The cylindrical part of an architectural column has a height of 325 cm and a diameter of 30 cm.find the volume of the c

When \(\theta\) terminates in quadrant III, both \(\cos\theta\) and \(\sin\theta\) are negative, and

\(\sin^2\theta+\cos^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac{12}{13}\)

When \(\varphi\) terminates in quadrant II, \(\cos\varphi\) is negative and \(\sin\varphi\) is positive, so

\(1+\tan^2\varphi=\sec^2\varphi\implies\sec\varphi=-\dfrac{17}{15}\)

which gives

\(\cos\varphi=\dfrac1{-\frac{17}{15}}=-\dfrac{15}{17}\)

\(\tan\varphi=\dfrac{\sin\varphi}{\cos\varphi}=-\dfrac8{15}\implies\sin\varphi=\dfrac8{17}\)

Now,

\(\sin(\theta+\varphi)=\sin\theta\cos\varphi+\cos\theta\sin\varphi=-\dfrac{21}{221}\)

Answer:

  14400 cm³/s

Step-by-step explanation:

Find the rate of change of volume in terms of edge length, and evaluate the expression for the given conditions.

  V = s³ . . . . volume in terms of edge length (s)

  dV/dt = 3s²·ds/dt . . . . . . derivative of volume with respect to time

For the given values of s and ds/dt, this is ...

  dV/dt = 3(40 cm)²(3 cm/s) = 14400 cm³/s

Answer:

48 cents each pound

Step-by-step explanation:

Divide $12 by 25 pounds.

12÷25=0.48

The total cost is $44.50

Since the rug costs $27, the posters altogether cost : 44.50 - 27 = $17.50

We're given that the posters cost $2.50 each, and since they cost $17.50, the number of posters he bought was : 17.50 : 2.50 = 7 (posters)

(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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Answer:

6.75 miles

Step-by-step explanation:

Since it is 2.25 per 1/2 hour to get to 1 1/2 hour you multiply by 3. Then you do 2.25 times 3 and it gives you 6.75 miles.

hope that helps

Answer:

6.75 miles

Step-by-step explanation:

How many 1/2 hours in 1 1/2 hour? 1.5 ÷ 0.5 = 3

2.25 x 3 = 6.75

OR

Find the unit rate = 2.25 x 2 = 4.50 (we multiply it by 2 because there 2 half hours in an hour)
4.50 x 1.50 = 6.75

Answer:

2x^(2)+34x-12

Step-by-step explanation:

Use the FOIL method. I've attached a link that explains it: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:multiply-binomial/v/multiplying-binomials

Answer: 2x√5

Step-by-step explanation:

Answer:

\( → \sqrt{10x} \times \sqrt{2x} \\ = \sqrt{20 {x}^{2} } \\ = \sqrt{2 \times 2 \times 5 \times x \times x} \\ = \boxed{2 \sqrt{5} x}✓\)

The equation of the new function, if we vertically compress the absolute value parent function, f(x) = |x| by a factor of 3: y = 1/x |x|

In this question we have been given an absolute value function f(x) = |x|

We need to find the equation of the function, if we vertically compress the absolute value parent function, f(x) = |x| by a factor of 3.

We know in function transformtaion there are two types of dilations.

1) Horizontal Dilation: a function y = f(x) into the form y = f(kx)

2) Vertical Dilation: a function y = f(x) into the form y = k f(x)

In both the cases, if k > 1, then the graph stretches and if 0 < k < 1, then the graph shrinks.

Since we vertically compress the absolute value parent function f(x) = |x| by a factor of 3, a scaling factor k must be 0 < k < 1

So, k = 1/3

And the required function wuld be, y = 1/3 * f(x)

y = 1/3 |x|

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The absolute value parent function is f(x)= x. When we vertically compress the absolute value parent function f(x)= x by a factor of 3, the new equation is f(x)=⅓x.

The vertical compression by a factor of 3 means that the original graph will be compressed to a vertically scaled-down version of the original graph. This means that the graph will be shorter by a factor of 3.

To calculate the new equation, we must first determine the value of the constant “a”. The equation of the original absolute value parent function is f(x)=x. When we vertically compress the absolute value parent function f(x)=x by a factor of 3, the new equation is f(x)=ax. The value of “a” is equal to ⅓. Therefore, the new equation of the absolute value parent function f(x)=x when it is vertically compressed by a factor of 3 is f(x)=⅓x.

The graph of the new equation is shown below. The graph is shorter than the original absolute value parent function by a factor of 3.

From the graph, we can also see that the new equation has a minimum value of -1/3, a maximum value of 1/3, and the graph is symmetrical along the y-axis.

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Answer:

Money in the cash box is $150

Step-by-step explanation:

Let

x = money in the cash box

1/5 of the money in a cash box is 30 dollars

1/5 of x = $30

1/5 * x = 30

1/5x = 30

Divide both sides by 1/5

x = 30 ÷ 1/5

= 30 × 5/1

= 150/1

x = $150

Money in the cash box is $150

Answer:

Step-by-step explanation:

We know that a triangle angles total equals 180 so we could use the numbers and the equation, add it up and then find the value of x

(7x + 3) + 85 + 50 = 180

7x + 138 = 180

7x = 180-138

7x = 42

x = 6

Now that we found the value of x we can know substitute the value into the equation to find the value of the angle.

7x+3

42+3

45

Answer:

The cost of parking in the garage for 75 minutes is 4.875.

Step-by-step explanation:

The costs of parking h hours is given by the following function:

\(f(h) = 4.5 + 1.5(h-1)\)

Cost of parking 75 minutes.

1 hour is 60 minutes. How many hours are 75 minutes?

1h - 60 min

xh - 75 min

\(60x = 75\)

\(x = \frac{75}{60}\)

\(x = 1.25\)

75 minutes is 1.25 hours. So we have to find f(1.25).

\(f(1.25) = 4.5 + 1.5*(1.25-1) = 4.875\)

The cost of parking in the garage for 75 minutes is 4.875.

The number of different arrangements possible will be 600.

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

6 people go to a movie and sit next to each other in 6 adjacent seats in the front row of the theatre. If "A" cannot sit to the right of "F".

The total number of sitting will be

⇒ 6!

⇒ 6 x 5 x 4 x 3 x 2 x 1

⇒ 720

If A and F sit together, then the number of arrangements will be

⇒ 5!

⇒ 5 x 4 x 3 x 2 x 1

⇒ 120

Then the number of different arrangements possible will be

⇒ 720 - 120

⇒ 600

Thus, the number of different arrangements possible will be 600.

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Answer:

The height of the tree is 6.12 meters and the height of the building is 33.12 meters.

Step-by-step explanation:

Since the person is 1.8 meters tall, HC = 1.8

And since their shadow is 10 meters long, HD = 10.

We are also given that GH is 24 meters and that FG is 150 meters.

Height of the Tree:

The height of the tree is given by GB.

Again, since m∠BGD = m∠CHD = 90°, ∠BGD ≅ ∠CHD.

Likewise, ∠D ≅ ∠D. So, by AA-Similarity:

\(\displaystyle \Delta BGD\sim \Delta CHD\)

Corresponding parts of similar triangles are in proportion. Therefore:

\(\displaystyle \frac{GB}{GD}=\frac{HC}{HD}\)

Note that:

\(GD=GH+HD\)

Find GD:

\(GD=(24)+(10)=34\)

Substitute the known values into the proportion:

\(\displaystyle \frac{GB}{34}=\frac{1.8}{10}\)

Cross-multiply:

\(10GB=61.2\)

Therefore:

\(GB=6.12\text{ meters}\)

The height of the tree is 6.12 meters.

Height of the Building:

The height of the building is given by FA.

Since m∠AFD = m∠CHD = 90°, ∠AFD ≅ ∠CHD.

∠D ≅ ∠D. So, by AA-Similarity:

\(\Delta AFD\sim \Delta CHD\)

Corresponding parts of similar triangles are in proportion. Therefore:

\(\displaystyle \frac{FA}{FD}=\frac{HC}{HD}\)

Note that:

\(FD=FG+GH+HD\)

Find FD:

\(FD=(150)+(24)+(10)=184\)

Substitute the known values into the proportion:

\(\displaystyle \frac{FA}{184}=\frac{1.8}{10}\)

Cross-multiply:

\(10FA=331.2\)

Therefore:

\(FA=33.12\text{ meters}\)

The height of the building is 33.12 meters.

Answer:

The height of the area is (x - 3) ft.

Step-by-step explanation:

You can do this a few ways.  You could use long division to divide the area by the width, or you could just factor the area, which is guaranteed to have the width as a factor, leaving you with the height.

Let's go with factoring, as that's probably what this question is intended as:

\(= \frac{2x^2 - 9x + 9}{2x - 3} \\\\= \frac{2x^2 - 6x - 3x + 9}{2x - 3} \\\\= \frac{2x(x - 3) - 3(x - 3)}{2x - 3} \\\\= \frac{(2x - 3)(x - 3)}{2x - 3} \\\\= x - 3\)

By performing the desired calculation using each arrangement and squaring the difference between the result and the target value, you can determine the arrangement that yields the largest squared difference.

To find the arrangement of the 6 numbers that generates the biggest difference squared, you need to consider all possible permutations of the numbers. For each arrangement, perform the desired calculation using the given, such as addition, subtraction, multiplication, or any other specified operation.

Once you have the calculated result for each arrangement, calculate the squared difference between the result and the target value. This is done by subtracting the target value from the calculated result and then squaring the difference.

By comparing the squared differences obtained for each arrangement, you can identify the arrangement that yields the largest squared difference. This arrangement will have the maximum difference squared between the calculated result and the target value.

It's important to note that the specific calculation or operation to be performed is not mentioned in the question. Therefore, you need to specify the operation or provide more information to determine the exact steps for performing the calculation.

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Answer: 14a²b³c⁴ = 2 x 7 x a x a x b x b x b x c x c x c

28ab²c².​ = 2 x 2 x 7 x a x b x b x c x c

Step-by-step explanation: is this what your looking for?

Answer:

Step-by-step explanation:

Both will be equal ,

4x-7 =3x +2

solve it we will get ,

x =9 degree

Answer:

answer is x=9

vertical angles have same angle measure.

so:

(4x-7)=(3x+2)

x=9

lets see if it correct. put x values in

4×9-7=3×9+2

29=29

There are 266 number of  ways to park 3 distinct cars in 9 consecutive parking slots such that at least one parking slot remains vacant between any two cars.

To determine the number of ways to park 3 distinct cars in 9 consecutive parking slots such that at least one parking slot remains vacant between any two cars, we need to consider the possible arrangements.

Let's analyze the scenario:

1. All three cars are parked in adjacent slots

In this case, there are 7 possible positions where the first car can be parked (as it needs at least one vacant slot on the right side), 6 possible positions for the second car (as it also needs one vacant slot on the right side), and the third car will occupy the remaining slot.

Total arrangements for Case 1 = 7 * 6 = 42.

2. One vacant slot between the cars

In this case, there are 7 possible positions where the first car can be parked (as it needs at least one vacant slot on the right side).

After parking the first car, there will be 5 remaining slots where the second car can be parked (one vacant slot between the first and second car).

The third car will occupy one of the remaining 4 slots.

Total arrangements for Case 2 = 7 * 5 * 4 = 140.

3. Two vacant slots between the cars

In this case, there are 7 possible positions where the first car can be parked (as it needs at least one vacant slot on the right side).

After parking the first car, there will be 4 remaining slots where the second car can be parked (two vacant slots between the first and second car).

The third car will occupy one of the remaining 3 slots.

Total arrangements for Case 3 = 7 * 4 * 3 = 84.

Total number of ways = Total arrangements for Case 1 + Total arrangements for Case 2 + Total arrangements for Case 3

Total number of ways = 42 + 140 + 84 = 266.

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Answer:

\(\mathbf{6xe^xy+y^2e^x = C}\) which implies that C is the integrating factor

Step-by-step explanation:

The correct format for the equation given is:

\(y(6x+y +6)dx +(6x +2y)dy=0\)

By the application of the general differential equation:

⇒ Mdx + Ndy = 0

where:

M = 6xy+y²+6y

\(\dfrac{\partial M}{\partial y}= 6x+2y+6\)

and

N = 6x +2y

\(\dfrac{\partial N}{\partial x}= 6\)

∴

\(f(x) = \dfrac{1}{N}\Big(\dfrac{\partial M}{\partial y}- \dfrac{\partial N}{\partial x} \Big)\)

\(f(x) = \dfrac{1}{6x+2y}(6x+2y+6-6)\)

\(f(x) = \dfrac{1}{6x+2y}(6x+2y)\)

f(x) = 1

Now, the integrating factor can be computed as:

\(\implies e^{\int fxdx}\)

\(\implies e^{\int (1)dx}\)

the integrating factor = \(e^x\)

From the given equation:

\(y(6x+y +6)dx +(6x +2y)dy=0\)

Let us multiply the above given equation by the integrating factor:

i.e.

\((6xy+y^2 +6y)dx +(6x +2y)dy=0\)

\((6xe^xy+y^2 +6e^xy)dx +(6xe^x +2e^xy)dy=0\)

\(6xe^xydx+6e^xydx+y^2e^xdx +6xe^xdy +2ye^xdy=0\)

By rearrangement:

\(6xe^xydx+6e^xydx+6xe^xdy +y^2e^xdx +2ye^xdy=0\)

Let assume that:

\(6xe^xydx+6e^xydx+6xe^xdy = d(6xe^xy)\)

and:

\(y^2e^xdx +e^x2ydy=d(y^2e^x)\)

Then:

\(d(6xe^xy)+d(y^2e^x) = 0\)

\(6d (xe^xy) + d(y^2e^x) = 0\)

By integration:

\(\mathbf{6xe^xy+y^2e^x = C}\) which implies that C is the integrating factor

Answer:

54 years

Step-by-step explanation:

Given that :

Let :

Ann's age = x

Mary's age = x/2

Donald's age = x/3

x + x/2 + x/3 = 99

Take the L. C. M

(6x + 3x + 2x) / 6 = 99

11x / 6 = 99

11x = 99 * 6

11x = 594

x = 594 / 11

x = 54

Hence, Ann is 54 years

Protractor postulate: given any angle, we can express its measure as a unique real number from 0 to 180 degrees.

The protractor postulate is a fundamental concept in geometry that establishes a way to measure angles using a protractor. According to this postulate, every angle can be uniquely represented by a real number between 0 and 180 degrees.

A protractor is a geometric tool with a semicircular shape and marked degrees along its edge. To measure an angle using a protractor, we align the center of the protractor with the vertex of the angle and the baseline of the protractor with one side of the angle. We then read the degree measure where the other side of the angle intersects the protractor.

The protractor is divided into 180 degrees, with 0 degrees being the starting point at the baseline of the protractor, and 180 degrees being at the opposite end of the baseline. By aligning the protractor with an angle, we can determine its measure as a real number within this range.

For example, if we measure an angle using a protractor and find that the other side intersects the protractor at 45 degrees, we can express the measure of the angle as 45 degrees. Similarly, if the intersection point is at 90 degrees, the angle measure would be 90 degrees. The protractor postulate guarantees that these angle measures are unique within the range of 0 to 180 degrees.

It is important to note that the protractor postulate assumes that angles can be measured using a protractor and that the measurement is accurate and reliable. The postulate provides a consistent and standardized way to assign a numerical value to an angle, allowing for precise communication and comparison of angles in geometric contexts.

In summary, the protractor postulate establishes that the measure of any angle can be expressed as a unique real number between 0 and 180 degrees. This concept is fundamental in geometry and allows for the measurement, comparison, and communication of angles using a protractor.

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Answer:

See graph below.

Answer:

x < -10

Step-by-step explanation:

First, let x = unknown number. Then create the algebraic equation to solve for x. The equation would be 2x + 7 < -13, so 2x < -20, thus x < -10.

Answer:

If you wanted the in equality equation then your answer is 2n + 7 < -13

If you want the answer to the inequality then its n < -10

Step-by-step explanation:

2n + 7 < -13

     -7     -7

    2n < -20

    /2      /2

     n < -10

Answer:

26

Step-by-step explanation:

DE+EF=DF

Subsitue thise x values for DE,  and DF

12+x=38

=26

Answer:

u must sketch what u see when u close ur

Using trigonometry we obtain the bearing of the ship ≈ 41.8 degrees.

To obtain the bearing of the ship given the values of x and y, we can use trigonometry.

The bearing represents the angle in degrees measured clockwise from the north direction.

First, we need to determine the angle θ between the positive x-axis and the line connecting the origin (0,0) and the point (x, y).

We can use the inverse tangent function (arctan) to find this angle:

θ = arctan(y/x)

Substituting the values x = 9.4 and y = 10.1 into the equation:

θ = arctan(10.1/9.4)

Using a calculator, we find that θ is approximately 48.2 degrees.

However, this angle corresponds to the angle counterclockwise from the positive x-axis.

To convert it to the bearing (measured clockwise from the north direction), we subtract this angle from 90 degrees:

Bearing = 90 - θ = 90 - 48.2 = 41.8 degrees.

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Step-by-step explanation:

1296.84 / 12 = $108.07 earned per day

Answer:

B. 8π

Step-by-step explanation:

4×2=8 to find the diameter

8×π=8π

answer is B