Download Plug in what t is

I am stuck on a few problems completely, and I guess on another few just looking for
reassurance. Please help if you can. Thank you ----Thank you---Thank you!!!!
1. Find a linear function perpendicular to the function y= -5x + 12 at the point (2,5) in
standard form, point slope form, and slope-intercept form.
The orginal line is y = -5x + 12 (slope is -5), so the perpindicular line will be y = 1/5x + ?
5 = (1/5)2 + ?.
4 3/5 = ?
y = 1/5x +4 3/5
2. A ball is thrown up into the air.Measurements are ta ken and a function is found to model the
height of the ball versus the time the ball is in the air. The function derived from the data,
H(t) = -4.92 + 40.5t + 25.3, is the model for the height of the ball, H(t) in meters, at time t
(in seconds)
a) Calculate H(1.672) and interpret the meaning of this result?
b) Find the domain & range of the function H(t)
h=0
h(t)=function notation
Acceleration near earth = 9.7 m/s
h =-4.9t2+40.5t+25.3
10
y-max = 20
10
(t)x –10
Plug in what t is
At t=1, h=-4.9(1)2 = 40.5(1)+25.3 =60.9 m x-min=-1
At t=2, h=-4.9(2)2 = 40.5(2)=25.3 = 86.7m
x-max = 5
-10
y (h)
Avg. Slope= h = change in height (m) 60.9 – (86.7) = -25.8 m/s =25.8m/s
t
change in time (s)
1-2
Represents the average speed traveled between pt. 1& pt. 2
Avg. slope = avg. rate of chg. (speed) from t=1sec to t=2 sec which is 13.2 m/s downwards
3.A business has a product that is sold in m any local outlets. This product sells for $39.95
each. The weekly fixed cost of the business is $2675/week and each additional unit sold costs
the company $17.85 to produce and sell.
a. How much revenue is generated on the sale of 349 units? What is the cost of selling
units?
b. Create models for the revenue and the cost of sales for the sales of this product.
c. Remembering that profit is revenue minus cost of sales, create a profit model from the
revenue and the cost of sales models.
d. Find the number of units you need to sell to “breakeven”.
e. What is the inverse of the profit function? Use this function to determine the number
of units needed to be sold so that the profit is $13,000.
I am sure there is a simple way to figure this all out but for some reason I can’t figure it
out!
a)Revenue is 349 units x $39.95 each = $13,942.55
Cost of sales is (349 units x $17.85 each) + $2675 fixed costs = $8,904.65
Profit is $13,942.55 revenue - $8,904.65 cost of sales = $5,037.90
or do I take 39.95(1)+ 348(17.85)=$6251.75 would I minus the 2675 here =3576.75 then
would I divide the 349 by the final revenue? = $10.25ea
b) I'm not sure of the technical way to write a "model" but it must have to do with... (# of
units sold x price each) - (cost of unit to produce + fixed costs) = p rofit
c) No clue
d) I believe it's around 121 units to breakeven. Basically I just calculated the costs for 121
units [(121 x $17.85) + $2,675] and then the revenue for 121 units [121 x $39.95] until the
two numbers are the same such that revenue - costs = zero. I think it's about121
4) The height of a football (as a function of the horizontal distance traveled) is given by the
function h(x) = 0.75x – 0.0192x2, where all measurements are in meters. Rewrite the function
in vertes form and use the information to determine the initial horizontal and vertical position
of the football.
I honestly do not know how to start this??
5)Find a linear equation (in slope-intercept, point-slope and standard forms) for the line
through the points (2,4) and (-1,5)
Another one!!!
I know the formulas: a)
y= mx+b
(slope-intercept form)
b)
y – y1 = m(x-x1)
(point-slope form)
c)
ax =by =c
(standard form)
a) 4=m(-1)+b I need more info don’t I?
b)m = 5 - 4
-1 - 2 = -1/3
y = -1/3x + b
4 = (-1/3)2 + b
4 2/3 = b
y = -1/3x + 4 2/3.
b) What are a & b?
6) Find the inverse of the following functions:
a) f(x) = -5x + 7
b) g(t) = 3t+6
a) f-1(y) =-7y + 5 =x Not to sure about this?
b) g-1(t) = 1/3 (t+6)3 I think this is it’s inverse?
7) Find the following functions f(x) = -6x+5 and g(x) = 3x2 – 10 simplify results
a) (fg)(x) =(-6x+5)(3x2-10) = (-6x + -50)3x2
b) (g+f)(x) = 3x2-10+ -6x+5=-5+6x+3x2
c) 3g(x-4) = 3(3x2-10)-4 = 3x2-30-4 = 3x2-26