-11c-35/4 = 4c- 2

-11c-35 ÷4 = 4c -2

We can express the forcing function (the piecewise expression on the right side) in terms of the step function as [tex]e^{-t}(u(t) - u(t-1))[/tex] where

[tex]u(t) = \begin{cases}1&\text{for }t\ge0\\0&\text{otherwise}\end{cases}[/tex]

Let F(s) be the Laplace transform of a function f(t). Now recall the transform pair

[tex]f(t-c) u(t-c) \mapsto e^{-cs} F(s)[/tex]

This means

[tex]e^{-t} u(t) \mapsto \dfrac1{s+1}[/tex]

[tex]e^{-t} u(t-1) = \dfrac1e \times e^{-(t-1)} u(t-1) \mapsto  \dfrac{e^{-(s+1)}}{s+1}[/tex]

I assume you're familiar with the transform rule for derivatives of y(t). Now we're ready to take the transform of both sides of the ODE:

[tex]y'' + 3y' + 2y = e^{-t}(u(t) - u(t-1))[/tex]

[tex]\implies \left(s^2 Y(s) - s y(0) - y'(0)\right) + 3 \left(s Y(s) - y(0)\right) + 2 Y(s) = \dfrac{1 - e^{-(s+1)}}{s+1}[/tex]

Plug in the initial values and solve for Y(s) :

[tex]\left(s^2 Y(s) - s + 1\right) + 3 \left(s Y(s) + 1\right) + 2 Y(s) = \dfrac{1 - e^{-(s+1)}}{s+1}[/tex]

[tex](s^2 + 3s + 2) Y(s) - s + 4 = \dfrac{1 - e^{-(s+1)}}{s+1}[/tex]

[tex]Y(s) = \dfrac{1 - e^{-(s+1)} + (s-4)(s+1)}{(s+1)(s^2 + 3s + 2)}[/tex]

[tex]Y(s) = \dfrac{1 - e^{-(s+1)} + (s-4)(s+1)}{(s+1)^2 (s+2)}[/tex]

Consider the partial fraction expansion

[tex]\dfrac1{(s+1)^2(s+2)} = \dfrac a{s+1} + \dfrac b{(s+1)^2} + \dfrac c{s+2}[/tex]

Solve for the coefficients:

[tex]1 = a(s+1)(s+2) + b(s+2) + c(s+1)^2[/tex]

[tex]s = -1 \implies b = 1[/tex]

[tex]s = -2 \implies c = 1[/tex]

[tex]1 = (a+c)s^2 + \cdots \implies a+c = 0 \implies a = -1[/tex]

Hence we can expand Y(s) as

[tex]Y(s) = \dfrac1{(s+1)^2} + \dfrac1{s+2}  + \dfrac{e^{-(s+1)}}{s+1} - \dfrac{e^{-(s+1)}}{(s+1)^2} - \dfrac{e \times e^{-(s+2)}}{s+2}[/tex]

The last transform pair we need is

[tex]e^{ct} f(t) \mapsto F(s - c)[/tex]

Now, taking inverse transforms of everything yields

[tex]\dfrac1{(s+1)^2} \mapsto te^{-t}[/tex]

[tex]\dfrac1{s+2} \mapsto e^{-2t}[/tex]

[tex]\dfrac{e^{-(s+1)}}{s+1} \mapsto e^{-t} u(t-1)[/tex]

[tex]\dfrac{e^{-(s+1)}}{(s+1)^2} \mapsto e^{-t} (t-1) u(t-1)[/tex]

[tex]\dfrac{e \times e^{-(s+2)}}{s+2} \mapsto e^{-(2t-1)} u(t-1)[/tex]

and putting everything together gives the same solution as the one provided.

box one
box three
box four

box two is incorrect because 0.80/100 x 400 is 3.2
and we are looking for the common denominator of 320 :)

how do i know the common denominator is 320? it's is 80% of 400!

i hope this helps

Answer:

first box, second box and third box.

Step-by-step explanation:

This is because they shared the same answer which is 320.

hope it helps =)

Answer:

B. 1 :)

Step-by-step explanation:

Every time the x value gets bigger, the y laue does too. Positive numbers are larger than negative ones so every time we get closer to 0, our values get bigger :)

Have an amazing day!!

Please rate and mark as brainliest!!

7:13

hope it helps...!!

Answer:

I'm not sure if you are allowed to use improper fractions but that would be the only way to have an answer be greater than both of its factors if one of the factors has to be a fraction.

I would do something simple like:

[tex]\frac{2}{1} * 2 = 4[/tex]

Step-by-step explanation:

Since both factors are greater than 1 the product will be greater than both the factors.

Answer:

Equation is below. See model attached.

6/4 x 3 = 18/4

Answer:

There were 29 adult admissions; and 72 child's.

Answer:

A = $2,779.16

Step-by-step explanation:

A = $2,779.16

A = P + I where

P (principal) = $1,778.00

I (interest) = $1,001.16

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 1,778.00(1 + 0.03/2)^(2)(15)

A = 1,778.00(1 + 0.015)^(30)

A = $2,779.16

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $1,778.00 at a rate of 3% per year compounded 2 times per year over 15 years is $2,779.16.

Using the box plot, it is found that:

It is a plot that focuses the interquartile range of the population, that is, it gives:

In this problem, the box plot starts at 5, hence the least amount of snowfall in any of the cities was of 5 inches.

The data was most concentraded in the third quarter, betwen 35 and 40, as it is the smallest quarter in the graph.

The data was most spread out in the second quarter, betwen 13 and 35, as it is the greater quarter in the graph.

More can be learned about box plots at https://brainly.com/question/27353162

Answer:

a) 5

b) 35 - 40 this is the smallest part in the purple bar

c) 13 - 35, this is the biggest part of the purple bar

Step-by-step explanation:

(this is off my test!)

By looking at the plot, you can see where everything is, and since it asks how you know, there you go.

Answer:

The answer is six I think

Answer:

a = -4, b = 5, c = -2

(the third option)

The values are a = -4, b = 5  and  c = -2 in the quadratic equation.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We are given to determine the values of a, b and c in the following quadratic equation :

0 = 5x - 4x² - 2

We know that a general quadratic equation is of the following form :

ax² + bx + c = 0

where a is the coefficient of x², b is the coefficient of x and c is the constant term.

Comparing the general equation with equation (i), we have that;

coefficient of x², a = -4,

coefficient of x, b = 5

and the constant term, c = -2.

Thus, the values are; a = -4, b = 5  and  c = -2.

Learn more about quadratic equations;

https://brainly.com/question/17177510

#SPJ7

The worth of the boat of Maya which goes for 15% deprication this year at the end of the first year of purchase, with the considered purchase price, is $15,589

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Deprecated price = Initial price- amount of deprication

We have:

Initial price = $18,340

And the amount of deprication = 15% of $18,340

= [tex]\dfrac{18340}{100} \times 15 = 2751 \: \rm dollars[/tex]

(as deprication on first year was by 15% of the original price, and we want to know the deprication for the first year only)

Thus, we get:

Depricated price of Maya's boat = $18,340 - $2,751 = $15,589

Thus, the worth of the boat of Maya which goes for 15% deprication this year at the end of the first year of purchase, with the considered purchase price, is $15,589

Learn more about percent here:

https://brainly.com/question/11549320

#SPJ1

Answer:

The answer is 68

Step-by-step explanation:

Plug -5 into each x value then solve.

Answer:

D

Step-by-step explanation:

We want to find the values of x such that:

[tex]\displaystyle -x^2 + 7x + 5 = 0[/tex]

We can use the quadratic formula. Recall that:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = -1, b = 7, and c = 5. Substitute and evaluate:
[tex]\displaystyle \begin{aligned} x & = \frac{-(7)\pm\sqrt{(7)^2-4(-1)(5)}}{2(-1)}\\ \\ & = \frac{-7\pm\sqrt{49+20}}{-2} \\ \\ & = \frac{-7\pm\sqrt{69}}{-2}\end{aligned}[/tex]

In conclusion, the answer is D.

Answer:

d

Step-by-step explanation:

hahaha

Answer:

$428

Step-by-step explanation:

you can do 72*24= the 2 year period and then you get 1728

you then do 1728-1300 and you will get $428 more

Answer: 31.4

Step-by-step explanation:

Circumference = πd  or 2πr

π = 3.14

Since the diameter is given we will use Circumference = πd

So

3.14 * 10 = 31.4

Answer:

C ≈ 31.4

Step-by-step explanation:

The circumference of a circle can be calculated using either of the following formulas: C=d or C=2r.

The circumference of a circle is the distance around the outside of the circle. It is like the perimeter of other shapes like squares. You can think of it as the line that defines the shape. For shapes made of straight edges this line is called the perimeter but for circles this defining line is called the circumference.

The radius (r) and the diameter (d) are two more crucial distances on a circle (d). Every circle has three distinguishing features: a radius, a diameter, and a circumference. The circumference may be calculated using the radius or diameter and pi. The diameter of a circle is the distance between one side and the other at its widest points. The circumference of a circle will always pass through its center. This distance is divided in half by the radius. The radius may alternatively be thought of as the distance between the circle's center and its edge.

You can calculate the circumference of a circle if you know its diameter or radius. To begin, keep in mind that pi is an irrational number represented by the symbol. 3.14 is a close approximation.

The formula for calculating a circle's circumference is:

The circumference of a circle is equal to its diameter multiplied by its circumference.

C = d is a common notation for this. This indicates that the circle's circumference is three "and a half" times its diameter. 

Given radius (R) = 5

⇒ Diameter =  2R =  10

⇒ Circumference =  2πR

=  10π

=  31.415926535898

≈     31. 4

Answer:

Stay after school more often with your math teacher or come early to school to practice math or to see what your stuggling at.

Answer:

68

Step-by-step explanation:

62+50=112

180-112=68

Answer:  [tex]E \ge 31[/tex]

Reason:

"at least 31 points" means "31 or more".

So either E = 31 or E > 31 (meaning Embiid scored 31 points or he scored more than 31 points).

Choice A looks like the closest match assuming the inequality sign is [tex]\ge[/tex]

Saying E > 31 instead of [tex]E \ge 31[/tex] would be false because it leaves out the case E = 31.

Answer:

Step-by-step explanation:

To solve this inequality, you have to isolate the term of x from one side of the equation.

-9<x-4<9

First, add by 4 from both sides.

x-4+4>-9+4

Solve.

-9+4=-5

Add by 4 from both sides.

x-4+4<9+4

Solve.

Add the numbers from left to right.

9+4=13

x<13

I hope this helps. Let me know if you have any questions.

Answer:

b = 10 mm

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex]bh ( b is the base and h the height )

given A = 30 and h = 6 , then

[tex]\frac{1}{2}[/tex]b × 6 = 30 , that is

3b = 30 ( divide both sides by 3 )

b = 10

Answer:

139

Step-by-step explanation:

Using the Empirical Rule, it is found that the desired probabilities are given as follows.

a) P(x > 158)  = 0.16.

b) P(149 < x < 152) = 0.135.

It states that, for a normally distributed random variable:

Additionally, considering the symmetry of the normal distribution, 50% of the measures are below the mean and 50% are above.

Item a:

158 is one standard deviation above the mean, hence the probability is given by, considering that 32% of the measures are more than 1 standard deviation from the mean:

P(x > 158) = 0.5 x 0.32 = 0.16.

Item b:

Between one and two standard deviations below the mean, hence:

P(149 < x < 152) = 0.5 x (0.95 - 0.68) = 0.5 x 0.27 = 0.135.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

Answer:

R = 4cm

Step-by-step explanation:

V = π(R)²h = 480π

Divide by π

(R)²h = 480

Substitute h with 30

30*(R)² = 480

Divide by 30

(R)² = 16

Square root

R = 4cm

We do not accept R= -4 because it's a length, so it must be positive.

Answer:

x=3,-2

Step-by-step explanation:

take the first part ;(x+2)=0. x=-2 x_3=0 so x=3