Answer:
42,47,91
Step-by-step explanation:
Let the first angle = x
Second angle = 5 degree more = 5 + x
3rd angle = 7 degree more than two times = 7 + 2x
NOTE : sum of angles in a triangle = 180
X + 5+ x + 7 + 2x = 180
Collect like terms
X+x+2x +5 +7 = 180
4x + 12 = 180
4x = 180 - 12
4x = 168
Divide both sides by 4
4x/4 = 168/4
X = 42 degree
First angle = 42 degree
2nd angle = 5 + x = 5+42 = 47 degree
3rd angle = 7 + 2x = 7 + 2(42)
=7 + 84 = 91 degree
I hope this was helpful, Please mark as brainliest
Answer:
65,000 g is equivalent to 65 kilograms
Answer:
Explanation:
<u>1. Assume she runs up to a point that is x miles to the east of the coral reef:</u>
- distance running =
![9-x\text{ }miles](https://tex.z-dn.net/?f=9-x%5Ctext%7B%20%7Dmiles)
- distance swimming =
![\sqrt{x^2+6^2}=\sqrt{x^2+36}\text{ }miles](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%2B6%5E2%7D%3D%5Csqrt%7Bx%5E2%2B36%7D%5Ctext%7B%20%7Dmiles)
<u>2. Times:</u>
time= distance / speed
- time running =
![\dfrac{9-x}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7B9-x%7D%7B4%7D)
- time swimming =
![\dfrac{\sqrt{x^2+36} }{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7Bx%5E2%2B36%7D%20%7D%7B2%7D)
<u>3. Total time</u>
- time running + time swimming:
![T=\dfrac{9-x}{4}+\dfrac{\sqrt{x^2+36} }{2}](https://tex.z-dn.net/?f=T%3D%5Cdfrac%7B9-x%7D%7B4%7D%2B%5Cdfrac%7B%5Csqrt%7Bx%5E2%2B36%7D%20%7D%7B2%7D)
<u>4. Minimize time</u>
The minimum time is when the derivative of the function of time is zero.
Find the derivative of T(x), using rule of the sum, the derivative of the sum is the sum of the derivatives, and the chain rule:
![\dfrac{dT}{dx}=\dfrac{-1}{4}+\dfrac{1}{2}\cdot \dfrac{1}{2}\dfrac{2x}{\sqrt{x^2+36}}=0](https://tex.z-dn.net/?f=%5Cdfrac%7BdT%7D%7Bdx%7D%3D%5Cdfrac%7B-1%7D%7B4%7D%2B%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D%5Cdfrac%7B2x%7D%7B%5Csqrt%7Bx%5E2%2B36%7D%7D%3D0)
Solve for x:
![\dfrac{2x}{\sqrt{x^2+36}}=1\\ \\ \\ 2x=\sqrt{x^2+36\\ } \\ \\ (2x)^2=x^2+36\\ \\ \\ 4x^2=x^2+36\\ \\ \\ 3x^2=36\\ \\ \\ x^2=12\\ \\ \\ x=2\sqrt{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%7D%7B%5Csqrt%7Bx%5E2%2B36%7D%7D%3D1%5C%5C%20%5C%5C%20%5C%5C%202x%3D%5Csqrt%7Bx%5E2%2B36%5C%5C%20%7D%20%5C%5C%20%5C%5C%20%282x%29%5E2%3Dx%5E2%2B36%5C%5C%20%5C%5C%20%5C%5C%204x%5E2%3Dx%5E2%2B36%5C%5C%20%5C%5C%20%5C%5C%203x%5E2%3D36%5C%5C%20%5C%5C%20%5C%5C%20x%5E2%3D12%5C%5C%20%5C%5C%20%5C%5C%20x%3D2%5Csqrt%7B3%7D)
<u>5. Distance the visitor should run to minimize the time</u>
Hence, the visitor should run
miles.
4+4i
(4)^2+(4)^2=32
sqrt(32)=5.66
So your answer would be D
Salutations!
A master plan is devised for -----
A master plan is devised for long term goals. You need to have a proper master plan in order to achieve your long term goal. Becoming a doctor needs to have a master plan.
Thus, your answer is option C.
Hope I helped (:
Have a great day!