Hey there!!
( a ) 1 + 3/x²-1 = 2/x-1
x²-1+3/x²-1 = 2/x-1
x²+2/x²-1 = 2/x-1
Note : we can write x²-1 as (x-1)(x+1)
I wrote this with the identity a²-b² = (a+b)(a-b)
x²+2/(x-1)(x+1) = 2/x-1
Multiplying (x-1)(x+1) on both sides
x²+2 = 2(x-1)(x+1) / (x-1)
x²+2 = 2(x+1)
x²+2 = 2x+2
x²-2x = 0
x(x-2)=0
x=0
x-2=0
x=2
x = 0 and 2
( b ) ( √x+3 ) - 1 = x
√x+3 = x+1
x+3 = ( x+1)²
x+3 = x²+2x+1
x+3-x²-2x-1=0
-x+2-x²=0
-x²-x+2=0
x = -b plus or minus √b2 -4ac / 2a
x = -1 plus or minus √ 1 + 8 / 2
-1 plus or minus √9 / 2
-1 plus or minus 3/2
-1 +3 / 2
x = 1
-1 - 3 / 2
-4/2
x = -2
negative cannot be a value
Hence, the answer is
x = 1
Hope my answer helps!
where x represents the car's speed in miles per hour. Determine the fuel economy
when the car is traveling 40, 50, and 60 miles per hour.
Answer:
a) 29.50 miles per gallon b) 29.87 miles per gallon c) 28.19 miles per gallon
Step-by-step explanation:
A specific car fuel economy (miles/gallon) = f(x) = 0.00000056x^4 - 0.000018x^3 - 0.016x^2 + 1.38x - 0.38
where x represents the car speed in miles per hour.
when x = 40 miles per hour
A specific car fuel economy (miles/gallon) = f(x) = 0.00000056(40)^4 - 0.000018(40)^3 - 0.016(40)^2 + 1.38(40) - 0.38 = 1.4336 - 1.152 - 25.6 + 55.2 - 0.38 = 29.50 miles per gallon
Similarly,
when x = 50
A specific car fuel economy (miles/gallon) = f(x) = 0.00000056(50)^4 - 0.000018(50)^3 - 0.016(50)^2 + 1.38(50) - 0.38 = 3.5 - 2.25 - 40 + 69 - 0.38 = 29.87 miles per gallon
Similarly,
when x = 60
A specific car fuel economy (miles/gallon) = f(x) = 0.00000056(60)^4 - 0.000018(60)^3 - 0.016(60)^2 + 1.38(60) - 0.38 = 7.26 - 3.89 - 57.6 + 82.8 - 0.38 = 28.19 miles per gallon