A right circular cylinder has a diameter of 12 in and a height of 12 in. if water is flowing in at the rate of 4π in3 per minute, find the rate of change of the height when the height is 4 in?

The view of war doves with respect to the Vietnam War was that: B. as a localized civil war that should not include the United States of America (US).

The Vietnam War is also referred to as Second Indochina War or the Vietnam conflict and it can be defined as a short, costly, protracted and divisive conflict between the communist government of North Vietnam and South Vietnam, which ended on the 30th of April, 1975.

Based on historical information and records, the Vietnam War officially started on the 1st of November, 1955 in the following locations:

In conclusion, we can infer and logically deduce that the view of war doves with respect to the Vietnam War was that it is a a localized civil war and as such should not include the United States of America.

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Answer:

5296.125 days

Step-by-step explanation:

1 year = 365.25 days

14.5 years × 365.25 days/year = 5296.125 days

177.8 centimeters.

The shortest distance between the tip of the cone and its rim:

cos θ= base/Hypotenuse

cos 77°=[tex]\frac{40}{H}[/tex]

[tex]0.22495=\frac{40}{H}[/tex]

[tex]H=177.8[/tex]

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The shortest distance between the tip of the cone and its rim exits 51.11cm.

If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.

Cos 38.5 = 40 / x

Solving the value of x, we get

Multiply both sides by x

[tex]$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x[/tex]

[tex]$\cos \left(38.5^{\circ}\right) x=40[/tex]

Divide both sides by [tex]$\cos \left(38.5^{\circ}\right)$[/tex]

[tex]$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]

simplifying the above equation, we get

[tex]$x=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]

x = 51.11cm

The shortest distance between the tip of the cone and its rim exits 51.11cm.

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Using the law of sines, it is found that the measure of angle x is given as follows:

x = 69.9º.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

sin(A)/A = sin(B)/B = sin(C)/C

Considering the given triangle, the following relation can be established:

sin(x)/11 = sin(28º)/x

Hence, applying cross multiplication:

sin(x) = 2sin(28º)

sin(x) = 0.938943126

x = arcsin(0.938943126)

x = 69.9º.

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The test That holds true for this inequality is given as 1/4 and 1

3/2 y - 2x > 1

The goal is to make y the subject

then

3/2 y > 2x + 1

We have to divide through the equation by 3/2

Such that  y  > 4/3 x + 2/3

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Answer:

The value of x will be 2.5cm.

Step-by-step explanation:

Volume = Length*Width*Height

where,

[tex]v = l \times w \times h \: ...substitute \: values \\ 120cm {}^{3} = 12cm \times w \times 4cm \\ 120cm {}^{3} = 48cm {}^{2} \times w \: ...divide \: both \: \\ sides \:by \: 48cm {}^{2} \\ \frac{120cm {}^{3} }{48cm {}^{2} } = w \\ w = 2.5cm[/tex]

Answer: 42 and 31

Step-by-step explanation:

       Let x be one number and y be the other.

       We will write mathematical equations for these two numbers.

The sum of 2 numbers is 73.

x + y = 73

Their difference is 11.

x - y = 11

       See attached for the graph.

       The point of intersection is our solution.

Answer:

150

Step-by-step explanation:

because full capacity is 3/3, therefore you time 50 by 3, which will be 150 gallons

           [tex]\boldsymbol{\sf{-2x + 7x +34 = -2(1-7x) \ \ \longmapsto \ \ [Add \ -2x+7x]}}[/tex]

                        [tex]\boldsymbol{\sf{5x+34=-2(1-7x)}}[/tex]

Use the distributive property to multiply −2 by 1−7x.

                            [tex]\boldsymbol{\sf{5x+34=-2+14x}}[/tex]

Subtract 14x on both sides.

                              [tex]\boldsymbol{\sf{5x+34-14x=-2}}[/tex]

Combine 5x and −14x to get −9x.

                                [tex]\boldsymbol{\sf{-9x+34=-2 }}[/tex]

Subtract 34 from both sides.

                              [tex]\boldsymbol{\sf{-9x=-2-34 \ \ \longmapsto \ \ \ [Subtract] }}[/tex]

                               [tex]\boldsymbol{\sf{-9x=-36}}[/tex]

Divide both sides by −9.

                                      [tex]\boldsymbol{\sf{x=\dfrac{-36}{-9} \ \ \longmapsto \ \ [Split] }}[/tex]

                                       [tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ x=4 }}}}}[/tex]

[tex] \quad\quad\quad \huge \underline{ \tt{ANSWER}}[/tex]

[tex]\quad\quad\quad\quad\quad\quad[/tex]

[tex]\tt{- 2x + 7x + 34 = - 2(1 - 7x)}[/tex]

[tex]\tt{5x + 34 = - 2(- 7x + 1)}[/tex]

[tex]\tt{5x + 34 = - (- 2 * 7x + 2)}[/tex]

[tex]\tt{5x + 34 = - (- 14x + 2)}[/tex]

[tex]\tt{(5x + 34) + (- 34 - 14x) = (14x - 2) + (- 34 - 14x)}[/tex]

[tex]\tt{5x + 34 - 34 - 14x = 14x - 2 - 34 - 14x}[/tex]

[tex]\tt{5x - 14x + 34 - 34 =14x-14x-2 - 34}[/tex]

[tex]\tt{- 9x = - 36}[/tex]

[tex]\tt{\frac{9x}{9} = \frac{36}{9}}[/tex]

[tex]\tt{x = 4}[/tex]

Answer:

B {3/2, -5/3}

Step-by-step explanation:

6x² + x - 15 = 0

6x² + 10x - 9x - 15 = 0

2x(3x + 5) - 3(3x + 5) = 0

(3x + 5)(2x - 3) = 0

3x + 5 = 0  or  2x - 3 = 0

3x = -5  or  2x = 3

x = -5/3  or  x = 3/2

Answer: B {3/2, -5/3}

Answer:

[tex]\left\{\dfrac{3}{2},\ -\dfrac{5}{3}\right\}[/tex]

Step-by-step explanation:

Given quadratic equation: [tex]6x^2+x-15=0[/tex]

[tex]\implies a=\textsf{6},b=\textsf{1},c=\textsf{-15}[/tex]

..................................................................................................................................................

[tex]{\large \textsf{ Quadratic Formula: }}x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]

..................................................................................................................................................

Step 1: Substitute the given values into the formula and simplify.

[tex]\implies x=\dfrac{-{(\textsf1})\pm \sqrt{\textsf{(1)}^2-4(\textsf{6}){(\textsf{-15})}}}{2{(\textsf{6})}}[/tex]

[tex]\implies x=\dfrac{-1\pm \sqrt{1-4(-90)}}{12}[/tex]

[tex]\implies x=\dfrac{-1\pm \sqrt{1+360}}{12}[/tex]

[tex]\implies x=\dfrac{-1\pm \sqrt{361}}{12}[/tex]

[tex]\implies x=\dfrac{-1\pm 19}{12}[/tex]

Step 2: Separate into two cases.

[tex]x_1=\dfrac{-1+19}{2}[/tex]

[tex]x_2=\dfrac{-1-19}{2}[/tex]

Step 3: Solve both cases.

[tex]\implies x_1=\dfrac{-1+19}{12}=\dfrac{18}{12}=\dfrac{6\times3}{6\times2}=\boxed{\dfrac{3}{2}}[/tex]

[tex]\implies x_2=\dfrac{-1-19}{12}=\dfrac{-20}{12}=\dfrac{-4\times5}{4\times3}=\boxed{-\dfrac{5}{3}}[/tex]

The solutions to this quadratic are: [tex]x_1=\dfrac{3}{2},\ x_2=-\dfrac{5}{3}[/tex]

..................................................................................................................................................

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Answer: ||||||| n=41° |||||| m=59° IIIII p=260° IIII

Step-by-step explanation:

Alternate angle:

<m=<59°

m=59°

<n=<41°

n=41°

______________

p+41°+59°= 360°

p+100°=360°

p=360°-100°

p=260°

Answer:

n = 49

m= 31

p= 280

Step-by-step explanation:

41 + n = 90

n= 90 -41 = 49

59 + m = 90

m = 90 - 59 = 31

Hope this helps!

p + n + m = 360

p = 360 - 49 - 31 = 280

By applying the definition of exponential function, we find that the function f(x) = 3 · 2ˣ match with the graph of the picture. (Correct choice: A)

In this question we have the graph of a exponential function, whose expression have to be found based on the definition of exponential function:

y = a · bˣ      (1)

Where:

Now we find the values for a and b:

Initial value (x = 0, y = 3)

3 = a · b⁰

a = 3

Base of the exponential function (x = 1, a = 3, y = 6)

6 = 3 · a

a = 6 / 3

a = 2

By applying the definition of exponential function, we find that the function f(x) = 3 · 2ˣ match with the graph of the picture. (Correct choice: A)

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Based on the thickness of the rubber insulation and outside diameter, the diameter of the copper conductor is 0.376 inch.

The diameter of the copper wire can be found by the formula:

= Outer diameter - ( 2 x cotton insulation) - (2 x rubber insulation)

Solving gives:

= 500/ 1,000 - (2 x 12/ 1,000) - (2 x 50 / 1,000)

= 0.5 - (2 x 0.12) - (2 x 0.05)

= 0.376 inch

= 376 / 1,000 inch

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By critically observing the graph, we can infer and logically deduce the following points:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, the data of a linear graph are directly proportional and as such, as the value on the x-axis increases or decreases, the values on the y-axis also increases or decreases.

By critically observing the graph which models the changes in temperature over a specific period of time (in years), we can infer and logically deduce the following points:

In conclusion, there are four (4) points of intersection on this graph.

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Answer: 180 meters

Step-by-step explanation: To solve this we need to find the square root of 3600. 6x6 = 36 so we know the square root is 60. That means that each side of the square lot is 60 meters. If they fence 3 sides they will need to purchase 60x3= 180 meters of fence.

The expected value or mean of binomial distribution is also increased by increasing the number of trials.

The standard deviation of binomial distribution is also increased by increasing the number of trials.

According to the question

There is binomial experiment.

The condition given in the question is 'if the number of trials is increased, what happens to the expected value and to the standard deviation'.

We all know,

In binomial distribution, The mean or expected value is given by np whereas the variance is given by np(1 - p) where (1 - p) taken as q is the probability of failure and p is the probability of success.

The standard deviation of binomial distribution is [tex]\sqrt{npq}[/tex].

From the expected value formula we can see that number number of trials is directly proportional to mean or expected value.

Thus we can say that

If the number of trials is increasing, then the expected value is also increasing.

From the standard deviation of binomial distribution we can see that if the number of trials increasing then the standard deviation also increasing because standard deviation is directly proportional to number of trials.

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Answer:

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

Inequality:

1. Distribute:

2. Multiply:

3. Collect like terms:

4. Addition:

5. Divide both sides by 6:

Interval notation for this solution is:

Answer:

[tex]x < -3[/tex]

Interval notation:  (-∞, 3)

Step-by-step explanation:

Given inequality:

[tex]-4 \left(\dfrac{5}{2}+\dfrac{3}{2}x\right) > 8[/tex]

Divide both sides by -4 (remembering to change the direction of the inequality sign, since we are dividing by a negative):

[tex]\implies \dfrac{ -4 \left(\dfrac{5}{2}+\dfrac{3}{2}x\right)}{-4} > \dfrac{8}{-4}[/tex]

[tex]\implies \dfrac{5}{2}+\dfrac{3}{2}x < -2[/tex]

Subtract ⁵/₂ from both sides:

[tex]\implies \dfrac{5}{2}+\dfrac{3}{2}x-\dfrac{5}{2} < -2-\dfrac{5}{2}[/tex]

[tex]\implies \dfrac{3}{2}x < -\dfrac{9}{2}[/tex]

Multiply both sides by 2:

[tex]\implies \dfrac{2 \cdot 3}{2}x < -\dfrac{2 \cdot 9}{2}[/tex]

[tex]\implies \dfrac{\diagup\!\!\!\!2 \cdot 3}{\diagup\!\!\!\!2}x < -\dfrac{\diagup\!\!\!\!2 \cdot 9}{\diagup\!\!\!\!2}[/tex]

[tex]\implies 3x < -9[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3x}{3} < \dfrac{-9}{3}[/tex]

[tex]\implies x < -3[/tex]

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Answer:

Option 2

Step-by-step explanation:

There is an amplitude of 1/2, a period of pi, and a non-zero y-intercept.

See attached images for the graph.

The answer is 10.73 years.

Here, the formula we can use is :

[tex]\boxed {Children = \frac{Boys+Girls}{2}}[/tex] (for the average)

Substitute the values mentioned in the question.

10.54 = (10.35 + Girls)/2

21.08 = 10.35 + Girls

Girls = 10.73 years

Answer:

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

Step-by-step explanation:

To find y-intercept of a graph, we have to substitute x = 0 to find it - consider each functions:

First Choice

[tex]\displaystyle{f(x) = 2x(x+14)-64}\\\\\displaystyle{f(0) = 2\cdot 0(0+14)-64}\\\\\displaystyle{f(0) = 0\cdot 14-64}\\\\\displaystyle{f(0) = -64}[/tex]

Second Choice

[tex]\displaystyle{f(x) = (x+4)^2+2x}\\\\\displaystyle{f(0) = (0+4)^2 + 2(0)}\\\\\displaystyle{f(0) = 4^2}\\\\\displaystyle{f(0) = 16}[/tex]

Third Choice

[tex]\displaystyle{f(x) = (x-16)^2 + 4}\\\\\displaystyle{f(0) = (0-16)^2 + 4}\\\\\displaystyle{f(0) = (-16)^2 + 4}\\\\\displaystyle{f(0) = 256 + 4}\\\\\displaystyle{f(0) = 260}[/tex]

Fourth Choice

[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}\\\\\displaystyle{f(0) = -2(0-3)^2 + 2}\\\\\displaystyle{f(0) = -2(-3)^2 + 2}\\\\\displaystyle{f(0) = -2\cdot 9 + 2}\\\\\displaystyle{f(0) = -18+2}\\\\\displaystyle{f(0) = -16}\\[/tex]

Therefore, fourth choice is correct.

Answer:

6 2 point shots 2 3 points

Step-by-step explanation:

3 two point shot 1 3 point shot = 9

6 two point shot 2 3 point shot =18

Step-by-step explanation:

This is trigonometry. Focusing on Y initially, we can see that Y is the opposite, and 32 is the hypotenuse. Therefore, we must use sin:

[tex] \sin(60) = \frac{y}{32} [/tex]

[tex]y = \sin(60) \times 32[/tex]

[tex]y \approx28[/tex]

Next X. We can see that X is the adjacent, and 32 is the hypotenuse, so we must use cos:

[tex] \cos(60) = \frac{x}{32} [/tex]

[tex]x = \cos(60) \times 32[/tex]

[tex]x = 16[/tex]

Now let's look at A. We can see that a is the adjacent, and 12 is the opposite, so we must use tan:

[tex] \tan(60) = \frac{12}{a} [/tex]

[tex]a = \frac{12}{ \tan(60) } [/tex]

[tex]a \approx7[/tex]

Now, B. We can see that B is the hypotenuse, and 12 is the opposite, so we must use sin:

[tex] \sin(60) = \frac{12}{b} [/tex]

[tex]b = \frac{12}{ \sin(60) } [/tex]

[tex]b \approx14[/tex]

Answer:

Below in bold.

Step-by-step explanation:

The first triangle is a 30-60-90 triangle,

so the sides are in the ratio 2 : 1 : √3,  where 2 is the hypotenuse, the 1 is adjacent to 60 degree angle and the √3 is opposite the 60 degree angle.

So x = 1/2 * 32 = 16

and y = 16√3  or 27.71 to nearest hundredth.

The second one is the same special triangle, so

√3/2 = 12/b

b = 24/√3

 = 8√3  or 13.86  to nearest hundredth.

a = 1/2 b = 4√3 or 6.93 to nearest hundredth.

The polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].

The vertices of ellipse are (−1,0) and (3,0).

The polar equation of an ellipse can be represented as

[tex]r=\frac{ep}{1+ecos\theta}[/tex]

where e is the eccentricity.

Eccentricity, e = [tex]\frac{c}{a}[/tex]

c is the distance from the center to the focus and a is the distance from the center to the vertex

[tex]c=\frac{3-(-1)}{2}[/tex]

⇒ [tex]c=\frac{4}{2}[/tex]

⇒ c = 2

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

⇒ [tex]a=\frac{2}{2}[/tex]

⇒ a = 1

Then, e = [tex]\frac{2}{1}[/tex]

⇒ e = 2

Now, the polar equation of an ellipse becomes as,

⇒ [tex]r=\frac{2p}{1+2cos\theta}[/tex] ------- (1)

Now plug in a vertex point such as (-1,0) and solve for p,

⇒ [tex]-1=\frac{2p}{1+2cos0}[/tex]

⇒ [tex]-1=\frac{2p}{1+2(1)}[/tex]               [∵ cos 0 = 1]

⇒ [tex]-1=\frac{2p}{3}[/tex]

⇒ [tex]-3=2p[/tex]

⇒ [tex]p=-\frac{3}{2}[/tex]

Thus the polar equation of an ellipse (1) becomes as,

⇒ [tex]r=\frac{2(-\frac{3}{2} )}{1+2cos\theta}[/tex]

⇒ [tex]r=-\frac{3}{1+2cos\theta}[/tex]

Hence we can conclude that the polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].

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The surface area of the given figure is 288 km²

From the question, we are to determine the surface area of the figure

The given figure is a square-base pyramid

Surface area of the pyramid = (10×10) + 4× 1/2(10×9.4)

Surface area of the pyramid = (100) + 2(94)

Surface area of the pyramid = 100 + 188

Surface area of the pyramid = 288 km²

Hence, the surface area of the given figure is 288 km²

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The true and false statement about the mean salary is illustrated below.

The true false statement about the mean salary include:

When Tom's salary has a z-score of 0.5, the amount that he earns will be:

0.5 = (x - 29300)/5400

0.5 × 5400 = x - 29300

2700 = x - 29300

x = 29300 + 2700.

x = 32000

The amount he earns is 32000.

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Answer:

Step-by-step explanation:

The approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.

In this question,

The differential equation is

yʹ=y(3−ty) ------- (1)

Here, y(0)=0. 5,h=0. 1, 0≤t≤0. 5.

By Euler's method,

[tex]y_{n+1}=y_n+hf_n[/tex]

where [tex]f_n=f(t_n,y_n)[/tex]

For, t = 0, y = 0,

[tex]y_{1}=y_0+hf_0[/tex] and

[tex]f_0=f(t_0,y_0)[/tex]

Substitute in equation 1,

⇒ f(0,0.5) = 0.5(3-(0)(0.5))

⇒ f(0,0.5) = 0.5(3-0)

⇒ f(0,0.5) = 0.5(3)

⇒ f(0,0.5) = 1.5

Then, [tex]y_{1}=y_0+hf_0[/tex] becomes,

⇒ y₁ = 0.5 + (0.1)(1.5)

⇒ y₁ = 0.5 + 0.15

⇒ y₁ = 0.65

For, t = 1, y = 1,

[tex]y_{2}=y_1+hf_1[/tex] and

[tex]f_1=f(t_1,y_1)[/tex]

⇒ f(0.1,0.65) = 0.65(3-(0.1)(0.65))

⇒ f(0.1,0.65) = 0.65(3-0.065)

⇒ f(0.1,0.65) = 1.90

Then, [tex]y_{2}=y_1+hf_1[/tex] becomes,

⇒ y₂ = 0.65+(0.1)(1.90)

⇒ y₂ = 0.84

For t = 2, y = 2,

[tex]y_{3}=y_2+hf_2[/tex] and

[tex]f_2=f(t_2,y_2)[/tex]

⇒ f(0.2,0.84) = 0.84(3-(0.2)(0.84))

⇒ f(0.2,0.84) = 0.84(3-0.168)

⇒ f(0.2,0.84) = 2.3788

Then, [tex]y_{3}=y_2+hf_2[/tex]

⇒ y₃ = 0.84+(0.1)(2.3788)

⇒ y₃ = 1.0778

For t = 3, y = 3,

[tex]y_{4}=y_3+hf_3[/tex] and

[tex]f_3=f(t_3,y_3)[/tex]

⇒ f(0.3,1.0778) = 1.0778(3-(0.3)(1.0778))

⇒ f(0.3,1.0778) = 1.0778(3-0.32334)

⇒ f(0.3,1.0778) = 2.8848

Then, [tex]y_{4}=y_3+hf_3[/tex] becomes

⇒ y₄ = 1.0778+(0.1)(2.8848)

⇒ y₄ = 1.3584

For t = 4, y = 4,

[tex]y_{5}=y_4+hf_4[/tex] and

[tex]f_4=f(t_4,y_4)[/tex]

⇒ f(0.4,1.3584) = 1.3584(3-(0.4)(1.3584))

⇒ f(0.4,1.3584) = 1.3584(3-0.5433)

⇒ f(0.4,1.3584) = 3.3372

Then, [tex]y_{5}=y_4+hf_4[/tex] becomes

⇒ y₅ = 1.3584 + (0.1)(3.3372)

⇒ y₅ = 1.6921

For t = 5, y = 5,

[tex]y_{6}=y_5+hf_5[/tex] and

[tex]f_5=f(t_5,y_5)[/tex]

⇒ f(0.5,1.6921) = 1.6921(3-(0.5)(1.6921))

⇒ f(0.5,1.6921) = 1.6921(3-0.84605)

⇒ f(0.5,1.6921) = 3.6447

Then, [tex]y_{6}=y_5+hf_5[/tex] becomes

⇒ y₆ = 1.6921 + (0.1)(3.6447)

⇒ y₆ = 2.05657

Hence we can conclude that the approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.

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