Plane A leaves Tulsa at 2:00 p.m., averaging 300 mph and flying in a northerly direction. Plane B leaves Tulsa at 2:30 p.m., averaging 225 mph and flying due east. At 5:00 p.m., how far apart will the planes be?
Answers
Answer 1061
Step-by-step explanation:
Answer:
At 5:00 p.m. the planes will be [tex]1061.323[/tex] miles apart.
Step-by-step explanation:
To solve this problem, I add a picture of the situation.
We know that speed is distance over time ⇒
[tex]Speed=\frac{distance}{time}[/tex] (I)
The first step to solve this exercise is to graph the situation. We can draw a right triangle which vertices will be ''Tulsa'', and the planes ''A'' and ''B'' at 5:00 p.m.
In order to know the measures of the sides, we are going to calculate them using the equation (I)
Plane A leaves Tulsa at 2:00 p.m.
Therefore, at 5:00 p.m. it will have flown 3 hours ⇒
[tex]300\frac{mi}{h}=\frac{distance}{3h}[/tex] ⇒
[tex]distance=(300\frac{mi}{h}).(3h)[/tex]
[tex]distance=900mi[/tex]
At 5:00 p.m. the distance from the plane A to Tulsa is 900 mi
Plane B leaves Tulsa at 2:30 p.m.
Therefore, at 5:00 p.m. it will have flown 2.5 hours ⇒
[tex]225\frac{mi}{h}=\frac{distance}{2.5h}[/tex]
[tex]distance=(225\frac{mi}{h}).(2.5h)[/tex]
[tex]distance=562.5mi[/tex]
At 5:00 p.m. the distance from the plane B to Tulsa is 562.5 mi
Finally, we can find the distance between the plane A and the plane B using the Pythagorean theorem :
[tex](900mi)^{2}+(562.5mi)^{2}=(Distance_{A-B})^{2}[/tex]
[tex]810000mi^{2}+316406.25mi^{2}=(Distance_{A-B})^{2}[/tex]
[tex](Distance_{A-B})^{2}=1126406.25mi^{2}[/tex]
[tex]Distance_{A-B}=\sqrt{1126406.25mi^{2}}[/tex]
[tex]Distance_{A-B}=1061.322877mi[/tex] ≅ [tex]1061.323mi[/tex]
At 5:00 p.m. the planes will be 1061.323 miles apart.
Related Questions
Find the simple interest on a $2,219 principal, deposited for six years at a rate of 5.11%
Answers
hope this helped!
When invested at an annual rate of 5%, an amount earned Php 15,000.00 of simple interest in 2 years. How much money was initially invested?
Answers
r = 8% = 0.05, simple interest rate
t = 2 years, duration
A = 15,000.00, value after 2 years
Let P = principal, the amount invested.
Then
P(1+ 2*0.05) = 15000
P = 15000/1.1 = 13636.36
Answer: Php 13,636.36
A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s average speed in miles per hour? Show your work.
Answers
60 seconds per minute, 60 minutes per hour
60*60 = 3600 seconds per hour
5280 feet per mile
300/5280 = 0.0568 of a mile
2.92/3600 = 0.000811 of an hour
0.0568 / 0.000811 = 70.028 miles per hour
round to 70 miles per hour
What is the intersection of the sets A = {2, 3, 5, 7, 11} and B = {5, 11, 13, 15, 17}?
Answers
The intersection of sets is composed of the common elements.
The given sets have two common elements: 2 and 5.
{2;3;5;7}∩{2;5;11;13}={2;5}
Answer:
A ∩ B = {5, 11}
Step-by-step explanation:
Hello, the intersection of two sets A and B (A B), is the set that contains all elements of A that also belong to B , I mean , the common elements
Step 1
Let
A = {2, 3, 5, 7, 11}
B = {5, 11, 13, 15, 17}
you have to verify the common elements, first order the data from least to greatest to make it easier, here they are already sorted
A ∩ B = {5, 11}
Have a great day
Which expression is equal to 2−√ 32 ?
8i√2
−8√2
8√2i
−8i√2
Answers
Answer:
A. [tex]8i\sqrt{2}[/tex]
Step-by-step explanation:
We have been given a radical expression [tex]2\sqrt{-32}[/tex]. We are asked to find equivalent expression to our given expression.
Using radical rule [tex]\sqrt{-a}=\sqrt{-1}\cdot \sqrt{a}[/tex], we can write [tex]\sqrt{-32}[/tex] as product of [tex]\sqrt{-1}\cdot\sqrt{32}[/tex].
[tex]2\sqrt{-32}=2\cdot \sqrt{-1}\cdot\sqrt{32}[/tex]
Substitute [tex]\sqrt{-1}=i[/tex]:
[tex]2\sqrt{-32}=2i\cdot\sqrt{32}[/tex]
[tex]2\sqrt{-32}=2i\cdot\sqrt{2\cdot 16}[/tex]
[tex]2\sqrt{-32}=2i\cdot\sqrt{2\cdot 4^2}[/tex]
[tex]2\sqrt{-32}=2*4i\cdot\sqrt{2}[/tex]
[tex]2\sqrt{-32}=8i\sqrt{2}[/tex]
Therefore, the equivalent expression would be [tex]8i\sqrt{2}[/tex].
The expression which is equal to 2√-32 is; 8i√2
According to the question, we have been given the radical expression; 2√-32
First, the expression can be evaluated as follows;
=2√-32= 2√-1 × 32We must recall that, In complex numbers, √-1 = i.
= 2i√32= 2i√16 ×2= 8i√2Therefore, the expression which is equal to 2√- 32 is:. 8i√2
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There are 2.54 centimeters in an inch how many inches are in 51.78 centimeters round to the nearest tenths
Answers
51.78 / 2.54 = 20.4 inches <==
or this way...
2.54 / 1 = 51.78 / x....2.54 cm to 1 in = 51.78 cm to x inches
cross multiply
(2.54)(x) = 51.78)(1)
2.54x = 51.78
x = 51.78 / 2.54
x = 20.4 inches <==
A scientist inoculates mice, one at a time, with a disease germ until he finds 2 that have contracted the disease. if the probability of contracting the disease is 1/6, what is the probability that 8 mice are required?
Answers
Need help with problem number 10
Answers
9x - 6 + 58 = 16x - 4
9x + 52 = 16x - 4
9x - 16x = -4 - 52
-7x = -56
x = 8
hope it helps
Whats The Number name for 43,080,700
Answers
forty-three million, eighty thousand, seven hundred!! hope this helps
Use a calculator to round the nearest hundredth
Answers
= -5.87 / 2
= - 2.94
hope it helps
At the movie theatre, child admission is $5.50 and adult admission is $9.40 . On Monday, four times as many adult tickets as child tickets were sold, for a total sales of $1379.20 . How many child tickets were sold that day?
Answers
a = 4c
5.50c + 9.40(4c) = 1379.20
5.50c + 37.6c = 1379.20
43.1c = 1379.20
c = 1379.20 / 43.10
c = 32 <=== 32 kids tickets
a = 4c
a = 4(32)
a = 128 <=== 128 adult tickets
35 points in a game if the team scored 21 points the first half the fraction of the total scored in the second half was
Answers
35 -21 = 14
14/35 reduces to 2/5
For about 10 years after the french revolution, the french government attempted to base measures of time on multiples of ten: one week consisted of 10 days, one day consisted of 10 hours, one hour consisted of 100 minutes, and one minute consisted of 100 seconds. what are the ratios of (a) the french decimal week to the standard week and (b) the french decimal second to the standard second? assume that the definition of a "day" remains the same.
Answers
Explanation of the ratios of French decimal time to standard time after the French Revolution.
Explanation:Ratio of French Decimal Week to Standard Week:
1 French decimal week = 10 days, whereas 1 standard week = 7 days. So, the ratio is 10/7.
Ratio of French Decimal Second to Standard Second:
1 French decimal second = 0.01 standard second since 1 hour = 100 French decimal minutes = 100 x 0.01 = 1 standard hour.
(a) The ratio of the French decimal week to the standard week is [tex]\( \frac{10}{7} \)[/tex].
(b) The ratio of the French decimal second to the standard second is [tex]\( \frac{5}{3} \)[/tex].
To find the ratios of the French decimal week to the standard week and the French decimal second to the standard second, we'll compare the durations of these units in the French decimal system to those in the standard system.
(a) Ratio of the French decimal week to the standard week:
In the French decimal system:
- One French decimal week consists of 10 days.
In the standard system:
- One standard week consists of 7 days.
So, the ratio of the French decimal week to the standard week is:
[tex]\[ \text{Ratio} = \frac{\text{French decimal week}}{\text{Standard week}} = \frac{10 \text{ days}}{7 \text{ days}} \][/tex]
(b) Ratio of the French decimal second to the standard second:
In the French decimal system:
- One minute consists of 100 seconds.
In the standard system:
- One minute consists of 60 seconds.
So, the ratio of the French decimal second to the standard second is:
[tex]\[ \text{Ratio} = \frac{\text{French decimal second}}{\text{Standard second}} = \frac{100 \text{ seconds}}{60 \text{ seconds}} \][/tex]
Now, let's simplify these ratios:
(a) Ratio of the French decimal week to the standard week:
[tex]\[ \frac{10}{7} \][/tex]
(b) Ratio of the French decimal second to the standard second:
[tex]\[ \frac{100}{60} = \frac{5}{3} \][/tex]
So, the ratios are:
(a) for the French decimal week to the standard week.
(b) [tex]\( \frac{5}{3} \)[/tex] for the French decimal second to the standard second.
Best buy shoes had a back to school special. The total bill for four pairs of shoes came to $69.24 ( before tax ) What was the average price for each pair of shoes?
QUESTION 2 If you only purchased 1 pair of shoes at Best Buy Shoes instead of the four described in problem 20, how much would you have paid, based on the average price?
Answers
Answer: a) $17.31, b) $17.31.
Step-by-step explanation:
Since we have given that
Total bill for four pairs of shoes = $69.24
Number of pairs of shoes = 4
We need to find the average price for each pair of shoes .
So, Average price would be
[tex]\dfrac{\text{Total amount}}{\text{Number of pairs of shoes}}\\\\=\dfrac{69.24}{4}\\\\=\$17.31[/tex]
If he purchased only 1 pair of shoes, the amount he has to pay based on average price would be $17.31.
Hence, a) $17.31, b) $17.31.
Final answer:
The average price for each pair of shoes from the total bill of $69.24 is $17.31. If only one pair of shoes was purchased, it would also cost $17.31.
Explanation:
To find the average price for each pair of shoes in the first question, you divide the total bill by the number of pairs of shoes. In this case, the total bill is $69.24 for four pairs of shoes.
Step-by-step calculation:
Divide the total cost ($69.24) by the number of pairs (4).
The calculation will be $69.24 / 4 = $17.31.
The average price for each pair of shoes is $17.31.
For the second question, if you were to purchase only one pair of shoes, the cost would be equal to this average price, which is $17.31.
When the sun is at 31 above the horizon, a tree casts a 42 ft. shadow. how tall is the tree?
Answers
This question can be solved by a trigonometric equation. Shadow formed when something with height like a tree, so it can be pictured as a vertical line. Shadow is a length of and can be pictured as a horizontal line.
In trigonometric, to find the vertical line length with horizontal line you need tan function. The sun angle will be used in the function, so the calculation would be: tan(31) x 42ft = 25.2361459992ft
I need help please I’m lost
Answers
3, 1, 2
3 is the most likely because the chances are out of 2 classes instead of 2, which is one class.
1 is the number of people is also included in 2.
Hope this helps!
What is the sum of the polynomials
Answers
Answer:
B its 100% this one i promise
Step-by-step explanation:
The sum of the polynomials (17m - 12n - 1) and (4 - 13m - 12n) will be
⇒ 4m - 24n + 3
Option B is true.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The polynomials are,
⇒ (17m - 12n - 1) and (4 - 13m - 12n)
Now, Sum of the polynomial is find as;
The polynomials are,
⇒ (17m - 12n - 1) and (4 - 13m - 12n)
It can be written as;
The polynomials are,
⇒ 17m - 12n - 1
- 13m - 12n + 4
---------------------------
4m - 24n + 3
---------------------------
Thus, (17m - 12n - 1) + (4 - 13m - 12n) = 4m - 24n + 3
Therefore, The sum of the polynomials (17m - 12n - 1) and (4 - 13m - 12n) will be
⇒ 4m - 24n + 3
Option B is true.
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Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.
Can any of the roots have multiplicity?
How can you find a function that has these roots?
Answers
Work backwards to find the factors from the roots, then multiply the factors together.y=x3−10x2+31x−30
Answer:
The roots cannot have multiplicity because the function is specified as cubic and 3 roots are given.
To find the function, write f(x) = (x – 2)(x – 3)(x – 5), and simplify the right side.
Idk how to do this please help me
Answers
HIJ = 176
ZIJ = x
HIJ is the whole thing, and HIZ is a part, therefore
36 + x = 176
176 - 36 = 140
x = 140
ZIJ = 140 degrees
hope this helps
On a farm, there are 20 fewer cows than twice the number of pigs. If there are 50 cows, how many pigs are there? Write a two step equation to model the scenario and answer it.
Answers
50=2p-20
p=35
please answer both questions thank you.
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Can someone please help me with this problem?
Let f(x)=(x-2)^3+8.
Show that this function is one-to-one algebraically.
I've been stuck on this problem for quite some time now. I'm not asking for answers just a little explanation on what I need to do to solve it.
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Which of the following phrases would represent this expression?
the quotient of x and 3
the quotient of 3 and x
the product of 3 and x
the difference of x and 3
Answers
sorry if i got it wrong
Answer:
The quotient of x and 3 is the answer i hope it works
Jennifer is saving money to buy a bike. The bike costs $245. She has $125 saved, and each week she adds $15 to her savings. How long will it take her to save enough money to buy the bike?
Answers
120/15=8
Write the equation of a line that has a slope 1/3 and y-intercept 4.
Answers
In slope-intercept form, y = (1/3)x + 4 can be used to represent the equation of a line with a slope of 1/3 and a y-intercept of 4.
Explanation:In mathematics particularly in algebra, the equation of a line is usually formulated in the slope-intercept form, which is y = mx + b. Where m is the slope of the line and b is the y-intercept. For a line with a slope of 1/3 and y-intercept of 4, you would substitute 1/3 for m and 4 for b. Therefore, the equation of the line would be y = (1/3)x + 4
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Please help me! Im really confused on how to solve problems like this
Answers
÷-c ÷-c
b = a ÷ -c
a= -bc
Firstly, divide -bc by c
a/c=-bc/c
The c on -bc cancels out
a/c=-b
Transfer the negative to he other side of the equation
b= -a/c
If f(x)=x^2-3x,find f(-18). Show work
Answers
-------------------------------------
-------------------------------------
Work Shown:
f(x) = x^2 - 3x
f(x) = ( x )^2 - 3*( x )
f(-18) = ( -18 )^2 - 3*( -18 ) ... replace every x with -18; now use PEMDAS
f(-18) = 324 - 3*( -18 )
f(-18) = 324 + 54
f(-18) = 378
The function f(x) = 800(1.09)3x shows the growth due to interest that Jim earns on an investment. The steps to calculate an equivalent function are shown below: [Step 1] f(x) = 800(1.09)3x
[Step 2] f(x) = 800(1.093)x
[Step 3] f(x) = 800(1.09 ⋅ 3)x
[Step 4] f(x) = 800(3.27)x Which of the following is the first incorrect step?
A. There is no mistake in the work.
B. Step 1
C. Step 2
D. Step 3
E. Step 4
Answers
Answer:
the answer is Step 3
Step-by-step explanation:
i took the test
ax+2xy=14 solving for y
Answers
Answer:
[tex]y=\dfrac{14-Ax}{2x}[/tex]
Step-by-step explanation:
The given expression is :
[tex]Ax+2xy=14[/tex].............(1)
We need to find the value of y. Subtracting "Ax" on both sides of equation (1) as :
[tex]Ax-Ax+2xy=14-ax[/tex]
[tex]2xy=14-Ax[/tex]
Dividing both sides of above equation by "2x" as :
[tex]\dfrac{2xy}{2x}=\dfrac{14-Ax}{2x}[/tex]
[tex]y=\dfrac{14-Ax}{2x}[/tex]
So, the value of y is, [tex]y=\dfrac{14-Ax}{2x}[/tex]. Hence, this is the required solution.
Identify the property that is demonstrated below:
ab = ba
a. commutative property of addition
b.commutative property of multiplication
c. identity property of multiplication
d.associative property of multiplication