the volume of a cyliner is V= πR^2x
where R= radius and x= height
if the radius is 3 times the height and the volume increases at 18 cm^2/s
how fast does the radius increase when the radius= 6cm

Answer:

21.4 * 10^(-5)

\(\\ \sf\longmapsto 2.14\times 10^{-5}\)

\(\\ \sf\longmapsto 0.214\times 10^{-4}\)

\(\\ \sf\longmapsto 0.0214\times 10^{-3}\)

\(\\ \sf\longmapsto 0.00214\times 10^{-2}\)

\(\\ \sf\longmapsto 0.000214\times 10^{-1}\)

\(\\ \sf\longmapsto 0.0000214\)

The area of the walkway is 24π square meters.

To find the area of the walkway, we need to subtract the area of the inner circle from the area of the outer circle.

The inner circle has a radius of 5 meters, so its area can be calculated using the formula for the area of a circle: A_inner = π * \((r_inner)^{2}\).

A_inner = π * \(5^{2}\) = 25π square meters.

The outer circle has a radius equal to the sum of the inner radius and the width of the walkway. In this case, the outer radius is 5 + 2 = 7 meters.

The area of the outer circle can be calculated in the same way: A_outer = π * \((r_outer)^{2}\).

A_outer = π * \(7^{2}\) = 49π square meters.

Now, we can find the area of the walkway by subtracting the area of the inner circle from the area of the outer circle: A_walkway = A_outer - A_inner.

A_walkway = 49π - 25π = 24π square meters.

The area of the walkway is 24π square meters, where π (pi) is a mathematical constant approximately equal to 3.14159.

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According to the information, the numbers are classified as follows: Greater than 8.2 x 104 = None; between 8.2 x 10⁴ and 8.2 x 10⁻⁶ : 2.1 x 10⁻⁴, 9.2 x 10⁻⁴, 3.4 x 10⁻⁵, 2.1 x 10⁻³, 8.3 x 10⁻⁵, 7.2 x 10⁻⁵; and less than 8.2 x 10⁻⁵: 2.8 x 10⁻⁷.

To find the classification of numbers we must know how scientific notation works and know how to classify these numbers. According to its scientific notation, if we want to classify numbers greater than 8.2 x 10⁴ we must take the following into account:

All numbers with a power greater than 10⁴ would be greater than 8.2. Therefore, none of the options would be greater than this number.

In the second case, to find the numbers that are between 8.2 x 10⁴ and 8.2 x 10⁻⁶ we must look at the same element, that is, the numbers that have a power less than 10⁴ and greater than 10⁶ would be in the range of this exercise. So the numbers in this range would be:

In the third case, to identify the numbers that are less than 8.2 x 10⁻⁵ we must take into account the same element. If power is less than 10⁻⁵, they would classify in this interval. So the values that classify are:

Note: This question is incomplete because there is some information missing. Here is the complete information:

Greater than 8.2 x 104

Between 8.2 x 104

and 8.2 x 10-6

Less than 8.2 x 10-5

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In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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x = (c - y3) / m
y = m*x + c

Let's prove this using the coordinates of the three points A, B, and C that form triangle ABC. If we take line AB, it will intersect the triangle in the point P.

To prove that the only points of line AB that lie on the triangle are the points of the side AB, we must prove that point P is either point A or point B. We do this by showing that the coordinates of P are the same as the coordinates of either A or B.

The equation of line AB is given by y = mx + c, where m is the slope and c is the y-intercept. We can calculate m and c using the coordinates of points A and B:

m = (y2-y1)/(x2-x1)
c = y1 - m*x1

We can now calculate the coordinates of point P using the equation of line AB and the coordinates of point C:

x = (c - y3) / m
y = m*x + c

Finally, we can compare the coordinates of point P with the coordinates of points A and B. If the coordinates are the same, then point P is either point A or point B, and so line AB intersects the triangle ABC only in the points of side AB.

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Answer:

It's 510!

Step-by-step explanation:

15% of 600 = 90

600-90 = 510

\( = 1 \frac{1}{5} - \frac{1}{2} \)

\( = \frac{6}{5} - \frac{1}{2} \)

\( = \frac{12}{10} - \frac{5}{10} \)

\( = \frac{7}{10} \)

Answer:

7/10

Step-by-step explanation:

Answer:

Jim: 30 Feet

Carla: 28 Feet

Step-by-step explanation:

Answer:

$7.50

Step-by-step explanation:

25% of $30 is $7.50

Answer:

7.50

Step-by-step explanation:

100%-> 30

1%->0.30

25%-> 7.50

Answer:

Extremely sorry if my answer is wrong or doesn't make sense! Also sorry that I couldn't solve it farther, I solved it using sense and haven't made it this far in math!

Step-by-step explanation:

If red is 2:3 then that means red to green is either 2:2 or 2:1. Same goes with blue.

If green is 6:19 then we can figure out the 2 possibilities for red to green.

First Possibility:

If the red to green ratio is 2:2, then the red to green to blue is 6:6:13 because 6 + 19 - 12 = 13.

Second Possibility:

If the red to green ratio is 2:3, then the red to green to blue ratio is 4:6:15 because 6 + 19 - 10 = 15.

Answer:

I think It would be B

Step-by-step explanation:

There is a∥b, Converse of the Alternate Interior Angles Theorem, which is the correct answer that would be an option (B).

Interior angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles.

Given ∠4≅∠14, which lines,

If a transversal connects two parallel lines, we know that the corresponding angles and vertically opposed angles are equivalent.

Therefore,

⇒ ∠15 = ∠3 ...(i) [Corresponding angles]

⇒ ∠15 = ∠13 ...(ii) [Vertically opposite angles]

From equations (i) and (ii), we get

⇒ ∠3 = ∠13    [Alternate interior angles]

Similarly,

⇒ ∠4 = ∠14

Hence, it is proven.

Therefore, we conclude that a∥b, Converse of the Alternate Interior Angles Theorem.

Hence, the correct answer would be an option (B).

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Answer:

x < 1

Step-by-step explanation:

2(x-7)<-12

Divide by 2

2(x-7)/2<-12/2

x-7 < -6

Add 7 to each side

x-7+7 < -6+7

x < 1

Answer:

i = the square root of -1

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given

\(\frac{2-i}{2+i}\)

Multiply the numerator/ denominator by the conjugate of the denominator.

The conjugate of 2 + i is 2 - i , then

= \(\frac{(2-i)(2-i)}{(2+i)(2-i)}\) ← expand numerator/ denominator using FOIL

= \(\frac{4-4i+i^2}{4-i^2}\)  [ i = \(\sqrt{-1}\) ⇒ i² = - 1 ]

= \(\frac{4-4i-1}{4+1}\)

= \(\frac{3-4i}{5}\)

= \(\frac{3}{5}\) - \(\frac{4}{5}\) i → A

Answer: a. (-2, -2)

Step-by-step explanation:

The point at which the two lines intersects is at (-2, -2), which is the solution.

The statement holds for k + 1. To prove that an = n^(2n-1) for all positive integers n using induction, we will follow the steps of mathematical induction:

Step 1: Base Case

Show that the statement holds true for the base case, which is n = 1.

For n = 1, we have a1 = 1^(2*1-1) = 1^1 = 1.

Since a1 = 1, the base case holds.

Step 2: Inductive Hypothesis

Assume that the statement is true for some positive integer k, i.e., ak = k^(2k-1). This is called the inductive hypothesis.

Step 3: Inductive Step

We need to prove that if the statement holds for k, it also holds for k + 1. That is, we need to show that ak+1 = (k + 1)^(2(k + 1)-1).

Using the recursive definition of the sequence, we have:

ak+1 = 2ak - 2(ak/2)

= 2k^(2k-1) - 2((k/2)^(2(k/2)-1))

= 2k^(2k-1) - 2(k/2)^(2(k/2)-1)

= 2k^(2k-1) - 2(k^(k-1))^2

= 2k^(2k-1) - 2k^(2k-2)

= k^(2k-1)(2 - 2/k)

Now, let's simplify further:

ak+1 = k^(2k-1)(2 - 2/k)

= k^(2k-1)(2k/k - 2/k)

= k^(2k-1)(2k - 2)/k

= k^(2k-1)(2(k - 1))/k

= 2k^(2k-1)(k - 1)/k

We notice that (k - 1)/k = 1 - 1/k.

Substituting this back into the equation, we have:

ak+1 = 2k^(2k-1)(k - 1)/k

= 2k^(2k-1)(1 - 1/k)

Next, let's simplify further by expanding the term (1 - 1/k):

ak+1 = 2k^(2k-1)(1 - 1/k)

= 2k^(2k-1) - 2(k^(2k-1))/k

Now, observe that k^(2k-1)/k = k^(2k-1-1) = k^(2(k-1)).

Using this simplification, we get:

ak+1 = 2k^(2k-1) - 2(k^(2k-1))/k

= 2k^(2k-1) - 2k^(2(k-1))

= 2k^(2k-1) - 2k^(2k-2)

= k^(2k-1)(2 - 2/k)

We can see that ak+1 is of the form k^(2k-1)(2 - 2/k). Simplifying further:

ak+1 = k^(2k-1)(2 - 2/k)

= k^(2k-1)((2k - 2)/k)

= k^(2k-1)(k - 1)

Finally, we have arrived at ak+1 = (k + 1)^(2(k + 1)-1). Therefore, the statement holds for k + 1.

By completing the three steps of mathematical induction, we have proven that an = n^(2n-1) for all positive integers n.

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To find the subtransient current in per unit for a three-phase fault on bus 4, we need to calculate the fault current using the bus impedance matrix.

Given bus impedance matrix Zbus:

| j0.15 j0.08 j0.04 j0.07 |

| j0.08 j0.15 j0.06 j0.09 |

| j0.04 j0.06 j0.13 j0.05 |

| j0.07 j0.09 j0.05 j0.12 |

To find the fault current on bus 4, we need to find the inverse of the Zbus matrix and multiply it by the pre-fault voltage vector.

The pre-fault voltage vector V_pre-fault is given as:

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

Let's calculate the inverse of the Zbus matrix:

Zbus_inverse = inv(Zbus)

Now, we can calculate the fault current using the formula:

I_fault = Zbus_inverse * V_pre-fault

Calculating the fault current, we have:

I_fault = Zbus_inverse * V_pre-fault

Substituting the values and calculating the product, we get:

I_fault = Zbus_inverse * V_pre-fault

= Zbus_inverse * | 1.0/0° |

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

Please provide the values of the Zbus matrix and the pre-fault voltage vector to obtain the specific values for the fault current and the per-unit current from generator 2.

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Answer:

area of hexagon = 600√3 m²

explanation:

apothem² = 20² - 10² = 400 - 100 = 300

apothem of hexagon = √300 = 10√3 m²

area of hexagon = 1/2(6 x 20)(10√3) = 600√3 m²

Answer:

Step-by-step explanation:

One way to find the area of the hexagon is to use the formula \(A=\frac{1}{2}ap\), where p is the perimeter and a is the apothem (distance from the center to the midpoint of one side).

The problem says the side length is 20, so the perimeter is 6 x 20 = 120.

The apothem is the distance marked by the dotted line. The rectangles height is \(20\sqrt{3}\), so the apothem is half of that, \(10\sqrt{3}\).

The area is \(\frac{1}{2}\cdot 10\sqrt{3} \cdot 120=600\sqrt{3}\)

Answer:

x = 10.5

Step-by-step explanation:

\(cos 65 =\frac {adjacent}{hypotenuse} \\\\0.4226 = \frac{x}{25}\\\\0.4226 \times 25 = x \\\\x = 10.565\)

Answer:

Step-by-step explanation:

take 65 degree as reference angle

using cos rule

cos 65=adjacent/hypotenuse

0.42=x/25

0.42*25=x

10.5=x

Answer:7

Step-by-step explanation:

Answer: 51 degrees

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

\(12-9x=-3x-30\)

\(12=6x-30\)

\(6x-42\)

\(x=-7\)

Hey there! I'm happy to help!

Let's call our hours h. Here is what we have going on.

42-9h

4:00 PM is 7 hours after 9:00 AM. So, we will replace the h with 7 and evaluate.

42-9(7)

42-63=-21

Therefore, the temperature would be -21°F.

Have a wonderful day! :D

\(a {y}^{2} + by + c = 0 \)

\(3 {y}^{2} + 8y + 2 = 0 \)

\(a = 3\)

\(b = 8\)

\(c = 2\)

_________________________________

\(∆ = {b}^{2} - 4ac \)

\(∆ = ({8})^{2} - 4 \times (3) \times (2) \)

\(∆ = 64 - 24\)

\(∆ = 40\)

_________________________________

\(y = \frac{ -b ± \sqrt{∆} }{2a} \\ \)

##############################

\(y(1) = \frac{ - 8 + \sqrt{40} }{6} \\ \)

\(y(1) = \frac{ - 8 + \sqrt{4 \times 10} }{6} \\ \)

\(y(1) = \frac{ - 8 + 2 \sqrt{10} }{6} \\ \)

\(y(1) = \frac{2( - 4 + \sqrt{10}) }{2 \times 3} \\ \)

\(y(1) = \frac{ - 4 + \sqrt{10} }{3} \\ \)

+++++++++++++++++++++++++++++++++++++++

\(y(2) = \frac{ - 8 - \sqrt{40} }{6} \\ \)

\(y(2) = \frac{ - 8 - \sqrt{4 \times 10} }{6} \\ \)

\(y(2) = \frac{ - 8 - 2 \sqrt{10} }{6} \\ \)

\(y(2) = \frac{2( - 4 - \sqrt{10}) }{2 \times 3} \\ \)

\(y(2) = \frac{ - 4 - \sqrt{10} }{3} \\ \)

##############################

_________________________________

And we're done.....♥️♥️♥️♥️♥️

So you are solving for x? If so, I believe that your answer would be \(x=\frac{22}{r}\).

Hope this helps! If not, feel free to explain further on this question/topic in the comments and I'll see what I can do to help you out further. Thanks and good luck!

We can eliminate x from the second equation by differentiating it and substituting for x' using the first equation:

y'' = (x + 2y)' = x' + 2y' = x + 2(x + 2y) = 3x + 4y

So we have the system:

x' = x

y'' = 3x + 4y

The characteristic equation is:

r^2 - 1 = 0

which has roots r = ±1. So the general solution is:

x = c1e^t + c2e^(-t)

y = c3e^(2t) + c4e^(-2t) - (3/4)x

where c1, c2, c3, and c4 are arbitrary constants.

To write this as a linear combination of two vector solutions, we can let:

u1 = [e^t, e^(2t)]

u2 = [e^(-t), e^(-2t)]

Then the general solution can be written as:

[x, y] = c1 u1 + c2 u2 - (3/4)[e^t, e^(2t)]

b. We can eliminate y from the second equation by adding the two equations together:

x' + y' = (x - y) + (x + y) = 2x

So we have the system:

x' - y' = x - y

x' + y' = 2x

Multiplying the first equation by 2 and adding it to the second equation gives:

2x' = 3x

So x = c1e^(3t/2) and y = c2e^(t/2) + c3e^(-t/2) - (1/2)x. The general solution is:

x = c1e^(3t/2)

y = c2e^(t/2) + c3e^(-t/2) - (1/2)c1e^(3t/2)

To write this as a linear combination of two vector solutions, we can let:

u1 = [e^(3t/2), e^(t/2)]

u2 = [0, e^(-t/2)]

Then the general solution can be written as:

[x, y] = c1 u1 + c2 u2 - (1/2)[e^(3t/2), 0]

c. We can eliminate y from the first equation by differentiating it and substituting for y' using the second equation:

x'' = (x + 2y)' = x' + 2y' = x' + 2x = 3x

So we have the system:

x' = x + 2y

x'' = 3x

The characteristic equation is:

r^2 - r - 2 = 0

which has roots r = -1, 2. So the general solution is:

x = c1e^(-t) + c2e^(2t)

y = (1/2)(c2-c1)e^(2t) + c3

where c1, c2, and c3 are arbitrary constants.

To write this as a linear combination of two vector solutions, we can let:

u1 = [e^(-t), (1/2)e^(2t)]

u2 = [e^(2t), (1/2)e^(2t)]

Then the general solution can be written as:

[x, y] = c1 u1 + c2 u2 + [0, c3]

d. We can eliminate y from the second equation by differentiating it and substituting for y' using the first equation:

y'' = 2x - y' = 2x - (-x - 2y) = 3x + 2y

So we have the system:

x' = -x - 2y

y'' = 3x + 2y

The characteristic equation is:

r^2 + r + 2 = 0

which has roots r = (-1 ± i√7)/2. So the general solution is:

x = e^(-t/2)(c1cos((√7/2)t/2) + c2sin((√7/2)t/2))

y = (-1/√7)e^(-t/2)((c1/2)sin((√7/2)t/2) - (c2/2)cos((√7/2)t/2)) + c3e^(-t)

where c1, c2, and c3 are arbitrary constants.

To write this as a linear combination of two vector solutions

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Answer:

341

STEPS:

an = a1 + (n-1) d

a1 is the first number

d = is the difference between each number = 6

a11 = 1 + (11 - 1)6

a11 = 61

Sn = n (a1 + an)/2

S11 = 11 (1 + 61)/ 2

S11 = 682/2

S11 = 341 = answer

The 11th partial sum of the arithmetic sequence {1, 7, 13, 19, …} = 341

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.

\(a_{n} = a_{1} + (n-1)d\\\\\)

Given : {1, 7, 13, 19.....}

\(a_{1} = 1\\\\d = a_{2} - a_{1} = 7 - 1 = 6\\\\a_{n} = 1 + 6(n-1) = 1 + 6n - 6 = 6n -5\\\\a_{11} = 6*11 -5 = 61\\\\S_{n} = \frac{n(a_{1} + a_{n})}{2} \\\\S_{11} = \frac{11(1+ 61)}{2} = 11 * 31 = 341\)

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height = 24.4in

hope it helps...!!!

Answer:

24.4in.

Step-by-step explanation:

31.25 x 15.5 = 484.375

11818.75 / 484.375 = 24.4in.

Answer:

The answer is -(1. 2)

GIVE ME BRAINLIEST

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

2/3 x2= 1.5

1.5 x4=  6

2x4=8