Algebra Help Please! Very Urgent! Bless you!?

-----------Question 1-----------

Instantaneous height of the balloon at time t (in min) is given by the expression 120t (ft)

(Since the speed of the balloon is 120 ft/min)

The second balloon is descending from a height 2500 ft with a speed of 75 ft/min.

So, instantaneous height of the second balloon from the ground is 2500 ─ 75t.

When the balloons are at the same height,

120t = 2500 ─ 75t

which implies,

195t = 2500

t = 2500/195 = 12.821 minutes

That is, both the balloons will be at the same height after 12.821 minutes from start.

Common height of the balloons = 120 X 12.821 = 1538.52 ft.

-----------Question 2-----------

h = ax² + b

Given that at x = 0, h = 40

Substituting x = 0 in the above equation,

40 = 0 + b

That is, b = 40.

At x = 300, h = 0

So,

0 = a(300²) + b

90000a = ─b = ─40

a = ─40 / 90000 = ─4.44 x 10^(─4)

Hence, h = ─[4.44 x 10^(─4)] x² + 40

At x = 25,

h = ─[─4.44 x 10^(─4)] (25²) + 40 = 40 ─ 4.44x10^(─4)x625

· = 40 ─ 0.2775 = 39.7225 units

-----------Question 3-----------

Reggie gets a mileage of 28mpg on gasoline.

Capacity of the car tank = 20gallon

Distance he can travel with one tank full of gasoline

= 28 X 20 = 560 miles.

Cost of 20 gallon of gasoline = $1.10 X 20 = $22

Expenditure incurred per mile with gasoline = 22/560 = $0.0393

He gets a mileage of 24mpg on gasohol.

Distance he can travel with one tank full of gasohol

= 24 X 20 = 480 miles.

In gasohol the ratio of gasoline to alcohol = 4:1

Hence in one tank full(20 gallon) of gasohol, there will be 16gallon of gasoline and 4gallon of alcohol.

Cost of one gallon of alcohol = $0.40

Hence total cost of 20 gallon of gasohol = 1.1X16 + 0.4X4 = $19.2

Expenditure incurred per mile with gasohol = 19.2 / 480 = $0.04

Expenditure incurred per mile with gasohol is more than that with gasoline. This implies that he loses $0.0007 per mile and using gasoline is mire economical.

Amount that he saves on one tank full of gasohol = $22.00 ─ $19.20 = $2.80

-----------Question 4-----------

Instantaneous height of the balloon from ground at time t (t in seconds) is

500 + 2t (in ft)

Instantaneous height of blimp = 10000 ─ 4t

When the balloon and blimp meet,

500 + 2t = 10000 ─ 4t

6t = 9500

t = 9500 / 6 = 1583.33s

The balloon and blimp will be at same height after 1583.33 s from start.

Height from ground at that instant = 500 + 2(1583.33) = 3666.66 ft.

-----------Question 5-----------

One is 2% solution and the other is 9% solution.

Volume of the combination should be 1L and the concentration should be 7%.

Let x(in L) be the amount of 2% solution to be taken. Then the amount to 9% solution to be taken = 1 ─ x

Since the concentration of the combination should be 7%,

[2x + 9(1─x)] / [x + (1─x)] = 7

9 ─7x = 7

7x = 2

x = 2/7 = 0.2857L

Volume of 2% solution to be taken = 0.2857L

Volume of 2% solution to be taken = 1 ─ 0.2857L = 0.7143L

-----------Question 6-----------

This question is similar to the first question. You can solve it for yourself if you understand the first one. Anyway, I’m giving you the answers.

The kites will meet after 116.67 s from start.

The height when they are at the same altitude is 466.68 ft.

ALL THE BEST