Trans truck get very poor gas mileage. if tran pays $84 to fill his truck with gas and is able to drive m miles on a full tank, what expression shows his gas cost per mile? what operation does "per" indicate? check your expression by substituting 200 miles for m. does your answer make sense?

Money paid by Trans to completely fill his truck's gas tank = $84

Miles traveled by Trans' truck on full tank = m miles

Part A (Expression to show gas cost per mile)

Total Cost = (Gas Cost per Mile) × (Number of Miles)

⇒ 84 = (Gas Cost per Mile) × m

⇒ Gas Cost per Mile = 84 / m

Part B (Meaning of per)

In Gas Cost per Mile, the word 'per' indicates the division (÷) operation.

Part C (Substitute 200 miles for m)

Substituting 200 for m in the expression, we get:

Gas Cost per Mile = 84 ÷ 200

⇒ Gas Cost per Mile = $ 0.42

This indicates that to travel 1 mile, Trans needs to spend $0.42

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)