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3 years ago

Determine the intercepts of a line. x-intercept: (,) y-intercept: (,)

Mathematics

2 answers:

nlexa [21]3 years ago

8 0

<h2>The x intercept is -250, and the y intercept is 100. x is the horizontal line, and the intercept is where the line goes through the x axis. Same thing for y only for the vertical line. So,</h2><h2>(-250, 0)</h2><h2>(0, 100)</h2>

natka813 [3]3 years ago

3 0

Step-by-step explanation:

In x- intercept: -250

In y- intetcept: 100

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(10 points) Consider the initial value problem y′+3y=9t,y(0)=7. Take the Laplace transform of both sides of the given differenti

Rashid [163]

Answer:

The solution

$Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3 t}$

Step-by-step explanation:

Explanation:-

Consider the initial value problem y′+3 y=9 t,y(0)=7

Step(i):-

Given differential problem

y′+3 y=9 t

Take the Laplace transform of both sides of the differential equation

L( y′+3 y) = L(9 t)

Using Formula Transform of derivatives

L(y¹(t)) = s y⁻(s)-y(0)

By using Laplace transform formula

$L(t) = \frac{1}{S^{2} }$

Step(ii):-

Given

L( y′(t)) + 3 L (y(t)) = 9 L( t)

$s y^{-} (s) - y(0) + 3y^{-}(s) = \frac{9}{s^{2} }$

$s y^{-} (s) - 7 + 3y^{-}(s) = \frac{9}{s^{2} }$

Taking common y⁻(s) and simplification, we get

$( s + 3)y^{-}(s) = \frac{9}{s^{2} }+7$

$y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}$

Step(iii):-

By using partial fractions , we get

$\frac{9}{s^{2} (s+3} = \frac{A}{s} + \frac{B}{s^{2} } + \frac{C}{s+3}$

$\frac{9}{s^{2} (s+3} = \frac{As(s+3)+B(s+3)+Cs^{2} }{s^{2} (s+3)}$

On simplification we get

9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Put s =0 in equation(i)

9 = B(0+3)

B = 9/3 = 3

Put s = -3 in equation(i)

9 = C(-3)²

C = 1

Given Equation 9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Comparing 'S²' coefficient on both sides, we get

9 = A s²+3 A s +B(s)+3 B +C(s²)

0 = A + C

put C=1 , becomes A = -1

$\frac{9}{s^{2} (s+3} = \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}$

Step(iv):-

$y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}$

$y^{-}(s) =9( \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}) + \frac{7}{s+3}$

Applying inverse Laplace transform on both sides

$L^{-1} (y^{-}(s) ) =L^{-1} (9( \frac{-1}{s}) + L^{-1} (\frac{3}{s^{2} }) + L^{-1} (\frac{1}{s+3}) )+ L^{-1} (\frac{7}{s+3})$

By using inverse Laplace transform

$L^{-1} (\frac{1}{s} ) =1$

$L^{-1} (\frac{1}{s^{2} } ) = \frac{t}{1!}$

$L^{-1} (\frac{1}{s+a} ) =e^{-at}$

Final answer:-

Now the solution , we get

$Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3t}$

5 0

3 years ago

help me (a) The total cost of rent is determined by recording x months of rent at $1400 per month, plus a $150 application fee.

xxTIMURxx [149]

Answer:

$1400x + $150

Step-by-step explanation:

Let the total cost of rent used for a month be $1400 plus a $150 application fee.

This means that;

Total cost (1 month) = $1400(1) + $150 = $1550

TO calculate the cost for x months, we will simply multiply x with the cost of rent for 1 month as shown.

The cost of rent for x month = 1400x * $150

The cost of rent for x month = $1400x + $150 (application fee are paid only once)

6 0

2 years ago

1.) If I am selling a dozen at $3, how much would each egg cost?

riadik2000 [5.3K]

Answer:

1.$3÷12=0.25

each egg would cost 25 cents

2.12×18=216

216×25=5,400

6 0

3 years ago

Find the sum of 1.3 + 0.4

Archy [21]

Answer:

1.7

Step-by-step explanation:

8 0

2 years ago

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Biased or Unbiased:

Crazy boy [7]

Biased or Unbiased: Take 20 packages off the top of the load of packages being shipped by a truck and measure the amount of damage expected to the whole truckload.

Answer: It is a biased way of taking sample. Because the top layer of packages has less weight resting on it and may have less damage. Therefore, the given statement is biased and based on these 20 packages of the top of the load, we can not make a decision about how much damage a truckload contains.

4 0

2 years ago

Determine the intercepts of a line. x-intercept: (__,__) y-intercept: (__,__)

Determine the intercepts of a line. x-intercept: (,) y-intercept: (,)