Answer:
[tex]e^t+e^{-4t}[/tex]
Step-by-step explanation:
We have to simplify the original function using partial fraction, hence:
[tex]\frac{5s}{s^2+3s-4} =\frac{5s}{(s-1)(s+4)}\\\\=\frac{A}{s-1}+\frac{B}{s+4}\\\\Therefore:\\\\\frac{A(s+4)+B(s-1)}{(s-1)(s+4)}=\frac{5s}{(s-1)(s+4)}\\\\Eliminating\ the \ denominator:\\\\A(s+4)+B(s-1)=5s\\\\substitute\ s=1:\\\\A(1+4)+B(1-1)=5(1)\\\\5A=5\\\\A=1\\\\tsubstitute\ s=-4:\\\\A(-4+4)+B(-4-1)=5(-4)\\\\-5B=-20\\\\B=4\\\\Therefore\ substituting\ A\ and\ B\ gives:\\\\\frac{5s}{s^2+3s-4}=\frac{1}{s-1}+ \frac{4}{s+4}\\\\[/tex]
[tex]From\ Laplace\ inverse:\\\\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}\\\\L^{-1} [\frac{5s}{s^2+3s-4}]=e^{t}+4e^{-4t}[/tex]
Find the total surface area of this square based pyramid
Given:
Length of a side of base of a square base pyramid = 6 cm
Height of each triangular surface = 4 cm.
To find:
The total surface area of the square based pyramid.
Solution:
Area of a square with side length a is
[tex]\text{Area of square}=a^2[/tex]
Area of square with side length 6 cm is
[tex]\text{Area of square}=(6)^2[/tex]
[tex]\text{Area of square}=36[/tex]
So, area of square with side length 6 cm is 36 cm².
Area of triangle is
[tex]\text{Area of a triangle}=\dfrac{1}{2}\times base\times height[/tex]
Area of each triangular surface is
[tex]\text{Area of each triangular surface}=\dfrac{1}{2}\times (6)\times (4)[/tex]
[tex]\text{Area of each triangular surface}=12[/tex]
Total area of 4 triangular surfaces is
[tex]\text{Area of 4 triangular surfaces}=4\times 12[/tex]
[tex]\text{Area of 4 triangular surfaces}=48[/tex]
So, area of all triangular surfaces is 48 cm².
Now, total area of pyramid is the sum of base area and area of all triangular sides.
[tex]Area=36+48[/tex]
[tex]Area=84[/tex]
Therefore, the area of given square pyramid is 84 cm².
What is the value of - |-60| ?
Answer:
-60
Step-by-step explanation:
absolute value cancels the negative
then the negative outside the absolute value makes it negative.
N is an integer.
Write the values of n such that -15<3n≤6
Answer:
n = - 4, - 3, - 2, - 1, 0, 1, 2
Step-by-step explanation:
Given
- 15 < 3n ≤ 6 ( divide the 3 intervals by 3 )
- 5 < n ≤ 2
Thus n ≠ - 5 but n can equal the upper limit of 2
Hence
n = - 4, - 3, - 2, - 1, 0 , 1, 2
what 1/3 X 1/6 in simplest form?
1/18 would be your answer because 3 * 6 = 18. so 18 is your denominator. 1 * 1 is still 1 so that would be your numerator. You cant simplify the numerator because it's a one and can't be simplified by any other number but 18 can be simplified but it wouldn't make sense to just simplify the denominator and not the numerator so It would stay as 1/18.
Math Club members are selling games and puzzles. They make a profit of $10 per game and $8 per puzzle. They would like to make a profit of at least $200.
Answer:
a) [tex]10x+8y \geq 200[/tex]
b) The members should sell at least 15 puzzles
Step-by-step explanation:
Let x represents selling games
and y represents puzzles
The statement given is: They make a profit of $10 per game and $8 per puzzle. They would like to make a profit of at least $200.
a) The inequality will be:
[tex]10x+8y \geq 200[/tex]
at least 200 means the profit can be equal to 200 or greater than that.
b) If the members sell 8 games, how many puzzles would they have to sell?
Number of puzzles sold can be solved by solving the inequality [tex]10x+8y \geq 200[/tex]
Put x =8 and find value of y
[tex]10x+8y \geq 200\\10(8)+8y\geq 200\\80+8y\geq 200\\8y\geq 200-80\\8y\geq 120\\y\geq \frac{120}{8}\\y\geq 15[/tex]
So, the members should sell at least 15 puzzles to make the inequality true. because the profit should be at least $200.
What are the solutions of x^2+6x-6=10
Answer:
ifhofgoefouegf
Step-by-step explanation:
Answers (there are two solutions):
x = -8x = 2I hope this helps!
what phrase represents this expression x/3
Answer:
X PARTS OF AN INTEGER DIVIDED INTO 3 PARTS
Step-by-step explanation:
X PARTS OF AN INTEGER DIVIDED INTO 3 PARTS
help !! asap
!!!!!!!!!
which of the following is a proper fraction
Answer:
Ummm... You didn't put any pictures or wrote any fractions lol.
Step-by-step explanation:
Have a great day! Thanks!
Answer:
where is the picture????????
In 2003, the average combined SAT score (math and verbal) for college-bound students in the United States was 1026. Suppose that approximately 45% of all high school graduates took this test and that 100 high school graduates are randomly selected from among all high school grads in the United States. Which of the following random variables has a distribution that can be approximated by a binomial distribution? Whenever possible, give the values for n and p.
a. The number of students who took the SAT
b. The scores of the 100 students in the sample
c. The number of students in the sample who scored above average on the SAT
d. The amount of time required by each student to complete the SAT
e. The number of female high school grads in the sample
Answer:
The random variables which has a distribution that can be approximated by a binomial distribution is:
c. The number of students in the sample who scored above average on the SAT.
Step-by-step explanation:
The binomial distribution in this scenario will be between the number of students in the sample who scored below average on the SAT and the number of students who scored above average. Variables that have a binomial distribution must meet these four conditions:
1: The observed number of students who sat for the SAT 'n' is not variable.
2: Each student's score (observation) is purely independent of each other, either above or below average scores.
3: Each student's score (observation) shows one of the two outcomes ("success" or "failure"). Those below average are "failures." Those above average are "successes."
4: The outcome probability of "success" 'p' for each student is the same.
What is this? Please answer with an explanation
Answer:
No
Step-by-step explanation:
Given
f(x) = [tex]\sqrt{x-10}[/tex] + 11 ← substitute x = 1
f(1) = [tex]\sqrt{1-10}[/tex] + 11
= [tex]\sqrt{-9}[/tex] + 11
[tex]\sqrt{-9}[/tex] is not real and therefore x = 1 does not have a real output for f(x)
Della bought 3 new dresses for a total cost of $203. The
sales tax was 7.5%. What is the best estimate for the
amount of sales tax?
Answer:
$15.23
Step-by-step explanation:
Expand 4(-2y+ 3).
2y+7
0:-8 y + 12
2 y + 12
-8 y+ 3
NEED HELP ASAP WILL GIVE BRAINLIEST
Answer:
The answer is option A.
Step-by-step explanation:
If both equations are graphed side by side, will produce same figure.
Will give BRAINLIEST
Answer:
post office, Library, Park, town hall
Step-by-step explanation:
A soda pop manufacturer runs a contest and places a winning bottle cap on every sixth bottle. If a person buys the soda pop, find the probability that the person will win for the first time on his third purchase.
Answer:
[tex]\dfrac{25}{216}[/tex]
Step-by-step explanation:
From the given information:
The probability (p) of winning a bottle cap = [tex]\dfrac{1}{6}[/tex]
The probability of not winning a bottle cap will be (q) = 1 - p
[tex]= 1- \dfrac{1}{6}[/tex]
[tex]= \dfrac{5}{6}[/tex]
Since we are told that the winning is placed once on every sixth bottle
Then the required probability = P( of not winning the first purchase) × P( of not winning the second purchase) × P( of winning the third purchase)
[tex]= \dfrac{5}{6} \times \dfrac{5}{6} \times \dfrac{1}{6}[/tex]
[tex]= \dfrac{25}{216}[/tex]
Which of the following is true about the linear function 4x+2y=12
1.it has a slope of -2 and a y intercept of 6
2. It has a slope of -2 and a y intercept of 12
3 it has a slope of -1/2 and a y intercept of 6
4 it has a slope of -4 and a y intercept of 12
Answer:
i believe is 4
Step-by-step explanation:
If you 2y=-4x+12
need to get the Y by it self
Which point could represent 5/3?
B -3
A -1/2
D 1/2
C 1 1/2
Answer:
(D)
Step-by-step explanation:
is the correct because is 1/2
Answer:
C. 1 1/2
Step-by-step explanation:
a hummingbird egg's mass
Answer:
A hummingbird eggs mass is approximately 0.374 mg.
Answer:
Hummingbird Nesting Habits. First of all, we must remember that there are about 17 species of hummingbirds found in the US and not all of these different species have the same nesting habits. The most prominent difference lies in their choice of location for the nest (but more on this later), nevertheless there is not much difference in the way they build their nests and tend to their young.
Step-by-step explanation:
give all credit to my brain
A line has slope -1. It passes through the point Q(2, -n) and R(4, -3). What is the value of n?
A-5
B 1
C 4
D5
Answer:
i need this answer too
Step-by-step explanation:
lol
If P = Set of all triangles, Q = Set of scalene triangles, R = Set of isosceles triangles and
S = Set of equilateral triangles.
State which of the following statements are true or false.
(a) QCР
(b) RCS
(c) SCR
Given:
P = Set of all triangles,
Q = Set of scalene triangles,
R = Set of isosceles triangles and
S = Set of equilateral triangles.
To find:
Which of the following statements are true or false?
Solution:
We know that,
Scalene triangles : All sides are different.
Isosceles triangles : Two sides are equal.
equilateral triangles : All sides are equal.
Set of all triangles contains all scalene triangles. So, set of scalene triangles Q is a subset of Set of all triangles P.
[tex]Q\subset P[/tex]
So, (a) is true.
All isosceles triangles are not equilateral triangles. So, set of isosceles triangles R is not a subset of set of equilateral triangles S.
[tex]R\nsubseteq S[/tex]
So, (b) is false.
Set of all isosceles triangles contains all equilateral triangles. So, set of equilateral triangles S is a subset of set of isosceles triangles R .
[tex]S\subset R[/tex]
So, (c) is true.
How many groups of 1/3 inch are in 3/4 inch?
Answer: There are 2 1/4 groups of 1/3 inch in 3/4 inch.
Step-by-step explanation:
1. Find a common denominator. 3 and 4 are both multiples of 12, so 12 would be the common denominator.
2. Convert each fraction to have the common denominator of 12.
1/3 * 4/4 = 4/12
3/4 * 3/3 = 9/12
3. Divide using the keep, change, flip method.
9/12 * 12/4 = 108/48
108/48 = 2 1/4
16 and 1/3 reciprocal
A: 30/6 = 6/1
B: 30/45 = 10/15
C: 32/8 = 20/4
Which two fractions are equivalent?
Step-by-step explanation:
B and A are equal. :) hope I helped!
Answer:
b. 30/45 = 10/15; reduce by 3
Step-by-step explanation:
a. 30/6 = 5 not 6 so no
c. 32/8 = 4. even if you reduced by 2, it would be 16/4 so no
In which number does the digit 7 have a value that is 10 times as great as the digit 7 in the number 0.975
Answer:
ten :)))))))))))))))))))))))))
Please help, it’s math! Give me the answers for 50+ points
Answer:
1. 0.45
2. 0.30
3. 0.583 with a bar over 3
4. 0.80
5. 0.6 with a bar over 6
6. 0.83 with a bar over 3
7. 0.16 with a bar over 6
8. 0.9375
9. 0.13 with a bar over 3
10. 0.36 with a bar over 36
11. 0.625
12. 0.8125
13. 0.12
14. 0.4 with a bar over 4
15. 0.8 with a bar over 8
16. 0.6875
17. 0.56
18. 0.73 with a bar over 3
can anyone help me thanks
Answer:
Option B: 1.3 hours is the correct answer.
Step-by-step explanation:
Given that:
Total distance = 140 miles
Speed on city roads = 35 miles per hour
Time travelled = 1.5 hours
Distance covered on city roads:
[tex]Distance = Speed * Time\\Distance = 35 * 1.5\\Distance = 52.5 miles[/tex]
Distance travelled on highway = Total distance - Distance on city roads
Distance travelled on highway = 140 - 52.5 = 87.5 miles
Speed on highway = 65 miles per hour
Time = [tex]\frac{Distance}{Speed}[/tex]
[tex]Time =\frac{87.5}{65}\\Time = 1.3\ hours[/tex]
Hence,
Option B: 1.3 hours is the correct answer.
what means ratio with explanation
1.
A toy store is preparing for the
winter holiday season. The
manager is reviewing the current
inventory and comparing it to the
forecasted inventory needed that
is based on last year's sales.
What is the forecasted need for
board games?
Toy Inventory, 2016
Which of the following is an open statement?
A) An angle that measures 40° is an acute angle.
B) An angle that measures 95° is an obtuse angle.
C)
XYZ is an acute angle.
OD) An angle that measures 95° is an acute angle
Answer:
OD
Step-by-step explanation:
an angle that is more than 90 is considered a acute angles
The correct option for an open statement is:
C) XYZ is an acute angle.
The answer is C. We don't know if it's true or false.
Here, we have,
we know that,
An open statement is one that can be true or false depending on the value or condition being discussed.
In this case, the statement "An angle that measures 95° is an acute angle" is an open statement because it can be evaluated as true or false based on the definition of an acute angle.
An acute angle is defined as an angle that measures less than 90 degrees.
Since 95° is greater than 90°, the statement is false.
However, if we were discussing a different angle measure, the statement could be true or false depending on its value.
Options A and B are not open statements because they provide specific angle measures (40° and 95°) and classify them as either acute or obtuse, which can be determined as true or false based on their given measures.
Option C does not provide any specific information or condition,
We don't know if it's true or false.
The correct option for an open statement is:
C) XYZ is an acute angle.
To learn more on angle click:
brainly.com/question/28451077
#SPJ2