Answer: x = 133 degrees
Step-by-step explanation:
Well this problem becomes a lot easier when you break it down into steps and understand parallel lines and the angles that are formed from them. We are trying to work out what x would be so the first step would be to find an easy way to accomplish this. If you know the different types of angles that are formed from parallel lines we would know that corresponding angles are = to each other. This means that the 47 degree angle is the same as the angle directly above this, which I hope you too can visualize in the image as well. Since this new 47 degree angle that we figured out is right next to the angle we want to find out the value for the next step is quite simple. Since we of course know that a straight line is 180 degrees we just need to subtract 47 from 180 to find this x value as it would be whatever forms a straight line. 180-47=133 so the answer is x = 133 degrees. I hope this has helped you and please do no hesitate to ask further follow up questions! Have a wonderful rest of your day :)
Step-by-step explanation:
The height, h in feet, of a rocket is given by, where t is time in seconds.
...(1)
We need to find the maximum height of the rocket and find the time the rocket was in the air. For maximum height, put ![\dfrac{dh}{dt}=0](https://tex.z-dn.net/?f=%5Cdfrac%7Bdh%7D%7Bdt%7D%3D0)
![\dfrac{d(-16t^2+64t+190)}{dt}=0\\\\-32t+64=0\\\\t=\dfrac{64}{32}\\\\t=2\ s](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%28-16t%5E2%2B64t%2B190%29%7D%7Bdt%7D%3D0%5C%5C%5C%5C-32t%2B64%3D0%5C%5C%5C%5Ct%3D%5Cdfrac%7B64%7D%7B32%7D%5C%5C%5C%5Ct%3D2%5C%20s)
So, it will reach its maximum height in 2 seconds.
Now put t = 2 in equation (1) as follows :
![h(2)=-16(2)^2+64(2)+190\\\\=254\ \text{feet}](https://tex.z-dn.net/?f=h%282%29%3D-16%282%29%5E2%2B64%282%29%2B190%5C%5C%5C%5C%3D254%5C%20%5Ctext%7Bfeet%7D)
So, the maximum height of the rocket and find the time the rocket was in the air is 254 feet and 2 seconds respectively.
<span>Since 1' = 12'', so the scale 1/4'' to 1' is 1/4'' to 12'', or, multiplying both sides by 4, 1 to 48. </span>
<span>Convert all dimensions given from foot/inches to inches, then scale them down, dividing by 48. </span>
10ft 6in=10*12+6=126+6=132 dividing by 48. 132/48=2.75/48=0.0572*1000=57.2 inches
<span>18' 8'' = 18 * 12 + 8 inches = 216 + 8 = 224 inches. Dividing by 48: 224/48 = 4 32/48 = 4 2/3 inch*1000=66.6
</span>
Answer:
<em>y = 150</em>
Step-by-step explanation:
<u>Proportions</u>
It's given y is directly proportional to the square of x-1. It can be expressed as:
![y=k(x-1)^2](https://tex.z-dn.net/?f=y%3Dk%28x-1%29%5E2)
Where k is the constant of proportionality. We know y=24 when x=3. Substituting:
![24=k(3-1)^2](https://tex.z-dn.net/?f=24%3Dk%283-1%29%5E2)
![24=k(2)^2=4k](https://tex.z-dn.net/?f=24%3Dk%282%29%5E2%3D4k)
Solving for k:
k = 24/4 = 6
Thus, the equation is:
![y=6(x-1)^2](https://tex.z-dn.net/?f=y%3D6%28x-1%29%5E2)
When x=6:
![y=6(6-1)^2=6(5)^2=6*25](https://tex.z-dn.net/?f=y%3D6%286-1%29%5E2%3D6%285%29%5E2%3D6%2A25)
y = 150