 when x = 4, so that

exp((-2)²) = exp(4) + C

exp(4) = exp(4) + C

==>   C = 0

Then the particular solution to this DE is

exp(y ²) = exp(x)

Solving for y as a function of x gives

y ² = x

y = ±√x

But bearing in mind that y = -2 < 0 when x = 4, only the negative square root solution satisfies the DE. So

y(x) = -√x

Answer:

7.3

Step-by-step explanation:

y=2.5x+5.8

=2.5×0.6+5.8

= 1.5+.8

=7.3

Answer: He can make 36 different salds

Step-by-step explanation:

[tex]\huge{\colorbox{pink}{Solution}}[/tex]

Step 1 : Equation at the end of step 1

(((7•(x^10 ))-5)•x)•(5x^10-8)

Step 2 : Equation at the end of step 2 :

((7x^10 - 5) • x) • (5x^10 - 8)

Step 3 :

Trying to factor as a Difference of Squares:

3.1 Factoring: 7x^10-5

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A² - AB + BA - B² =

A² - AB + AB - B² =

[tex] \: \: \: \: \: \blue {A² - B²}[/tex]

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 7 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares.

Equation at the end of step 3 :

x • (7x10 - 5) • (5x10 - 8)

Step 4 :

4.1 Factoring: 5x^10-8

Check : 5 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares.

Final result : ☞ x • (7x10 - 5) • (5x10 - 8)

→ 3.5 × 10^-12

____________________________

Hope It Helps You ✌️

Answer:

3/5 so A.

Step-by-step explanation:

Answer:

slope = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (1, 5)

m = [tex]\frac{5-2}{1-(-4)}[/tex] = [tex]\frac{3}{1+4}[/tex] = [tex]\frac{3}{5}[/tex]

Answer:

a) [tex]E(\bar x) = \mu_{1} = 22[/tex] inches

The sampling distribution of the sample means annual rainfall for California is 1.278.

b)

[tex]E(\bar x) = \mu_{2} = 42[/tex] inches

The sampling distribution of the sample means annual rainfall for New York is 1.0435.

c)

Here, The standard error of New York is smaller because the sample size is larger than for California.

Step-by-step explanation:

California:

[tex]\mu_{1} = 22[/tex] inches.

[tex]\sigma_{1}[/tex] = 7 inches.

[tex]n_{1}[/tex] = 30 years.

New York:

[tex]\mu_{2} = 42[/tex] inches.

[tex]\sigma_{2}[/tex] = 7 inches.

[tex]n_{2}[/tex] = 45 years.

a)

[tex]E(\bar x) = \mu_{1} = 22[/tex] inches

[tex]\sigma^{p} _{\bar x} = \frac{\sigma_{1} }{\sqrt n_{1} } \\\\\\\sigma^{p} _{\bar x} = \frac{7}{\sqrt 30} \\\\\sigma^{p} _{\bar x} = 1.278[/tex]

b)

[tex]E(\bar x) = \mu_{2} = 42[/tex] inches

[tex]\sigma _{\bar x} = \frac{\sigma_{2} }{\sqrt n_{2} } \\\\\\\sigma_{\bar x} = \frac{7}{\sqrt45} \\\\\sigma _{\bar x} = 1.0435[/tex]

c)

Here, The standard error of New York is smaller because the sample size is larger than for California.

Answer:

Step-by-step explanation:

You need to put parentheses around the radicands.

√z · √(30z²) · √(35z³) = √(z·30z²·35z³)

= √(1050z⁶)

= √(5²·42z⁶)

= √5²√z⁶√42

= 25z³√42

The obtained expression would be 25z³√42 which is determined by the multiplication of the terms of expression.

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

We have been the expression as:

⇒ √z · √(30z²) · √(35z³)

Multiply and remove all perfect squares from inside the square roots

⇒ √(z·30z²·35z³)

⇒ √(1050z⁶)

⇒ √(5²·42z⁶)

Assume z is positive.

⇒ √5²√z⁶√42

⇒ 25z³√42

Therefore, the obtained expression would be 25z³√42.

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Answer:

The answer is "0.59".

Step-by-step explanation:

Please find the whole question in the attached file.

Given:

[tex]\mu=26.8\\\\\sigma=6.4\\\\X=30.6[/tex]

Using formula:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

   [tex]=\frac{30.6-26.8}{6.4}\\\\=\frac{3.8}{6.4}\\\\=\frac{380}{640}\\\\=\frac{38}{64}\\\\=\frac{19}{32}\\\\=0.59375\approx 0.59[/tex]

Explanation:

For any rectangle, the diagonals are the same length.

AC = BD

7x-35 = 3x+45

7x-3x = 45+35

4x = 80

x = 80/4

x = 20

Answer:

7/26

Step-by-step explanation:

Add all of it up.

9 + 8 + 4 +5 = 26

26 cookies, but done twice so,

26 × 2 = 52

14/52 = 7/26

Answer:

1. (i) 7, 21, 63, 189

(ii) 20, 10, 5, 2.5

2. (i) n²+n (where n = 1, 2, 3, ..)

(ii) 8/(10^n) (where n = 1, 2, 3, ..)

(iii) 1/(n+1) (where n = 1, 2, 3, ..)

Given:

The cost function is:

[tex]C(x)=0.28x^2-0.7x+1[/tex]

where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands.

To find:

The minimum production cost.

Solution:

We have,

[tex]C(x)=0.28x^2-0.7x+1[/tex]

It is a quadratic function with positive leading efficient. It means it is an upward parabola and its vertex is the point of minima.

If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex of the parabola is:

[tex]\text{Vertex}=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]

In the given function, [tex]a=0.28, b=-0.7, c=1[/tex]. So,

[tex]-\dfrac{b}{2a}=-\dfrac{-0.7}{2(0.28)}[/tex]

[tex]-\dfrac{b}{2a}=1.25[/tex]

Putting [tex]x=1.25[/tex] in the given function to find the minimum production cost.

[tex]C(x)=0.28(1.25)^2-0.7(1.25)+1[/tex]

[tex]C(x)=0.28(1.5625)-0.875+1[/tex]

[tex]C(x)=0.4375+0.125[/tex]

[tex]C(x)=0.5625[/tex]

Therefore, the minimum production cost is 0.5625 million dollars.

Answer:

The minimum cost is 0.5625.

Step-by-step explanation:

The cost function is

C(x) = 0.28x^2 - 0.7 x + 1

Differentiate with respect to x.

[tex]C = 0.28x^2 - 0.7 x + 1\\\\\frac{dC}{dt} = 0.56 x - 0.7\\\\\frac{dC}{dt} = 0\\\\0.56 x - 0.7 = 0\\\\x = 1.25[/tex]

The minimum value is

c = 0.28 x 1.25 x 1.25 - 0.7 x 1.25 + 1

C = 0.4375 - 0.875 + 1

C = 0.5625

Answer:

4.) 10^2 + 24^2

Step-by-step explanation:

From the attached diagram, the area of a square A is given by the measure of the square of its hypotenus :

The hypotenus is given by :

Hypotenus² = opposite² + Adjacent²

Hypotenus² = 10² + 24²

The square of hypotenus =  10^2 + 24^2

P(Z ≥ z) = 1 - P(Z ≤ z) = 0.06

==>   P(Z ≤ z) = 0.94

==>   z ≈ 1.7507

Answer:

Range → {y| y ≥ -11}

Step-by-step explanation:

Range of a function is the set of of y-values.

Given function is,

f(x) = 2x² + 6x - 8

By converting this equation into vertex form,

f(x) = [tex]3(x^2+2x-\frac{8}{3})[/tex]

     = [tex]3(x^2+2x+1-1-\frac{8}{3})[/tex]

     = [tex]3[(x+1)^2-\frac{11}{3}][/tex]

     = [tex]3(x+1)^2-11[/tex]

Vertex of the parabola → (-1, -11)

Therefore, range of the function will be → y ≥ -11

The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}

The range of a function is the set of output values of the function

Since f(x) = 3x² + 6x - 8, we differentiate f(x) = y with respect to x to find the value of x that makes y minimum.

So, df(x)/dx = d(3x² + 6x - 8)/dx

= d(3x²)/dx + d6x/dx - d8/dx

= 6x + 6 + 0

= 6x + 6

Equating the experssion to zero, we have

df(x)/dx = 0

6x + 6 = 0

6x = -6

x = -6/6

x = -1

From the graph, we see that this is a minimum point.

So, the value of y = f(x) at the minimum point is that is a t x = - 1 is

y = f(x) = 3x² + 6x - 8

y = f(-1) = 3(-1)² + 6(-1) - 8

y = 3 - 6 - 8

y = -3 - 8

y = -11

Since this is a minimum point for the graph, we have that y ≥ -11.

So, the range of the function is {y|y ≥ -11}

So, the range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}

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Answer:

No

Step-by-step explanation:

16x + y = −48

Substitute the point into the equation and see if it is true

16(3) +0 = -48

48 = -48

This is not true so the point is not a solution

Answer:

x = ±sqrt(26)

Step-by-step explanation:

ln ( x^2 -25) = 0

Raise each side to base e

e^ln ( x^2 -25) = e^0

x^2 -25 = 1

Add 25 to each side

x^2 -25 +25 = 1+25

x^2 = 26

Take the square root of each side

sqrt(x^2) = ±sqrt(26)

x = ±sqrt(26)

Answer:

The third option

Step-by-step explanation:

If we rewrite this in log form, we get

[tex]e {}^{0} = {x}^{2} - 25[/tex]

Remeber anything to the 0 power is 1, so simplifying the equation first

[tex]1 = {x}^{2} - 25[/tex]

Add 25 to both sides

[tex]26 = {x}^{2} [/tex]

Take the square root of both sides

[tex]x = \sqrt{26} [/tex]

Square root are both so

[tex]x = - \sqrt{26} [/tex]

Is also a answer.

The third option is the answer

Answer:

60 sq in

Step-by-step explanation:

Perimeter = 2l + 2w

If l = w+4

Perimeter = 2(w+4) + 2w

Perimeter = 4w+8

32 = 4w + 8

24 = 4w

6 = w

If w = 6, l = 6+4 = 10

Area = l * w

Area = 10 * 6

Area = 60

Answer:

[tex]R(x) = -0.00051x^2 + 5x[/tex]

[tex]P(x) = -0.00049x^2 + 3x-600[/tex]

Step-by-step explanation:

Given

[tex]p = -0.00051x + 5[/tex] [tex]\to[/tex] [tex](0 \le x \le 12,000)[/tex]

[tex]C(x) = 600 + 2x - 0.00002x^2[/tex] [tex]\to[/tex] [tex](0 \le x \le 20,000)[/tex]

Solving (a): The revenue function

We have:

[tex]R(x) = x * p[/tex]

Substitute [tex]p = -0.00051x + 5[/tex]

[tex]R(x) = x * (-0.00051x + 5)[/tex]

Open bracket

[tex]R(x) = -0.00051x^2 + 5x[/tex]

Solving (b): The profit function

This is calculated as:

We have:

[tex]P(x) = R(x) - C(x)[/tex]

So, we have:

[tex]P(x) =-0.00051x^2 + 5x - (600 + 2x - 0.00002x^2)[/tex]

Open bracket

[tex]P(x) =-0.00051x^2 + 5x -600 - 2x +0.00002x^2[/tex]

Collect like terms

[tex]P(x) = 0.00002x^2-0.00051x^2 + 5x - 2x-600[/tex]

[tex]P(x) = -0.00049x^2 + 3x-600[/tex]

Answer:

see explanation

Step-by-step explanation:

Using the identities

tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x = 1 - cos²x

sin2x = 2sinxcosx

Consider left side

cosθ × sin2θ

= [tex]\frac{sin0}{cos0}[/tex] × 2sinθcosθ ( cancel cosθ )

= 2sin²θ

= 2(1 - cos²θ)

= 2 - 2cos²θ

= right side , then established

Answer:

D

Step-by-step explanation:

X intercept=y=0. 0=tan(x-5pi/6). x-5pi/6=0, x=5pi/6

f(x) = 2x³ - 3x² + 7

f(-1) = 2(-1)³ - 3(-1)² + 7

=> f(-1) = 2(-1) - 3(1) + 7

=> f(-1) = -2 -3 + 7

=> f(-1) = 2

f(1) = 2(1)³ - 3(1)² + 7

=> f(1) = 2(1) - 3(1) + 7

=> f(1) = 2 -3 + 7

=> f(1) = 6

f(2) = 2(2)³ - 3(2)² + 7

=> f(2) = 2(8) - 3(4) + 7

=> f(2) = 16 - 12 + 7

=> f(2) = 11

Answer: Volume of Cylinder A is                          pi times the area of the base times the height

                                                             π r2 h = (3.1416)(4)(4)(15) = 753.98 ft3

Volume of Cylinder B is likewise             pi times the area of the base times the height

                                                             π r2 h = (3.1416)(6)(6)(7)   = 791.68 ft3

After pumping all of Cyl A into Cyl B

there will remain empty space in B         791.68 – 753.98 = 37.7 ft3  

The percentage this empty space is

of the entire volume is                            37.7 / 791.68 = 0.0476 which is 4.8% when rounded to the nearest tenth  

.

Step-by-step explanation: I hope that help you.

Note: you may not need to type in the percent sign.

===========================================================

Explanation:

Let's find the volume of water in container A.

Use the cylinder volume formula to get

V = pi*r^2*h

V = pi*5^2*8

V = 200pi

The full capacity of tank A is 200pi cubic feet, and this is the amount of water in the tank since it's completely full.

We have 200pi cubic feet of water transfer to tank B. We'll keep this value in mind for later.

-----------------------

Now find the volume of cylinder B

V = pi*r^2*h

V = pi*6^2*6

V = 216pi

Despite being shorter, tank B can hold more water (since it's more wider).

-----------------------

Now divide the results of each section

(200pi)/(216pi) = 200/216 = 25/27 = 0.9259 = 92.59%

This shows us that 92.59% of tank B is 200pi cubic feet of water.

In other words, when all of tank A goes into tank B, we'll have tank B roughly 92.59% full.

This means the percentage of empty space (aka air) in tank B at this point is approximately 100% - 92.59% = 7.41%

Then finally, this value rounds to 7.4% when rounding to the nearest tenth of a percent.

Step-by-step explanation:

10v-6v=28

4v=28

v=28/4

v=7

Answer:

10v-6v=28

or, 4v = 28

or, v = 28/4

or, v = 7

hence 7 is the required value of v

Answer:

Here is your answer.....

Hope it helps you....