Daniel’s answer was wrong because he used square root instead of the cubed root.
How can we calculate this?From the expression , which is [tex]t = 5.825 \sqrt[3]{3590/p}[/tex]
Then we can perform some operations to Solve for the value of p.
Then we can make division on the both sides of the equation using 5.825 , then we have
2.304 = [tex]} (3590/p)^{\frac{1}{3}[/tex]
We can cube the both side of the equation to will eliminate the radical and we will have
12.174 = 3590/p
then , p = 294.89 which implies that Natasha’s answer is correct.
Therefore , Daniel’s answer was wrong because he used square root instead of the cubed root.
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If six cans of soda cost nine dollars, how much would it cost for 8 cans.
Answer:
Solution:
here,
6 cans cost = 9 dollars
1 can costs = 9÷6 dollars
= 1.5 dollars
Now,
8 cans cost = 8×1.5 dollars
= 12 dollars
4m^2-5m when m= -4 solve
Answer:
84
Step-by-step explanation:
4 (-4)^2 - 5(-4)
4 × 16 - 5 × -4
64 + 20
84
If the probability of a new employee in a fast-food chain still being with the company at the end of the year is 0. 5, what is the probability that out of 8 newly hired people?
Using binomial distribution, the probability of
a. 5 will still be with the company after 1 year is 28%.
b. at most 6 will still be with the company after 1 year is 89%.
The probability of a new employee in a fast-food chain still being with the company at the end of the year is given to be 0.6, which can be taken as the success of the experiment, p.
We are finding probability for people, thus, our sample size, n = 8.
Thus, we can show the given experiment a binomial distribution, with n = 8, and p = 0.6.
(i) We are asked for the probability that 5 will still be with the company.
Thus, we take x = 5.
P(X = 5) = (8C5)(0.6⁵)((1 - 0.6)⁸⁻⁵),
or, P(X = 5) = (56)(0.07776)(0.064),
or, P(X = 5) = 0.27869184 ≈ 0.28 or 28%.
(ii) We are asked for the probability that at most 6 will still be with the company.
Thus, our x = 6, and we need to take all values below it also.
P(X ≤ 6)
= 1 - P(X > 6)
= 1 - P(X = 7) - P(X = 8)
= 1 - (8C7)(0.6)⁷((1 - 0.6)⁸⁻⁷) - (8C8)(0.6)⁸((1 - 0.6)⁸⁻⁸)
= 1 - 8*0.0279936*0.4 - 1*0.01679616*1
= 1 - 0.08957952 - 0.01679616
= 0.89362432 ≈ 0.89 or 89%.
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The provided question is incomplete. The complete question is:
If the probability of new employee in a fast-food chain still being with the company at the end of 1 year is 0.6, what is the probability that out of 8 newly hired people,
a. 5 will still be with the company after 1 year?
b. at most 6 will still be with the company after 1 year?
PLEASE HELP IM STUCK PLS
Step-by-step explanation:
the general slope-intercept form is
y = ax + b
a is the slope, b is the y-intercept.
we need to transform x + 2y = 6, so that we end up with y being all alone on one side, and the rest on the other side.
x + 2y = 6
2y = -x + 6
y = -x/2 + 6
Miguel created the ratio table below to show how he uses the money he earns at work.
Miguel’s Money
Money Earned
(dollars)
Money Saved
(dollars)
10
8
50
40
120
?
150
120
How much money will he save if he earns 120 dollars?
The amount of money that Miguel would save when he earns $120 is $96.
How much would Miguel save?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
A ratio table can be described as table that shows equivalent values between two or more numbers and helps us to understand the relationship between the numbers.
The first step is to determine the ratio between the money earned and the money saved.
Ratio = money saved / money earned
8/10 = 0.8
Now, multiply the ratio gotten in the previous step by the amount earned to determine the amount saved.
Amount saved = amount earned x ratio
0.8 x 120 = $96
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Answer:
96
Step-by-step explanation:
I took the quiz edge 2022
A sampling method is _________ when the individuals selected for one sample are used to determine the individuals in the second sample.
Answer:
someone please help me check my page
someone please help me check my pageStep-by-step explanation:
Complete the inequality statement.
13.01 ___ 13.1
1. =
2. >
3.
13.1 = 13.10
---> 13.1 > 13.01
---> 13.01 < 13.1
The correct answer is <
A cone has a radius of 3 and a height given by the expression 2a. which expression represents the volume of the cone?2aπ units34a2π units36aπ units324aπ units3
The expression that represents the volume of the cone is 6aπ.
What is called cone?
A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the vertex.The volume of a cone is expressed as;V = (1/3)πr²hWhere r is the radius, h is height and π is pieGiven the data in the question;
Radius r = 3
Height h = 2a
Volume of the cone V = ?
We substitute our given values into the expression above.
V = (1/3) × π × r² × h
V = (1/3) × π × (3)² × 2a
V = (1/3) × π × 9 × 2a
V = 18aπ / 3
V = 6aπ
Therefore, the expression that represents the volume of the cone is 6aπ.
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A restaurant was hiring for 6 positions, each with a different hourly wage. These wages were all between 15$ and 20$ per hour, v except for one position whose wage was 40$ per hour. The manager at the restaurant looked at the mean and median of the wages. Then, she decided to remove the 40$ per hour wage from the set and recalculate the mean and median.
How will removing this wage affect the mean and median?
Choose 1 answer:
(A) Both the mean and median will increase, but the mean will increase by more than the median.
(B) Both the mean and median will increase, but the median will increase by more than the mean.
(C)
Both the mean and median will decrease, but the mean will decrease by more than the median.
(D) Both the mean and median will decrease, but the median will decrease by more than the mean.
Help pls
Answer: its C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
A written contract is not legally binding until _____. a. money is exchanged b. it is signed by all parties involved c. all requirements of the contract have been fulfilled d. it is signed by all parties involved and notarized by an authorized notary official please select the best answer from the choices provided a b c d
Answer: Answer is B, Mark me brainliest please
Step-by-step explanation:
Alina measured a distance to be 2.18 miles. what is the margin of error? 2.1 miles to 2.2 miles 2.175 miles to 2.185 miles 2.185 miles to 2.195 miles 2.2 miles to 2.3 cm
Answer:
(b) 2.175 miles to 2.185 miles
Step-by-step explanation:
When a value is rounded, the original "exact" value is presumed to be within 1/2 of the value of one least-significant unit of the rounded number.
ApplicationA rounded value of 2.18 has a least-significant digit with a place value of 0.01 units. Half that value is the "margin of error". That is, the range of numbers that would be rounded to 2.18 is ...
2.18-0.005 ≤ x < 2.18+0.005
2.175 ≤ x < 2.185 . . . . miles
Quadrilateral ABCD has vertices at A(0,0), B(0,3), C(5,3), and D(5,0). Find the vertices of the quadrilateral after a dilation with scale factor 2.5.
PLS ANSWER ASAP
The vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)
How to determine the vertices of the quadrilateral after a dilation with scale factor 2.5?The coordinates of the quadrilateral ABCD are given as:
A(0,0), B(0,3), C(5,3), and D(5,0)
When dilated by a scale factor of 2.5, we have the following equation
A' = A * 2.5
So, we have:
A' = (0,0) * 2.5
A' = (0, 0)
B' = (0,3) * 2.5
B' = (0, 7.5)
C' = (5,3) * 2.5
C' = (12.5, 7.5)
D' = (5,0) * 2.5
D' = (12.5, 0)
Hence, the vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)
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need answer
solve for w
w + 7.1
———- = 2.87
3
Answer: 1.51
Step-by-step explanation:
[tex]\frac{w + 7.1}{3} =2.87[/tex]
[tex]3(\frac{w+7.1}{3})=3(2.87)[/tex]
w + 7.1 = 8.61
w + 7.1 - 7.1 = 8.61 - 7.1
w = 1.51
What’s 400.00 - 172.98 I know the answer I just need to know how to get it
Answer:
227.02
Step-by-step explanation:
[tex]400.00-172.98 \\ \\ =300 - 72.98 \\ \\ =230-2.98 \\ \\ =228-0.98 \\ \\ =227.02[/tex]
Answer:
227.02
Step-by-step explanation:
[tex]400.00\\-172.98[/tex]
To solve: First subtract 172 from 400, resulting in 228, then you may subtract the 0.98, leaving 227.02.
I need help to complete this question
The complete fractional question given in the above picture is 55/3 = 1 + 52/3 = 2 + 49/3 = 5 + 40/3 = 8 + 31/3 = 10 + 25/3
FractionLet
Each empty box = x55/3 = 1 + x/3
55/3 = (3+x) / 3
55/3 × 3 = 3 + x
55 = 3 + x
55 - 3 = x
52 = x
55/3 = 2 + x/3
55/3 =(6+x) / 3
55/3 × 3 = 6+x
55 = 6 + x
55 - 6 = x
49 = x
55/3 = x + 40/3
55/3 = (3x+40) / 3
55/3 × 3 = 3x + 40
55 = 3x + 40
55 - 40 = 3x
15 = 3x
x = 15/3
x = 5
55/3 = x + 31/3
55/3 = (3x+31) / 3
55/3 × 3 = 3x + 31
55 = 3x + 31
55 - 31 = 3x
24 = 3x
x = 24/3
x = 8
55/3 = 10 + x/3
55/3 = (30+x) / 3
55/3 × 3 = 30 + x
55 = 30 + x
55 - 30 = x
25 = x
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Wich of the following is not a way to represent the solution of inequality 2(x-2)<2? A number line with a closed circle on 3 and shading to the right x<3 3>x a number line with a closed circle on 3 and shading to the left
Answer:
The solution is x < 3. To represent that on a number line, you'd have an open (not filled in) circle on 3 and shading to the left.
Step-by-step explanation:
You would only have a closed (solid/filled in) circle if the inequality had a ≤
There are 61 boxes of pencils in a store there are 14 pencils in each box how many pencils are in the store
Can someone help me with this?
20 points for the Answer to this
Thank You for leaving your answer here!
Answer:
182000
Step-by-step explanation:
4.82 x 10^5
1.
10^5 is equal to 10 being multiplied 5 times. So this can be expressed as:
10 x 10 x 10 x 10 x 10.
When you multiply 10s, you just add the number of zeros next to one.
==> 100000 (5 zeros total)
2.
We multiply 100000 to 4.82.
100000 x 4.82 = 182000
So our final answer will be 182000.
Answer:
482,000.
Step-by-step explanation:
The 5 tells us this number is 6 digits long.
The answer is
482,000
johns first three test scores out of 100 are 84,78,82. what did he score on his fourth test if the average for all four tests is 80 out of 100
Answer:
76
Step-by-step explanation:
Formula
[tex]\sf Average=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]
Given values:
First three test scores: 84, 78 and 82Total number of tests = 4Average score for all four tests = 80Let x be the score of the fourth test.
To find the score of the fourth test, substitute the given values into the formula and solve for x:
[tex]\begin{aligned} \sf Average & =\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}\\\\\implies \sf 80 & = \sf \dfrac{84+78+82+x}{4}\\\sf 80 & = \sf \dfrac{244+x}{4}\\\sf 80 \cdot 4 & = \sf 244 + x \\\sf 320 & = \sf 244 + x\\\implies \sf x & = \sf 320 - 244\\& = \sf 76\end{aligned}[/tex]
Therefore, John scored 76 on his fourth test.
Quick algebra 1 question for 50 points!
Only answer if you know the answer, Tysm!
Answer:
A) f(x) = x^2 +8(x+2)
Step-by-step explanation:
We will start by putting y=0
0 = x^2+8(x+2) -Apply distributive property
0 = x^2+8x+16
0=(x+4)(x+4)
0=x+4, 0=x+4
x=-4
There is only one zero, and that is x=-4
Brainiest would be appreciated.
First one
Because
If we solve for x
x²+8(x+2)=0x²+8x+16=0x²+4x+4x+16=0(x+4)(x+4)=0x=-4Option A
B is the midpoint of segment AC. Which statement best describes the relationship between triangles ABD and CBD? (1 point)
The statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A
What are similar triangles?
It is important to note the following;
"Two triangles are similar when their corresponding angles are equal and corresponding sides are in equal proportion."
The SSS congruence states that ; "Two triangles are congruent if all three sides of a triangle are congruent to corresponding three sides of other triangle."
SSS similarity postulates that; "Two triangles are similar if all the three sides of a triangle are in proportion to the three sides of another triangle."
SAS similarity postulates that ; "Two triangles are similar if the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle between the two sides in both the triangle are equal."
SAS congruence postulates that ; "Two triangles are congruent if two sides and the angle between these two sides of one triangle are congruent to the corresponding two sides and the included angle of a second triangle."
For given question,
We have been given triangles ABD and CBD.
B is the midpoint of line AC
⇒ AB = BC
For triangles ABD and CBD,
side AB = side CB; since, B is the midpoint of line AC
side BD = side BD ; they have common sides
side AD = side CD = 15 units each
So, by SSS postulates of triangle congruence triangles ABD and CBD are congruent triangles.
Therefore, the statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A
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what part of an hour passes between 11:24 am and 415 am
Using proportions, it is found that 1685% of an hour passes between 11:24 am and 415 am.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
One hour is composed by 60 minutes. Between 11:24 am and 4:15 am, there are 16 hours and 51 minutes, hence the number of minutes is given by:
M = 16 x 60 + 51 = 1011 minutes.
As a percentage of one hour = 60 minutes, we have that this measure is:
1011/60 x 100% = 1685%.
Hence 1685% of an hour passes between 11:24 am and 415 am.
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A long distance runner started on a course running at an average speed of 6mph. half an hour later, a second runner began the same course at an average speed of 7mph. how long after the second runner started will the second runner overtake the first runner?
9 hours long after the second runner started will the second runner overtake the first runner.
What does it mean to do speed?
Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector.Runner I = 6 mph
Runner II = 7 mph
Difference in time= 90 minutes
Train A will have covered 9 miles before Runner II starts
catch up distance= 9 miles
catch up speed = 7-6 mph
catch up speed = 1 mph
Catchup time = catchup distance/catch up speed
catch up time= 9/1
catch up time= 9 hours
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I was wondering what C and how to solve for it because i dont really understand the problem
The measure of angle C is 35°.
Given that, ΔABC≅ΔDEF, ∠A=70°, ∠E=3x and ∠F=x+10.
What are congruent triangles?Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
In ΔABC and ΔDEF, corresponding angles are equal.
That is, ∠A=∠D=70°, ∠B=∠E=3x and ∠C=∠F=x+10
Now, ∠A+∠B+∠C=180° (∵angle sum property)
⇒70°+3x+x+10=180°
⇒4x=100°
⇒x=25°
Thus, ∠C=x+10=35°.
Therefore, the measure of angle C is 35°.
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4. Use the following images to answer the question:
a.
Write a truth statement about each
picture using Euclidean postulates.
b. Write the matching Euclidean postulate.
C.
Describe the deductive reasoning you used.
Truth statement exists statements or assertions that exist true yet of whether the constituent premises exist true or false.
What is the Euclidean Postulate?There exist five Euclidean Postulates or axioms.
1. Any two ends can be bound by a straight line segment.
2. In a straight line, any straight line segment can be extended indefinitely.
3. A circle can be created utilizing any straight line segment as the radius and one endpoint as the center.
4. Right angles exist all the exact.
5. If two lines meet a third in a manner that the totality of the inner angles on one side exists smaller than two Right Angles, the two lines will inevitably collide on that side if they exist extended far enough.
What are the true statements connecting to the pictures and their equivalent Euclidean Axiom?1. The right angle on the first page of the book offered and the right angles on the last page of the book shown exist all the exact. (Axiom 4)
2. If the string from the Yoyo dangling from the hand in the picture exists circled for 360° such that the length of the string stays equivalent to all thought, and the point from where it exists attached stays fixed, it will trace a circular trajectory. (Axiom 3)
3. The swords held by the fighters can be extended into infinity because they exist in in straight lines. (Axiom 5)
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Let f(x)=147+2e−0.6x.
What is f(3)?
The value of f(3) is 147.3306
How to evaluate the function?The function is given as:
[tex]f(x)=147+2e^{-0.6x[/tex]
Substitute 3 for x
[tex]f(3)=147+2e^{-0.6*3[/tex]
Evaluate the product
[tex]f(3)=147+2e^{-1.8[/tex]
Evaluate the exponent
f(3)=147 + 2* 0.1653
Evaluate the sum
f(3) = 147.3306
Hence, the value of f(3) is 147.3306
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please help with this i genuinely have no clue how to figure it out
Answer: c = 520
Step-by-step explanation:
f(2) = 578 means that when x = 2, the value is equal to 578. We will plug these knowns in and then solve for c.
Given:
f(x) = 4x³ + 7x² - x + c
Substitute:
578 = 4(2)³ + 7(2)² - (2) + c
Distribute:
578 = 4 * 2³ + 7 * 2² - 2 + c
Raise to the power of 3 and 2:
578 = 4 * 8 + 7 * 4 - 2 + c
Multiply:
578 = 32 + 28 - 2 + c
Add:
578 = 60 - 2 + c
Subtract:
578 = 58 + c
Subtract 58 from both sides:
520 = c
Reflexive property:
c = 520
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:
[tex]\longrightarrow\bold{f(x) = 4x^3 + 7x2 −x + c}[/tex]
[tex]\longrightarrow\sf{578= 32+28 −2+ c}[/tex]
[tex]\longrightarrow\sf{578 =58+ c}[/tex]
[tex]\longrightarrow\sf{c = 578-58}[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex]\longrightarrow\sf{c= 520}[/tex]
Apyrotechnician plans for two fireworks to explode together at the same
height in the air. They travel at speeds shown below. Firework B is launched
0.25 s before Firework A. How many seconds after Firework B launches will
both fireworks explode?
Firework A Firework B
320 fts
240 fuis
Both fireworks will explode _?seconds after Firework B launches.
Pls help me,this is Canadian MO 1998 question,i'm very confuse with this
The solution to the equation is x = 1.62
How to solve the equation?The equation is given as:
[tex]x =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]
Next, we split the equations as follows:
y = x
[tex]y =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]
Next, we graph the equations (see attachment)
From the attached graph, the equations intersect at
(x, y)= (1.62, 1.62)
Remove the y value
x = 1.62
Hence, the solution to the equation is x = 1.62
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Rationalize the right side first. Expand and simplify.
[tex]x = \sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}[/tex]
[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}\right) \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right)[/tex]
[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x}\right)^2 - \left(\sqrt{1 - \dfrac1x}\right)^2[/tex]
[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(x - \dfrac1x\right) - \left(1 - \dfrac1x\right)[/tex]
[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = x - 1[/tex]
Rearrange terms as
[tex]\dfrac{x - 1}x = \sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}[/tex]
[tex]\dfrac{x - 1}x + \sqrt{\dfrac{x - 1}x} = \sqrt{x - \dfrac1x}[/tex]
Substitute
[tex]y = \sqrt{\dfrac{x-1}x} = \sqrt{1 - \dfrac1x} \\\\ \implies y^2 = 1 - \dfrac1x \implies x = \dfrac1{1-y^2}[/tex]
(noting that [tex]y>0[/tex]) so that
[tex]x - \dfrac1x = \dfrac1{1-y^2} - (1-y^2) = \dfrac{2y^2 - y^4}{1-y^2}[/tex]
and the equation transforms to
[tex]y^2 + y = \sqrt{\dfrac{2y^2 - y^4}{1-y^2}}[/tex]
[tex]y + 1 = \sqrt{\dfrac{2 - y^2}{1-y^2}}[/tex]
Solve for [tex]y[/tex].
[tex](y+1)^2 = \left(\sqrt{\dfrac{2-y^2}{1-y^2}}\right)^2[/tex]
[tex]y^2 + 2y + 1 = \dfrac{2 - y^2}{1 - y^2}[/tex]
[tex]-y^4 - 2y^3 + 2y + 1 = 2 - y^2[/tex]
[tex]y^4 + 2y^3 - y^2 - 2y + 1 = 0[/tex]
[tex]\left(y^4 + 2y^3 + y^2\right) - 2y^2 - 2y + 1 = 0[/tex]
[tex](y^2 + y)^2 - 2(y^2 + y) + 1 = 0[/tex]
[tex]\left(y^2 + y - 1\right)^2 = 0[/tex]
[tex]y^2 + y - 1 = 0[/tex]
[tex]y = \dfrac{-1 \pm \sqrt5}2[/tex]
Since [tex]y>0[/tex], we take the positive root. Then
[tex]y = \sqrt{\dfrac{x-1}x} = \dfrac{-1 + \sqrt5}2[/tex]
Solve for [tex]x[/tex].
[tex]\left(\sqrt{\dfrac{x-1}x}\right)^2 = \left(\dfrac{-1 + \sqrt5}2\right)^2[/tex]
[tex]\dfrac{x-1}x = \dfrac{6 - 2\sqrt5}4 = \dfrac{3 - \sqrt5}2[/tex]
[tex]x - 1 = \dfrac{3-\sqrt5}2x[/tex]
[tex]\dfrac{-1+\sqrt5}2 x = 1[/tex]
[tex]x = \dfrac2{-1+\sqrt5}[/tex]
Rationalize to clean up the answer.
[tex]x = \dfrac2{-1+\sqrt5}\cdot\dfrac{-1-\sqrt5}{-1-\sqrt5} = \boxed{\dfrac{1+\sqrt5}2} \approx 1.6108[/tex]
i.e. the golden ratio constant.
Write the function in terms of unit step functions. find the laplace transform of the given function. f(t) = t, 0 ≤ t < 5 0, t ≥ 5
The Laplace transform of the given function is [tex]f(s)=\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]
Given,
[tex]f(t)=\left \{ {{t, 0\leq t < 5} \atop {0,t\geq 5}} \right.[/tex]
Write the function in unit step function.
[tex]f(t)=t(u_{0}(t)-u_{5} (t))[/tex]
= [tex]t(1-u_{5}(t))[/tex] ∵[tex]u_{0} (t)=1[/tex]
= [tex]t-tu_{5} (t)[/tex]
[tex]f(t)=t-tu_{5} (t)[/tex]
In order to make it easier to take the Laplace transform of the function, we can follow the steps:
[tex]f(t)=t-tu_{5} (t)[/tex]
= [tex]t-(t-5+5)u_{5} (t)[/tex]
= [tex]t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]
[tex]f(t)=t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]
We need to find the Laplace transform of f(t).
Apply Laplace transform on both sides,
£[tex][f(t)=[/tex]£[tex](t)-[/tex]£[tex](t-5)u_{5} (t))+5[/tex]£[tex](u_{5} (t))[/tex]
= [tex]\frac{1}{s^{2} } -e^{-s}[/tex]£[tex](t)+5(\frac{e^{-5s} }{s} )[/tex]
= [tex]\frac{1}{s^{2} } -e^{-5s} (\frac{1}{s^{2} } )+\frac{5se^{-5s} }{s^{2} }[/tex]
= [tex]\frac{1-e^{-5s}+5se^{-5s} }{s^{2} }[/tex]
= [tex]\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]
[tex]f(s) =\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]
Learn more about Laplace transform here: https://brainly.com/question/17190535
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