Answer:
Grocery mart=1.495 per pound
baldwin hills=1.33 per pound
Step-by-step explanation:
-5
Write tan in terms of sin and cos.
![\displaystyle \lim_{t\to0}\frac{\tan(6t)}{\sin(2t)} = \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B%5Ctan%286t%29%7D%7B%5Csin%282t%29%7D%20%3D%20%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B%5Csin%286t%29%7D%7B%5Csin%282t%29%5Ccos%286t%29%7D)
Recall that
![\displaystyle \lim_{x\to0}\frac{\sin(x)}x = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%5Csin%28x%29%7Dx%20%3D%201)
Rewrite and expand the given limand as the product
![\displaystyle \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)} = \lim_{t\to0} \frac{\sin(6t)}{6t} \times \frac{2t}{\sin(2t)} \times \frac{6t}{2t\cos(6t)} \\\\ = \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B%5Csin%286t%29%7D%7B%5Csin%282t%29%5Ccos%286t%29%7D%20%3D%20%5Clim_%7Bt%5Cto0%7D%20%5Cfrac%7B%5Csin%286t%29%7D%7B6t%7D%20%5Ctimes%20%5Cfrac%7B2t%7D%7B%5Csin%282t%29%7D%20%5Ctimes%20%5Cfrac%7B6t%7D%7B2t%5Ccos%286t%29%7D%20%5C%5C%5C%5C%20%3D%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%20%5Cfrac%7B%5Csin%286t%29%7D%7B6t%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B2t%7D%7B%5Csin%282t%29%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B3%7D%7B%5Ccos%286t%29%7D%5Cright%29)
Then using the known limit above, it follows that
![\displaystyle \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right) = 1 \times 1 \times \frac3{\cos(0)} = \boxed{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%20%5Cfrac%7B%5Csin%286t%29%7D%7B6t%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B2t%7D%7B%5Csin%282t%29%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B3%7D%7B%5Ccos%286t%29%7D%5Cright%29%20%3D%201%20%5Ctimes%201%20%5Ctimes%20%5Cfrac3%7B%5Ccos%280%29%7D%20%3D%20%5Cboxed%7B3%7D)
Answer:
27, 90 and 63
Step-by-step explanation:
Given
Ratio of triangle sides
![Ratio = 3 : 10 : 7](https://tex.z-dn.net/?f=Ratio%20%3D%203%20%3A%2010%20%3A%207)
Required:
The length of each side
Triangles in a triangle add up to 180.
The side with ratio 3 is:
![S_1 = \frac{3}{3 + 10 + 7} *180](https://tex.z-dn.net/?f=S_1%20%3D%20%5Cfrac%7B3%7D%7B3%20%2B%2010%20%2B%207%7D%20%2A180)
![S_1 = \frac{3 *180}{20}](https://tex.z-dn.net/?f=S_1%20%3D%20%5Cfrac%7B3%20%2A180%7D%7B20%7D)
![S_1 = \frac{540}{20}](https://tex.z-dn.net/?f=S_1%20%3D%20%5Cfrac%7B540%7D%7B20%7D)
![S_1 = 27](https://tex.z-dn.net/?f=S_1%20%3D%2027)
The side with ratio 10 is:
![S_2 = \frac{10}{3 + 10 + 7} *180](https://tex.z-dn.net/?f=S_2%20%3D%20%5Cfrac%7B10%7D%7B3%20%2B%2010%20%2B%207%7D%20%2A180)
![S_2 = \frac{10 *180}{20}](https://tex.z-dn.net/?f=S_2%20%3D%20%5Cfrac%7B10%20%2A180%7D%7B20%7D)
![S_2 = \frac{1800}{20}](https://tex.z-dn.net/?f=S_2%20%3D%20%5Cfrac%7B1800%7D%7B20%7D)
![S_2 = 90](https://tex.z-dn.net/?f=S_2%20%3D%2090)
Lastly:
The side with 7 as its ratio
![S_3 = \frac{7}{3 + 10 + 7} *180](https://tex.z-dn.net/?f=S_3%20%3D%20%5Cfrac%7B7%7D%7B3%20%2B%2010%20%2B%207%7D%20%2A180)
![S_3 = \frac{7 *180}{20}](https://tex.z-dn.net/?f=S_3%20%3D%20%5Cfrac%7B7%20%2A180%7D%7B20%7D)
![S_3 = \frac{1260}{20}](https://tex.z-dn.net/?f=S_3%20%3D%20%5Cfrac%7B1260%7D%7B20%7D)
![S_3 = 63](https://tex.z-dn.net/?f=S_3%20%3D%2063)
Hence, the angles are: 27, 90 and 63
<h2>
Answer:</h2>
y=
*x+4.5
<h2>
Step-by-step explanation:</h2>
We are given a slope and a point. That is why we will use point slope form.
The default equation is:
(y-a)=m*(x-b)
a is the y coordinate of our point and b is the x coordinate of our point
m is the slope.
We will plug in the values.
(y-10.5)=3/2*(x-4)
Now we just manipulate the equation
y=
*x+4.5