Question

Mariela and Jelena are biking to LA for charity. They have to buy some supplies and gear before they leave, which they calculate to be $240. They will receive $1.50 in donations for every mile they bike from San Jose to LA. (a) Write an equation in slope-intercept form for the money raised biking M miles, that factors in all costs. (b) How much will Mariela and Jelena raise once they get to LA? (hint: it's 340 miles biked one way) 11. Let sin(θ) and be in Quadrant II. Find sin (θ/2), cos (θ/2), and tan (θ/2)

Answer 1

Answer: 240 x 1.50 /2 (340)

Explanation:

Answer 2

(a) The equation in slope-intercept form for the money raised biking M miles, that factors in all costs is:

y = 1.50M - 240

where y is the total money raised (including the $240 in costs) and M is the number of miles biked.

(b) Mariela and Jelena will bike a total of 680 miles (340 miles each way) to LA and back. Thus, the total money raised will be:

y = 1.50(680) - 240 = $840

Therefore, Mariela and Jelena will raise $840 for charity once they get to LA.

(c) Given that sin(θ) and is in Quadrant II, we know that sin(θ) is positive and cos(θ) is negative.

Using the half-angle formulas, we can find:

sin(θ/2) = ±sqrt((1 - cos(θ)) / 2) = ±sqrt((1 - sqrt(1 - sin²(θ))) / 2)

cos(θ/2) = ±sqrt((1 + cos(θ)) / 2) = ±sqrt((1 + sqrt(1 - sin²(θ))) / 2)

tan(θ/2) = sin(θ) / (1 + cos(θ)) = sqrt(1 - sin²(θ)) / (1 - sqrt(1 - sin²(θ)))

Since sin(θ) is positive and cos(θ) is negative in Quadrant II, we know that:

sin²(θ) + cos²(θ) = 1
sin²(θ) + (-cos(θ))² = 1
sin²(θ) + cos²(θ) = 1

Thus, we can find:

sin(θ/2) = sqrt((1 - sqrt(1 - sin²(θ))) / 2) = sqrt((1 - sqrt(1 - (-0.8)²)) / 2) = sqrt((1 - sqrt(0.36)) / 2) = sqrt(0.32) ≈ ±0.5657

cos(θ/2) = -sqrt((1 + sqrt(1 - sin²(θ))) / 2) = -sqrt((1 + sqrt(1 - (-0.8)²)) / 2) = -sqrt((1 + sqrt(0.36)) / 2) = -sqrt(1.18