The angle between the two tangents drawn from an external point to a circle and the angle subtended by the line segment joining the points of the contact at the Centre are supplymentary,
So,
15.) let the unknown angle be x
=》x + 55° = 180°
=》x = 180° - 55°
=》
![\boxed{x = 125°}](https://tex.z-dn.net/?f=%20%5Cboxed%7Bx%20%3D%20125%C2%B0%7D)
16. let the unknown angle be n
=》n + 80° = 180°
=》n = 180° - 80°
=》
![\boxed{n = 100°}](https://tex.z-dn.net/?f=%20%5Cboxed%7Bn%20%3D%20100%C2%B0%7D)
![\bf f(x)=\cfrac{x}{x^2+2}\implies \cfrac{dy}{dx}=\cfrac{1(x^2+2)-(x)(2x)}{(x^2+2)^2}\\\\\\ \cfrac{dy}{dx}=\cfrac{x^2+2-2x^2}{(x^2+2)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{2-x^2}{(x^2+2)^2}\implies 0=2-x^2\implies x=\pm\sqrt{2} \\\\\\ \textit{now }-\sqrt{2}\textit{ is outside the range of }[0,4],\textit{ so is only }\sqrt{2}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%3D%5Ccfrac%7Bx%7D%7Bx%5E2%2B2%7D%5Cimplies%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3D%5Ccfrac%7B1%28x%5E2%2B2%29-%28x%29%282x%29%7D%7B%28x%5E2%2B2%29%5E2%7D%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3D%5Ccfrac%7Bx%5E2%2B2-2x%5E2%7D%7B%28x%5E2%2B2%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%3D%5Ccfrac%7B2-x%5E2%7D%7B%28x%5E2%2B2%29%5E2%7D%5Cimplies%200%3D2-x%5E2%5Cimplies%20x%3D%5Cpm%5Csqrt%7B2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Bnow%20%7D-%5Csqrt%7B2%7D%5Ctextit%7B%20is%20outside%20the%20range%20of%20%7D%5B0%2C4%5D%2C%5Ctextit%7B%20so%20is%20only%20%7D%5Csqrt%7B2%7D)
the denominator yields no critical points, so is only that one, which IS within the range of [0, 4].
f(0) = 0 and f(4) is about 0.2222... whilst f(√2) is about 0.3536
now, doing a first-derivative test, the √2 points is a maximum, and and the 0 and 4 are both minima, from which the 0 is lowest than the 4, notice f(0) = 0 and f(4) is up above that.
so the absolute minimum is f(0), and the absolute maximum is f(√2).
Answer:
A
Step-by-step explanation:
B - 11,015 = 2t ( add 11,015 to both sides )
B = 2t + 11,015 , that is
B(t) = 2t + 11,015
Answer:
II case.
Step-by-step explanation:
Given that a catering company prepared and served 300 meals at an anniversary celebration last week using eight workers.
The week before, six workers prepared and served 240 meals at a wedding reception.
Productivity is normally measured by number of outputs/number of inputs
Here we can measure productivity as
no of meals served/no of workers
In the I case productivity =![\frac{300}{8} \\=37.5](https://tex.z-dn.net/?f=%5Cfrac%7B300%7D%7B8%7D%20%5C%5C%3D37.5)
In the II case productivity = ![\frac{240}{6} \\=40](https://tex.z-dn.net/?f=%5Cfrac%7B240%7D%7B6%7D%20%5C%5C%3D40)
Obviously II case productivity is more as per worker 40 meals were served which is more than 37.5 meals per worker in the I case.
Evaluate j k − 0.2 k k j −0.2kstart fraction, j, divided by, k, end fraction, minus, 0, point, 2, k when j = 25 j=25j, equals,
maria [59]
Answer:
4
Step-by-step explanation:
Fill in the numbers and do the arithmetic:
![\dfrac{25}{5}-0.2\cdot 5=5-1=4](https://tex.z-dn.net/?f=%5Cdfrac%7B25%7D%7B5%7D-0.2%5Ccdot%205%3D5-1%3D4)
For the given values, the expression evaluates to 4.