Let x and y represent the numbers of gallons used by the 40 mpg and 35 mpg cars, respectively.
.. x +y = 40 . . . . . . . . . . .total consumption is 40 gallons
.. 40x +35y = 1525 . . . . total miles driven = 1525

Multiply the first equation by 40 and subtract the second.
.. 40(x +y) -(40x +35y) = 40(40) -(1525)
.. 5y = 75
.. y = 15
.. x = 40 -15 = 25

The 40 mpg car consumed 25 gallons.
The 35 mpg car consumed 15 gallons.

7 0

3 years ago

Solve the equation on the interval 0 less than or equals theta less than 2 pi 0≤θ<2π. 2 cosine theta plus 1 equals 0 2cosθ+1=

VARVARA [1.3K]

Answer:

θ = 2π/3 or 5π/3

Step-by-step explanation:

2 cosθ + 1= 0

when + 1 goes to R H S Side than it becomes negative by transposition method

2 cos = -1

now by dividing by 2 both sides we get

cosθ = - $\frac{1}{2}$

since cosθ is negative

Cosθ = - cos 60°

it means either cosθ lies in 2nd or third quadrant

θ = π - π/3

θ = 2π- π/3

so θ = 2π/3 or 5π/3

6 0

3 years ago