Amodel rocket is launched with an initial upward velocity of 151 ft/s. the rockets height "h" (in feet) after "t" seconds is given by the following. h=151t-16t squared. find the values of "t" for which the rockets height is 88 feet. round your answer to the nearest hundredth.

t=8.81s and t=0.62s

Step-by-step explanation:

Asking for H=88ft and putting units leaves us with the formula:

Which can be also written as:

We want t, and this is a quadratic formula of the form , which we know has the solutions:

So we put the relevant values (a=16ft/s^2, b=-151ft/s, c=88ft) on that equation we get:

Which for the plus sign gives t=8.81345408729s and for the minus sign gives t=0.6240459127s, which rounding to the nearest hundredth are t=8.81s and t=0.62s

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.