Answer: B) 4 & 1/6
Nice work on getting the correct answer.
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Explanation:
x is opposite the marked acute angle
5 is opposite the corresponding acute angle
So x and 5 are proportional to each other. We can form the ratio x/5
Similarly, 10 and 12 are proportional to one another. We can form the ratio 10/12.
Set those ratios equal to each other and solve for x
x/5 = 10/12
12x = 5*10 ... cross multiply
12x = 50
x = 50/12 ...... divide both sides by 12
x = (25*2)/(6*2)
x = 25/6
x = (24+1)/6
x = 24/6 + 1/6
x = 4 + 1/6
x = 4 & 1/6 which shows why <u>choice B</u> is the answer.
Side note: 25/6 = 4.167 approximately
Answer:
Y= 2e^(5t)
Step-by-step explanation:
Taking Laplace of the given differential equation:
s^2+3s-10=0
s^2+5s-2s-10=0
s(s+5)-2(s+5) =0
(s-2) (s+5) =0
s=2, s=-5
Hence, the general solution will be:
Y=Ae^(-2t)+ Be^(5t)………………………………(D)
Put t = 0 in equation (D)
Y (0) =A+B
2 =A+B……………………………………… (i)
Now take derivative of (D) with respect to "t", we get:
Y=-2Ae^(-2t)+5Be^(5t) ....................... (E)
Put t = 0 in equation (E) we get:
Y’ (0) = -2A+5B
10 = -2A+5B ……………………………………(ii)
2(i) + (ii) =>
2A+2B=4 .....................(iii)
-2A+5B=10 .................(iv)
Solving (iii) and (iv)
7B=14
B=2
Now put B=2 in (i)
A=2-2
A=0
By putting the values of A and B in equation (D)
Y= 2e^(5t)
8/45 is the correct answerrrrrr
Answer:
(g ￮ f)(- 5) = 4
Step-by-step explanation:
evaluate f(- 5) then substitute the value obtained into g(x)
f(- 5) = (- 5)² + 6(- 5) + 3 = 25 - 30 + 3 = - 2 , then
g(- 2) = 2(- 2) + 8 = - 4 + 8 = 4
(g ￮ f)(- 5) = 4
Answer:
He worked 40 regular hours.
He 4 hours beyond 40.
He worked 40 + 4(1.5) = 40 + 6 = 46 adjusted hours
Step-by-step explanation:
John worked 44 hours and a regular work week is 40 hours. This means John worked 40 regular hours plus 4 hours over time. He receives time and a half or 1.5 for each hour over 40.
So 40 + 4(1.5) = 40+6=46 adjusted hours.
