Answer:
11) Here given Function,
![f(x) = \sqrt{2x-11}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%7B2x-11%7D)
And, ![g(x) = -|0.1|x+5](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-%7C0.1%7Cx%2B5)
For f(x) = g(x)
![\sqrt{2x-11}=-|0.1|x+5](https://tex.z-dn.net/?f=%5Csqrt%7B2x-11%7D%3D-%7C0.1%7Cx%2B5)
![2x-11=(-|0.1|x+5)^2](https://tex.z-dn.net/?f=2x-11%3D%28-%7C0.1%7Cx%2B5%29%5E2)
![2x-11=0.01x^2 - 10|0.1|x+25](https://tex.z-dn.net/?f=2x-11%3D0.01x%5E2%20-%2010%7C0.1%7Cx%2B25)
![2x=0.01x^2 - 10|0.1|x+25+11](https://tex.z-dn.net/?f=2x%3D0.01x%5E2%20-%2010%7C0.1%7Cx%2B25%2B11)
![2x=0.01x^2 - 10|0.1|x+36](https://tex.z-dn.net/?f=2x%3D0.01x%5E2%20-%2010%7C0.1%7Cx%2B36)
![0.01x^2 - 10|0.1|x - 2x+36=0](https://tex.z-dn.net/?f=0.01x%5E2%20-%2010%7C0.1%7Cx%20-%202x%2B36%3D0)
When we solve this equation,
We found,
x = 12.5227 ≈ 12.53
Thus, the required solution is, x = 12.53
12) Here the height of rocket A in x second,
![f(x) = -16x^2+74x+9](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-16x%5E2%2B74x%2B9)
And, The height gain by the rocket B in x seconds,
![g(x) = -16x^2+82x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-16x%5E2%2B82x)
If at x seconds both A and B gain the same height,
That is, f(x) = g(x)
⇒ ![-16x^2+74x+9= -16x^2+82x](https://tex.z-dn.net/?f=-16x%5E2%2B74x%2B9%3D%20-16x%5E2%2B82x)
⇒![74x + 9 = 82x](https://tex.z-dn.net/?f=74x%20%2B%209%20%3D%2082x)
⇒ ![82x - 74x = 9](https://tex.z-dn.net/?f=82x%20-%2074x%20%3D%209)
⇒ ![8x = 9](https://tex.z-dn.net/?f=8x%20%3D%209)
⇒ x = 1.125 ≈ 1.13
Thus, the required solution is x = 1.13 seconds (approx)
Answer:
90
Step-by-step explanation:
Answer:
C. 2^x+1
Step-by-step explanation:
Graph
<h3>
Answer: 9 meters</h3>
===========================================
Work Shown:
- side a = 8
- side b = 5
- angle C = 88 degrees
Applying the law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 8^2 + 5^2 - 2*8*5*cos(88)
c^2 = 64 + 25 - 80*cos(88)
c^2 = 86.2080403
c = sqrt(86.2080403)
c = 9.2848285
c = 9
Technically he needs 10 meters of rope because of the extra 0.28 portion, but I'll stick with 9 meters since your teacher said to round to the nearest whole number.
Answer:
£10,200
Step-by-step explanation:
Simple interest = principal × rate × time
Principal = £6000
Rate = 7% = 0.07
Time = 10 years
Simple interest = principal × rate × time
= £6000 × 0.07 × 10
= £4,200
Total = simple interest + principal
= £4,200 + £6,000
= £10,200
He would have to pay back a total of £10,200 in 10 years