The function h(t) = 210 – 15t models the altitude of a hot air balloon over time t, in minutes.

2 answers:

7 0

If we substitute 10 for t we get the height of the balloon after being in the air 10 minutes

h(10) = 210 - 15(10) = 210 - 150 = 60

sukhopar [10]3 years ago

3 0

Answer:

on edg: t represents time, which is the input of the function, so we know that 10 is the time in minutes. h(t) represents the altitude, which is the output of the function after time, t. So, we need to substitute 10 into 210 – 15t in place of t. Simplifying 210 – 15(10), we get that 60 is the altitude in feet. So, after 10 minutes, the hot air balloon is at 60 feet.

Step-by-step explanation:

thats the sample response

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A box with a square base and open top must have a volume of 32,000 cm3. find the dimensions of the box that mini- mize the amoun

zmey [24]

Alrighty

squaer base so length=width, nice

v=lwh
but in this case, l=w, so replace l with w
V=w²h

and volume is 32000
32000=w²h

the amount of materials is the surface area
note that there is no top
so
SA=LW+2H(L+W)
L=W so
SA=W²+2H(2W)
SA=W²+4HW

alrighty

we gots
SA=W²+4HW and
32000=W²H

we want to minimize the square foottage
get rid of one of the variables
32000=W²H
solve for H
32000/W²=H
subsitute

SA=W²+4WH
SA=W²+4W(32000/W²)
SA=W²+128000/W

take derivitive to find the minimum
dSA/dW=2W-128000/W²
where does it equal 0?

0=2W-1280000/W²
128000/W²=2W
128000=2W³
64000=W³
40=W

so sub back
32000/W²=H
32000/(40)²=H
32000/(1600)=H
20=H

the box is 20cm height and the width and length are 40cm

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3 years ago

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Dafna11 [192]

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