Answer:
The midpoint is (-1,-1)
This is in quadrant III
Step-by-step explanation:
The x coordinate of the midpoint is
(-4+2)/2 = -2/2 = -1
The y coordinate of the midpoint is
(1+-3)/2 = -2/2 = -1
The midpoint is (-1,-1)
The quadrant with both negative points is quadrant III
a. Let
be the number of daytime calls Eshwa makes, and
the number of evening calls. Then the cost
(in pence) of making
calls is
![C = \boxed{50d + 40e}](https://tex.z-dn.net/?f=C%20%3D%20%5Cboxed%7B50d%20%2B%2040e%7D)
b. £1 = 100p, so the cost
(in £) is 1/100 of the cost found in part (a),
![C' = \dfrac{50d + 40e}{100} = \boxed{\dfrac d2 + \dfrac{2e}5}](https://tex.z-dn.net/?f=C%27%20%3D%20%5Cdfrac%7B50d%20%2B%2040e%7D%7B100%7D%20%3D%20%5Cboxed%7B%5Cdfrac%20d2%20%2B%20%5Cdfrac%7B2e%7D5%7D)
c. If Eshwa makes 30 of each type of call in a month, then the total cost (in £) is
![C' = \dfrac{30}2 + \dfrac{2\cdot30}5 = \boxed{27}](https://tex.z-dn.net/?f=C%27%20%3D%20%5Cdfrac%7B30%7D2%20%2B%20%5Cdfrac%7B2%5Ccdot30%7D5%20%3D%20%5Cboxed%7B27%7D)
c2. If Eshwa makes 20 daytime calls and 50 evening calls, then the total cost (in £) is
![C' = \dfrac{20}2 + \dfrac{2\cdot50}5 = \boxed{30}](https://tex.z-dn.net/?f=C%27%20%3D%20%5Cdfrac%7B20%7D2%20%2B%20%5Cdfrac%7B2%5Ccdot50%7D5%20%3D%20%5Cboxed%7B30%7D)
d. Let
and
. Solve for
.
![42 = \dfrac d2 + \dfrac{2\cdot40}5](https://tex.z-dn.net/?f=42%20%3D%20%5Cdfrac%20d2%20%2B%20%5Cdfrac%7B2%5Ccdot40%7D5)
![42 = \dfrac d2 + 16](https://tex.z-dn.net/?f=42%20%3D%20%5Cdfrac%20d2%20%2B%2016)
![\dfrac d2 = 26](https://tex.z-dn.net/?f=%5Cdfrac%20d2%20%3D%2026)
![d = \boxed{52}](https://tex.z-dn.net/?f=d%20%3D%20%5Cboxed%7B52%7D)
<span>fifty-eight and seven-tenths</span>
Answer:
the height of the tree to the nearest tenth of a meter is 13.8 meters
Step-by-step explanation:
The computation of the height of the tree is shown below:
Given that
Distance from the tree is 10 meters
And, the angle of elevation of the tree is 54 degrees
Now here we used the trigonometry
![tan \theta = \frac{Height}{distance} \\\\tan 54^{\circ} = \frac{height}{10}](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%3D%20%5Cfrac%7BHeight%7D%7Bdistance%7D%20%5C%5C%5C%5Ctan%2054%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7Bheight%7D%7B10%7D)
So, the height is
= 10 × 1.38
= 13.8 meters
hence, the height of the tree to the nearest tenth of a meter is 13.8 meters