Ya, calculus and related rates, such fun!
everything is changing with respect to t
altitude rate will be dh/dt and that is 1cm/min
dh/dt=1cm/min
area will be da/dt which is increasing at 2cm²/min
da/dt=2cm²/min
base=db/dt
alright
area=1/2bh
take dervitivie of both sides
da/dt=1/2((db/dt)(h)+(dh/dt)(b))
solve for db/dt
distribute
da/dt=1/2(db/dt)(h)+1/2(dh/dt)(b)
move
da/dt-1/2(dh/dt)(b)=1/2(db/dt)(h)
times 2 both sides
2da/dt-(dh/dt)(b)=(db/dt)(h)
divide by h
(2da/dt-(dh/dt)(b))/h=db/dt
ok
we know
height=10
area=100
so
a=1/2bh
100=1/2b10
100=5b
20=b
so
h=10
b=20
da/dt=2cm²/min
dh/dt=1cm/min
therefor
(2(2cm²/min)-(1cm/min)(20cm))/10cm=db/dt
(4cm²/min-20cm²/min)/10cm=db/dt
(-16cm²/min)/10cm=db/dt
-1.6cm/min=db/dt
the base is decreasing at 1.6cm/min
Answer:
Please see attached image for the graph
Step-by-step explanation:
To graph the elevation versus time, we start by plotting the first point at time zero (when the climb begins) when Zane is 20 meters below the edge (-20 meters). This corresponds to the point (0, -20).
One second later (1 in the horizontal axis), Zane has moved up 4 meters, now reaching -16 meters. This is the point (1, -16) on the graph.
One second later at time 2 seconds, he is another 4 meters up which corresponds to the point (2, -12) on the graph.
you can go on like this plotting more points on the graph.
Please see the attached image that illustrates this and shows the appropriate line that represents Zane's position versus time (pictured in red)
Answer:
csc θ = 
/6
sec θ = /7
tan θ = 6/7
Step-by-step explanation:
The first thing to do will be to compute the length of the hypotenuse using the Pythagoras theorem;
6^2 +7^2 = hypotenuse^2
hypotenuse =
csc θ = 1/sinθ
sinθ = opposite side/hypotenuse
= 6/
csc θ = /6
sec θ = 1/cosθ
cosθ = adjacent side/hypotenuse
sec θ = hypotenuse/adjacent side
= /7
tan θ = Opposite side/adjacent side
= 6/7
Answer:
The first piece is 15 in and the second piece is 21 in
Step-by-step explanation:
5 + 7 = 12
3 ft = 3 x 12 in = 36 in
36 ÷ 12 = 3
5 x 3 = 15 7 x 3 = 21
The first piece is 15 in and the second piece is 21 in
Answers:
1. a) 4.1x + 29
2. b) 1/5(m – 100)
3. c) nine over five y + 9 (9/5y + 9)
Explanations:
1. The formula for perimeter of a triangle is P = side a + side b + side c, so with these values it is:
2.3x + 14 + 2x – .2x + 15
Combine like terms:
4.1x + 29
2. Test the options to see which ones work out to the answer. You know that 1/5 of 100 = 20, so you need one with a 100 and a 1/5 in it. The only possible answer is:
1/5(m – 100)
3. Distribute the 3/5:
3/5 • 3y + 3/5 • 15 = 9/5y + 45/5 = 9/5y + 15
