Write an equation of a line that passes through the given point and has slope m
(-4,3) m=2

Answers

Answer 1

Answer: y - y₁ = m(x - x₁)
y - 3 = 2(x - (-4))
y - 3 = 2(x + 4)
y - 3 = 2x + 8
+ 3 + 3
y = 2x + 11

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Inverse laplace of [(1/s^2)-(48/s^5)]

Answers

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I am not familiar with Laplace transforms, so my explanation probably won't help, but given that for two Laplace transform $F(s)$ and $G(s)$ , then $\mathcal{L}^(-1)\{aF(s)+bG(s)\} = a\mathcal{L}^(-1)\{F(s)\}+b\mathcal{L}^(-1)\{G(s)\}$

Given that $(1)/(s^2) = (1!)/(s^2)$ and $-(48)/(s^5) = -2\cdot(4!)/(s^5)$

So you have $\mathcal{L}^(-1)\left\{(1)/(s^2) - 2\cdot(4!)/(s^5)\right\} = \mathcal{L}^(-1)\left\{(1)/(s^2)\right\} - 2\mathcal{L}^(-1)\left\{(4!)/(s^5)\right\}$

From Table of Laplace Transform, you have $\mathcal{L}\{t^n\} = (n!)/(s^(n+1))$ and hence $\mathcal{L}^(-1)\left\{(n!)/(s^(n+1))\right\} = t^n$

So you have $\mathcal{L}^(-1)\left\{(1)/(s^2)\right\} - 2\mathcal{L}^(-1)\left\{(4!)/(s^5)\right\} = \boxed{t-2t^4}$ .

Hope this helps...

Final answer:

To find the inverse Laplace transform of the given expression, use partial fraction decomposition to simplify it into individual fractions and then find their inverse transforms.

Explanation:

To find the inverse Laplace transform of the given expression, we can use partial fraction decomposition. First, we factor the denominator: s2*(s3-48). The next step is to represent the expression as a sum of simpler fractions:

1/s2 - 48/s5 = A/s + B/s2 + C/(s - 2) + D/(s + 2) + E/(s + 4) + F/(s2 - 4)

Next, we solve for A, B, C, D, E, and F by performing algebraic manipulations and equating the corresponding coefficients. Finally, we can look up the inverse Laplace transform of each individual fraction term in tables or by using known formulas.

Learn more about Inverse Laplace Transform here:

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The product of 8/15 6/5 and 1/3 is?

Answers

its 16/75 if its one of ur options hope it helps

16/75
there, that should work, hope that this helps you! =)

On august 1st, a plant was 79 centimeters tall. in june of that year it grew 12 centimeters, then 9 more centimeters in july. how many centimeters tall was it on june 1st?a.67
b.70
c.100
d.5

Answers

Answer: d. 58

The height of the plant in June 1st is 58 centimeters.

Step-by-step explanation:

Given : On August 1st, a plant was 79 centimeters tall.

In June of that year it grew 12 centimeters, then 9 more centimeters in July.

Order of Month = June → July → August

Then , the height of the plant on June 1st would be

Height in August 1st - Height grew in June - height grew in July

= 79-12-9 centimeters

= 67-9 centimeters

= 58 centimeters

Therefore , the height of the plant in June 1st = 58 centimeters

Hence, the correct answer is d. 58

Suppose gil can write a poem in 1 hour, holly can write a poem in 2 hours, and ivan can write a poem in 3 hours. Each person spends 12 hours per day writing poems and requires a wage of $10 per hour to do so. How much more would it cost a literary magazine to commission 19 poems per day than 18 poems per day?

Answers

A poem wage for Gil = number of hours* wage per hour

= 1*10 = 10$

A poem wage for Holly = number of hours*wage per hour

= 2*10 = 20$

A poem wage for Ivan = number of hours * wage per hour

= 3*10 = 30$

And all 3 of them works for 12 hours per day.

Since Gil charges least for a poem, it is always betterr to take Gil for first 12 poems.

Let us find wage for 18 poems = (wage for 12 poems from Gil) + (wage for 6 poems from Holly) = 12*10 + 6*20 = 240$

Since both Gil and Holly worked for 12 hours to complete 18 poems.

Remaining 1 poem should be written by Ivan.

And that will cost 30$.

Hence It will cost 30$ more to commission 19 poems per day than 18 poems per day.

Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale.
a. x = 8, y = 17
b. x = 6, y = 8
c. x = 8, y = 10
d. x = 8, y = 6

Answers

D. X = 8 , Y = 6

3x - 14 = x + 2
3x - x = 2 + 14
2x = 16
2x / 2 = 16/2
x = 8

To check: 3x - 14 = x + 2 ; 3(8) - 14 = 8 + 2 ; 24 - 14 = 10 ; 10 = 10

4y - 7 = y + 11
4y - y = 11 + 7
3y = 18
3y / 3 = 18 / 3
y = 6

To check: 4y - 7 = y + 11 ; 4(6) - 7 = 6 + 11 ; 24 - 7 = 17 ; 17 = 17

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