Consider the initial value problem y" + 16 = 48t, y(0) = 5, y'(0) = 2. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(S). Do not move any terms from one side of the equation to the other (until you get to part (b) below). 48/s^2 help (formulas) b. Solve your equation for Y(s). Y(s) = L{y(t)} = (58^3+2s^2+48)/(s^2(s^2+16)) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t).

Answer:

82 percent

Step-by-step explanation:

really simple

Answer:

2

Step-by-step explanation:

a2 = a1×3

a3 = a2×3 = a1×3×3

=>

an = an-1 × 3 =

\(a1 \times {3}^{n - 1} \)

a5 = 162 = a1×3⁴ = a1×81

a1 = 162/81 = 2

Answer:

Rotation of 90 degrees counterclockwise about the origin

Step-by-step explanation:

well counterclockwise means you rotate the figure to the left and this figure is rotated to the left

Given data: Current population of a small town = 2681 people.

The town's population is tripling every 12 years.

We need to approximate the population of the town 6 years from now.

Solution: Let P be the population of the town after 6 years.

The population of the town triples every 12 years, which means that for every 12 years, the population is multiplied by 3.

Therefore, the population P after 6 years from now will be:\(P = (2681 people) x 3^{(6 years / 12 years)}P = (2681 people) x 3^{0.5}P = 2681 people x 1.732P = 4642 people.\)

Therefore, the approximate population of the town 6 years from now is 4642 people.

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Answer:

Hopefully this is the question: 7\(x^{2}\) + 3x - \(x^{2}\)

Step-by-step explanation:

7\(x^{2}\) + 3x -\(x^{2}\)

= 6\(x^{2}\) + 3x

= 3x ( 2x + 1 )

Hopefully this helps.

Answer:

(1, 2 )

Step-by-step explanation:

x + y = 3 (subtract x from both sides )

y = 3 - x → (1)

2x - y = 0 → (2)

Substitute y = 3 - x into (2)

2x - (3 - x) = 0

2x - 3 + x = 0

3x - 3 = 0 ( add 3 to both sides )

3x = 3 ( divide both sides by 3 )

x = 1

Substitute x = 1 into (1)

y = 3 - 1 = 2

solution is (1, 2 )

Answer:

Angle BFC.

Step-by-step explanation:

Because angle BFD is a right angle because angle AFE is equal to BFD because of vertical angles

a The product of a constant factor of four and a factor with the sum of two terms.

We can estimate that B × T is roughly 0.57, or equivalently, T is roughly 0.57 / B.

Assuming that the rumor spreads according to the logistic law, we can use the following formula to estimate the number of people who will hear the rumor by 5 pm:

\(P(t) = K / (1 + A \times e^{(-B\times t)})\)

where:

P(t) is the number of people who have heard the rumor by time t,

K is the maximum possible number of people who can hear the rumor (in this case, the total population of the town, which is 10,000),

A and B are constants that determine the shape of the logistic curve, and

e is the mathematical constant approximately equal to 2.71828.

To solve for A and B, we need to use the information given in the problem. We know that at noon, 4,000 people have heard the rumor. Let's assume that "noon" corresponds to t=0 (i.e., we start counting time from noon). Then we have:

\(P(0) = 4,000 = K / (1 + A \times e^{(-B\times 0)})\)

4,000 = K / (1 + A)

1 + A = K / 4,000

We also know that the logistic law predicts that the number of people who hear the rumor will eventually level off and approach the maximum value K. Let's assume that the leveling off occurs after a long time T (which we don't know). Then we have:

P(T) = K

We can use these two equations to solve for A and B:

A = (K / 4,000) - 1

B = ln((K / 4,000) / (1 - K / 4,000)) / T

where ln denotes the natural logarithm.

Unfortunately, we don't know the value of T, so we can't calculate B directly. However, we can make an educated guess based on the shape of the logistic curve. Typically, the curve starts out steeply and then levels off gradually. Therefore, we can assume that the time it takes for the curve to reach 90% of its maximum value is roughly equal to T. In other words, we want to solve for T such that:

\(P(T) = 0.9 \times K\)

Substituting the expression for P(t) into this equation, we get:

\(0.9 \times K = K / (1 + A \times e^{(-BT)})\\0.9 = 1 / (1 + A \times e^{(-BT)})\\1 + A \times e^{(-BT)} = 1 / 0.9\\A \times e^{(-BT)} = 1 / 0.9 - 1\\e^{(-B\times T)} = (1 / 0.9 - 1) / A\\B \times T = -ln((1 / 0.9 - 1) / A)\)

Plugging in the values for K and A, we get:

A = (10,000 / 4,000) - 1 = 1.5

\(B \times T = -ln((1 / 0.9 - 1) / 1.5) = 0.57\)

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Answer: the product of this question is 858

Step-by-step explanation:

In the graph of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

The simple linear regression equation represents a linear relationship between a dependent variable and an independent variable. It can be written as y = ß0 + ß1x, where ß0 is the intercept and ß1 is the slope of the regression line.

The slope (ß1) determines the rate of change in the dependent variable (y) for each unit change in the independent variable (x). It represents the steepness or inclination of the regression line. The sign of ß1 indicates whether the line has a positive or negative slope, indicating the direction of the relationship between the variables.

Thus, in the context of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

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Answer:

x>3

Step-by-step explanation:

put an open circle where the number 3 goes on the numberline, then make an arrow to the right signifying that x is greater than 3

The degrees of freedom and t-critical for a two-tailed t-test for a zero slope at α=0.05 are 18 and ±2.101, respectively.

To calculate the degrees of freedom for the two-tailed t-test, we need to subtract 2 from the sample size, which gives us n-2 = 20-2 = 18. The t-critical value can be obtained from a t-distribution table with 18 degrees of freedom and a significance level of α/2=0.025. Looking up the table, we find that the t-critical value is ±2.101.

Therefore, for a two-tailed t-test with a significance level of α=0.05 and a sample size of 20, we would have 18 degrees of freedom and a t-critical value of ±2.101. This means that if our calculated t-value falls outside of this range, we can reject the null hypothesis that the slope is zero.

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Answer:

174\(m^{2}\)

Step-by-step explanation:

22 + 75 + 77 = 174

hope this makes more sense

so, I've divided the figure into 3 different rectangles

in order to get the surface area of the original figure, you'll need to figure out the surface areas of those 3 rectangles and then add them up

YELLOW RECTANGLE

the lenght is 11, the width is 2

in order to get the surface area, you'll need to multiply the length (11) by the width(2)

so you'll get

11 * 2 = 22

PURPLE RECTANGLE

the lenght is 15, the width is 5

in order to get the surface area, you'll need to multiply the length (15) by the width(5)

so you'll get

15 * 5 = 75

RED RECTANGLE

the lenght is 11, the width is 7

in order to get the surface area, you'll need to multiply the length (11) by the width(7)

so you'll get

11 * 7 = 77

THEN YOU JUST ADD UP THESE 3 SURFACE AREAS

you'll get 22 + 75 + 77 = 174

Answer:

Point G and Point B

Step-by-step explanation:

The quadrant on the top right is quadrant 1 and the quadrant on the top left is quadrant 2. The quadrant on the bottom right is quadrant 4 and the quadrant on the bottom left is quadrant 3.

one solution of the equation is approximately 1.8925469 radians.

The equation is:

tan(x) + 3 = 0

Subtracting 3 from both sides, we get:

tan(x) = -3

Taking the inverse tangent of both sides, we get:

x = arctan(-3)

However, the tangent function is periodic with period π, which means that there are infinitely many solutions to this equation. In general, the solutions are given by:

x = arctan(-3) + nπ, where n is an arbitrary integer.

Using a calculator to approximate arctan(-3), we get:

arctan(-3) ≈ -1.2490458

Therefore, the general solution to the equation is:

x ≈ -1.2490458 + nπ, where n is an arbitrary integer.

If we substitute n = 1, we get:

x ≈ -1.2490458 + π

Using a calculator to approximate this value, we get:

x ≈ 1.8925469

So one solution of the equation is approximately 1.8925469 radians.

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Work Shown:

sin(angle) = opposite/hypotenuse

sin(35) = 10/x

x*sin(35) = 10

x = 10/sin(35)

x = 17.434467956211 make sure your calculator is in degree mode

x = 17.4

Answer:

\(\boxed{17.4}\)

Step-by-step explanation:

sin \(\theta\) = \(\frac{opposite}{hypotenuse}\)

sin (35) = \(\frac{10}{x}\)

x = \(\frac{10}{sin(35)}\)

x = 17.4344679562...

x ≈ 17.4

Answer:

62.5% , and a decrease

Step-by-step explanation:

random characters ahagahsvxkxnd

Answer:

The value of k is 4 and q is 16.

Step-by-step explanation:

First, you have to expand the brackets by applying :

\( {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} \)

\( {x}^{2} + 8x + q = {(x + k)}^{2} \)

\( {x}^{2} + 8x + q = {x}^{2} + 2kx + {k}^{2} \)

Next, you have to do it by comparison :

\( {x}^{2} + 8x + q = {x}^{2} + 2kx + {k}^{2} \)

\(by \: comparison\)

\(8x = 2kx\)

\(8 = 2k\)

\(k = 4\)

\(q = {k}^{2} \)

\(q = {4}^{2} \)

\(q = 16\)

Looking at the right triangle that has been shown here, the statements that are not true are; ABC .

A right triangle is a particular kind of triangle with a right angle, which is an angle that measures 90 degrees. The other two angles in a right triangle are acute, which means that they have a degree value below 90. The hypotenuse is the side that forms the right angle; the legs are the other two sides.

The length of the hypotenuse squared in a right triangle is equal to one leg's squared length plus the other leg's squared length. The Pythagorean theorem, which refers to this relationship, is a cornerstone of geometry.

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The coin purse hit the ground in 3 seconds.

Given :

\($\mathrm{f}(\mathrm{t})=16 \mathrm{t}^2$\) ----- (represent the distance(in feet) a dropped object falls in t seconds)

\($\mathrm{g}(\mathrm{t})=\mathrm{s}_0=144 \mathrm{ft}$\) ------ (represent the initial height (in feet) of the coin purse)

The function that represents the distance a dropped coin purse falls in t seconds,

\($f(t)=144-16 t^2$\)

When the coin purse touches the ground,

\($f(t)=0$\)

\($0=144-16 t^2$\)

\($t^2=\frac{144}{16}=9$\)

t = +3 and t = -3

So we take positive t.

Therefore, the coin purse hit the ground in 3 seconds.

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Answer:

I think it is 1.25

Step-by-step explanation:

Sorry if I'm wrong

Answer:

-1.25

Step-by-step explanation:

The given functions are

Trade discount is the discount given to a retailer or wholesaler in the list price of a product for purchasing a specific amount or achieving a certain volume of sales.

It is a discount given to traders to encourage them to buy products in bulk. Here is the calculation of trade discount amount for a product with a list price of $440 and a trade discount rate of 30%

:Given, list price of the product = $440Trade discount rate = 30%Discount amount = Trade discount rate × List price

Discount amount = 30% × $440Discount amount = 0.3 × $440Discount amount = $132Therefore, the trade discount amount for the product with a list price of $440 and a trade discount rate of 30% is $132.

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Answer:

A. Zero

Step-by-step explanation:

The upside down parabolic graph has no roots because it not linear

An equation of the tangent line to the curve \(x e^y+y e^x=4\) at the point (0, 4) is \(y=-(4+e^4) x+4\).

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  \(\left.y^{\prime}\right|_{x=0, y=4}\) as-

Consider the given equation;

\(x e^y+y e^x=4\)

Differentiate both side with respect to x;

\(\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}\)

Now apply product rule;

\(\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}\)

Applying exponential and power rule;

\(\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}\)

Solve the value of y'

\(y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}\)

Now, find the value of slope m.

\(m=\left.y^{\prime}\right|_{x=0, y=4}\)

\(\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4\)

Now, using the point-slope formula, obtain the line equation as follows.

\(\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}\)

Therefore, an equation of the tangent line to the curve is   \(y=-(4+e^4) x+4\).

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