A 1/17th scale model of a new hybrid car is tested in a wind tunnel at the same Reynolds number as that of the full-scale prototype. The drag coefficient of the model is the same as that of the prototype. Assuming the model and prototype are both tested in air, find the ratio of the drag on the scale model (Fm) to the drag on the prototype (Fp), i.e., Fm/Fp. Since the size of the model is 1/17th of the size of the prototype, the projected area of the model is (1/17)2 of the projected area of the prototype. Round your answer to the nearest tenth.
Answer:
The ratio of the drag coefficients [tex]\dfrac{F_m}{F_p}[/tex] is approximately 0.0002
Step-by-step explanation:
The given Reynolds number of the model = The Reynolds number of the prototype
The drag coefficient of the model, [tex]c_{m}[/tex] = The drag coefficient of the prototype, [tex]c_{p}[/tex]
The medium of the test for the model, [tex]\rho_m[/tex] = The medium of the test for the prototype, [tex]\rho_p[/tex]
The drag force is given as follows;
[tex]F_D = C_D \times A \times \dfrac{\rho \cdot V^2}{2}[/tex]
We have;
[tex]L_p = \dfrac{\rho _p}{\rho _m} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_m} \right)^2 \times L_m[/tex]
Therefore;
[tex]\dfrac{L_p}{L_m} = \dfrac{\rho _p}{\rho _m} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_m} \right)^2[/tex]
[tex]\dfrac{L_p}{L_m} =\dfrac{17}{1}[/tex]
[tex]\therefore \dfrac{L_p}{L_m} = \dfrac{17}{1} =\dfrac{\rho _p}{\rho _p} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_p} \right)^2 = \left(\dfrac{V_p}{V_m} \right)^2[/tex]
[tex]\dfrac{17}{1} = \left(\dfrac{V_p}{V_m} \right)^2[/tex]
[tex]\dfrac{F_p}{F_m} = \dfrac{c_p \times A_p \times \dfrac{\rho_p \cdot V_p^2}{2}}{c_m \times A_m \times \dfrac{\rho_m \cdot V_m^2}{2}} = \dfrac{A_p}{A_m} \times \dfrac{V_p^2}{V_m^2}[/tex]
[tex]\dfrac{A_m}{A_p} = \left( \dfrac{1}{17} \right)^2[/tex]
[tex]\dfrac{F_p}{F_m} = \dfrac{A_p}{A_m} \times \dfrac{V_p^2}{V_m^2}= \left (\dfrac{17}{1} \right)^2 \times \left( \left\dfrac{17}{1} \right) = 17^3[/tex]
[tex]\dfrac{F_m}{F_p} = \left( \left\dfrac{1}{17} \right)^3[/tex]= (1/17)^3 ≈ 0.0002
The ratio of the drag coefficients [tex]\dfrac{F_m}{F_p}[/tex] ≈ 0.0002.
AB = 5, AP = 4, and DP = 12, then find the length of PC
Answer:
[tex]PC = 0.333[/tex]
Step-by-step explanation:
Given
[tex]AB = 5[/tex]
[tex]AP = 4[/tex]
[tex]DP =12\\[/tex]
See attachment
Required
Find PC
When two chords intersect, the product of the segments are always equal.
In chord DC, the segments are DP and PC
In chord AB, the segments are AP and PB
So:
[tex]DP * PC = AP * PB[/tex]
This gives:
[tex]12 * PC = 4 * PB[/tex] --- (1)
In chord AB, we have:
[tex]AB = AP + PB[/tex]
Make PB the subject
[tex]PB = AB - AP[/tex]
This becomes
[tex]PB = 5 - 4[/tex]
[tex]PB = 1[/tex]
[tex]12 * PC = 4 * PB[/tex] --- (1) becomes
[tex]12 * PC = 4 * 1[/tex]
[tex]12 * PC = 4[/tex]
Make PC the subject
[tex]PC = \frac{4}{12}[/tex]
[tex]PC = 0.333[/tex]
what's the distance between (-9,-6) and (-2,-2)
Answer:
the distance formula is square root (x2-x1)^2 + (y2-y1)^2
7^2 + 4^2 = 49+16 = 65
squarroot of 65 = 8.06
Step-by-step explanation:
Step-by-step explanation:
The distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]. I don't provide answers for problems like these but will give the equations.
What is the equation of the following line?
Answer:
Answer is F. y = 6x
Step-by-step explanation:
simplify 3 times x² times y times 4z times x times 2y times z
Answer:
3(x^2 x Y)(4z x X)(2y x Z)
Step-by-step explanation:
Answer:
[tex]3(x^{3} * 2y^2*4z^2)[/tex]
Step-by-step explanation:
x^2(x) = x^3
2y(y) = 2y^2
4z(z) = 4z^3
Multiple it all by 3
3.294e6 standard form
Answer:
3.294
Step-by-step explanation:
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest inch, how many inches are in 8 meters?
Answer:
314.96in
Step-by-step explanation:
Will give the brainliest answer and 20 points to anyone who can give a complete answer and not a scam link or a joke answer or begging for points (those 3 types of answers will be reported)
Courtney and Christy both leave the coffee shop at the same time, but in opposite directions. If Christy travels 9 mph faster than Courtney and after 7 hours they are 189 miles apart, how fast is each traveling?
Courtney is traveling ___________ mph.
Christy is traveling _____________ mph.
Answer:
Courtney is travelling at 9mph
Christy is travelling at 18mph
Step-by-step explanation:
Courtney's speed = x
Christy's speed = y
Christy travels 9 mph faster than Courtney: x+9=y
Distance = speed * time
Courtney's distance after 7 hours = 7x
Christy's distance after 7 hours = 7y
After 7 hours, they're 189 miles apart:
7x+7y=189
x+y=27
x+y=27
x+x+9=27
2x=18
x=9
y=x+9
y=9+9
y=18
What is the area of the parallelogram?
Answer:
im not 100 percent sure but i think its
140 inches squared
Step-by-step explanation:
Please explain step by step I dont get it.
Answer: B
Step-by-step explanation:
108 divide by 54 = 2
That equation means she paid 2 dollars per ticket, not 1 dollar for 2 tickets
(There is no 1 in the equation also)
Find all the missing elements : C=120degrees
b= 5
c=11
Answer:
A = 36.8°
B = 23.2°
a = 7.6
Step-by-step explanation:
Given:
C = 120°
b = 5
c = 11
Required:
Find A, B, and a.
Solution:
✔️To find B, apply the Law of Sines
[tex] \frac{sin(B)}{b} = \frac{sin(C)}{c} [/tex]
Plug in the values
[tex] \frac{sin(B)}{5} = \frac{sin(120)}{11} [/tex]
Cross multiply
Sin(B)*11 = sin(120)*5
Divide both sides by 11
[tex] sin(B) = \frac{sin(120)*5}{11} [/tex]
[tex] sin(B) = \frac{sin(120)*5}{11} [/tex]
Sin(B) = 0.3936
B = [tex] sin^{-1}(0.3936) [/tex]
B = 23.1786882° ≈ 23.2° (nearest tenth)
✔️Find A:
A = 180° - (B + C) (sum of triangle)
A = 180° - (23.2° + 120°)
A = 36.8°
✔️To find a, apply the Law of sines:
[tex] \frac{sin(A)}{a} = \frac{sin(B)}{b} [/tex]
Plug in the values
[tex] \frac{sin(36.8)}{a} = \frac{sin(23.2)}{5} [/tex]
Cross multiply
a*sin(23.2) = 5*sin(36.8)
Divide both sides by sin(23.2)
[tex] a = \frac{5*sin(36.8)}{sin(23.2) [/tex]
a = 7.60294329 ≈ 7.6 (nearest tenth)
Nettlefield primary school have you heard
Answer:
No, I have not heard. Give me brainliest plz, I neeeeeeeeeeed it to level up
Step-by-step explanation:
How many odd numbers are between 10 and 50?
Answer: 19 odd numbers: 11 , 13, 15, 17 , 19, 23, 25, 27, 29, 31, 33 , 35, 37, 39, 41, 43, 45, 47, 49
Hope that helped! :)
Solve for x:
2x + 9 = 3
Answer:
x = -3
Step-by-step explanation:
2x + 9 = 3
2x = 3 - 9
2x = -6
x = -3
Answer:
- 3
Step-by-step explanation:
given
2x + 9 = 3
2x = 3 - 9
2x = - 6
x = - 6/2
x = - 3
hope it helps :)
NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6. In an earlier study, the population proportion was estimated to be 0.3 . How large a sample would be required in order to estimate the fraction of people who black out at 6 or more Gs at the 80% confidence level with an error of at most 0.03
Answer:
A sample of 383 would be required.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In an earlier study, the population proportion was estimated to be 0.3.
This means that [tex]\pi = 0.3[/tex]
80% confidence level
So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].
How large a sample would be required in order to estimate the fraction of people who black out at 6 or more Gs at the 80% confidence level with an error of at most 0.03?
A sample of n is needed.
n is found when M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.28\sqrt{\frac{0.3*0.7}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.28\sqrt{0.3*0.7}[/tex]
[tex]\sqrt{n} = \frac{1.28\sqrt{0.3*0.7}}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.28\sqrt{0.3*0.7}}{0.03})^2[/tex]
[tex]n = 382.3[/tex]
Rounding up:
A sample of 383 would be required.
The management of KSmall Industries is considering a new method of assembling a computer. The current assembling method requires a mean time of 66 minutes with a standard deviation of 3.0 minutes. Using the new method, the mean assembly time for a random sample of 24 computers was 61 minutes.
a. Using the 0.10 level of significance, can we conclude that the assembly time using the new method is faster?
b. What is the probability of a Type II error? (Round "Critical values" to 2 decimal places and round your final answer to 4 decimal places.)
Answer:
Part a:
Since the calculated z= 8.1649 falls in the critical region z < ± 1.28 we reject H0 and conclude that the assembly time using the new method is faster.
Part b:
P (Type II Error)= 0.6628
Step-by-step explanation:
The null and alternate hypothesis are
H0: μ1 ≥ μ2 against the claim Ha: μ1 < μ2
This is left tailed test
The critical region for this test at 0.10 ∝ is z < ± 1.28
The test statistic
z= x1-x2/ s/√n
z= 66-61/ 3/√24
z= 5/0.61238
z= 8.16486
Since the calculated z= 8.1649 falls in the critical region z < ± 1.28 we reject H0 and conclude that the assembly time using the new method is faster.
Part b:
P (Type II Error) = P ( accept H0/ H0 is false)
z ( ∝)= X-u/s/√n
1.28= X-61/0.61238
X= 61.7838
So I will incorrectly fail to reject the null as long as a draw a sample mean that greater than 61.7838
The probability of a Type II error is given by
P (z> 61.7838-66/24)
P (z>- 0.42161)
From the tables
P (z>- 0.42161)= 0.6628
The groundhog population of Punxsutawny, Pennsylvania is closely monitored each year. Two years ago the population decreased by 12%. Last year the number of groundhogs increased by 6%. This year the population also increased by 9%. What was the percentage increase/decrease of groundhogs over these three years? Round your answer to the nearest tenth of a percentage poin
Answer:
There was a increase of 1.7% over these three years
Step-by-step explanation:
Multipliers:
For a decrease of a%, we multiply by: [tex]\frac{100-a}{100}[/tex]
For a increase of a%, we multiply by: [tex]\frac{100+a}{100}[/tex]
What was the percentage increase/decrease of groundhogs over these three years?
Decrease of 12%(multiplication by 0.88).
Increase of 6%(multiplication by 1.06).
Increase of 9%(multiplication by 1.09).
After these three years:
0.88*1.06*1.09 = 1.017
1.017 - 1 = 0.017
0.017*100% = 1.7%
There was a increase of 1.7% over these three years
I NEED HELPPP
PLEASEEEEEEEEEEEEEE
Find mean & margin of error if 28.4 < µ < 38.8
Answer:
The mean is of 33.6
The margin of error is of 5.2.
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
In this question:
Lower bound: 28.4
Upper bound: 38.8
Mean
(28.4+38.8)/2 = 33.6.
The mean is of 33.6
Margin of error:
(38.8 - 28.4)/2 = 5.2
The margin of error is of 5.2.
ted is twice his sister's age and three years younger than joe. ted's sister is half of a century plus ten. how old is ted how old is ted's sister
Answer:
120, 60
Step-by-step explanation:
half a century = 60 + 10 x 2 = ted.
she is 60.
Solve the equation below.
Answer:
D
Step-by-step explanation:
Just divide by 2/3
Help pleaseeeeeeeeeeee
Answer:
3Step-by-step explanation:
When looking at a graph, the greatest speed will be the steepest part. Even though one line is further than another, does not mean it is faster.
Find the Perimeter of this figure. I do y get it
Answer:
56m
Step-by-step explanation:
5+7+5+11+7+16+5
= 56
Use the remainder theorem to determine which of the following is not a factor of x^3-5x^2-x+5
Answer:
The answer is A
Step-by-step explanation:
x to the power of 1 is the lowest x and when you multiply -5 and -5 you get 5 so the answer is A.
The dot plot below shows the number of movies rented last month by students in Ms. Underwood's class.
What is the median number of movies rented?
A.
4
B.
6
C.
3
D.
2
Answer:
the answer gonna be 3
Answer: I the answer is 3 100%
Step-by-step explanation: I took the test
What do those emojis mean in words?
The dot plots show the numbers of children’s books purchased by customers at two different bookstores on one day.
Which statement is supported by the information in the dot plots?
A) The mean of the data for Store 1 is greater than the mean of the data for Store2
B) The mode of the data for Store 2 is greater than the mode of the data for Store1
C) The median of the data for Store 2 is greater than the median of the data for Store1
D) The range of the data for Store 1 is greater than the range of the data for Store2
Answer:
A
Step-by-step explanation:
since mean is the most annoying to calculate I went through and did everything else, the range is the same as both charts go 0-6. The median is is the middle number which means store 1 has a higher number of 3' s but our option says store 2 is greater and B is the mode, the number that shows up the most.
Evaluate the piecewise function when x = -1.
Step-by-step explanation:
-2<-1<1, so f(-1)=-1-2=-3
measure of each exterior angle of a regular 30-gon?
7. An exterior angle of a regular polygon measures 22.5°. How many sides does it have?
8. An interior
Answer:
I'm not sure would love to help but dont know the answer
Can someone help me with this problem please. ( I need it as fast as possible).
Answer:
D-B-A-C
Step-by-step explanation: