Answer:
ab = 49
abc=253
bac=156
acb=311
Step-by-step explanation:
Answer:
Equal to
Step-by-step explanation:
The angle of depression from object A to object B is always Equal to the angle of elevation from object B to object A.
It was in the notes in slide 7 in the bottom
Answer:
4.41 feet per second.
Step-by-step explanation:
Please find the attachment.
We have been given that a man flies a kite at a height of 16 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. We are asked to find how fast must he let out the string when the kite is flying on 34 ft. of string.
We will use Pythagoras theorem to solve for the length of side x as:
![x^2+16^2=34^2](https://tex.z-dn.net/?f=x%5E2%2B16%5E2%3D34%5E2)
![x^2=34^2-16^2](https://tex.z-dn.net/?f=x%5E2%3D34%5E2-16%5E2)
![x^2=900\\\\x=30](https://tex.z-dn.net/?f=x%5E2%3D900%5C%5C%5C%5Cx%3D30)
Now, we will use Pythagorean theorem to relate x and y because we know that the vertical side (16) is always constant.
![x^2+16^2=y^2](https://tex.z-dn.net/?f=x%5E2%2B16%5E2%3Dy%5E2)
Let us find derivative of our equation with respect to time (t) using power rule and chain rule as:
![2x\cdot \frac{dx}{dt}+0=2y\cdot \frac{dy}{dt}](https://tex.z-dn.net/?f=2x%5Ccdot%20%5Cfrac%7Bdx%7D%7Bdt%7D%2B0%3D2y%5Ccdot%20%5Cfrac%7Bdy%7D%7Bdt%7D)
We have been given that
,
and
.
![2(30)\cdot 5=2(34)\cdot \frac{dy}{dt}](https://tex.z-dn.net/?f=2%2830%29%5Ccdot%205%3D2%2834%29%5Ccdot%20%5Cfrac%7Bdy%7D%7Bdt%7D)
![300=68\cdot \frac{dy}{dt}](https://tex.z-dn.net/?f=300%3D68%5Ccdot%20%5Cfrac%7Bdy%7D%7Bdt%7D)
![\frac{dy}{dt}=\frac{300}{68}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%3D%5Cfrac%7B300%7D%7B68%7D)
![\frac{dy}{dt}=4.4117647058823529](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%3D4.4117647058823529)
![\frac{dy}{dt}\approx 4.41](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%5Capprox%204.41)
Therefore, the man must let out the string at a rate of 4.41 feet per second.
Answer:
The scale factor of given coordinate
A is correct.
Step-by-step explanation:
We are given two coordinate O and K. The dilation with respect to origin.
![D_{O,K}(6,12)\rightarrow (3,6)](https://tex.z-dn.net/?f=D_%7BO%2CK%7D%286%2C12%29%5Crightarrow%20%283%2C6%29)
For scale factor,
![(x,y)\rightarrow (ax,ay)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28ax%2Cay%29)
a is scale factor of coordinate.
If we divide new coordinate with old coordinate to get scale factor.
![\text{ scale factor}=\dfrac{\text{x-value of new coordinate }}{\text{x-value of old coordinate}}](https://tex.z-dn.net/?f=%5Ctext%7B%20scale%20factor%7D%3D%5Cdfrac%7B%5Ctext%7Bx-value%20of%20new%20coordinate%20%7D%7D%7B%5Ctext%7Bx-value%20of%20old%20coordinate%7D%7D)
![\text{ scale factor}=\dfrac{3}{6}=\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Ctext%7B%20scale%20factor%7D%3D%5Cdfrac%7B3%7D%7B6%7D%3D%5Cdfrac%7B1%7D%7B2%7D)
Hence, The scale factor of given coordinate