If an object is dropped from a height of 256 feet above the ground (initial height), then its velocity, V in ft/sec, at time t is given by the equation V(t)=-32t a. Find the height (h) of the object at time by solving the initial value problem. (Hint: h(0)=256) b. Find the height of the object at time = 2 seconds. c. Find how long it will the object to hit the ground.

The radius and height, in two decimal places are mathematically given as

r=10.60

Generally, the equation for the volume is mathematically given as

\(V=\pi r^{2} h+\frac{2}{3} \pi r^{3}\)

Therefore

\(5000 &=\pi 0^{2} h+\frac{2}{3} \pi r^{3}\)

\(V(r, h) &=\pi r^{2} h+\frac{2}{3} \pi r^{3}-5000 \\\nabla V &=\left\langle 2 \pi r h+2 \pi r^{2}, \pi r^{2}\right\rangle \\\)

\(\cos t &=100\left(2 \pi r^{2}\right)+75(2 \pi r h) \\\\\cos t &=200 \pi r^{2}+150 \pi r h \\\\\nabla C(r, h) &=\langle 400 \pi r+150 \pi h, 150 \pi r\rangle\)

Using Lagrange method

\($\langle 400 \pi \gamma+150 \pi \gamma h, 150 \pi \gamma\rangle=\lambda\left\langle 2 \pi \gamma h+2 \pi \gamma^{2}, \pi r^{2}\right\rangle$\)

\($400 \pi r+150 \pi r=\left(2 \pi r h+2 \pi r^{2}\right) \lambda$\)

\($400 \pi \gamma+150 \pi h=300 \pi h+300 \pi r \\\\\)

\($400 \pi r-300 \pi r=150 \pi h$\)

\($160 \pi r=150 \pi h \quad \\\\\\\)

with

\(h=\frac{2}{3} r $\)

\($\pi r^{2} h+\frac{2}{3} \pi r^{3}=5000$\)

\(\pi r}\left(\frac{2}{3} r \right)+\frac{2}{3} \pi^{3}=5000$\)

\($\frac{4 \pi \gamma^{3}}{3}=5000 \quad\)

\(r^{3}=\left(\frac{5000 \times 3}{4 \pi}\right)$\)

r=10.60

In conclusion, the radius and height, in two decimal places is

r=10.60

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Answer:

135.42

Step-by-step explanation:

Find area of all sides then add them together

Answer:

hi

Step-by-step explanation:

84⁰+103⁰+120⁰=307⁰

360⁰-307⁰=53⁰

x is 53⁰

have a nice day

Answer:

x=53

Step-by-step explanation:

A quadrilateral has four sides, four vertices and its  interior angles that add to 360 degrees:.

360 -120-103-84-= x

360-307 = x

53 = x

The smallest positive integer n for which the polynomial x^4 - nx - 63 can be factored as a product of two nonconstant polynomials with integer coefficients is 97.

To find the smallest positive integer n that satisfies the given condition, we need to consider the factors of the constant term -63 and check if any combination can be used to factorize the polynomial x^4 - nx - 63.

The constant term -63 can be factored as (-1) * 3^2 * 7, giving us several possible combinations of factors to consider: {-1, 1, -3, 3, -7, 7, -9, 9, -21, 21, -63, 63}.

We try each combination and check if it is possible to factorize the polynomial with those factors. After testing these combinations, it is found that n = 97 is the smallest positive integer for which the given polynomial can be factored as a product of two nonconstant polynomials with integer coefficients.

Thus, the polynomial x^4 - 97x - 63 can be written as a product of two nonconstant polynomials with integer coefficients, and 97 is the smallest positive integer that satisfies this condition.

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Answer:

y=-2x+3

Step-by-step explanation:

-2y=-6+4x

-2y/-2=(4x-6)/-2

y=-2x+3

Answer:

Step-by-step explanation:

Hope this helps! <3

x = 11, TV = 10

According to the Thales theorem:

RU = 8

US = 14

TV = x - 1

VS = 17.5

Substitute these values into the equation for the thales theorem

8/14 = (x-1) / 17.5

Cross multiply

8 (17.5) = 14(x - 1)

140 = 14 (x - 1)

140/14 = x - 1

10 = x - 1

x = 10 + 1

x = 11

To get the value of TV, substitute x = 11 into TV = x - 1

TV = x - 1

TV = 11 - 1

TV = 10

The measure of the smallest angle is 30° in an octagon when the interior angles are in the ratio 1:2:3:4:5:6:7:8.

The sum of the interior angles of an octagon is (8 - 2) x 180° = 1080°.

Let x be the minimum angle measure and write down the other angle equations concerning x using the ratios given.

2x, 3x, 4x, 5x, 6x, 7x, 8x.

by adding all the angles we get,

x + 2x + 3x + 4x + 5x + 6x + 7x + 8x = 36x.

Since the sum of the interior angles of an octagon is 1080°,

Simplifying the equation:

36x = 1080

x = 30

The minimum angular dimension is x = 30°. 

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If the function given is f(x), with f(0) = 16 and no other information provided, we cannot determine the values of corresponding to local maxima or minima. We can only say that there is no local maximum at x = 4 and no local maximum or minimum at x = -4, but there is a local minimum at x = -4. Without more information about the function and its behavior, we cannot provide a more specific response.

Hi there! Based on your question, I understand that you are looking for an appropriate response to determine local maximum and minimum values of a given function f(x). Here is my answer:

For a function f(x), a local maximum occurs when the value of the function is greater than its neighboring values, and a local minimum occurs when the value is smaller than its neighboring values. To find these points, you can analyze the critical points (where the derivative of the function is zero or undefined) and use the first or second derivative test.

In the given question, there seems to be some information missing or unclear. Please provide the complete function f(x) and any additional details to help me better understand your question and provide a more accurate response.

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The expression n⁸ is equivalent to the exponent expression n⁸ = (n⁴)²

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Given the equation:

n⁸

Simplifying the equation using the Power Rule for Exponents:

n⁸ = (n⁴)²

The expression n⁸ is equivalent to the exponent expression n⁸ = (n⁴)²

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The probability that a white cat escapes, followed by a black cat, is 7/26.

To find the probability of a white cat escaping followed by a black cat, we need to consider the total number of possible outcomes and the number of favorable outcomes.

The total number of cats in the cage is 8 white cats + 6 black cats = 14 cats.

When the first cat escapes, there are now 13 cats in the cage, and the number of white cats is reduced to 7. Therefore, the probability of the first cat being white is 7/13.

After the first white cat escapes, there are 12 cats left in the cage, and the number of black cats remains the same at 6. So the probability of the second cat being black is 6/12.

To find the probability of both events happening (a white cat followed by a black cat), we multiply the probabilities:

P(white cat and black cat) = P(white cat) * P(black cat | white cat)

P(white cat and black cat) = (7/13) * (6/12)

Simplifying the expression:

P(white cat and black cat) = (7/13) * (1/2) = 7/26

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Answer:

A.36m

C.-11m

D.2m

E.20m

Step-by-step explanation:

Sorry I forgot b

The final elevation of the given animals is as follows 1)Bird = 36m  2) butterfly = 4m 3) diver = -11m below sea level 4) whale = 2m 5) fish= -20 m

To get the sum of a negative and a positive number, use the sign of the larger number and subtract. For example: (–7) + 4 = –3. 6 + (–9) = –3.

Given here,1)  A bird starts at 20 m and changes 16m in a positive direction therefore net elevation is  20 + 16 = 36m

2)  A butterfly starts at 20 m and changes -16m, thus again net elevation is      

20-16 = 4m

3)  A diver starts at 5 m and changes -16m, the net depth of the diver below sea level is 5+(-16) = -11m

4)  A whale starts at -9 m and changes 11 m in the positive direction then net depth is -9+11 = 2m

5) A fish starts at -9 meters and changes -11 meters in the negative direction thus net depth is = 9-11= -20m below sea level

Hence these are the final answers.

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The integer would be -250, since it is a decrease.

Answer:

\(m=-3\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in your 2 coordinates into the slope formula to find slope m:

\(m=\frac{-7-5}{6-2}\)

\(m=\frac{-12}{4}\)

\(m=-3\)

The equipment acquired at the beginning of the year had a value of $7,620.

⇒ Debit: Cash/Bank Account = $59,200

   Debit: Accumulated Depreciation = $26,140

   Debit/Credit: (Gain) or Loss on Sale of Equipment = $6,920 (if gain) or        ($6,920) (if loss)

   Credit: Equipment = $78,420

At the beginning of the year, equipment with a value of $7,620 was acquired. The equipment's cost was $78,420, and it was depreciated using the straight-line method over an estimated useful life of 6 years with an estimated residual value.

a. To calculate the depreciation expense for the first year, we need to determine the annual depreciation amount. The formula for straight-line depreciation is:

Annual Depreciation Expense = (Cost - Residual Value) / Useful Life

Given that the cost is $78,420, the estimated residual value is not provided in the question, so we assume it to be $0, and the useful life is 6 years, we can calculate the annual depreciation expense as follows:

Annual Depreciation Expense = ($78,420 - $0) / 6 = $13,070

Therefore, the depreciation expense for the first year is $13,070.

b. To determine the gain or loss on the sale of the equipment at the end of the second year, we need to compare the selling price with the equipment's book value. The book value can be calculated as follows:

Book Value = Cost - Accumulated Depreciation

Given that the cost is $78,420 and the depreciation expense for the first year is $13,070, we can calculate the accumulated depreciation for the first year:

Accumulated Depreciation (Year 1) = Depreciation Expense (Year 1) = $13,070

The accumulated depreciation for the second year would be twice the first-year depreciation expense:

Accumulated Depreciation (Year 2) = 2 * Depreciation Expense (Year 1) = 2 * $13,070 = $26,140

Now we can calculate the book value at the end of the second year:

Book Value (Year 2) = Cost - Accumulated Depreciation (Year 2) = $78,420 - $26,140 = $52,280

Given that the equipment was sold for $59,200, we can determine the gain or loss on the sale:

Gain or Loss = Selling Price - Book Value = $59,200 - $52,280 = $6,920

Therefore, there is a gain of $6,920 on the sale of the equipment.

c. Journal entry to record the sale:

Debit: Cash/Bank Account = $59,200

Debit: Accumulated Depreciation = $26,140

Debit/Credit: (Gain) or Loss on Sale of Equipment = $6,920 (if gain) or ($6,920) (if loss)

Credit: Equipment = $78,420

The journal entry debits the cash/bank account for the selling price, debits the accumulated depreciation to remove the accumulated depreciation up to the sale date, credits the gain or loss on the sale of equipment, and credits the equipment account to remove the equipment from the books.

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a) MPC = 0.93, i.e., for every additional dollar of disposable income, 93 cents is spent on consumption.

b) Use a t-test to compare MPC to 1.

c) Prime rate is included as a measure of the cost of borrowing.

d) Yes,

e) Use an F-test

f) Standard Error = (Square root of Sum of squared residuals / Degrees of freedom) / Square root of Sum of squared deviations from mean.

The answers are as follows:

a. The MPC is 0.93, which means that for every additional dollar of disposable income, 93 cents will be spent on consumption.

b. To test if the MPC is statistically different from 1, we can use a t-test with the null hypothesis that the MPC = 1. Using the t-value and degrees of freedom provided in the regression output, we calculate the p-value to be less than 0.05, indicating that the MPC is statistically different from 1.

c. The prime rate variable is included in the model to account for the effect of interest rates on borrowing and spending. A negative sign is expected as higher interest rates would discourage borrowing and spending.

d. The coefficient for X2 (disposable income) is statistically significant with a t-value of 249.06 and a p-value of less than 0.05, indicating that it has a significant effect on PCE. The coefficient for X3 (prime rate) is also statistically significant with a t-value of -3.09 and a p-value of less than 0.05, indicating that it has a significant negative effect on PCE.

e. To test the hypothesis that R^2 = 0, we can use an F-test with the null hypothesis that R^2 = 0. Using the F-value and degrees of freedom provided in the regression output, we calculate the p-value to be extremely low, indicating that the model is a good fit and R^2 is significantly different from 0.

The regression model shows the relationship between personal consumption expenditure (PCE) and disposable income and the prime rate variable. The MPC indicates how much additional spending occurs for each additional dollar of disposable income. In this case, the MPC is 0.93, indicating that most of the additional disposable income is spent on consumption.

To test if the MPC is statistically different from 1, we use a t-test with the null hypothesis that the MPC equals 1. The p-value is less than 0.05, which means we reject the null hypothesis and conclude that the MPC is statistically different from 1.

The prime rate variable is included in the model to account for the effect of interest rates on borrowing and spending. The negative sign for the coefficient indicates that higher interest rates will discourage borrowing and spending, which is expected.

The coefficients for both X2 and X3 are statistically significant, indicating that they have a significant effect on PCE. To test the hypothesis that R^2 equals 0, we use an F-test with the null hypothesis that R^2 equals 0. The p-value is extremely low, indicating that the model is a good fit and that R^2 is significantly different from 0.

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Answer:

3

Step-by-step explanation:

answer: 35%

Step-by-step explanation: 1/4 is 25 so add 25 and 40, you get 65. Subtract 65 by 100 and u get 35. Therefor, 35% is your answer! plz mark brainliest or rate :D

Step-by-step explanation:

Total = 600

Screen 1 = 1/4 × 600 = 150

Screen 2 = 40/100 × 600 = 240

Screen 3 = 600 - (150 + 240) = 600 - 390 = 210

Answer:

Question 1:

The sum of interior angles of a polygon can be found by the following formula:

(n-2) × 180

Where n is the no. of sides

A pentagon has 5 sides

So,

= (5-2) × 180

= (3) × 180

= 540 degrees

Question 2:

Since The sum of interior angles of a regular octagon is 1080 and the total interior angle are 8

So, Measure of interior angle = \(\frac{1080}{8}\)

Measure of interior angle = 135 degrees

Question 3:

Since, one interior angle in a hexagon measures 120 degrees.

So,

The interior angle should be subtracted by 180 to get the exterior angle.

Exterior angle = 180-120

Exterior Angle = 60 degrees

Answer:

2x10+6=16

that's the equation

the expression doesn't have an answer so it would look like this:

2x10+6

The standard deviation for this sample data set is 1.93.

What is deviation ?

Deviation refers to the difference between an individual value or observation and the average or mean value of a set of data. It can also refer to the extent to which a variable or set of data deviates from a standard or expected value.

To calculate the standard deviation for a sample data set, we first need to find the mean (average) of the data. In this case, the mean of the data set {5, 7, 6, 9, 6, 4, 4, 6, 5, 2, 5} is 5.45.

Once we have the mean, we can calculate the variance by taking the average of the squared differences between each data point and the mean. The variance is given by:

(1/n) * Σ(x_i - mean)^2

where n is the number of data points and x_i is the i-th data point.

The variance for this data set is 3.70.

Finally, we take the square root of the variance to get the standard deviation.

So, the standard deviation for this sample data set is 1.93.

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Answer:

Step-by-step explanation:

1-1=0

Answer:You will have 0 moms.

Step-by-step explanation:

First you take 1 away from 1.

After that you get your answer of 0.

As we know 1 kilometer = 39370.079 inches

and, 8.39 kilometer = 330,315 inches.

Kilometers: - It is a unit of length in the international system of units (SI) equal to one thousand meters. It is now the measurement unit used for expressing distances between geographical places on land in most of the world.

Inches: - It is a unit of length in the British imperial and united states customary system of measurement. It is equal 1/36 yard or 1/12 of a foot.

To convert a kilometer measurement to an inch measurement, multiply the length by the conversion ratio.

Since 01 kilometer = 39,370.07874 inches,

We can use this simple formula to convert:

          inches = kilometers × 39,370.079

Now, according to the question:

inches = 8.39 × 39370.079

inches = 33.315

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We can substitute this result back into our original equation: ∫(π/4) Jo(x) sin(2x) dx = -(π/8) Jo(x) cos(2x) + (1/2) [(1/2) Jo'(x) sin(2x) + (1/4) ∫Jo''(x) sin(2x) dx].

To evaluate the integral ∫(π/4) Jo(x) sin(2x) dx using integration by parts, we first need to identify the two functions to be differentiated and integrated.

Let's assign u = Jo(x) and dv = sin(2x) dx.

Using the integration by parts formula, which states ∫u dv = uv - ∫v du, we can differentiate u and integrate dv.

Differentiating u:

du = d(Jo(x)) = -Jo'(x) dx.

Integrating dv:

v = -1/2 cos(2x).

Now, we can apply the integration by parts formula:

∫(π/4) Jo(x) sin(2x) dx = uv - ∫v du.

Plugging in the values:

∫(π/4) Jo(x) sin(2x) dx = (π/4) Jo(x) (-1/2 cos(2x)) - ∫(-1/2 cos(2x)) (-Jo'(x)) dx.

Simplifying, we have:

∫(π/4) Jo(x) sin(2x) dx = -(π/8) Jo(x) cos(2x) + (1/2) ∫Jo'(x) cos(2x) dx.

Now, we need to evaluate the integral on the right-hand side. The integral ∫Jo'(x) cos(2x) dx can be further simplified using integration by parts.

Assigning u = Jo'(x) and dv = cos(2x) dx, we have:

du = d(Jo'(x)) = -Jo''(x) dx,

v = (1/2) sin(2x).

Applying the integration by parts formula again:

∫Jo'(x) cos(2x) dx = u v - ∫v du.

Plugging in the values:

∫Jo'(x) cos(2x) dx = Jo'(x) (1/2) sin(2x) - ∫(1/2) sin(2x) (-Jo''(x)) dx.

Simplifying, we have:

∫Jo'(x) cos(2x) dx = (1/2) Jo'(x) sin(2x) + (1/4) ∫Jo''(x) sin(2x) dx.

At this point, we have reduced the problem to evaluating the integral ∫Jo''(x) sin(2x) dx. To proceed further, we would need additional information or apply other techniques specific to the Bessel function.

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The volume of the right cone is calculated as: 100.48 units³.

The volume of a right cone with a radius of r, and an height of h, is calculated using the formula given as:

Volume of a right cone = 1/3 × π × r² × h.

The right cone has the following parameters:

Radius (r) of the right cone = 4 units

Height (h) of the right cone = 6 units

π = 3.14

Plug in the values into 1/3 × π × r² × h:

Volume of a right cone = 1/3 × 3.14 × 4² × 6

Volume of a right cone = 1/3 × 3.14 × 16 × 6

Volume of a right cone = 1 × 3.14 × 16 × 2

Volume of a right cone = 100.48 units³

In conclusion, the volume of the right cone is calculated as: 100.48 units³.

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Answer:

very late but the answer is pi 32 units by the power of 3!

Step-by-step explanation:

Answer:

18-24-30

Step-by-step explanation:

18^2 + 24^2 = 30^2

  so via pythagorean theorem  18 24 30   forms a right triangle

Answer:

Step-by-step explanation:

Given that the principal p= $4760

rate r= 1.6%  1.6/100 =0.016  

time t= 7years

by applying the expression

\(V = Pe^{rt}\)

We have

\(V = 4760e^{0.016*7}\\\\ V=4760e^{0.112}\\\\ V=4760*1.11851286065\\\\ V=$5324.12\)

Hence after 7 years the money in the account will be $5324.12

Answer:

Always

Step-by-step explanation:

if two points lie in a plane, then the entire line containing those points lies in that plane

Answer:

y = -1/4x +3

Step-by-step explanation:

Hope this helps!