MATHEMATICS HIGH SCHOOL

What is the average rate of change from x = −3 to x = −4?
The parabola is open upward

Answers

Answer 1
Answer: The rate of change is +(-1) or -1

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Solve the system of equations using substitution. 3x + 2y = 7y = –3x + 11

Find the solutions of y= x+2
y=4-x

Answers

y= x+2

y=4-x

so

x + 2 = 4 - x

2x = 2

x = 1


y = 1 + 2

y = 3


Answer

x = 1, y = 3

y= x + 2

y= 4 - x


Let (y= x+2) be y

x+2 = 4- x

x + x = 4 - 2

2x = 2

Therefore x= 1


Lets now find y;

y= x+2

lets replace x with 1 ( x=1)

y= 1+2

y= 3

The answer therefore is y=3 and x= 1

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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How many solutions does the equation 6s – 3s – 9 = –2 + 3 have? Only one
None
Two
Infinitely many

Answers

The answer to this question is Infinitely many
only one the answer is A

What is 563 rounded to nearest 10

Answers

The answer is 560 because if say you had to round 567 to the nearest ten, that would be 570 because the nearest 10 to 67 is 70, but here you have 563 so the nearest 10 to 63 is 60 :)

You are building a rectangular deck. The area of the deck should be 250 ft.² . You want the lengths of the deck to be 5 feet longer than twice its width. What should the dimensions of the deck be?

Answers

et the width be x 
"the length of the deck to be 5 ft longer than twice its width" --- >length = 2x+5 

then 
x(2x+5) = 250 
2x^2 + 5x - 250 = 0 
(x - 10)(2x + 25) = 0 
x = 10 or x is a negative, which makes no sense 

width = 10 
length = 25 

check: 
is the length 5 more than twice the width ?? yes 
is the area 250 ? yes

f(x)=4 x^(3)+a x^(2) +bx+c and there is a local min at x=-1 and an inflection point at x=-2. Find the values of a and b

Answers

f'(x)=12x^2+2ax+b\n0=12\cdot(-1)^2+2a\cdot(-1)+b\n0=12-2a+b\n\nf''(x)=24x+2a\n0=24\cdot(-2)+2a\n2a=48\na=24\n\n0=12-48+b\nb=36\n\n\boxed{a=24,b=36}
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