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3 years ago

Solve the following simultaneous linear equations by the substitution method.

Mathematics

1 answer:

anyanavicka [17]3 years ago

5 0

Answer:

p = 2 and q = 2

Step-by-step explanation:

hope this helps please like and mark as brainliest

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Please help me with the below question.

Snezhnost [94]

6a. By the convolution theorem,

$L\{t^3\star e^{5t}\} = L\{t^3\} \times L\{e^{5t}\} = \dfrac6{s^4} \times \dfrac1{s-5} = \boxed{\dfrac5{s^4(s-5)}}$

6b. Similarly,

$L\{e^{3t}\star \cos(t)\} = L\{e^{3t}\} \times L\{\cos(t)\} = \dfrac1{s-3} \times \dfrac s{1+s^2} = \boxed{\dfrac s{(s-3)(s^2+1)}}$

7. Take the Laplace transform of both sides, noting that the integral is the convolution of $e^t$ and $f(t)$ .

$\displaystyle f(t) = 3 - 4 \int_0^t e^\tau f(t - \tau) \, d\tau$

$\implies \displaystyle F(s) = \dfrac3s - 4 F(s) G(s)$

where $g(t) = e^t$ . Then $G(s) = \frac1{s-1}$ , and

$F(s) = \dfrac3s - \dfrac4{s-1} F(s) \implies F(s) = \dfrac{\frac3s}{\frac{s+3}{s-1}} = 3\dfrac{s-1}{s(s+3)}$

We have the partial fraction decomposition,

$\dfrac{s-1}{s(s+3)} = \dfrac13 \left(-\dfrac1s + \dfrac4{s+3}\right)$

Then we can easily compute the inverse transform to solve for f(t) :

$F(s) = -\dfrac1s + \dfrac4{s+3}$

$\implies \boxed{f(t) = -1 + 4e^{-3t}}$

6 0

1 year ago

How to do this!!! Help me ASAP!!!!

BARSIC [14]

Answer:

idk either sorry but

Step-by-step explanation:

I think you need a protractor to help you find the other angles to find x

5 0

3 years ago

Mariah spent $9.50 on 9 pounds of limes and pears. Limes cost $0.50 per pound and pears cost $1.50 per pound. Let l be the numbe

Mashcka [7]

Answer:

4 pounds of lime and 5 pounds of pears

Step-by-step explanation:

I + P = 9

0.5l + 1.5P = 9.5

I = 9 - P

0.5(9 - P) + 1.5P = 9.5

4.5-0.5P + 1.5P = 9.5

4.5 + P (1P) = 9.5

P = 9.5-4.5 = 5

I = 9 - 5 = 4

Answer: 4 pounds of lime and 5 pounds of pears

5 0

2 years ago

To the nearest tenth, what is the perimeter of the triangle with vertices at (−2, 3), (3, 6), and (2, −2)?

katovenus [111]

9514 1404 393

Answer:

20.3

Step-by-step explanation:

The distance formula can be used to find the side lengths.

d = √((x2 -x1)^2 +(y2 -y1)^2)

For the first two points, ...

d = √((3 -(-2))^2 +(6 -3)^2) = √(5^2 +3^2) = √34 ≈ 5.83

For the next two points, ...

d = √((2 -3)^2 +(-2-6)^2) = √(1 +64) = √65 ≈ 8.06

For the last and first points, ...

d = √((-2-2)^2 +(3-(-2)^2) = √(16 +25) = √41 ≈ 6.40

Then the sum of the side lengths is ...

5.83 +8.06 +6.40 = 20.29 ≈ 20.3

The perimeter of the triangle is about 20.3 units.

7 0

2 years ago

xYou volunteer to help drive children at a charity event to the zoo, but you can fit only 6 of the 16 children present in your

brilliants [131]

There are 8008 groups in total, in other to drive the children

<h3>How to determine the number of groups?</h3>

From the question, we have

Total number of children, n = 16
Numbers to children at once, r = 6

The number of group of children that could be carried at once is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 16 and r = 6

Substitute the known values in the above equation

Total = ¹⁶C₆

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 16!/10!6!

Evaluate

Total = 8008

Hence, the number of groups is 8008