Answer:
The speed of the airplane is 300 miles per hour.
Step-by-step explanation:
Let consider that plane travels at constant speed, which is the sum of the velocity of the plane in still air (velocity of the plane relative to wind) and the velocity of the wind. Hence, the total time spent by the plane is described by following kinematic formula:
[tex]t = s\cdot \left(\frac{1}{v_{P}-v_{W}}+\frac{1}{v_{P}+v_{W}} \right)[/tex] (1)
Where:
[tex]t[/tex] - Total time, in hours.
[tex]s[/tex] - Distance between Los Angeles and San Jose, in miles.
[tex]v_{P}[/tex] - Velocity of the plane in still air, in miles per hour.
[tex]v_{W}[/tex] - Velocity of the wind, in miles per hour.
Then, we proceed to simplify the formula and clear the speed of the plane in still air:
[tex]\frac{t}{s} = \frac{2\cdot v_{P}}{v_{P}^{2}-v_{W}^{2}}[/tex]
[tex]\left(\frac{t}{s}\right)\cdot (v_{P}^{2}-v_{W}^{2}) = 2\cdot v_{P}[/tex]
[tex]\left(\frac{t}{s} \right)\cdot v_{P}^{2} - 2\cdot v_{P}- \left(\frac{t}{s} \right)\cdot v_{W}^{2} = 0[/tex]
Which is a Second Order Polynomial, whose roots can be found analytically by Quadratic Formula. If we know that [tex]t = 2\,h[/tex], [tex]s = 288\,mi[/tex] and [tex]v_{W} = 60\,\frac{mi}{h}[/tex], then we have the following polynomial:
[tex]\frac{1}{144}\cdot v_{P}^{2}-2\cdot v_{P} -25 = 0[/tex]
The two roots associated with this polynomial are, respectively:
[tex]v_{P,1} = 300\,\frac{mi}{h}[/tex], [tex]v_{P,2} = -12\,\frac{mi}{h}[/tex]
Since speed is the magnitude of velocity, then solution must be positive. First root satisfies all these conditions.
In a nutshell, the speed of the airplane is 300 miles per hour.
2. Use the distributive property to write an expression that is equivalent to 12 + 4x.
Answer:
4(x+3)
Step-by-step explanation:
So with the distrubutive property, you look at the numbers you have, and then take the greatest common factor between the two.
So lets think about it, what goes into both 12 and 4?
2 does, but is that the greatest common factor? No.
What about 4? That goes into 12 and 4. Is it the greatest common factor? Yup it is.
So, what do we get when we take 4 from 4x? We get 1x, or just x.
How about 12? Well, when we take 4 from 12, we get 3.
Now, lets take the common greatest factor, and our two new numbers and put them back into the expression.
Remember that the greatest common factor, the one you took from the other numbers, is what goes first:
4()
Remember to put the parethese there, or else you would only be multiplying the first number by 4, and not the second.
Next lets put the other numbers in. In most expressions, you should put the x number in first, and the normal number in second. So it should now be:
4(x+3)
This is your expression.
Hope this helps! ;)
9514 1404 393
Answer:
4(3 +x)
Step-by-step explanation:
The greatest common factor is 4, so any divisor of that can be factored out:
12 +4x = 2(6 +2x) = 4(3 +x)
Solve the equation 23+n=29 using the inverse operation.
Answer:
n=6
Step-by-step explanation:
i used math-way :P
2. Which of the following congruence statements is true?
(A) A = B
(B) CE = DE
(C) AED = CEB
(D) AED = BEC
GEOMETRY
Answer:
D)
hope it helps..........
Answer:
D is the correct answer
hope it is helpful to you ☺️☺️☺️
Jack has a bag of coins. The bag
contains 8 dimes, 4 nickels, 3
pennies, and 1 quarter. He will
randomly select 2 coins from the bag
at one time without replacement
What is the probability that Jack will
select 2 dimes?
a. 15/23
b. 7/30
c. 5/9
d. 1/2
Answer:
i think 1 half sorry if i am wrong
Step-by-step explanation:
which is equivalent to 3/8^1/4? 8^3/4
A.10
B.6
C.5
D.2
Answer:
B I'm pretty sure..............
Can someone help me? I am stuck on this question I would mean the world if u helped me! and tysm for the people who helped me!
Answer:
$10.10
Step-by-step explanation:
0.25 × 27 = 6.75
0.10 × 26 = 2.60
0.05 × 15 = 0.75
6.75 + 2.60 + 0.75 = $10.10
please help again once again 10 POINTS AND 15!
40 cubic units, just count them my guy
you got a chunk of 32 and a chunk that's 8
Find the area of the composite figure.
Answer:
B. [tex] 200.5 \: {m}^{2} [/tex]
Step-by-step explanation:
Area of the composite figure = Area of square with side length 12 m + Area of semicircle with radius (12/2= 6) 6 m
[tex] = {(12)}^{2} + \frac{1}{2} \pi {r}^{2} \\ \\ = 144 + \frac{1}{2} \times 3.14(6)^{2} \\ \\ = 144 + \frac{1}{2} \times 3.14 \times 36 \\ \\ = 144 + 56.52 \\ \\ = 200.52 \: {m}^{2} \\ \\ \approx \: 200.5 \: {m}^{2} [/tex]
Solve the following inequality.
-4x + 5 2 25 + 6x
A. X2
B. XS2
C. XS-2
OD. XX-2
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
Answer:
Step-by-step explanation:
Solve the system of equations
x + y = 24 both sides times 3 3x + 3y = 72
3x + 5y = 100
3x + 3y = 72 subtract the bottom equation from the top one
0x + 2y = 28
y = 14 five point questions 70 points
x + 14 = 24 the first equation with y set to 14
x = 10 three point questions 30 points
Find the total amount due on a loan of $650 at the annual simple interest rate 5% at the
end of 6 months
Answer:
$666.25
Step-by-step explanation:
Use the equation A = P(1 + rt)
P=16.25
$650+$16.25=666.25
Which vector below goes from (0,0) to (2,2)?
A. c
B. a
C. b
D. d
Answer:
i say it's A.c
I hope it helped
The volume of this rectangular prism is 53.72 cubic centimeters . what is the value of y?
Answer:
y = 1.7 cm
Step-by-step explanation:
V= lwh
w = [tex]\frac{V}{lh}[/tex] = [tex]\frac{53.72 cubic centimeters}{4cm(7.9cm)}[/tex] = 1.7 cm
Are 5x + 9 - 2x = 12 and 3x = 3 equivalent equations
Answer:
Yes
Step-by-step explanation:
If you simplify the 1st equation,
5x + 9 - 2x = 12
Add like terms
3x + 9 = 12
Subtract the 9 from both sides
3x = 3
It gives you the same equation as the other one
Answer:
yes they both equal 1
Step-by-step explanation:
2 1/6* 2 5/6 IN SIMPLEST FORM
Answer:
6 5/36
Step-by-step explanation:
MARK ME BRAINLIEST?
Which prism has the largest surface area?
Answer: a
Step-by-step explanation:
Link= REPORT
Х
5 ft.
8 ft. M
24 ft.
(A) 13
(B) 15
(C) 17
(D) 11
Please someone help!!
Answer:
I think the answer is c
explanation:
Ethan rolls the number cube and then spins the arrow on the
spinner. A list of all the possible outcomes is shown.
Answer:
B 1/2
Step-by-step explanation:
This is right
The probability that the sum of the two numbers is odd, given that the product is 6 will be 2/3. Option C is correct.
What is probability?Probability is synonymous with possibility. It is concerned with the occurrence of a random event. Probability can only have a value between 0 and 1.
Ethan cranks the arrow on the spinner after rolling the number cube. There is a list of all conceivable outcomes.
{(1, 1), (1, 2), (1,3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4,1),(4,2), (4,3), (5, 1), (5,2), (5,3), (6, 1), (6,2), (6,3)}
The no of sets having the sum of the number is odd=9
The no of sets having the product of the number is 6=3
The total number including the two conditions=3+9=12
Probability is found as;
P=12/18
P=2/3
The probability that the sum of the two numbers is odd, given that the product is 6 will be 2/3.
Hence, option C is correct.
To learn more about probability, refer to the link;
https://brainly.com/question/795909
#SPJ2
The front view of a square pyramid is in the shape of a triangle that
has a base of 30 yards and a height of 40 yards. What is the area
of the front view of the square pyramid?
600 sq yards
0 1200 square yards
250 yards
600 yards
Answer:
600 sq yards
Step-by-step explanation:
font view as in on triangle
30*40/2 = 600
B*H/2 = area of triangle
What is the distance between the points (4, 9) and (4, 2)? A) 2 B) 5 C) 7 D) 8
Answer:
The answer is 7
Step-by-step explanation:
I took the test and failed it cuz I put 5. Don't listen to that other dude. So I know what I'm talking about. Just listen to me and you won't fail.
Beginning at 8:30 A.M., tours of the National Capitol and
the White House begin at a tour agency. Tours for the
National Capitol leave every 15 minutes. Tours for the
White House leave every 20 minutes.
a) How often do the tours leave at the same time?
b) When is the next time the two tours will leave at
the same time?
Answer:
Step-by-step explanation:
if both tours start at 8:30 A.M, the NC (National Capitol) 8:45, and the WH (White House) leaves at 8:50.
NC
08:45 08:50
09:00 09:10
09:15 09:30
09:30 09:50
09:45 10:10
10:00 10:30
10:15 10:50
10:30 11:10
10:45
11:00
Both tours leave at 9:30, and then away at 10:30.
They leave at the same time every hour.
A special CPI is constructed to measure the variation of these products, so that coffee and bread have a weight of 0.35 of the total and egg, ham and cheese 0.1 of the total. variation of the CPI?
9514 1404 393
Answer:
The CPI increased 3.42% in Month 2.
Step-by-step explanation:
In a spreadsheet, the weighted sum is easily computed using the SUMPRODUCT( ) function. It multiplies the corresponding values of two arrays, then returns the sum of those products. If one of the values is a weight, then the result is a weighted sum.
Your CPI is computed as the weighted sum of the prices of the individual products. The percentage change is computed in the usual way:
pct change = ((new value)/(old value) -1) × 100%
Of course, the spreadsheet can format a fraction as a percentage, so the computation of the change can stop after 1 is subtracted from the ratio.
In a survey of 12 people, it was found that an average of $36 was spent on their child's last birthday gift with a standard deviation of $11. Estimate the mean amount people spend on their child's last birthday gift with 80% confidence using the appropriate critical value to three decimal places. Enter your answer as equations or as numbers rounded to four decimal places.
Answer:
(27.3692 ; 44.6308)
Step-by-step explanation:
Mean, xbar = 36
Standard deviation, s = 11
Sample size, n = 12
Tcritical at 0.2, df = 12 - 1 = 11 ; Tcritical = 2.718
Confidence interval :
Xbar ± Margin of error
Margin of Error = Tcritical * s/sqrt(n)
Margin of Error = 2.718 * 11/sqrt(12) = 8.6308
Confidence interval :
Lower boundary : 36 - 8.6308 = 27.3692
Upper boundary : 36 + 8.6308 = 44.6308
(27.3692 ; 44.6308)
if the area is 48 square meters what is the length of side R in meter
Answer:
12 m
Step-by-step explanation:
the area of a rectangle is length x width
we know the width, so we can proceed like this:
Lenght = A/width
Lenght = 48/4 = 12 m
can some help me plz I will give the brainlist
Answer:
A-0.125
B-15%
C- I think .15 would
Step-by-step explanation:
Sorry if i am incorrect
Answer:
A=.125
B=.14
Step-by-step explanation:
C=.15 would give him more candy.
Car A travels 18 miles every 20 minutes. Car B travels 13 miles every 12 minutes. Which statement best compares how far the two cars can travel in an hour?
Answer:
The answer is C) car b travels 11 more miles than car a in one hour
Step-by-step explanation:
Car A: 18/20(60)=54 mph
Car B: 13/12(60) = 65 mph
So car b travels 11 more miles than car a in one hour
Cambridge slim ate 11 sausages in the first 6 minutes of a high stakes eating contest assuming that he conuitnes at the same pace how many sausgaes would he have eaten by the end of the 15 minute contest
Cory has $24 more than twice as much as Stan. Together they have $150. How much money dose each have ?
Answer:
99 and 51
Step-by-step explanation:
a. Estimate Kevin rode 30 km in 2 hours. At that rate, how long would it take him to ride 75 km? Estimate an answer. Then use a case 1-case 2 ratio box to solve this problem.
Label each fifth on the number line. )
2.
3
4
2.
1
2
3
4
3
4
5
5
5
5
5
5
5
5
5
5
5
1
2
3
4
5
6
7
8.
0
Enter
Step-by-step explanation:
1 for 0/5
2 for 1/5
4 for 2\5
4 for 3\5
4 for 4\5
12 for 5\5
1 for 6\5
1 for 7\5
1 for 8\5
