Find the general solution of the differential equation y" – 7y' – 18y = –26t + 36t². NOTE: Use t as the independent variable. Use c₁ and c₂ as arbitrary constants. y(t) = ...

Answer:

x + 37 ≥ 65

Step-by-step explanation:

Given:

Money Micah wants = $65

Money Micah had = $37

Find:

Money Micah need

Computation:

Money Micah need(x)

x + 37 ≥ 65

So,

Money Micah need = 65 - 37

Money Micah need = $28

a) Consumption = $17 billion.

b) Investment = $6 billion.

c) Phoenicia's government runs a budget deficit.

a. To find Phoenicia's consumption, we can use the equation:

Consumption = 60

P - Private Saving.

Given that private saving is $5 billion, and 60P is $22 billion, we can calculate:

Consumption = $22 billion - $5 billion

= $17 billion.

b. To find the country's investment, we need to subtract government purchases, transfer payments, and taxes from the GDP.

Since the government purchases are $7 billion, transfer payments are $2 billion, and taxes are also $7 billion, we can calculate:

Investment = GDP - (Government purchases + Transfer payments + Taxes)

= $22 billion - ($7 billion + $2 billion + $7 billion)

= $6 billion.

c. To determine if the government runs a budget surplus or a budget deficit, we can compare government purchases, transfer payments, and taxes.

Given that government purchases are $7 billion, transfer payments are $2 billion, and taxes are also $7 billion, we can calculate:

Budget surplus/deficit = Taxes - (Government purchases + Transfer payments)

= $7 billion - ($7 billion + $2 billion)

= -$2 billion.

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The number n must be greater than or equal to 2.65 and less than 2.75 in order to round to 2.7 when rounded to one decimal place

If a number n rounded to one decimal place is 2.7, then we know that n lies between two numbers:

The lower bound is the number that is 0.05 less than 2.7, which is 2.65 (since the digit in the second decimal place is 5 or greater, we round up the last digit in the first decimal place).

The upper bound is the number that is 0.05 greater than 2.7, which is 2.75 (since the digit in the second decimal place is 5 or greater, we round up the last digit in the first decimal place).

Therefore, we can write the inequality as:

2.65 ≤ n < 2.75

This means that n must be greater than or equal to 2.65 and less than 2.75 in order to round to 2.7 when rounded to one decimal place.

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Answer:

just guess it there a 50% you get it right \(￣︶￣*\))

Step-by-step explanation:

Answer : The interval of convergence is (-2/9+7, 20/9+7), which simplifies to (61/9, 209/9).

To find the interval of convergence of the given power series, we can use the ratio test. The ratio test states that if lim |(a_n+1)/(a_n)| = L, then the series converges absolutely if L < 1 and diverges if L > 1.

In this case, we have a_n = (x-7)^n / (n*(-9)^n), so a_n+1 = (x-7)^(n+1) / ((n+1)*(-9)^(n+1)). Taking the ratio of a_n+1 and a_n and simplifying, we get:

|(a_n+1)/(a_n)| = |(x-7)*(-9)/((n+1)*n)|

Taking the limit as n approaches infinity, we get:

lim |(a_n+1)/(a_n)| = |(x-7)*(-9)/n^2|

If |(x-7)*(-9)/n^2| < 1, then the series converges absolutely. Solving for x, we get:

|x-7| < 1/9 * sqrt(n^2)

|x-7| < n/9

So the interval of convergence is (-2/9+7, 20/9+7), which simplifies to (61/9, 209/9). Therefore, the power series converges absolutely for all x in this interval.

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After the 10th iteration, the estimated value of the root obtained by the bisection method is approximately 0.517. Option B

To solve the equation cos(x) - x * e = 0 in the interval [0, 1] using the bisection method, we start by checking the function values at the endpoints of the interval.

For x = 0:

cos(0) - 0 * e = 1 - 0 = 1

For x = 1:

cos(1) - 1 * e ≈ 0.54 - 2.72 ≈ -2.18

Since the function values at the endpoints have opposite signs, we can apply the bisection method to find the root within the interval.

The bisection method involves repeatedly dividing the interval in half and checking the function value at the midpoint until a sufficiently accurate approximation is obtained. In this case, we will perform 10 iterations.

After the 10th iteration, the estimated value of the root obtained by the bisection method is approximately 0.517.

Therefore, the correct answer is OB) 0.517.

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Answer:

Step-by-step explanation:

Remark

The relationship that solves this is

The outside segment * the whole length of the secant = the outside segment of the other secant * the whole length of the second secant.

Put in symbolic (and hence easier language)

GF * EG = HG * SG

Givens

GF = 4

EG = 2x + 4

GH = 5

SG = x + 5

Equation

4*(2x + 4) = 5*(x + 5)               Remove the brackets

8x + 16 = 5x + 25                    Subtract 5x from both sides

8x - 5x + 16 = 25                    Combine

3x + 16 = 25                            Subtract 16 from both sides

3x = 25 - 16                        

3x = 9                                     Divide by 3

3x/3 = 9/3

x = 3

EF = 2 * 3

EF  = 6

The volume of the solid that lies within the sphere x2 y2 z2=1, above the xy plane, and outside the cone z=√(8x2/y2 is 4π/5.

To solve the problem, we first need to find the limits of integration. The cone intersects the sphere at z=√(8x2/y2) and x2 + y2 + z2 = 1, so we can solve for y in terms of x and z:

x2 + y2 + z2 = 1

y2 = 1 - x2 - z2

y = ±√(1 - x2 - z2)

We only need the upper half of the sphere, so we take the positive square root:

y = √(1 - x2 - z2)

Since the cone is defined by z=√(8x2/y2), we can substitute this into the equation for y to get:

√(1 - x2 - z2) = √(8x2/(z2 - x2))

Squaring both sides gives:

1 - x2 - z2 = 8x2/(z2 - x2)

(z2 - x2) - x2 - z2 = 8x2

2x2 + 2z2 = z2 - x2

3x2 = z2

So the cone intersects the sphere along the curve 3x2 = z2. Since we are only interested in the portion of the sphere above the xy plane, we can integrate over the region x2 + y2 ≤ 1, 0 ≤ z ≤ √(3x2):

∫∫∫V dV = ∫∫R ∫0^√(3x^2) dz dA

where R is the region in the xy-plane given by x2 + y2 ≤ 1. We can switch to cylindrical coordinates by letting x = r cos θ, y = r sin θ, and dA = r dr dθ, so the integral becomes:

∫0^2π ∫0^1 ∫0^√(3r^2) r dz dr dθ

Evaluating the inner integral gives:

∫0^√(3r^2) r dz = 1/2 (3r^2)^(3/2) = 3r^3/2

Substituting back and evaluating the remaining integrals gives:

∫0^2π ∫0^1 3r^3/2 dr dθ = 2π ∫0^1 3r^3/2 dr = 2π [2/5 r^(5/2)]_0^1 = 4π/5

So, the volume of the solid is 4π/5.

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Answer:

0.03215.

Step-by-step explanation:

The fraction  12/3+3/4÷(−1/3)−1/2is evaluated to give -114/10

A fraction can be defined as part of a whole element, variable or number

The several  types of fractions in mathematics are;

From the information, we have that;

12/3+3/4÷(−1/3)−1/2

The fraction given is a mixture of proper fractions and improper fractions

Expand the bracket, we get;

12/3 + 3/4 ÷ -1/3 -1/2

Find the lowest common denominator

48 + 9 /12 ÷ -2 - 3 /6

Add the numerators

57/12  ÷ -5/6

Take the inverse of the divisor and multiply

57/12 × 6/-5

-114/10

Hence, the value evaluated from the fraction is -114/10

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Answer:

a) 1/2 of 12 = 1/4 of 24

b) 1/3 of 90 = 2/3 of 45

Step-by-step explanation:

1/2 of 16 is 6, so 6 would be 1/4 of what? 6 x 4 = 24. 6 is 1/4 of 24. The other one is the same. 1/3 of 90 is 30, and 30 is 2/3 of 45.

Answer:

(B) 7.6, 8.8

Step-by-step explanation:

u are welcome

Answer:

B.(7.6, 8.8)

Step-by-step explanation:

Answer:WAIT HE IS TELLING THE TIME

Step-by-step explanation:

You will be able to withdraw approximately $3,076.32 at the end of 5 years.

To calculate the amount you will be able to withdraw at the end of 5 years, we can use the future value formula for compound interest.

The formula for calculating the future value (FV) of a present value (PV) invested at an annual interest rate (r) for a certain number of years (t) is:

\(FV = PV * (1 + r)^t\)

Given:

PV = $2,300

r = 6% = 0.06 (decimal representation)

t = 5 years

Substituting these values into the formula, we get:

FV = $2,300 * \((1 + 0.06)^5\)

Calculating the expression inside the parentheses:

\((1 + 0.06)^5 = 1.338225\)

Multiplying the present value by this factor:

FV = $2,300 * 1.338225

FV ≈ $3,076.32

Therefore, you will be able to withdraw approximately $3,076.32 at the end of 5 years.

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You deposit $2,300 into an account that pays 6% per year. Your plan is to withdraw this amount at the end of 5 years to use for a down payment on a new car. How much will you be able to withdraw at the end of 5 years? Do not round intermediate calculations. Round your answer to the nearest cent

We are asked to find the values needed for the length CB

The coordinates of points C and B are given as

C(-a, -5b)

Recall that the distance formula is given by

For the given case,

Let us substitute these coordinates into the above distance formula

Therefore, the required values are

Answer:

Your Answer is: 237 /20

Answer:

5 17/20

Step-by-step explanation:

The average drying time, based on the given sequence of 5 random numbers (r1 = 0.17, r2 = 0.22, r3 = 0.29, r4 = 0.31, and r5 = 0.42), is 0.282 seconds.

To calculate the average drying time, we sum up all the drying times and divide by the number of trials. In this case, the drying times are represented by the random numbers r1, r2, r3, r4, and r5.

Average drying time = (r1 + r2 + r3 + r4 + r5) / 5

Substituting the given values:

Average drying time = (0.17 + 0.22 + 0.29 + 0.31 + 0.42) / 5

                    = 1.41 / 5

                    = 0.282

Therefore, the average drying time, based on the given sequence of random numbers, is approximately 0.282 seconds. This average represents the expected value of the drying time based on the given trials. It provides a summary measure of central tendency for the drying times observed in the simulation.

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Answer:

Step-by-step explanation:

B.

A study has a 2 Ã 2 Ã 3 within-groups factorial design. This example has a total of _12_ cell(s). Researchers would need to investigate _three__ main effect(s), _Three two-way interactions __ two-way interaction(s), and _ One three-way interaction__ three-way interaction(s) in this study.

a 2 x 2 x 3 within-groups factorial design, you have:
A total of 2 x 2 x 3 = 12 cells
Three main effects to investigate (one for each factor)
Three two-way interactions to investigate (AxB, AxC, and BxC)
4. One three-way interaction to investigate (AxBxC)
So, in this study, there are 12 cells, researchers would need to investigate 3 main effects, 3 two-way interactions, and 1 three-way interaction.

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The correct simplification would be \(18x^4 - 36x^3 + 9x^2\) (option a).

To simplify the expression \(9x^2(4x - 2x^2\) - 1), we need to perform the multiplication and combine like terms.

1. Start by distributing the 9x^2 to each term inside the parentheses:

  \(9x^2 * 4x = 36x^3 9x^2 * (-2x^2) = -18x^4 9x^2 * (-1) = -9x^2\)

2. Now we can combine the terms obtained from the distribution:

\(36x^3 - 18x^4 - 9x^2\)

3. Rearranging the terms in descending order of exponents:

\(-18x^4 + 36x^3 - 9x^2\)

4. However, we can simplify this expression further by factoring out a common factor of \(-9x^2\):

\(-9x^2(2x^2 - 4x + 1)\)

5. Thus, the final simplified expression is:

\(18x^4 - 36x^3 + 9x^2\)

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Answer:

The two little blue boxes are going

Step-by-step explanation:

Lets start with the 0s.

Two zeros is 0. so its

_ _ _ _ 0.

Now we add 2 and 0 which is 2.

_ _ _ 2 0

now we add 6 and 4, which is 10. We have to put the 1 above the 7 and 5 and we are going to put 0 down below

_ _ 0 2 0

now we are going to add 7 +5, but dont forget the 1! Its going to be 13. Put the 3 down below and put the 1 above the 2!

_ 3 0 2 0

Now its 2 + 1 which is 3

your answer is

33020

For the construction of an inscribed circle the required construction that must be known is the angle bisector. The correct option is (A).

The angle bisector is a line that divides an angle into two equal parts. For a circle inscribed in a triangle the line joining the center to the vertex is the angular bisector of the interior angle.

The diagram for the given case can be drawn as follows,

For the circle inscribed in the circle, all the sides are tangents.

By the property of tangents to a circle ∠ODB and ∠OFB are right angles.

Now, in ΔODB and ΔOFB the relation is obtained as,

∠ODB = ∠OFB  (right angles)

OB = OB           (Common sides)

And, OD = OF  (radius of the circle)

⇒ ΔODB ≅ ΔOFB (by RHS criteria)

This implies that ∠ODB ≅ ∠OFB.

Thus, the line joining the centre and the vertex of triangle bisects its angles.

Hence, for the given case the required construction to be known is the angle bisector of triangle.

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The limit of the sequence (1) {2}, (2) {(-1)^n}, and (3) {n sin(n)}, converges to DNE (does not exist) or the sequence diverges. The limit of the sequence (4) {sin(nπ)} is undefined, as it oscillates between -1 and 1.

In the case of sequence (1) {2}, the limit is a constant value, and the sequence converges to that value. However, in the case of sequence (2) {(-1)^n}, the sequence oscillates between -1 and 1, and there is no single value that it approaches as n tends to infinity. Therefore, the limit does not exist, and the sequence diverges.

Sequence (3) {n sin(n)} also does not have a limit as n tends to infinity. The term n sin(n) oscillates between positive and negative values without approaching a specific value. Hence, the limit of this sequence is DNE, and it diverges.

In the case of sequence (4) {sin(nπ)}, the term sin(nπ) oscillates between -1 and 1 as n varies. Since there is no convergence to a specific value, the limit of this sequence is undefined.

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Answer:

2 cups left

Step-by-step explanation:

The general solution to the initial value problem is \(y(t) = y_h(t) + y_p(t).\)Substitute the initial conditions y(0) = 0 and y'(0) = 0 into the general solution to find the constants c1 and c2. The final solution to the initial value problem comes out as : \(y(t) = c1*e^t + c2*e^(-t) + u1(t)*e^t + u2(t)*e^(-t).\)

To solve the initial value problem \(y'' - y = g(t)\) with \(g(t) = -t if 0 ≤ t < 2\) and 0 if 2 ≤ t, and with y(0) = 0 and y'(0) = 0, we will use the method of variation of parameters.

The general solution to the homogeneous equation \(y'' - y = 0\). The characteristic equation is \(r^2 - 1\) = 0, which has roots r = 1 and r = -1. So the general solution is \(y_h(t) = c1*e^t + c2*e^(-t).\)
The particular solution to the non-homogeneous equation using variation of parameters. We will assume that the particular solution is of the form \(y_p(t) = u1(t)*e^t + u2(t)*e^(-t).\)

The first and second derivatives of \(y_p(t):\)
\(y'_p(t) = u1'(t)*e^t + u1(t)*e^t + u2'(t)*e^(-t) - u2(t)*e^(-t) y''_p(t) = u1''(t)*e^t + 2*u1'(t)*e^t + u1(t)*e^t + u2''(t)*e^(-t) - 2*u2'(t)*e^(-t) + u2(t)*e^(-t)\)

Substitute \(y_p(t), y'_p(t), and y''_p(t)\) into the original equation, simplify:
\(u1''(t)*e^t + 2*u1'(t)*e^t + u1(t)*e^t + u2''(t)*e^(-t) - 2*u2'(t)*e^(-t) + u2(t)*e^(-t) - u1(t)*e^t - u2(t)*e^(-t) = g(t) u1''(t)*e^t + 2*u1'(t)*e^t + u2''(t)*e^(-t) - 2*u2'(t)*e^(-t) = g(t)\)
\(u1''(t)*e^t + u2''(t)*e^(-t) = 0\) and \(2*u1'(t)*e^t - 2*u2'(t)*e^(-t) = g(t)\).

This gives us two equations: \(u1''(t) = -u2''(t)*e^(-2t) and 2*u1'(t) - 2*u2'(t)*e^(-2t) = g(t)*e^(-t)\)
Getting values for u1'(t) and u2'(t):
\(u1'(t) = (g(t)*e^(-t) + 2*u2'(t)*e^(-2t))/2 u2'(t) = (-g(t)*e^(t) + 2*u1'(t)*e^(2t))/2\)Integrate both equations to find u1(t) and u2(t):
\(u1(t) = ∫(g(t)*e^(-t) + 2*u2'(t)*e^(-2t))/2 dt u2(t) = ∫(-g(t)*e^(t) + 2*u1'(t)*e^(2t))/2 dt\)

Substitute g(t) = -t if 0 ≤ t < 2  0 if 2 ≤ t into the equations for u1(t) and u2(t) and solve for \(u1(t)\)and \(u2(t)\). Substitute \(u1(t)\) and\(u2(t)\)into the equation for y_p(t) to find the particular solution. The final solution to the initial value problem is \(y(t) = c1*e^t + c2*e^(-t) + u1(t)*e^t + u2(t)*e^(-t).\)

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using exponents, On simplifying the equation, we get =4m+8.

The PEMDAS order of operations must be followed when you want to simplify a mathematical equation without using parenthesis (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). There are no parenthesis in the expression, so you may start looking for exponents. If it does, first make that simpler.

Work simplification is to develop better work processes that boost output while cutting waste and costs.

Simplifying an expression is the same as solving a mathematical issue. When you simplify an equation, you essentially try to write it as simply as you can. There shouldn't be any more multiplication, dividing, adding, or deleting to be done when the process is finished.

Given equation,

m-(8-3m)

=m-8+3m

=4m+8

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9514 1404 393

Answer:

  (c)  1

Step-by-step explanation:

To find f(-2), locate -2 in the x column. Then find the corresponding f(x) value.

 -2 is in the second row, opposite f(x) = 1, so f(-2) = 1.

Answer: c

Step-by-step explanation:

The x-intercepts are the points (-2,0) and (4,0)

A parabola is a symmetrical, curved, U-shaped graph. Parabolas exist in everyday situations, such as the path of an object in the air, headlight shapes and the wire of suspension bridges. The equation of a parabolic graph is y = x² and all quadratic graphs have a line of symmetry which passes vertically through the minimum or maximum point

Find the x-intercepts of the parabola and write them as ordered pairs

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

For x=4 and x=-2 the equation is equal to zero

therefore

The x-intercepts are the points (-2,0) and (4,0)

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