the altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while the area of the triangle is increasing at a rate of 2.5 square cm/minute. at what rate is the base of the triangle changing when the altitude is 8.5 centimeters and the area is 92 square centimeters?

\(V = \pi(3)^2(21)\) is the equation that shows the volume of the given cylinder.

The following formula may be used to determine a cylinder's volume:

\(V=\pi r^2h\)

Where r is the radius of the cylinder's base, h is its height and is a mathematical constant that denotes the ratio of a circle's circumference to its diameter.

We must first determine the radius of the cylinder's base in order to utilize this formula to calculate the fulgurite's volume. The radius is equal to half of the base's diameter, or 3 inches since we know it to be 6 inches.

When we enter the values we are aware of into the formula, we obtain:

\(V = \pi(3)^2(21)\)

Therefore, the expression that represents the volume is \(V = \pi(3)^2(21)\)

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Answer: 45.9

Step-by-step explanation: its right trust

Answer:

45 9/10 0r 45.9

Step-by-step explanation:

0.54 * 85

45.9

45 9/10

Answer:

300 new employees

Step-by-step explanation:

1:3

x + 3x = 1,200

4x = 1200

x = 300

The parametric equation for the tangent line at t = 0 is:

\(x = 0 + (1/2)t\\y = 1\\z = 1 + (1/2)t\)

To find the tangent vector to the path at t = 0, we need to differentiate each component of the path with respect to t and evaluate it at t = 0.

Given the path c(t) = (sin(2t), cos(3t), 2sin(t) + cos(t)), we can differentiate each component as follows:

\(x'(t) = d/dt[\sin(2t)] \\= 2cos(2t)\\y'(t) = d/dt[\cos(3t)] \\= -3sin(3t)\\z'(t) = d/dt[2\sin(t) + cos(t)] \\= 2cos(t) - sin(t)\)

Now we can evaluate these derivatives at t = 0:

\(x'(0) = 2\cos(0) = 2(1) \\= 2\\y'(0) = -3\sin(0) \\= 0\\z'(0) = 2\cos(0) - \sin(0) \\= 2(1) - 0 \\= 2\)

Therefore, the tangent vector to the path at t = 0 is (2, 0, 2).

To find the parametric equation for the tangent line to the path at t = 0, we can use the point-slope form of a line. We already have the point (x0, y0, z0) = (sin(2(0)), cos(3(0)), 2sin(0) + cos(0)) = (0, 1, 1).

The equation of the tangent line is given by:

x - x0 y - y0 z - z0

------- = -------- = --------

a b c

Substituting the values we have:

x - 0 y - 1 z - 1

----- = ------- = -----

2 0 2

Simplifying, we get:

x y - 1 z - 1

--- = ------- = -----

2 0 2

The parametric equation for the tangent line at t = 0 is:

\(x = 0 + (1/2)t\\y = 1\\z = 1 + (1/2)t\)

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The tangent vector to this path at t=0 is (2, 0, 2) and the parametric equation for the tangent line to this path is;

r(t) = (2t, 1, 1 + 2t).

Given path is c(t) = (sin(2t),

cos(3t), 2sint + cost).

(a) The tangent vector to this path at t=0 is:

To find the tangent vector at t = 0, find the derivative of c(t) and substitute t = 0.

c(t) = (sin(2t),

cos(3t), 2sint + cost)

Differentiate with respect to t

c'(t) = (2cos(2t), -3sin(3t), 2cost-sint)

The tangent vector at t = 0 is c'(0) = (2cos(0), -3sin(0),

2cos(0)-sin(0)) = (2, 0, 2).

(b) The parametric equation for the tangent line to this path at t=0 is:

The equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept.

Here, the slope is the tangent vector we found in part (a), and the point (sin(0), cos(0), 2sin(0) + cos(0)) = (0, 1, 1) lies on the line. So, the parametric equation for the tangent line to this path at t=0 is:

r(t) = (0, 1, 1) + t(2, 0, 2)

= (2t, 1, 1 + 2t).

Conclusion: Therefore, the tangent vector to this path at t=0 is (2, 0, 2) and the parametric equation for the tangent line to this path is;

r(t) = (2t, 1, 1 + 2t).

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After traveling 16 miles east and 18 miles north, you would be approximately 23.4 miles away from your starting point by using Pythagorean theorem.

To find the distance from your starting point, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the distance traveled east and north form the legs of the right triangle, and the distance from the starting point to the final position is the hypotenuse.

Using the Pythagorean theorem, we can calculate the distance as follows:

Distance^2 = (16 miles)^2 + (18 miles)^2

Distance^2 = 256 miles^2 + 324 miles^2

Distance^2 = 580 miles^2

Distance ≈ √580

Distance ≈ 24.083 miles

Rounding to the nearest tenth, the distance from the starting point would be approximately 23.4 miles.

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We can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:

A parabola refers to the shape that traces the equation of the form ax² + bx + c.

A parabola's directrix is a vertical or horizontal line that never contacts the parabola and is located at p distance from the vertex and 2p distance from the focus.

The parabola created when the directrix is on the y coordinate called a vertical parabola.

If the directrix value is greater than the corresponding focus or vertex, there will be a negative p and the parabola will face downhill.

If the directrix value is less than the corresponding focus or vertex, there will be positive p and the parabola will face up.

From the given definition of the directrix, we can find the value of p;

2p = y coordinate of focus - equation of the directrix

2p = 1 - (-1)

2p = 2

p = 1

Vertex, v(h, k) compared with f(h, k + p), we will get;

k + p = 1

k = 0

Therefore, the vertex is (-8, 0).

Thus, we can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:

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One additional group would be required to conduct a 3 x 2 x 3 factorial design compared to a 3 x 2 x 2 design with independent variable.

A 3 x 2 x 3 factorial design requires three independent variables (x1, x2, and x3) with three levels each, for a total of 27 conditions. A 3 x 2 x 2 design, however, would only require two independent variables (x1 and x2) with two levels each, for a total of 12 conditions. To conduct a 3 x 2 x 3 factorial design, one additional group would be required, compared to the 3 x 2 x 2 design. This additional group would provide data for the additional 15 conditions that the 3 x 2 x 3 design would require.

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Let the selling price for walnuts be x and the selling price for the almonds be y.

On the first day, Erick sold 2 pounds of walnuts and 4 pounds of almonds for $28. This implies that

On the second day, 4 pounds of walnuts and 3 pounds of almonds for $31.

The domain of the quotient function (f/g)(x) consists of all numbers that belong to both the domain of f and the domain of g which is false.

A statement, opinion, or rule that forms a linking of two variables is characterized as a function. Mathematics has functions, which are necessary for the design of meaningful relationships.

The range refers to all potential values of y, and the domain refers to all conceivable values of x.

The denominator of the rational function shouldn't be 0. The function is not defined if the denominator is 0.

Thus, the given statement is false.

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Answer:

Step-by-step explanation:

Roll a number cube with 1 representing the first homeroom, 2 representing the second homeroom, 3 representing the third homeroom, and any other outcome representing the fourth homeroom.

Flip a coin 4 times, once for each homeroom, with heads up representing being assigned to the homeroom represented by that flip.

Draw a marble from a bag containing 5 white marbles, 5 black marbles, 5 red marbles, and 5 green marbles, with each color representing a different homeroom.

Spin a spinner with 8 congruent sections with 2 sections assigned to each homeroom.

Answer:

B. Draw a marble from a bag containing 5 white marbles, 5 black marbles, 5 red marbles, and 5 green marbles, with each color representing a different homeroom.

C. Use a random number generator with 1, 2, and 12 representing the first homeroom, 7, 9, and 10 representing the second homeroom, 3, 8, and 11 representing the third homeroom, and 4, 5, and 6 representing the fourth homeroom.

E. Spin a spinner with 8 congruent sections with 2 sections assigned to each homeroom.

Step-by-step explanation:

I just did the test and got this correct.

(please mark brainliest)

Have a good day!

Answer:

3:1

Step-by-step explanation:

It’s three times the original

Answer:

Trina is 45 years old.

Her grandfather is 50 years old.

Step-by-step explanation:

Trina is 5 years younger than grandfather, therefore:

45+50 = 95

True. When performing econometric analysis on time-series data, it is a best practice to sort the data in chronological order. Econometric analysis involves using statistical methods to study and understand economic relationships, trends, and patterns.

Time-series data refers to a set of observations collected at regular intervals over time, such as stock prices, GDP growth, or unemployment rates.

Sorting the data in chronological order is essential because it allows for a proper understanding of the temporal relationship between different data points. This ordering helps researchers identify patterns, trends, and potential causal relationships within the data. Additionally, many econometric models, such as autoregressive or moving average models, rely on the assumption that the data points are arranged sequentially in time.

In summary, when conducting econometric analysis on time-series data, it is crucial to sort the data in chronological order to accurately analyze patterns, trends, and relationships. This practice enables researchers to develop robust models that can be used for forecasting and understanding the underlying economic processes.

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a) You can afford a loan of approximately $91,862.33.

b) The total amount of money you will pay the loan company is $288,000.

c) Approximately $196,137.67 of that money is interest.

To determine how big of a loan you can afford, you need to consider your monthly mortgage payment, the loan term, and the interest rate. In this case, you can afford a $800 per month mortgage payment.

Using the formula for calculating the loan amount based on monthly payment, loan term, and interest rate, we can determine the loan amount you can afford. In this scenario, you have a 30-year loan at 8% interest.

Using the loan payment formula, we find that the loan amount you can afford is approximately $91,862.33.

To calculate the total amount of money you will pay the loan company, you multiply the monthly payment by the total number of payments over the loan term. In this case, it's $800 multiplied by 360 (30 years * 12 months). This gives a total payment of $288,000.

To determine how much of that total payment is interest, you subtract the loan amount from the total payment. In this case, it's $288,000 - $91,862.33, which equals approximately $196,137.67.

Therefore, you can afford a loan of approximately $91,862.33, the total amount you will pay the loan company is $288,000, and approximately $196,137.67 of that total is interest.

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Answer:

1/6

Since there are 6 sides on a dice, divide 100 by 6.

100 ÷ 6 = 16.67%

Now, convert 16.67% to a fraction.

16.67% = 1/6 fraction.

You get 1/6. That is your answer. Hope it helps!

The hexadecimal number 0x3d is equal to 61 in decimal (base 10).

To convert the hexadecimal number 0x3D to decimal (base 10), we need to understand the positional system of both bases. In hexadecimal, each digit represents a power of 16, starting from the rightmost digit. The digits range from 0 to 9, and then from A to F, where A represents 10 and F represents 15, In hexadecimal (base 16) representation, each digit can have values from 0 to 15. The digits from 0 to 9 represent their respective values, and the letters A to F represent the values 10 to 15.

To convert 0x3d to decimal, we can break down the number as follows:

0x3d = (3 * 16^1) + (13 * 16^0)

Simplifying the expression:

0x3d = (3 * 16) + 13

0x3d = 48 + 13

0x3d = 61

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Thus, the object travels a distance of 10π units along the given trajectory.

To find out how far an object travels along a given trajectory, we need to calculate the arc length of the curve. The formula for arc length is given by:

L = ∫_a^b √[dx/dt]^2 + [dy/dt]^2 dt

where L is the arc length, a and b are the start and end points of the curve, and dx/dt and dy/dt are the derivatives of x and y with respect to time t.

In this case, we have the trajectory r(t) = (10 cos 2t, 10 sin 2t) for 0 ≤ t ≤ π/2. Therefore, we can calculate the derivatives of x and y as follows:

dx/dt = -20 sin 2t
dy/dt = 20 cos 2t

Substituting these values into the formula for arc length, we get:

L = ∫_0^(π/2) √[(-20 sin 2t)^2 + (20 cos 2t)^2] dt
 = ∫_0^(π/2) √400 dt
 = ∫_0^(π/2) 20 dt
 = 20t |_0^(π/2)
 = 10π

Therefore, the object travels a distance of 10π units along the given trajectory.

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Answer:

through: (-4, 1) and (1, -3) how do u write the point slope form of the equation of the line through the given points ?

Step-by-step explanation:

to find slope you do delta y over delta x meaning 3 - 1 over 1 - (-4) you get 2/5 that is slope then you do to find b you take one of the points and you plug in for y = mx + b doesn't matter which one so -3 = 2/5 (1) + b

-3 = 2/5 + b

subtract 2/5 from both sides you get

-17/5 = b

so the equation is

y = 2/5x - 17/5

Answer:

take out or aluminate i think

Step-by-step explanation:

Answer: 50% I'm guessing but I cannot really answer unless you actually put a picture of it down

The length ||x||2 is positive, we must have λ

is positive. It follows that every eigenvalue λ

of A is real.

Recall that the eigenvalues of a real symmetric matrix are real.

Let λ be a (real) eigenvalue of A and let x be a corresponding real eigenvector. That is, we have

Ax=λx.

Then we multiply by xᵀ on left and obtain

xᵀAx = λxᵀx = λ || x || 2.

The left hand side is positive as A is positive definite and x is a nonzero vector as it is an eigenvector.

Since the length ||x||2 is positive, we must have λ

is positive. It follows that every eigenvalue λ

of A is real.

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The linear pair is the correct answer for a pair of adjacent angles whose opposite rays form their non-common sides.

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Therefore , the solution to this problem of resistance comes out to be  R = 50 ohms.

Resistance is the degree to which a substance obstructs or opposes an electric current. To better understand resistance, imagine how difficult it would be for a person to move from one shop to another in a crowded market.

Here,

Given: current = 2 amperes

and Voltage = 100 Volts

Using Ohm's Law,

V = I * R

At 100 v, current = 2 A

To calculate resistance

100 =  2 * R

R = 50 Ω

Resistance of material, R = 50 Ω

Therefore , the solution to this problem of resistance comes out to be  R = 50 ohms.

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Answer:

its b or c

Step-by-step explanation:

but I think C tho sorry if I'm wrong=)

have a great day

The wave interaction that is shown  in the given image is diffraction. Here, the incident wave is hitting on the obstacle and diffracting at different angles. Hence, option B is correct.

Diffraction is a phenomenon that occurs when waves encounter an obstacle or pass through an aperture (opening) in a barrier. When a wave encounters an obstacle or an aperture, it bends and spreads out, creating a pattern of interference that is characteristic of the wave.

Diffraction occurs with all types of waves, including sound waves, water waves, and electromagnetic waves (such as light waves). The amount of diffraction that occurs depends on the size of the obstacle or aperture relative to the wavelength of the wave.

When the obstacle or aperture is much smaller than the wavelength of the wave, the amount of diffraction is significant, and the wave bends sharply around the edges of the obstacle or aperture.

The diffraction pattern created by an aperture can be observed on a screen placed behind the aperture.  Hence, the given image is an example of diffraction.

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Answer:

y^2-y^1/x^2-x^1

Step-by-step explanation:

Answer:

x is equal to 105

solved!, brainliest pls! would help a lot! ;)

Explanation:

This is easy! Forget about the other numbers only the 75° and the line it's on, only focus on that. Then a straight line is equal to 180° so...

180° - 75° = 105° haha woohoo

It is given that the point G lies on the line segment FH and divides it in the ration 5:2.

So we will use the section formula to obtain the coordinates of the point G.

Now the x-coordinate of the point G will be:-

Now the y-ccordinate of the point G will be:-

So the coordinates of the point G are (-6, 14).

Hence the correct option is (D).