Answer:
[tex]e^{t}+4e^{-4t}[/tex].
Step-by-step explanation:
To find the Laplace inverse of the above problem, we have to first solve the problem as a partial fraction, hence:
[tex]\frac{5s}{s^2+3s-4}=\frac{5s}{s^2+4s-s-4} \\\\=\frac{5s}{s(s+4)-1(s+4)}\\\\=\frac{5s}{(s-1)(s+4)}=\frac{A}{s-1}+\frac{B}{s+4}\\\\= \frac{A(s+4)+B(s-1)}{(s-1)(s+4)}\\\\Hence:\\\\\frac{A(s+4)+B(s-1)}{(s-1)(s+4)}=\frac{5s}{(s-1)(s+4)}\\\\A(s+4)+B(s-1)=5s\\\\to\ find \ A,put\ s=1:\\\\A(1+4)+B(1-1)=5(1)\\\\5A=5\\\\A=1\\\\to\ find \ B,put\ s=-4:\\\\A(-4+4)+B(-4-1)=5(-4)\\\\-5B=-20\\\\B=4\\\\Hence:\\\\\frac{5s}{s^2+3s-4}=\frac{1}{s-1}+ \frac{4}{s+4}\\\\[/tex]
[tex]L^{-1} [\frac{5s}{s^2+3s-4}]=L^{-1}[\frac{1}{s-1} ]+L^{-1}[\frac{4}{s+4} ]\\\\But\ L^{-1}[\frac{1}{s-a} ]=e^{at}\\\\Hence:\\\\L^{-1} [\frac{5s}{s^2+3s-4}]=L^{-1}[\frac{1}{s-1} ]+L^{-1}[\frac{4}{s+4} ]=e^{t}+4e^{-4t}\\\\=e^{t}+4e^{-4t}[/tex]
What are some of the more significant limitations of mathematical models as imitators/predictors of natural phenomena
Answer:
See explanation
Step-by-step explanation:
A mathematical model refers to a mathematical function that describes natural phenomena.
Models are used to approximate natural phenomena hence they are not really exact representations of reality. Thus mathematical models are inherently imperfect and so is our understanding of natural phenomena represented by these mathematical models.
The mathematical parameters used in models to represent real processes are uncertain since they are determined from experiment or represent more than one process.
Lastly, the initial and the boundary conditions in a model may not be explicitly established.
What is the domain and range for the function graphed below
Answer:
c
Step-by-step explanation:
if you look, the x values will go on forever, however in the y value, the lowest value is -6, but the y values afterwards are infinite
Pls help I need it don’t understand
Answer: one solution.
Joseph paid $10 for six avocado at a grocery mart he wants to know what the price will be buying different numbers of avocado what is the price of 9 out of avocado
Answer: $15
9 avocados = $15
Step-by-step explanation:
1 x 3 = 9
5 x 3 = 15
Our Data:
Avocados Price (dollars)
3 5
6 10
9 15
So, our answer is $15
Factor 64b - 16c to identify the equivalent expressions.
2 correct answers
Answer:
16(4b - 1c)
Step by step explanation:
The gcf is 16.
so you divide 16 by both numbers
and
you have to start forming the equation
16(4b - 1c)
Please help me answer this!
Answer:
the answer is c
Step-by-step explanation:
4x = 4 x 2=8
8+12=20
which is equal to or greater than 8
Hope this helps plz mark brainliest
How many degrees are in a 29 sided figure?
Answer:
4860 degrees
Step-by-step explanation:
Triangle=180
Square=360.
The pattern: increase by 180.
Triangle=3 sides.
29-3 is 26.
26*180+180
4860.
Hope this helps :D
Bamboo grows at a rate of 3 inches every month. Gina planted Bamboo when it was initially only 11 inches. -Create an explicit formula for this situation. -How tall will the plant be after 6 months?
I’ll give brainliest if you are correct.
Please answerrrrr
Answer:
Step-by-step explanation:
initial growth = 11
growth in 6 months= 3*6= 18
Final growth = 29 inches (11+18)
A dragon is given 630 ounces of magical potion to sustain her journey from Arlandia to Gargandua. While flying 4/7 of the distance, she drinks 2/9 of the potion. Suppose she continues to drink the magical potion at this rate for the remainder of her journey. How much potion remains when she reaches Gargandua?
Can someone help me with this question? I can't even start!
P.S. Answering this question will give you the highest credit!
Step-by-step explanation:
4/7 of distance = 2/9 of potion
=> 7/7 of distance = 2/9 * (7/4) = 7/18 of potion.
The dragon has used 7/18 of the potion for the journey, and only have 11/18 of it left.
Amount left = 630 ounces * 11/18 = 385 ounces.
2 circle graphs. One circle graph is titled Freshmen Movie Preference. 38 percent is comedy, 27 percent is horror, 23 percent is drama, 9 percent is romance, 3 percent is documentary. Circle graph 2 is titled Senior Movie Preference. 19 percent is comedy, 4 percent is horror, 71 percent is drama, 1 percent is romance, 6 percent is documentary. The freshman and senior classes were surveyed on movie preference. Each class has 100 students. Which statements are true? Check all that apply. More seniors like drama than freshmen. More freshmen like comedy than seniors. Only 4 seniors prefer horror movies. Twice as many seniors like horror than freshmen. Twice as many freshmen like comedy than seniors.
Answer:
you probably got the answer already but its a, b, c, and e
Step-by-step explanation:
i just got the answer
Answer:
abce
Step-by-step explanation:
The sides of an equilateral triangle are reduced by 12 units, 13 units and 14 units respectively and a right-angle triangle is formed. Find the length of each side of the equilateral triangle?
Answer:
the length of each side of the equilateral triangle = 17
Step-by-step explanation:
suppose the side length of equilateral triangle = x
The 3 side of right triangle formed (by side length): x-12 , x-13, x-14
(x-13)² + (x-14)² = (x-12)² .... Pythagorean theorem
x² -26x + 169 + x² -28x + 196 = x² -24x + 144
x² - 30x +221 = 0
(x- 17) (x - 13) = 0
x = 17 or x = 13
if x = 13 the right triangle will have a side length of 13-13=0 ... not solution
x = 17
check: 17-12=5 17-13=4 17-14=3
3²+4² = 25 = 5²
Could someone help me please it’s a math question !
Answer:
1/4
Step-by-step explanation:
The answer the other guy told is wrong.
The probability of choosing an orange marble is 2/8 and 2/8 simplified equals 1/4
Find the slope and Y intercept from the equation 12x+3y=6
Answer:
slope = -4 y-intercept = (0, 2)
Step-by-step explanation:
12x + 3y = 6
-12x -12x
-----------------------------------------------
3y = -12x + 6
3y/3 = -12x/3 + 6/3
-----------------------------------------------
y = -4x + 2 ( this is in y = mx + b form, m representing the solpe and b representing the y-intercept)
This being said, the slope = -4 and the y-intercept = (0, 2).
y'all i need help immediately
Answer:
Option B
Step-by-step explanation:
Don't trust answers teachers don't bother to spell correctly. Plus, finding the 100th term is very easy.
However, the explicit formula will take a long time to use, because it's explicit.
Option C is just wrong. You're supposed to multiply in the recursive formula.
Option D might be correct, but never trust those answers. Teachers do that to trip you up
A runner leaves his house at 7:45 for a morning run. If he travels at an average speed of 6 mph and gets back home at 10:00, how many miles did he run
Answer:
13.5
Step-by-step explanation:
no explenation needed
Complete the given operation and write the expression in standard form.
Step-by-step explanation:
Using synthetic division of polynomials 3x⁴-2x²+4x+9÷x+2. Rewrite the dividend as 3x⁴+0x³-2x²+4x+9
2 | 3 0 -2 4 9
| 6 -12 20 -32
3 -6 10 -16 41
So the quotient is 3x³-6x²+10x-16 with a remainder of 41
Therefore, 3x³-6x²+10x-16+(41/x+2)
party trays, which cost $14.00 to make not including labor, are sold for $35.00. if two people work 8 hour shifts making the trays at $7.00 per hour, how many trays must be sold to cover all cost including labor?
Answer:
I think its $76
Step-by-step explanation:
please help https://brainly.com/question/20406553
help me now pleaseeeeeeeeeee
Answer:
how and i dont want to sdfsadfsdfasdfsdafdsa
A fair charges a $15 entry fee plus $3 for every
ride. Write an expression to represent the total
cost of the fair? HELLPP
Answer:
15 + 3r
Step-by-step explanation:
$15 entry fee plus $3 for every
ride.
Solve for x. Round your answer to the nearest tenth.
Answer:
a^2 + b^2 = c^2
9.9^2 + 4.9^2 = c^2
[tex]c = \sqrt{{9.9}^{2} + {4.9}^{2} } \: = 11[/tex]
Please simplify: 5x + 2 (x - 3) = -2 (x - 1)
Answer:
x= 8/9
Step-by-step explanation:
Open everything up to get 5x+2x-6=-2x+2. Move numbers with an x to the left side and without to the right to have 5x+2x+2x=2+6. Simplify to have 9x=8. Divide by 9 which leaves you with x= 8/9
500 - 237 in subtraction standard algorithm
Answer:
is 267 the answer your looking for
Answer:263
Step-by-step explanation:
Start from the ones place and subtract.
HELP ME PLZ
Find the slope of the line that passes through (-7,8) and (- 6, 5)
Answer:
-3
Step-by-step explanation:
Y = mx + c
m is the slope or the gradient and b is the y-intercept.
m = 5-8 / -6 - -7
m = -3
An on-demand printing company has monthly overhead costs of $1,900 in rent, $450 in electricity, $80 for phone service, and $230 for advertising and marketing. The printing cost is $40 per thousand pages for paper and ink. The average cost for printing x thousand pages can be represented by the function C(x)= 2660+40x/x
For a given month, if the printing company could print unlimited number of pages, what value would the average cost per thousand pages approach? What does this mean in the context of the problem?
Answer:
$40
It means that when an infinite number of pages are printed in a month then the fixed cost will be negligible.
Step-by-step explanation:
Given that:
Monthly overhead costs in rent = $1900
Costs in electricity = $450
Costs for phone service = $80
Costs for advertising and marketing = $230
Printing cost per thousand pages = $40
If number of pages printed are [tex]x[/tex] thousand then cost of printing for [tex]x[/tex] thousand pages = $40[tex]x[/tex]
Average cost to print [tex]x[/tex] thousand pages can be given as:
(Total fixed cost + Total cost of printing [tex]x[/tex] thousand pages) divided by [tex]x[/tex]
[tex]\dfrac{2660+40x}{x}[/tex]
Now, it is given that an infinite number of pages are printed in a month, and we have to find the value that average cost would approach to.
[tex]\lim_{x \to \infty} (\dfrac{2660+40x}{x})[/tex]
Let us solve the above limits.
[tex]\Rightarrow \lim_{x \to \infty} (\dfrac{2660}x+\dfrac{40x}{x})\\\Rightarrow \lim_{x \to \infty} (\dfrac{2660}x)+40\\\Rightarrow 40+\lim_{x \to \infty} (\dfrac{2660}x)[/tex]
When
[tex]x\rightarrow \infty\Rightarrow \frac{2660}{x} \rightarrow 0[/tex]
Putting the value in the limits, we get:
Average cost per thousand pages month would approach to [tex]\rightarrow \$40[/tex]
It means that when an infinite number of pages are printed in a month then the fixed cost will be negligible.
Find the value of the x in the equation 4(6x-9.5)=46
Answer:
3.5
Step-by-step explanation:
First you distribute. 24x-38=46.
Then add 38 to both sides
24x=84
Then divide both sides by 24
x=3.5
Answer:
x= 3.5
Step-by-step explanation:
[tex]4(6x-9.5)=46\\24x-38=46\\ +38 +38\\\\frac{24x}{24} = \frac{84}{24} \\ x=3.5[/tex].
If the value of x is -4, which inequality is true?
Cole’s backyard is rectangular an has a perimeter of 104 meters. The ratio of its length to its width is 6:2. What length is the long side of Cole’s backyard?
Help Me To Find The Answer Please !!!!!!!
Answer:
[tex]39\ m[/tex]
Step-by-step explanation:
[tex]We\ are\ given:\\Perimeter\ of\ Cole's\ backyard=104\ meters\\Now,\\Let\ the\ constant\ of\ proportionality\ between\ the\ length\ and\ the\ width\ of\\ Cole's\ backyard\ be\ x.\\Hence,\\Length\ of\ Cole's\ backyard=6x\\Breadth\ of\ Cole's\ backyard=2x\\Hence,\\As\ we\ know\ that,\\Perimeter\ of\ a\ rectangle=2(l+w)\\Hence,\\Here,\\Perimeter\ of\ Cole's\ backyard=2(6x+2x)=2(8x)=16x\\Hence,\\As\ the\ perimeter\ of\ Cole's\ backyard=104\ m,\\104=16x\\x=\frac{104}{16}=6.5\\Hence,\\[/tex][tex]Length\ of\ Cole's\ backyard=6x=6*6.5=39\ m\\Width\ of\ Cole's\ backyard=2x=2*6.5=13\ m\\Here,\\We\ are\ asked\ Length,\\Hence,\\Length\ of\ Cole's\ backyard=39\ m[/tex]
the perimeter of a rectangle is 40 feet. If the length is 15 feet, 6 inches ; what is the width? How to u get 4” 6
Answer:
Step-by-step explanation:
1 ft= 12 inches
we know l=15 ft and 6 inches
2L=31 inch
P=2L+2W=40ft
2W=40-2*(15ft6inches)
2W=40-31=9 inch
w=9inch/2=4 ft 6 inches
Four runners are training for long races. Noah ran 5.123 miles, Andre ran 6.34 miles, Jada ran 7.1 miles, and Diego ran 8 miles.
Jada ran how much farther than Noah?
Answer:
Jada ran 1.977 miles farther than Noah.
Step-by-step explanation:
Jada = 7.1m [J=7.1] & Noah = 5.123m [N=5.123] & Additional miles = AM
J-A=AM
7.1-5.123=AM
7-5=2, 0.1-0.123=-0.023
2-0.023=1.977
AM=1.977
a profit of 60$
( Write an integer for each situation )
I neeedd hellpppp
Given:
A profit of 60$.
To find:
An integer for the given situation.
Solution:
The given situation is "A profit of 60$".
We know that,
1. Negative integers are used to represent loss.
2. Positive integers are used to represent profit.
Here, the profit is 60$. So, the sign of required integer must be positive and the value of the integer is 60.
Therefore, the required integer is 60.