The speed rate at which the aircraft is gaining altitude is;
dx/dt = 250 miles per hour
Since the aircraft is climbing at 30° to the horizontal. it means there will be a vertical component which will be the altitude and also a horizontal component which will be the horizontal distance covered. while the hypotenuse will be how far it has climbed.
Let us call the vertical component x and the hypotenuse component z.
Thus, from trigonometric ratios, we can say that;
sin 30 = x/z
We are looking for how fast the aircraft is gaining altitude. Thus, using Liebniz notation, we can say this rate is; dx/dt. Thus;
sin 30 = (dx/dt)/(dz/dt)
0.5 = (dx/dt)/(dz/dt)
0.5 × (dz/dt) = dx/dt
Its' speed is 500 mph. This means dz/dt = 500
Thus;
dx/dt = 0.5 × 500
dx/dt = 250 mph
Hence, the speed rate at which the aircraft is gaining altitude is;
dx/dt = 250 miles per hour
Lead more about rate of change at;
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Answer:
d ≈ 11.4 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 5, 1 ) and (x₂, y₂ ) = (6, - 2 )
d = [tex]\sqrt{(6-(-5))^2+(-2-1)^2}[/tex]
= [tex]\sqrt{(6+5)^2+(-3)^2}[/tex]
= [tex]\sqrt{11^2+9}[/tex]
= [tex]\sqrt{121+9}[/tex]
= [tex]\sqrt{130}[/tex]
≈ 11.4 units ( to the nearest tenth )
1/2 (2x + 5) = 3/4 (x + 1) + 5/2 show your work!!:)
Answer: 0
Step-by-step explanation:
1/2(2x+5)=3/4(x+1)+5/2
distribute 1/2 to 2x and 5
distribute 3/4 to x and 1
1/4x+5/2=5/2
subtract 5/2 to 5/2
1/4=0
multiply 1/4 by the reciprocal
4/1*1/4=0*4/1
Answer= 0
You have averaged a score of 150 in the previous 12 bowling games and just bowled a 156. What score do you have to bowl in the next game to have an average of 152?
Group of answer choices
152
172
Below 150
Higher than 172
150
I need to score 172 in the 14th game to have an average of 152 in 14 games.
What is the weighted average?When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.
To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.
The total score of 12 games is (12×150) = 1800.
Again I scored 156 is the 13th game.
Let I score 'x' in the 14th game.
∴ (1800 + 156 + x)/12 + 1 + 1 = 152.
(1800 + 156 + x)/14 = 152.
(1956 + x)/14 = 152.
1956 + x = 2128.
x = 2128 - 1956.
x = 172.
So, I need to score 172 in order to have an average of 152 for 14 games.
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how do you graph 16x-4=2
Step-by-step explanation:
Manage into slope interrupt form
16x = 4y + 2
4y = 16x - 2
Separate by 4
Y = 4x -1/2
Because the equating is undeviating, find 3 points and plot ruling class
(0, -1/2), (1, 3.5), (-1, -4.5)
And last, set a limit through bureaucracy
Answer:
MC donalds is a scam
Step-by-step explanation: THEY KILL BABY CHICKENS THE ANSWER IS
Make it into slope intercept form
16x = 4y + 2
4y = 16x - 2
Divide by 4
Y = 4x -1/2
Since the equation is linear, find 3 points and plot them
(0, -1/2), (1, 3.5), (-1, -4.5)
And lastly, draw a line through them