A drawbridge has the shape of an isosceles trapezoid. The entire length of the bridge is 100 feet while the height is 25 feet. If the angle at which the bridge meets the land is approximately 60 degrees, how long is the part of the bridge that opens?

The solution of the given differential equation using the Laplace transform is y(t) =  1 −  [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].

Given differential equation is y″−2y = eˣ, y(0) = 0, y′(0) = 0. We will solve it using Laplace transforms.

To solve the given differential equation using the Laplace transform, take the Laplace transform of each term of the differential equation. Then solve for Y(s) and find y(t) by taking the inverse Laplace transform.

Here, we take L{y} for Y(s) and L{y''} and L{y'} for s²Y(s) and sY(s) respectively.

L[y′′] − 2L[y] = L[eˣ] s²Y(s) − s⋅y(0) − y′(0) − 2Y(s)

= 1s − 1.0 − 0 − 2Y(s)

= 1s − 1 

We have to rearrange the terms of the above equation in order to get Y(s) on one side.

Y(s) = 1s(s−2)(s−1) = As+Bs−2+Cs−1.

Using partial fraction expansion, A=1, B=1, and C=−2.

So,Y(s) = 1s+(1s−2)−2s−1.

We can write Y(s) as follows.Y(s) = 1s−(1s−2)+2s−1.

Then find the inverse Laplace transform of Y(s) to get the solution y(t).

y(t) = L − 1{Y(s)} = L − 1{1s} − L − 1{1s−2} + L − 1{2s−1}

= 1 −  [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].

Therefore, the solution of the given differential equation using Laplace transform is y(t) =  1 −  [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].

To know more about Laplace Transform,

https://brainly.com/question/30401252

#SPJ11

Answer:

20 x 4 = 60

Step-by-step explanation:

because it's says how many

Answer:

18 maybe

Step-by-step explanation:

it's either 20,19,or 18

but the secretary is the third to be elected so the answer is 18 maybe and if that doesn't work try one of the others trust me it's one of them.

hope this helps

Hey!

A = $4,785.00

I = A - P = $435.00

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 2%/100 = 0.02 per year.

Solving our equation:

A = 4350(1 + (0.02 × 5)) = 4785

A = $4,785.00

The total amount accrued, principal plus interest, from simple interest on a principal of $4,350.00 at a rate of 2% per year for 5 years is $4,785.00.

--------------------------------------------------

Hope you have a great day and this helped in some way <33

The probability of a vanilla taffy is given as follows:

P(vanilla) = 0.31.

Hence the probability of a vanilla or banana taffy is given as follows:

P(vanilla or banana) = 0.52.

The two parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

When we are given the relative frequencies, we must simply identify the desired outcomes, as follows:

Hence the probability is given as follows:

P(vanilla or banana) = P(vanilla) + P(banana) = 0.52.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

Answer:

Q7  0.2

Q8  0.17

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome. The probability that an event will happen when added to the probability that it will not happen is 1

Given that the probability that the bulb will grow is 0.8, the probability it would not grow

= 1 - 0.8

= 0.2

A match may be won lost or drawn

Given that the probability of a win is 0.28 and that of a draw is 0.55, the probability of  a loss

= 1 - (0.28 + 0.55)

= 0.17

Answer & Explanation:

Gross income is the total pay you earn before any reduction and adjustments (taxes, mortgage, etc.).

Net income is the amount of pay you get after taxes and other reductions are taken out of your gross income; it's the money that you "actually get to take home in your pocket with" on the payday.

Answer:

(Refer below:)

Step-by-step explanation:

Because there is no image, here's what I'm going to assume: there are multiple scenarios. Refer to each one below:

1) Where r = 6 and h = 7:

V = Bh

V = (π r²) (h)

V = (6² π) (7)

V = 36π (7)

V = 252π

2) Where r = 7 and h = 6:

V = Bh

V = (π r²) (h)

V = (7² π) (6)

V = 49π (6)

V = 294π

3) Where d = 6 and h = 7:

d = 2r = 6

r = 3

V = Bh

V = (π r²) (h)

V = (3² π) (7)

V = 9π (7)

V = 63π

4) Where d = 7 and h = 6:

d = 2r = 7

r = 3.5

V = Bh

V = (π r²) (h)

V = (3.5² π) (7)

V = 12.25π (7)

V = 87.75π ≈ 269.39

Answer:

43.5

divide 174 ÷ 4 and you get 43.5

Answer:

-13

Step-by-step explanation:

−2+3(1−4)−2

=−2+(3)(−3)−2

=−2+−9−2

=−11−2

=−13

hope it helped

please mark me as brainliest.

Answer:

Length=45 inches, width=15 inches

Step-by-step explanation:

Length=3w

Width=w

Can be written as 3w+w+3w+w

Combine like terms to get 8w

120/8=15

w=15

Width=15 inches

Length=3(15)=45

Length=45 inches

Answer:

x - 12 = 20

Step-by-step explanation:

If I'm wrong do x = 12 - 20

Answer:

im guessing 6 is your base and your height is 15 3/4.

Formula of a triangle we must remember:

BH x 1/2 (basically dividing by 2)

94.5 (fraction form will be: 94 1/2)

94.5 divided by 2 = 47.25 <---------- decimal form

94 1/2 divided by 2 = 47 1/4 <------- fraction form

Answer:

100

Step-by-step explanation:

Add all of the inches together including the parts you don't see.

one side is 9 inches. there are 8 sides. so 9x8. One side in the box is 7 inches. there are 4 sides. so 7x4.  9x8 + 7x4 is equal to 72 + 28.

72 + 28=100

Answer:

this is not a right triangle

Step-by-step explanation:

^  = squared

The formula forthe Pythagorean theorem is    a^+ b^   = c^

If this is a right triangle this must be true

6^ +    8^   =   14^

36 + 64 =  196

100  is not equal to 196

So this is not a right triangle

Answer:

12 feet

Step-by-step explanation:

Answer:

y1=4

x2=7

y2=-3

Answer:

13 hypotenuse

12 adjacent

5 opposite

Answer:

523.33 in^3

Step-by-step explanation:

A sphere is a 3-dimensional version of a circle. An example of a sphere is a ball

Volume of a sphere = [tex]\frac{4}{3}[/tex]π[tex]r^{3}[/tex]

Where

π = 3.14

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

diameter = 2r

Radius = 10 in / 2 = 5 inches

[tex]\frac{4}{3}[/tex] × 3.14 ×[tex]5^{3}[/tex] = 523.33 [tex]in^{3}[/tex]

Answer:

The answer is 175

The  mass of the rod is 15.9 grams.

To find the mass of the rod, we need to integrate the linear density function over the entire length of the rod. The linear density function is given by λ = 50.0 + 20.0x, where x is the distance from one end measured in meters.

The mass of an infinitesimally small element of length dx is given by dm = λ*dx. Substituting the linear density function, we have dm = (50.0 + 20.0x)*dx.

Integrating both sides from x = 0 to x = 0.3 meters (corresponding to the length of the rod), we get:

∫dm = ∫(50.0 + 20.0x)dx
m = ∫(50.0 + 20.0x)dx
m = [50.0x + 10.0x^2] evaluated from x = 0 to x = 0.3
m = 50.00.3 + 10.0(0.3)^2
m = 15.0 + 0.9
m = 15.9 grams.

Therefore, the mass of the rod is 15.9 grams.

Visit to know more about Mass:-

brainly.com/question/86444

#SPJ11

The given identities can be verified using basic rules of exponentials and algebra. Here are the steps to verify the given identities:

(a) 1 = ∑_(n=1) ^∞▒〖10^(x)+2(-1) ^nln⁡(x)〗0

Rewrite the sum to obtain two series, one for even values of n, and one for odd values of n. ∑_(n=1)^∞▒10^(x) = 10^x+10^x+...= (2/3) (10^x) (odd terms only)∑_(n=1)^∞▒〖(-1)^nln⁡(x)〗= ln(x)-ln(x)+ln(x)-ln(x)+...= (0) (even terms only)

Thus, we have 1= (2/3) (10^x) + (0) = (2/3) (10^x) (b) e^x = ∑_(n=1) ^∞▒〖10^x+2n(x)〗

Rewrite the sum to obtain two series, one for even values of n, and one for odd values of n.

∑_(n=1) ^∞▒10^(x) = 10^x+10^x+...= (1/2) (10^x) (even terms only) ∑_(n=1) ^∞▒〖2n(x)〗= 2(x)+2(2x) +2(3x) +...= 2x (1+2+3+...) = -x/(-1) ^2= -x

Thus, we have e^x= (1/2) (10^x) - x(c) e^(-x) = ∑_(n=1) ^∞▒〖10^x+2(-1) ^nln⁡(x)〗0

We can use the same series from part (a) with x replaced by -x.

Thus, we have e^(-x) = (2/3) (10^(-x)) + (0) = (2/3) (1/10^x)

Similarly, e^x= (2/3) (10^x) Subtracting these two equations, we get: e^x - e^(-x) = (2/3) (10^x + 1/10^x) (answer) (d)

Cosh x = ∑_(n=0) ^∞▒〖10^x+2n(x)〗

Similar to part (b), we have two series, one for even values of n, and one for odd values of n.∑_(n=0)^∞▒10^(x) = 1+10^x+10^x+...= (1/2) (10^x) (even terms only)∑_(n=0)^∞▒〖2n(x)〗= 0+2x+2(2x)+2(3x)+...= 2x (1+2+3+...)= 2x(1/(-1)^2)= 2xThus, we have Cosh(x) = 1 + (1/2) (10^x) + 2x (e^x)(e^x - e^(-x)) / 2= 1 + (1/2) (10^x) + 2x (1 + (2/3) (10^x + 1/10^x)) (answer)(e) Sinh x = ∑_(n=1)^∞▒〖2^(2n-1)(x)〗

Rewrite the sum to obtain two series, one for even values of n, and one for odd values of n.∑_(n=1)^∞▒〖2^(2n-1)(x)〗= 2x+2^3x+2^5x+...= 2x(1+2^2+2^4+...)= 2x(2^0+2^2+2^4+...)= 2x(1/ (1-2^2))= -2x/3Thus, we have Sinh(x) = ∑_(n=1)^∞▒〖2^(2n-1)(x)〗= 2x/3 (answer)

To know more about exponentials refer to:

https://brainly.com/question/12626186

#SPJ11

Answer:

this just confused me so much

Step-by-step explanation:

ooooooooooooooooooo

Answer:

B

Step-by-step explanation:

Given

x² - 9x + 18 = 0 ← in standard form

(x - 3)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 6 = 0 ⇒ x = 6

solution is x = 3, x = 6 → B

The given differential equation is not exact. To determine if a differential equation is exact, we need to check if its partial derivatives satisfy a specific condition.

In this case, the given equation is dy/dx = 9xe^x – y + 6x^2. Let's find the partial derivatives of the expression on the right-hand side with respect to y and x.∂/∂y (9xe^x – y + 6x^2) = -1∂/∂x (9xe^x – y + 6x^2) = 9e^x + 12x

The condition for exactness is that these partial derivatives are equal: ∂/∂y (∂/∂x) = ∂/∂x (∂/∂y). However, in this case, we have -1 ≠ 9e^x + 12x, which means the equation is not exact.As the equation is not exact, we cannot directly solve it by finding a potential function. Other methods, such as using integrating factors or applying specific techniques for solving non-exact equations, may be required.

Learn more about  partial derivatives click here: brainly.com/question/32554860

#SPJ11

Answer:

Step-by-step explanation:

That Would be 43/3

Answer:

Step-by-step explanation:

If you have $2250 as against an inflation rate of 2% every year, this then means that after the first year, the value of your money becomes

2250 * 2% =

2250 * 0.02 = 45

2250 - 45 = $2205

At the end second year

$2205 * 2% =

$2205 * 0.02 = 44.1

$2205 - 44.1 = 2160.9

At end of the third year

$2160.9 - 2% =

$2160.9 * 0.02 = 43.218

$2117.682

And so on, and so forth

Answer: [tex]4\times 3.5\ ft^2[/tex]

Step-by-step explanation:

Given

area of the rectangle is [tex]A=14\ ft^2[/tex]

Suppose width is given by w

So, length is [tex]l=2w-3[/tex]

The area of a rectangle is [tex]A=l\times w[/tex]

putting values

[tex]\Rightarrow A=(2w-3)w\\\Rightarrow 14=2w^2-3w\\\Rightarrow 2w^2-3w-14=0\\\Rightarrow 2w^2-7w+4w-14=0\\\Rightarrow w(2w-7)+2(2w-7)=0\\\Rightarrow (2w-7)(w+2)=0\\\\\Rightarrow w=\dfrac{7}{2}\ ft[/tex]

length is [tex]l=4\ ft[/tex]

If f(5) = 11, f ′ is cοntinuοus, and 6 5 f ′(x) dx = 19, then f(6) = 30.

Tο find the value οf f(6), we can use the Fundamental Theοrem οf Calculus. Accοrding tο the theοrem, if f(x) is cοntinuοus οn an interval [a, b] and F(x) is an antiderivative οf f(x) οn that interval, then the definite integral οf f(x) frοm a tο b is equal tο F(b) - F(a).

Given that f'(x) is cοntinuοus, we can apply the theοrem tο the integral:

∫₅₆ f'(x) dx = f(6) - f(5)

We are given that ∫₅₆ f'(x) dx = 19, and f(5) = 11. Plugging in these values, we have:

19 = f(6) - 11

Tο sοlve fοr f(6), we add 11 tο bοth sides:

f(6) = 19 + 11

f(6) = 30

Therefοre, the value οf f(6) is 30.

To know more about continuous, refer here:

https://brainly.com/question/31523914

#SPJ4