A ___________ ____________ can be written as a fraction or a ratio.
An airplane is preparing to land at an airport. It is 44,8000 feet above the ground and is descending at the rate of 3,100 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,500 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be? Use two other methods to solve the problem. Explain which methods are easier to use and which are more difficult to use for the situation.
Answer:
Time: 8 minutes
Altitude: 20000ft
Method 1 is easiest
Method 3 is easiest
Step-by-step explanation:
Given
Airplane 1:
[tex]Height = 44800 ft[/tex]
[tex]Descending\ Rate = 3100ft/min[/tex]
Airplane 2:
[tex]Ascending\ Rate = 2500ft/min[/tex]
Required
Determine when both planes would be at the same altitude?
Let the minute be represented by m
For Airplane 1, Its altitude at any height h is:
[tex]Airplane\ 1 = Height - Descending\ Rate * m[/tex]
It is minus (-) because the airplane is descending
[tex]Airplane\ 1 = 44800 - 3100 * m[/tex]
[tex]Airplane\ 1 = 44800 - 3100m[/tex]
For Airplane 2, Its altitude at any height h is:
[tex]Airplane\ 2 = Ascending\ Rate * m[/tex]
[tex]Airplane\ 2 = 2500 * m[/tex]
[tex]Airplane\ 2 = 2500m[/tex]
Method 1:
For both heights to be equal, we have that:
[tex]Airplane\ 1 = Airplane\ 2[/tex]
This gives:
[tex]44800 - 3100m = 2500m[/tex]
Collect Like Terms
[tex]44800 = 2500m + 3100m[/tex]
[tex]44800 = 5600m[/tex]
[tex]5600m = 44800[/tex]
[tex]m = 44800/5600[/tex]
[tex]m = 8\ min[/tex]
Hence, the time they will be at the same altitude is 8 minutes
Substitute 8 for m in
[tex]Airplane\ 2 = 2500m[/tex]
[tex]Airplane\ 2 = 2500 * 8[/tex]
[tex]Airplane\ 2 = 20000\ ft[/tex]
Hence, they will be at the same altitude at 20000ft
Method 2:
We have that:
[tex]Airplane\ 1 = 44800 - 3100m[/tex]
[tex]Airplane\ 2 = 2500m[/tex]
Since they are to be at the same altitude, then
The difference in their altitude must be 0
i.e.
[tex]Airplane\ 1 - Airplane\ 2 = 0[/tex]
This gives
[tex]44800 - 3100m - 2500m = 0[/tex]
[tex]44800 - 5600m = 0[/tex]
Collect Like Terms
[tex]5600m = 44800[/tex]
[tex]m = 44800/5600[/tex]
[tex]m = 8\ min[/tex]
Substitute 8 for m in
[tex]Airplane\ 1 = 44800 - 3100m[/tex]
[tex]Airplane\ 1 = 44800 - 3100 * 8[/tex]
[tex]Airplane\ 1 = 44800 - 24800[/tex]
[tex]Airplane\ 1 = 20000\ ft[/tex]
Method 3:
We have that:
[tex]Airplane\ 1 = 44800 - 3100m[/tex]
[tex]Airplane\ 2 = 2500m[/tex]
Since they are to be at the same altitude, then
The ratio of their altitudes must be 1
i.e.
[tex]\frac{Airplane\ 1}{Airplane\ 2} = 1[/tex]
[tex]\frac{44800 - 3100m}{2500m} = 1[/tex]
Cross Multiply
[tex]44800 - 3100m = 1 * 2500m[/tex]
[tex]44800 - 3100m = 2500m[/tex]
Collect Like Terms
[tex]44800 = 2500m + 3100m[/tex]
[tex]44800 = 5600m[/tex]
[tex]5600m = 44800[/tex]
[tex]m = 44800/5600[/tex]
[tex]m = 8\ min[/tex]
Substitute 8 for m in
[tex]Airplane\ 1 = 44800 - 3100m[/tex]
[tex]Airplane\ 1 = 44800 - 3100 * 8[/tex]
[tex]Airplane\ 1 = 44800 - 24800[/tex]
[tex]Airplane\ 1 = 20000\ ft[/tex]
Hence;
Their altitudes must be 20000ft
Though the three methods applied uses the same logic at some point, the first method applied is still the easiest and it is a straight forward method that could be applied in solving the question.
Method 3 is the most difficult.
what is the measure of the larger angle in this degree?
−3/4+(1/10÷2/5) plz hurry
Answer:
-.71
Step-by-step explanation:
-3/4+ ((1/10)/(2/5))
Part A: What is the measure of angle x? Show your work. (5 points)
Please hurry I'll give brainlest.
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
AB and CD are parallel lines, and PQ and PR are transversals which intersect AB at P and CD at Q and R. Angle APQ is labeled as 64 degrees, angle QPR is equal to x, angle PRD is equal to 110 degrees.
Answer:The missing part of ∠R = 70°. Hence, you can find the missing ∠R in the triangle (70°). 180°-110°=70°
Next x+64=110. The reason why you can do this is because ∠R is going to be an opposite interior angle. Subtract 64 from the left and right sides. x=46
I hope this helps!
Step-by-step explanation:
Answer:
Answer:The missing part of ∠R = 70°. Hence, you can find the missing ∠R in the triangle (70°). 180°-110°=70°
Next x+64=110. The reason why you can do this is because ∠R is going to be an opposite interior angle. Subtract 64 from the left and right sides. x=46
Can anyone teach mee.....................
Answer:
(i) The name of the part of the circle, OQ is a radius
(ii) The radius of the sector QOR is 21 cm
Step-by-step explanation:
The given figure is a sector of the circle O
∵ Any sector of a circle formed from 2 radii and an arc
∴ OQ is a radius
(i) The name of the part of the circle, OQ is a radius
The rule of the length of an arc of a circle is L = [tex]\frac{\alpha }{360}[/tex] × 2 π r, where
α is the angle of the sectorr is the radius of the circle∵ The length of the arc QR is 22 cm
∴ L = 22
∵ The measure of the angle of the arc is 60°
∴ α = 60°
∵ π = [tex]\frac{22}{7}[/tex]
→ Substitute them in the rule above
∵ 22 = [tex]\frac{60}{360}[/tex] × 2 × [tex]\frac{22}{7}[/tex] × r
∴ 22 = [tex]\frac{22}{21}[/tex] r
→ Divide both sides by [tex]\frac{22}{21}[/tex]
∴ 21 = r
(ii) The radius of the sector QOR is 21 cm
Sarah earns $9 an hour at a Mort’s Pizza Palace, working 20 hours per week. She spends $3 each week for snacks at work, but saves all her other earnings. How many hours must Sarah work to buy a new phone that costs $150?
Answer:
15h
Step-by-step explanation:
Answer:
17 hours
Step-by-step explanation:
she needs 150, she spends 3 and she makes 9 per hour
153/9 = 17
What is the slope of the line that runs through points (-7,-20) and (12,18)? Write the equation of that line.
Answer:
2
Step-by-step explanation:
-20 - 18 = -38
-7 - 12 = -19
-38/-19 = 2
Answer:
The slope is 2 which means the equation would be y=2x.
Step-by-step explanation:
in a certain code "VICTORY" is coded as "YLFWRUB", then how will "SUCCESS" be coded?
Answer:
VXFFHVV
Step-by-step explanation:
PLS GIVE BRAINLIEST
How do you do these two questions?
Answer:
y(t) → 2 as t → ∞
dP/dt = P (P/1850 − 1) (1 − P/16000)
Step-by-step explanation:
The graph shows how dy/dt changes as a function of y.
At t = 0, y = -0.5.
At y = -0.5, dy/dt > 0. Therefore, y is increasing.
y continues to increases until y = 2. At this point, dy/dt = 0, and changes signs from positive to negative, so y begins to decrease. dy/dt then becomes positive again, and the cycle repeats.
So y approaches 2 as t approaches infinity.
dP/dt is negative when P < 1850.
dP/dt is positive when 1850 < P < 16,000.
dP/dt is negative when P > 16,000.
dP/dt is 0 when P is 0.
Therefore, dP/dt = P (P/1850 − 1) (1 − P/16000).
What's the largest odd number you can make using all four digits 4, 5, 3, 6
Answer:
6543
Step-by-step explanation:
Not much to explain lol
Here,
Odd numbers are 3 and 5.
5>3The largest odd number =6543
A hiking trail down the side of Mt. Tom drops a vertical distance of 60 meters over a horizontal distance of 300 meters. What is the slope of the trail? Express your answer as a reduced fraction.
Answer:
Step-by-step explanation:
Slope of the trail is expressed as;
Slope = vertical distance/horizontal distance
Given
Vertical distance = 60metres
Horizontal distance= 300metres
Substitute
Slope = 60/300
Slope = 6×10/30×10
Slope = 6/30
Slope = 6×1/6×5
Slope = 1/5
Hence the slope of the trail in reduced fraction is 1/5
Cleo and her family fished for 3 days and caught 100 fish between them. They caught 12 fish on day 2 and 16 fish on day 3. How many fish did they catch on the first day.
Which equation is correct.
12x + 16 = 100
12x + 16 = 100
x + 12 + 16 = 100
x + 12 + 16 = 100
16x + 12 = 100
Answer:
x + 12 + 16 = 100
72 fishes
Step-by-step explanation:
Given parameters:
Number of days fished = 3days
Number of fishes caught = 100 fishes
Number of fish caught on day 2 = 12fishes
Number of fish caught on day 3 = 16fishes
Unknown:
Number of fish caught on the first day = ?
Solution:
Let the number of fishes caught on the first day = x;
Total number of fishes caught = No of fish on day 1 + No of fish on day 2 + number of fish on day 3
Insert the parameters and solve;
100 = x + 12 + 16
x = 100 - 28 = 72fishes
Which is the better buy?
48-fluid-ounce container of laundry detergent for
$5.28
3-gallon container of laundry detergent for $34.56
Answer:
3-gallon container of laundry detergent for $34.56
Step-by-step explanation:
48-fluid-ounce container of laundry detergent for $5.28
5.28 : 48 = 0.11
check your work: 0.11 x 48 = 5.28
so for the first offer you will be paying $0.11 per ounce of laundry detergent.
3-gallon container of laundry detergent for $34.56
1 gallon = 128 ounces
3 gallons = 384 ounces
34.56 : 384 = 0.09
check your work: 0.09 x 384 = 34.56
for the second offer you will be paying $0.09 per ounce of laundry detergent. 3-gallon container of laundry detergent for $34.56 is a better buy because you will be paying less for each ounce of detergent.
hope this helps!
There are 14 crayon and 30 markers in a pencil box. What is the ratio of crayon s to items in the pencil box?
Answer:
14 to 44
Step-by-step explanation:
14 + 30 = 44 (this number represents total items)
There are 14 crayons
Therefore the answer Is 14 to 44
D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is m∠DEF? A. 30° B. 45° C. 60° D. 90°
A random sample of size 1,000 is taken from a population where p = .20.
Find P( < .18).
A. .9429
B. .0571
C. .2643
D. .0793
The value of P( < 0.18) is 0.057.
What is p value?The probability, for a particular statistical model, that the statistical summary would be equal to or more extreme than the actual observed results if the null hypothesis were true is known as the P value.
Given:
Sample Size = 1000
and, p= 0.20
So, P( P' < 0.18)
= P ( P'- P / √ P(1- P)/ n < 0.18 - 0.20 / √ 0.2 (1- 0.2)/ 1000 )
= P ( P'- P / √ P(1- P)/ n < -0.02/ 0.0126)
= P ( P'- P / √ P(1- P)/ n < - 1.582)
= P( z < - 1.582)
= 0.056939
= 0.057
Learn more about p- value here:
https://brainly.com/question/14790912
#SPJ5
22 What is the circumference of the circle? Use 7 for yr. 35 cm 44 cm 55 cm
Answer:
B) 55 cm
Step-by-step explanation:
it’s correct from EDGE
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
67
Step-by-step explanation:
cause math
Answer:
It is 67
Step-by-step explanation:
Corina pays $5.00 for materials to make pillows. She makes 3 pillows and sells 2 for $10.00 each and 1 for 5.00 what is corinne’s profit.
Answer:
$20
Step-by-step explanation:
She has 5 dollars originally, she sells 2 pillows for $10 each that = $20 and then she sold one for $5 but she spent a original $5 on material so $25 - $5 = $20
Angle measures and segment lengths. Algebra Find the value of each variable.
(9)
x ° = 1/2 (130° - 30°) = 50°
(due to a theorem about intersecting secants/tangents)
(11) The labeled angle subtends a minor arc of meaure 120°, which means the larger arc has a measure of 360° - 120° = 240°. Then
x ° = 1/2 (240° - 120°) = 60°
(due to the same theorem)
(13) The labeling here is a bit confusing. I'm not sure what the 70° is referring to. It occurs to me that it might be info from a different exercise, so that y ° is the measure of the angle made by the tangent to the circle with a vertex of the pentagon, and x ° is the measure of each arc that passes over an edge of the pentagon.
Each arc makes up 1/5 of the circle's circumferece, so
x ° = 360°/5 = 72°
The pentagon is regular, so each of its interior angles have the same measure of 108°. (Why 108°? Each exterior angle measures 360°/5 = 72°, since the exterior angles sum to 360°. Interior and exterior angles are supplementary, so the interior angles measure 180° - 72° = 108° each.)
The angles formed by the tangent to the circle are supplementary, so that
y ° + 108° + y ° = 180°
2y ° = 72°
y ° = 36°
A recipe for chicken marinade says, "Mix 3 parts oil with 2 parts soy sauce and 1 part orange juice." If you need 42 cups of marinade in all, how much of each ingredient should you use?
Answer:
We will use;
21 parts oil
14 parts soy sauce
7 parts Orange
Step-by-step explanation:
We can have all of these as a ratio
That would be;
3 + 2 + 1 = 6
For oil
3/6 * 42 = 21 parts of oil
For Soy sauce
= 2/6 * 42 = 14 parts soy sauce
For Orange
= 1/6 * 42 = 7 parts orange juice
Answer: 7 14 21
Step-by-step explanation:
6x___=42 you fill in the blanks
what is the reciprocal of 11
Answer:
[tex]\frac{1}{11}[/tex]
Step-by-step explanation:
11 is [tex]\frac{11}{1\\}[/tex] so to get the reciprocal just flip it to [tex]\frac{1}{11}[/tex]
After driving 120 miles you completed 3/4 of the trip. How long was the entire trip
Answer:
160
Step-by-step explanation:
120/3 = 40
40 x 4 = 160
May I have brainliest please? :)
Give the slope between the points
(-2,4) (-8, 13)
Answer
Answer:
9/-6
Step-by-step explanation:
when you subtract (x2-x1) and (y2-y1) this is the answer you get.
[tex]-\frac{3}{2}[/tex]
Step-by-step explanation:Use the point slope formula
[tex]Slope = m = \frac{y_2-y_1}{x_2-x_1} = \frac{13-4}{-2-(-8)} = \frac{9}{6} = \frac{9}{6} = \frac{3}{2}[/tex]
This is the difference between two points with the rise (change in y) over the run (change in x)
Sorry it took so long for so little my girlfriend was distracting me
Hope this helps :)
You find a shirt that costs 24.67 for some clothes. To get ready for Black Friday there was a discount, and the discount was 32%. How much does it cost?
Made up question :D !!!
Answer:16.78
Step-by-step explanation:
Length of a rectangle is 8 inches and width of it is 3 inches. What is the area?
Answer:
24
Step-by-step explanation:
8 times 3=24
What is the result when the following equation is solved? 4/5x=1
Answer:
Step-by-step explanation: 0.8
SCREEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
2.4 m
Step-by-step explanation:
¿que son los grafos triviales?
Answer:
la respuesta
Step-by-step explanation:
perdon si no es