Find the cost to asphalt a circular racetrack if asphalt costs $90 per 100 f2. (Use 3.14 for it. Round to the nearest dollar.) r = 80 ft R = 145 ft
Small circle in a large circle
r= 80 ft
R=145 ft
Y
R
(Use 3.1 4 for a.)
Answers
Answer:
$41,330
Step-by-step explanation:
To find the cost to asphalt a circular path, first, calculate the area of the circular path:
Area of circular path = area of big circle (A1) - Area of small circle (A2)
Area of circle = πr²
Radius of big circle (R) = 145 ft
Area of big circle (A1) = 3.14*145²
= 3.14*21,025
A1 = 66,018.5 ft²
Radius of small circle (r) = 80ft
Area of small circle (A2) = 3.14*80²
= 3.14*6,400
A2 = 20,096 ft²
=>Area of path = 66,018.5 - 20,096 = 45,922.5 ft²
If 100ft = $90
45,922.5 ft = x
Cross multiply and find x (cost to asphalt the circular path)
100*x = 45,922.5*90
100x = 4,133,025
Divide both sides by 100
x = 4,133,025/100
x = $41,330.25
To the nearest dollar, $41,330 is needed to asphalt the circular path
Related Questions
Which value of x makes 7+5(x-3)=227+5(x−3)=227, plus, 5, left parenthesis, x, minus, 3, right parenthesis, equals, 22 a true statement? Choose 1 answer:
Answers
Answer:
7 + 5(x - 3) = 22
5(x - 3) = 15
x - 3 = 3
x = 6
Answer:
x = 6
Step-by-step explanation:
Step 1: Distribute 5
7 + 5x - 15 = 22
Step 2: Combine like terms
5x - 8 = 22
Step 3: Add 8 to both sides
5x = 30
Step 4: Divide both sides by 5
x = 6
Write an equation in slope-intercept form of the line that passes through the point (-6,-5) with slope 6.
Answers
Answer:
y=6x+31
Step-by-step explanation:
Since we are given a point and a slope, we can use the slope-intercept formula.
[tex]y-y_{1} =m(x-x_{1})[/tex]
where (x1,y1) is a point on the line and m is the slope.
The point given is (-6,-5) and the slope is 6.
x1= -6
y1= -5
m=6
[tex]y--5=6(x--6)[/tex]
A negative number subtracted from another number, or two negative signs, becomes a positive.
[tex]y+5=6(x+6)[/tex]
We want to find the equation of the line, which is y=mx+b (m is the slope and b is the y-intercept). Therefore, we must get y by itself on one side of the equation.
First, distribute the 6. Multiply each term inside the parentheses by 6.
[tex]y+5=(6*x)+(6*6)[/tex]
[tex]y+5=6x+36[/tex]
Subtract 5 from both sides, because it is being added on to y.
[tex]y+5-5=6x+36-5[/tex]
[tex]y=6x+36-5[/tex]
[tex]y=6x+31[/tex]
The equation of the line is y=6x+31
PLEASE HELP!
Fill in the reason for statement 3 in proof below:
SAS
AA
SSS
Answers
Answer:
SAS
Step-by-step explanation:
ΔABD ~ ΔECD is similar through:
S - because ED = CD (Given)
A - same angle ∠D (Statement 2)
S - because AD = BD (Given)
Cheers!
Answer:
SAS
Step-by-step explanation:
You can notice that you have ED/AB = CD/BD You have one common anglecompute the missing data in the table for the following exponential function f(x)={1/4}
Answers
Answer:
1/256
Step-by-step explanation:
The table shows a chain of fractions for f(x), x1 is 1/4, x2 is 1/16 and x3 is 1/64. All you need to do is multiply the denominator by 4 and put 1 over it. 64*4 = 256, adding the 1 as the numerator gives us the answer of 1/256 as x4.
A class of 30 music students includes 13 who play the piano, 15 who play the guitar, and 9 who play both the piano and the guitar. How many students in the class play neither instrument?
Answers
Answer: 2
Step-by-step explanation:
As given, out of 30 students, 15 play guitar and 13 play piano, thats 28.
Among these, 9 play both the guitar and the piano.
That means, only 2 remaining students play neither instrument. (30-15-13)
which equation represents the graph function?
Answers
Answer:
[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]
Step-by-step explanation:
First, notice that since the graph of the function is a line, we have a linear function.
To find the equations for linear functions, we need the slope and the y-intercept. Recall the slope-intercept form:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
We are given the point (0,3) which is the y-intercept. Thus, b = 3.
To find the slope, we can use the slope formula:
[tex]\displaystyle m=\frac{\Delta y}{\Delta x} =\frac{2-3}{3-0}=-1/3[/tex]
Therefore, our equation is:
[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]
pleassseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
The answer is 0.4
Step-by-step explanation:
2/5 is equal to 0.4
Answer:
0.4
Step-by-step explanation:
start with 2/5.
multipy the 5 by 20 to get 100, and the 2 by 20 to get 40.
so, now your fraction should look like this:
40/100
then, shift the decimal in 40 over 2 spots to get 0.40, or 0.4
hope this helps :)
Find the remainder when f(x)=2x3−x2+x+1 is divided by 2x+1.
Answers
Step-by-step explanation:
it can be simply done by using remainder theorem.
helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
0.25 = 1/4 because 25/100 = 1/4
▹ Step-by-Step Explanation
0.25 to a fraction → 25/100
25/100 = 1/4
Therefore, this statement is true. (0.25 = 1/4 because 25/100 = 1/4)
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
At her favorite sneakers store Nyeema saved $48 because of a
sale.
If the sneakers normally cost $120. How much did she save?
Answers
Answer:
40%
Step-by-step explanation:
We can find what percent 48 is of 120 by dividing:
48/120 = 0.4 or 40%
So, she saved 40% from the original price.
Select the correct answer.
If two angles of a triangle have equal measures and the third angle measures 90º, what are the angle measures of the triangle?
ОА.
60°, 60°, 60°
OB.
459,909, 90°
Ос.
30°, 30°, 90°
OD.
45°, 45°, 90°
Answers
Answer:
OD. 45,45,90
Step-by-step explanation:
If C(x) = 16000 + 600x − 1.8x2 + 0.004x3 is the cost function and p(x) = 4200 − 6x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)
Answers
Answer:
Quantity that will maximize profit=1000
Step-by-step explanation:
Assume quantity=x
Revenue=price*quantity
=(4200-6x)x
=4200x-6x^2
Marginal revenue(MR) =4200-12x
Cost(x)= 16000 + 600x − 1.8x2 + 0.004x3
Marginal cost(MC) =600-3.6x+0.012x^2
Marginal cost=Marginal revenue
600-3.6x+0.012x^2=4200-12x
600-3.6x+0.012x^2-4200+12x=0
0.012x^2-8.4x-3600=0
Solve the quadratic equation using
x= -b +or- √b^2-4ac/2a
a=0.012
b=-8.4
c=-3600
x=-(-8.4) +or- √(-8.4)^2- (4)(0.012)(-3600) / (2)(0.012)
= 8.4 +or- √70.56-(-172.8) / 0.024
= 8.4 +or- √70.56+172.8 / 0.024
= 8.4 +or- √243.36 / 0.024
= 8.4 +or- 15.6/0.024
= 8.4/0.024 +15.6/0.024
= 350+650
x=1000
OR
= 8.4/0.024 -15.6/0.024
= 350 - 650
= -300
x=1000 or -300
Quantity that maximises profits can not be negative
So, quantity that maximises profits=1000
Fake Question: Should Sekkrit be a moderator? (answer if you can) Real Question: Solve for x. [tex]x^2+3x=-2[/tex]
Answers
Answer:
x = -2 , -1
Step-by-step explanation:
Set the equation equal to 0. Add 2 to both sides:
x² + 3x = -2
x² + 3x (+2) = - 2 (+2)
x² + 3x + 2 = 0
Simplify. Find factors of x² and 2 that will give 3x when combined:
x² + 3x + 2 = 0
x 2
x 1
(x + 2)(x + 1) = 0
Set each parenthesis equal to 0. Isolate the variable, x. Note that what you do to one side of the equation, you do to the other.
(x + 2) = 0
x + 2 (-2) = 0 (-2)
x = 0 - 2
x = -2
(x + 1) = 0
x + 1 (-1) = 0 (-1)
x = 0 - 1
x = -1
x = -2 , -1
~
Answer:
x = -2 OR x = -1
Step-by-step explanation:
=> [tex]x^2+3x = -2[/tex]
Adding 2 to both sides
=> [tex]x^2+3x+2 = 0[/tex]
Using mid-term break formula
=> [tex]x^2+x+2x+2 = 0[/tex]
=> x(x+1)+2(x+1) = 0
=> (x+2)(x+1) = 0
Either:
x+2 = 0 OR x+1 = 0
x = -2 OR x = -1
P.S. Ummmm maybe...... Because he usually reports absurd answers! So, Won't it be better that he could directly delete it. And one more thing! He's Online 24/7!!!!!
Which expressions are equivalent to -3(2w+6)-4
Answers
Answer:
B is the answer
Step-by-step explanation:
-3(2w+6)-4
-6w-18-4
-6w-22
Answer:
B = 2(−3w + (−11)) is the answer.Step-by-step explanation:
-3(2w + 6) - 4
1. Distribute
= -3*2w = -6w
= -3 * 6 = -18
= -6w -18
2. Simplify like terms
= -18 - 4
= -22
3. Place variables and numbers together
= -6w - 22
-6w -22 is the answer.So, B is the answer.Explanation:
2 * -3w = -6w
2*-11 = -22
Place them together and you get the answer!
¿Cuál serie numérica tiene como regla general Xn = 2n +1?
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
Answers
Answer:
The series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
Step-by-step explanation:
We are given with the following series options below;
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].
For this, we will put the values of n in the above expression and then will see which series is obtained as a result.
So, the given expression is ; [tex]X_n=2n+1[/tex]
If we put n = 1, then;
[tex]X_1=(2\times 1)+1[/tex]
[tex]X_1 = 2+1 = 3[/tex]
If we put n = 2, then;
[tex]X_2=(2\times 2)+1[/tex]
[tex]X_2 = 4+1 = 5[/tex]
If we put n = 3, then;
[tex]X_3=(2\times 3)+1[/tex]
[tex]X_3 = 6+1 = 7[/tex]
If we put n = 4, then;
[tex]X_4=(2\times 4)+1[/tex]
[tex]X_4 = 8+1 = 9[/tex]
Hence, the series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
Find sets of parametric equations and symmetric equations of the line that passes through the two points (if possible). (For each line, write the direction numbers as integers.) (0, 0, 25), (10, 10, 0)
Answers
Answer:
a)Parametric equations are
X= -10t
Y= -10t and
z= 25+25t
b) Symmetric equations are
(x/-10) = (y/-10) = (z- 25)/25
Step-by-step explanation:
We were told to fin two things here which are ; a) the parametric equations and b) the symmetric equations
The given two points are (0, 0, 25)and (10, 10, 0)
The direction vector from the points (0, 0, 25) and (10, 10, 0)
(a,b,c) =( 0 -10 , 0-10 ,25-0)
= < -10 , -10 ,25>
The direction vector is
(a,b,c) = < -10 , -10 ,25>
The parametric equations passing through the point (X₁,Y₁,Z₁)and parallel to the direction vector (a,b,c) are X= x₁+ at ,y=y₁+by ,z=z₁+ct
Substitute (X₁ ,Y₁ ,Z₁)= (0, 0, 25), and (a,b,c) = < -10 , -10 ,25>
and in parametric equations.
Parametric equations are X= 0-10t
Y= 0-10t and z= 25+25t
Therefore, the Parametric equations are
X= -10t
Y= -10t and
z= 25+25t
b) Symmetric equations:
If the direction numbers image and image are all non zero, then eliminate the parameter image to obtain symmetric equations of the line.
(x-x₁)/a = (y-y₁)/b = (z-z₁)/c
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
In a particular year, the mean score on the ACT test was 19.6 and the standard deviation was 5.2. The mean score on the SAT mathematics test was 546 and the standard deviation was 126. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal placesFind the z-score for an ACT score of 26. The Z-score for an ACT score of 26 is ______ .
Answers
Answer:
0.11
Step-by-step explanation:
Let the random variable score, X = 26; mean, ∪ = 19.6; standard deviation, α = 5.2
By comparing P(0≤ Z ≤ 26)
P(Z ≤ X - ∪/α) = P(Z ≤ 26 - 19.6/5.2)
= P(Z ≤ 1.231)
Using Table: P(0 ≤ Z ≤ 1) = 0.39
P(Z > 1) = (0.5 - 0.39) = 0.11
∴ P(Z > 26) = 0.11
what is 3/5 of 1800
Answers
Answer:
1080
Step-by-step explanation:
first do 3 times 1800, because they are both the numerators. Then divide that number, which is 5400, by the denominator: 5. You will get 1080.
The following chart represents the record low temperatures recorded in Phoenix for April-November. Select the answer below that best describes the mean and the median of the data set (round answers to the nearest tenth). A graph titled Phoenix Low Temperatures has month on the x-axis and temperature (degrees Fahrenheit) on the y-axis. April, 32; May, 40; June, 50; July, 61; August, 60; September, 47; October, 34; November, 25. a. The mean is 43.5°F, and the median is 43.6°F. b. The mean is 60.5°F, and the median is 60.5°F. c. The mean is 60°F, and the median is 61°F. d. The mean is 43.6°F, and the median is 43.5°F.
Answers
Answer:
d. The mean is 43.6°F, and the median is 43.5°F.
Step-by-step explanation:
Hello!
The data corresponds to the low temperatures in Phoenix recorded for April to November.
April: 32ºF
May: 40ºF
June: 50ºF
July: 61ºF
August: 60ºF
September: 47ºF
October: 34ºF
November: 25ºF
Sample size: n= 8 months
The mean or average temperature of the low temperatures in Phoenix can be calculated as:
[tex]\frac{}{X}[/tex]= ∑X/n= (32+40+50+61+60+47+34+25)/8= 43.625ºF (≅ 43.6ºF)
The Median (Me) is the value that separates the data set in two halves, first you have to calculate its position:
PosMe= (n+1)/2= (8+1)/2= 4.5
The value that separates the sample in halves is between the 4th and the 5th observations, so first you have to order the data from least to greatest:
25; 32; 34; 40; 47; 50; 60; 61
The Median is between 40 and 47 ºF, so you have to calculate the average between these two values:
[tex]Me= \frac{(40+47)}{2} = 43.5[/tex] ºF
The correct option is D.
I hope this helps!
Answer:
it is d
Step-by-step explanation:
In a study of 205 adults, the average heart rate was 75 beats per minute. Assume the population of heart rates is known to be approximately normal, with a standard deviation of 8 beats per minute. What does a margin of error of 1.1 for the 95% confidence interval of the average beats per minute mean? There is a 95% chance that the population mean is between 67 and 83 beats per minute. There is a 95% chance that the population mean is between 73.9 and 76.1 beats per minute. There is a 5% chance that the population mean is less than 75 beats per minute. There is a 5% chance that the population mean is more than 75 beats per minute.
Answers
Answer:
There is a 95% chance that the population mean is between 73.9 and 76.1 beats per minute.
Step-by-step explanation:
i have the test
There is a 95% chance that the population mean is between 73.9 and 76.1 beats per minute.
Calculation of margin of error:Since
The average heart rate was 75 beats per minute.
The standard deviation is 8 beats per minute
And, there is the study of 205 adults
Now the following formula is to be used
Since
[tex]x \pm z \frac{\sigma}{\sqrt{n} }[/tex]
Here
z = 1.96 at 95% confidence interval
So,
[tex]= 75 \pm 1.96 \frac{8}{\sqrt{205} } \\\\= 75 - 1.96 \frac{8}{\sqrt{205} } , 75 + 1.96 \frac{8}{\sqrt{205} }[/tex]
= 73.9 ,76.1
Hence, the above statement should be true.
Learn more about standard deviation here: https://brainly.com/question/20529928
HELP !!!..... ASAP PLS
Answers
Step-by-step explanation:
the average change H = Δy/ Δx
so H = ( f(4) - f(2) )/ (4 -2) = ( 0 -1 ) / 2 = -1/2
Please help me I’ll mark brainliest
Answers
Explanation:
First let’s find angle D
D= 360-Q= 360-100=260
Now find angle A
Before the cut angle A = 90
Then A = 90-P=90-60=30
Now let’s find the missing x angle
We know that the interior of a quadrilateral is 360
Then 360= angle A + angle D + angle C + x
Find x:
x= 360- (30+ 260+30)= 40
So the answer is 40 degree
The two-way table shows the medal count for the top-performing countries in the 2012 Summer Olympics. A 5-column table has 5 rows. The first column has entries United notes, China, Russia, Great Britain, Total. The second column is labeled Gold with entries 46, 38, 24, 29, 137. The third column is labeled Silver with entries 29, 27, 26, 17, 99. The fourth column is labeled Bronze with entries 29, 23, 32, 19, 103. The fifth column is labeled Total with entries 104, 88, 82, 65, 339. Which statement is true?
Answers
Which statement is true?
The probability that a randomly selected silver medal was awarded to Great Britain is StartFraction 17 Over 99 EndFraction. The probability that a randomly selected medal won by Russia was a bronze medal is StartFraction 32 Over 103 EndFraction. The probability that a randomly selected gold medal was awarded to China is StartFraction 88 Over 137 EndFraction. The probability that a randomly selected medal won by the United States was a silver medal is StartFraction 104 Over 339 EndFraction.Answer:
(A)The probability that a randomly selected silver medal was awarded to Great Britain is 17/99.
Step-by-step explanation:
The table is given below:
[tex]\left|\begin{array}{l|c|c|c|c|c} &Gold&Silver & Bronze &Total\\United States &46 & 29 & 29 & 104\\China & 38 & 27 & 23 & 88\\Russia & 24 & 26 & 32 &82\\Great Britain & 29 & 17 & 19 & 65\\&&&&&\\Total &137 & 99 & 103 & 339\end{array}\right[/tex]
We calculate the probabilities given in the statements.
(A) The probability that a randomly selected silver medal was awarded to Great Britain
= 17/99
(B)The probability that a randomly selected medal won by Russia was a bronze medal
=32/82
(C)The probability that a randomly selected gold medal was awarded to China
=38/137
(D)The probability that a randomly selected medal won by the United States was a silver medal
=29/104
We can see that only the first statement is true.
Answer: A. The probability that a randomly selected silver medal was awarded to Great Britain is 17/99.
Step-by-step explanation:
I got it right on edge
Jina wants to measure the width of a river. She marks off two right triangles, as shown in the figure. The base of the larger triangle has a length of 56m, and the base of the smaller triangle has a length of 26m. The height of the smaller triangle is 20.9m. How wide is the river? Round your answer to the nearest meter.
Answers
Answer:
width of a river = 45m
Step-by-step explanation:
ration and proportion
let x = width of a river
x 20.9 m
------ = --------
56 m 26 m
x = (20.9 * 56) / 26
x = 45 m
therefore the width of a river is 45 m
Alexandra has $15 to buy drinks for her friends at the baseball game. Soda
costs $2.75 and bottled water costs $2.00. This relationship can be
represented by the inequality 2758+2w $ 15. Three of Alexandra's friends
asked for water. Which inequality represents the number of sodas she can
buy?
A. OS 85 3.27
B. 85 3.27
C. OSSS3
D. 853
Answers
Answer:
C
Step-by-step explanation:
write an equation for the costs:
if x is the number of sodas
and y is the number of waters
2.75x + 2y <= 15
(<= is less than or equal to)
if we substitute 3 for y
we get 2.75x + 2(3) <= 15
2.75x + 6 <= 15
2.75x <= 9
9 / 2.75 = 3.2727
however, you cannot buy part of a soda
so, round to 3
you also cannot buy negative sodas
so, the answer is C
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 418 gram setting. It is believed that the machine is underfilling the bags. A 9 bag sample had a mean of 413 grams with a standard deviation of 20. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?
Answers
Answer:
No. At a significance level of 0.1, there is not enough evidence to support the claim that the bags are underfilled (population mean significantly less than 418 g.)
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the bags are underfilled (population mean significantly less than 418 g.)
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=418\\\\H_a:\mu< 418[/tex]
The significance level is 0.1.
The sample has a size n=9.
The sample mean is M=413.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=20.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{20}{\sqrt{9}}=6.6667[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{413-418}{6.6667}=\dfrac{-5}{6.6667}=-0.75[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=9-1=8[/tex]
This test is a left-tailed test, with 8 degrees of freedom and t=-0.75, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-0.75)=0.237[/tex]
As the P-value (0.237) is bigger than the significance level (0.1), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.1, there is not enough evidence to support the claim that the bags are underfilled (population mean significantly less than 418 g.)
An industrial psychologist conducted an experiment in which 40 employees that were identified as "chronically tardy" by their managers were divided into two groups of size 20. Group 1 participated in the new "It's Great to be Awake!" program, while Group 2 had their pay docked. The following data represent the number of minutes that employees in Group 1 were late for work after participating in the program.
Does the probability plot suggest that the sample was obtained from a population that is normally distributed? Provide TWO reasons for your classification.
Answers
Answer:
The probability plot of this distribution shows that it is approximately normally distributed..
Check explanation for the reasons.
Step-by-step explanation:
The complete question is attached to this solution provided.
From the cumulative probability plot for this question, we can see that the plot is almost linear with no points outside the band (the fat pencil test).
The cumulative probability plot for a normal distribution isn't normally linear. It's usually fairly S shaped. But, when the probability plot satisfies the fat pencil test, we can conclude that the distribution is approximately linear. This is the first proof that this distribution is approximately normal.
Also, the p-value for the plot was obtained to be 0.541.
For this question, we are trying to check the notmality of the distribution, hence, the null hypothesis would be that the distribution is normal and the alternative hypothesis would be that the distribution isn't normal.
The interpretation of p-valies is that
When the p-value is greater than the significance level, we fail to reject the null hypothesis (normal hypothesis) and but if the p-value is less than the significance level, we reject the null hypothesis (normal hypothesis).
For this distribution,
p-value = 0.541
Significance level = 0.05 (Evident from the plot)
Hence,
p-value > significance level
So, we fail to reject the null or normality hypothesis. Hence, we can conclude that this distribution is approximately normal.
Hope this Helps!!!
The dimensions of a closed rectangular box are measured as 96 cm, 58 cm, and 48 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.
Answers
Answer:
161.6 cm²Step-by-step explanation:
Surface Area of the rectangular box = 2(LW+LH+WH)
L is the length of the box
W is the width of the box
H is the height of the box
let dL, dW and dH be the possible error in the dimensions L, W and H respectively.
Since there is a possible error of 0.2cm in each dimension, then dL = dW = dH = 0.2cm
The surface Area of the rectangular box using the differentials is expressed as shown;
S = 2{(LdW+WdL)+(LdH+HdL)+(WdH+HdW)]
Also given L = 96cm W = 58cm and H = 48cm, on substituting this given values and the differential error, we will have;
S = 2{(96*0.2+58*0.2) + (96*0.2+48*0.2)+(58*0.2+48*0.2)}
S = 2{19.2+11.6+19.2+9.6+11.6+9.6}
S = 2(80.8)
S = 161.6 cm²
Hence, the surface area of the box is 161.6 cm²
The length of a rectangle is 5M more than twice the width and the area of the rectangle is 63M to find the dimension of the rectangle
Answers
Answer:
width = 4.5 m
length = 14 m
Step-by-step explanation:
okay so first you right down that L = 5 + 2w
then as you know that Area = length * width so you replace the length with 5 + 2w
so it's A = (5 +2w) * w = 63
then 2 w^2 + 5w - 63 =0
so we solve for w which equals 4.5 after that you solve for length : 5+ 2*4.5 = 14
Use the Laplace transform to solve the given initial-value problem.
y' + 3y = f(t), y(0) = 0
where f(t) = t, 0 ≤ t < 1 0, t ≥ 1
Answers
Answer:
The solution to the given Initial - Value - Problem is [tex]y(t) = \frac{-1}{9} + \frac{1}{3}t + \frac{1}{9}e^{-3t} - [\frac{-1}{9} + \frac{1}{3}t - \frac{2}{9}e^{-3(t-1)}]u(t-1)[/tex]
Step-by-step explanation:
y' + 3y = f(t).................(1)
f(t) = t when 0 ≤ t < 1
f(t) = 0 when t ≥ 1
Step 1: Take the Laplace transform of the LHS of equation (1)
That is L(y' + 3y) = sY(s) + 3Y(s) = Y(s)[s + 3]..............(*)
Step 2: Get an expression for f(t)
For f(t) = t when 0 ≤ t < 1
f₁(t) = t (1 - u(t - 1)) ( there is a time shift of the unit step)
For f(t) = 0 when t ≥ 1
f₂(t) = 0(u(t-1))
f(t) = f₁(t) + f₂(t)
f(t) = t - t u(t-1)................(2)
Step 3: Taking the Laplace transform of equation (2)
[tex]F(s) = \frac{1}{s^2} - e^{-s} ( \frac{1}{s^2} + \frac{1}{s})[/tex]...............(**)
Step 4: Equating * and **
[tex]Y(s) [s + 3]=\frac{1}{s^2} - e^{-s} ( \frac{1}{s^2} + \frac{1}{s}) \\Y(s) = \frac{1}{s^2(s+3)} - e^{-s} ( \frac{1}{s^2(s+3)} + \frac{1}{s(s+3)})[/tex].......................(3)
Since y(t) is the solution we are looking for we need to find the Inverse Laplace Transform of equation (3) by first breaking every fraction into partial fraction:
[tex]\frac{1}{s^2 (s+3)} = \frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)}[/tex]
[tex]\frac{1}{s (s+3)} = \frac{1}{3s} + \frac{1}{3(s+3)}[/tex]
We can rewrite equation (3) by representing the fractions by their partial fractions.
[tex]Y(s) = \frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)} - e^{-s} [\frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)} + \frac{1}{3s} + \frac{1}{3(s+3)}]\\Y(s) = \frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)} - e^{-s}[\frac{2}{9s} + \frac{1}{3s^2} - \frac{2}{9(s+3)}][/tex]................(4)
step 5: Take the inverse Laplace transform of equation (4)
[tex]y(t) = \frac{-1}{9} + \frac{1}{3}t + \frac{1}{9}e^{-3t} - u(t-1)[\frac{2}{9} + \frac{1}{3}(t-1) - \frac{2}{9}e^{-3(t-1)}][/tex]
Simplifying the above equation:
[tex]y(t) = \frac{-1}{9} + \frac{1}{3}t + \frac{1}{9}e^{-3t} - [\frac{-1}{9} + \frac{1}{3}t - \frac{2}{9}e^{-3(t-1)}]u(t-1)[/tex]
The Laplace transform is use to solve the differential equation problem.
The solution for the given initial-value problem is,
[tex]y(t)=\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{1}{9}e^-3t-\left[\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{2}{9}e^{-3(t-1)}\right]u(t-1)[/tex]
Given:
The given initial value problem is [tex]y' + 3y = f(t)[/tex].
Consider the left hand side of the given equation.
[tex]y'+3y[/tex]
Take the Laplace transform.
[tex]L(y' + 3y) = sY(s) + 3Y(s) \\L(y' + 3y) = Y(s)[s + 3][/tex]
Consider the right hand side and get the expression for [tex]f(t)[/tex].
[tex]f(t) = t[/tex] when 0 ≤ t < 1
From time shift of the unit step
[tex]f_1(t) = t (1 - u(t - 1))[/tex]
For f(t) = 0 when t ≥ 1
Now,
[tex]f_2(t) = 0(u(t-1))f(t) = f_1(t) + f_2(t)f(t) = t - t u(t-1)[/tex]
Take the Laplace for above expression.
[tex]F(s)=\dfrac{1}{s^2}-e^{-s}\left(\dfrac{1}{s^2}+\dfrac{1}{s}\right)[/tex]
Now, the equate the above two equation.
[tex]Y(s)\left[s+3\right ]=\dfrac{1}{s^2}-e^{-s}\left(\dfrac{1}{s^2}+\dfrac{1}{s}\right)\\Y(s)=\dfrac {1}{(s^2(s+3))}-e^{-s}\left(\dfrac{1}{(s^2(s+3))}+\dfrac{1}{s(s+3)\right)}[/tex]
Find the inverse Laplace for the above equation.
[tex]\dfrac{1}{(s^2(s+3))}=\dfrac{-1}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}\\\dfrac{1}{(s(s+3))}=\dfrac{1}{3s}+\dfrac{1}{3(s+3)}[/tex]
Calculate the partial fraction of above equation.
[tex]Y(s)=\dfrac{-1}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}-e^{-s}\left[\dfrac{-1}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}+\dfrac{1}{3s}+\dfrac{1}{3(s+3)}\right]\\Y(s)=\dfrac{2}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}-e^{-s}\left[\dfrac{2}{9s}+\dfrac{1}{3s^2}-\dfrac{2}{9(s+3)}\right][/tex]
Take the inverse Laplace of the above equation.
[tex]y(t)=\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{1}{9}e^-3t-\left[\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{2}{9}e^{-3(t-1)}\right]u(t-1)[/tex]
Thus, the solution for the given initial-value problem is,
[tex]y(t)=\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{1}{9}e^-3t-\left[\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{2}{9}e^{-3(t-1)}\right]u(t-1)[/tex]
Learn more about what Laplace transformation is here:
https://brainly.com/question/14487937