Answer:
<em> </em><em>=0.5</em>
Step-by-step explanation:
1.) Add 0.25 to both sides of the equation
<em>4−0.25=1.75</em>
<em> </em><em> </em><em> </em><em> </em><em>4−0.25+0.25=1.75+0.25</em>
<em>2</em><em>.</em><em>)</em><em> </em>Simplify
⬇️
Add the numbers
⬇️
Add the numbers
<em> </em><em> </em><em> </em><em> </em><em>4=2</em>
<em>3</em><em>.</em><em>)</em><em> </em>Divide both sides of the equation by the same term
<em>4=2</em>
<em> </em><em> </em>
<em> </em><em> </em><em> </em><em>4</em><em>x</em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>2</em>
<em> </em><em> </em><em><u>_</u></em><em><u>_</u></em><em><u>_</u></em><em><u>_</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u> </u></em><em><u>___</u></em>
<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em>
<em> </em><em> </em><em> </em><em> </em><em> </em><em>4</em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>4</em>
<em>4</em><em>.</em><em>)</em><em>Simplify</em>
<em> </em><em> </em><em> </em><em> </em><em> </em>
<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>⬇️</em>
Cancel terms that are in both the numerator and denominator
⬇️
Divide the numbers
⬇️
=0.5
Answer:
all of the triangles are right triangles
Answer:
The number of minutes of the ride that are spent higher than 15 meters above the ground is 18 minutes.
Step-by-step explanation:
We will use the sin function for the height of the Ferris wheel.
![y=A\ sin(B(x+C))+D](https://tex.z-dn.net/?f=y%3DA%5C%20sin%28B%28x%2BC%29%29%2BD)
A = amplitude
C = phase shift
D = Vertical shift
2π/B = period
From the provided information:
A = 15/2 = 7.5 m
![Period=2\\\\\frac{2\pi}{B}=2\\\\B=\pi](https://tex.z-dn.net/?f=Period%3D2%5C%5C%5C%5C%5Cfrac%7B2%5Cpi%7D%7BB%7D%3D2%5C%5C%5C%5CB%3D%5Cpi)
Compute the Vertical shift as follows:
D = A + Distance of wheel from ground
= 7.5 + 1
= 8.5
The equation of height is:
![h(t)=7.5\cdot sin(\pi (t+C))+8.5](https://tex.z-dn.net/?f=h%28t%29%3D7.5%5Ccdot%20sin%28%5Cpi%20%28t%2BC%29%29%2B8.5)
Now at <em>t</em> = 0 the height is, h (t) = 1 m.
Compute the value of <em>C</em> as follows:
![h(t)=7.5\cdot sin(\pi (t+C))+8.5](https://tex.z-dn.net/?f=h%28t%29%3D7.5%5Ccdot%20sin%28%5Cpi%20%28t%2BC%29%29%2B8.5)
![1=7.5\cdot sin(\pi (0+C))+8.5\\\\-7.5=7.5\cdot sin\ \pi C\\\\sin\ \pi C=-1\\\\\pi C=sin^{-1}(-1)\\\\\pi C=\frac{3\pi}{2}\\\\C=\frac{3}{2}](https://tex.z-dn.net/?f=1%3D7.5%5Ccdot%20sin%28%5Cpi%20%280%2BC%29%29%2B8.5%5C%5C%5C%5C-7.5%3D7.5%5Ccdot%20sin%5C%20%5Cpi%20C%5C%5C%5C%5Csin%5C%20%5Cpi%20C%3D-1%5C%5C%5C%5C%5Cpi%20C%3Dsin%5E%7B-1%7D%28-1%29%5C%5C%5C%5C%5Cpi%20C%3D%5Cfrac%7B3%5Cpi%7D%7B2%7D%5C%5C%5C%5CC%3D%5Cfrac%7B3%7D%7B2%7D)
So, the complete equation of height is:
![h(t)=7.5\cdot sin(\pi (t+\frac{3}{2}))+8.5](https://tex.z-dn.net/?f=h%28t%29%3D7.5%5Ccdot%20sin%28%5Cpi%20%28t%2B%5Cfrac%7B3%7D%7B2%7D%29%29%2B8.5)
Compute the number of minutes of the ride that are spent higher than 15 meters above the ground as follows:
h (t) ≥ 15
![h(t)=15\\\\7.5\cdot sin(\pi (t+\frac{3}{2}))+8.5=15\\\\7.5\cdot sin(\pi (t+\frac{3}{2}))=6.5\\\\sin(\pi (t+\frac{3}{2}))=\frac{6.5}{7.5}\\\\(\pi (t+\frac{3}{2}))=sin^{-1}[\frac{13}{15}]\\\\\pi (t+\frac{3}{2})=60.074\\\\t+\frac{3}{2}=19.122\\\\t=17.622\\\\t\approx 18](https://tex.z-dn.net/?f=h%28t%29%3D15%5C%5C%5C%5C7.5%5Ccdot%20sin%28%5Cpi%20%28t%2B%5Cfrac%7B3%7D%7B2%7D%29%29%2B8.5%3D15%5C%5C%5C%5C7.5%5Ccdot%20sin%28%5Cpi%20%28t%2B%5Cfrac%7B3%7D%7B2%7D%29%29%3D6.5%5C%5C%5C%5Csin%28%5Cpi%20%28t%2B%5Cfrac%7B3%7D%7B2%7D%29%29%3D%5Cfrac%7B6.5%7D%7B7.5%7D%5C%5C%5C%5C%28%5Cpi%20%28t%2B%5Cfrac%7B3%7D%7B2%7D%29%29%3Dsin%5E%7B-1%7D%5B%5Cfrac%7B13%7D%7B15%7D%5D%5C%5C%5C%5C%5Cpi%20%28t%2B%5Cfrac%7B3%7D%7B2%7D%29%3D60.074%5C%5C%5C%5Ct%2B%5Cfrac%7B3%7D%7B2%7D%3D19.122%5C%5C%5C%5Ct%3D17.622%5C%5C%5C%5Ct%5Capprox%2018)
Thus, the number of minutes of the ride that are spent higher than 15 meters above the ground is 18 minutes.
Answer:
D cause it equals -45
Step-by-step explanation:
Answer:
the answer is b
Step-by-step explanation: