Response:
Step-by-step clarification:
Reply:
a) y-8 = (y₀-8), b) 2y -5 = (2y₀-5)
Clarification:
To address these equations, using direct integration is the simplest approach.
a) The equation provided is
dy / dt = -y + 8
dy / (y-8) = dt
We substitute variables
y-8 = u
dy = du
Substituting and integrating gives us
∫ du / u = ∫ dt
Ln (y-8) = t
Evaluating at the lower limits t = 0 for y = y₀
ln (y-8) - ln (y₀-8) = t-0
Simplifying the equation results in
ln (y-8 / y₀-8) = t
y-8 / y₀-8 =
y-8 = (y₀-8)
b) The equation here is
dy / dt = 2y -5
u = 2y -5
du = 2 dy
du / 2u = dt
Integrating now
½ Ln (2y-5) = t
Evaluating at limits gives
½ [ln (2y-5) - ln (2y₀-5)] = t
Ln (2y-5 / 2y₀-5) = 2t
2y -5 = (2y₀-5)
c) The equation here bears a strong resemblance to the previous one
u = 2y -10
du = 2 dy
∫ du / 2u = dt
ln (2y-10) = 2t
We evaluate this to get
ln (2y-10) –ln (2y₀-10) = 2t
2y-10 = (2y₀-10)
One method is to exert force (identify larger equivalent ratios and add them), so to increase them, we multiply both by the same number: 11:5. For instance, 11:5 added to itself gives us 16, but that's incorrect. If we scale both by 5, it translates to 55:25. When we sum those up, 55 + 25 equals 80. We can simply add the numbers prior to multiplying, then multiply afterwards. Thus, 11 + 5 equals 16, which leads us to divide each side by 16. This yields 1.125, meaning we must scale up both by 1.125. Hence, 11:5 multiplied by 1.125 results in 12.375:5.625, which totals 18. Thus, a equals 12.375 and b equals 5.625. Hope this aids you!)
Answer:
250
Step-by-step explanation:
60% translates to 3 out of every 5 shots taken. Thus, for every 5 attempts, the archer makes only 3 shots.
Consequently, they must take 250 shots to achieve 100 hits.
I hope this clarifies!
Please consider naming brainliest if you can!
Karina is right.
For clarity, the area Karina cleaned can be calculated as follows:
1/2*(6-0)(9-2) = 1/2*6*7 = 21.
The area cleaned by Petty is:
2*9 = 18.
Clearly, Karina cleaned a larger area than Petty, affirming her correctness.
