Answer:
18 is 6/10
18/1 = 6/10
Cross multiply
18x10 is 180
180/6 is 30 tiles total
Step-by-step explanation:
Following are the responses to the given points:
For point a:
![Diameter\ (d)= 16\ m\\\\](https://tex.z-dn.net/?f=Diameter%5C%20%28d%29%3D%2016%5C%20m%5C%5C%5C%5C)
Calculating the 3 rotations for every minute:
Calculating time for completing 1 rotation:
The standard form of the equation of the sine and cosine function is:
Calculating the Amplitue:
![A=\frac{max-min}{2}=\frac{17-1}{2}=\frac{16}{2}=8\\\\Period=\frac{2\pi}{B}\\\\20=\frac{2\pi}{B}\\\\B=\frac{2\pi}{20}\\\\B=\frac{\pi}{10}\\\\](https://tex.z-dn.net/?f=A%3D%5Cfrac%7Bmax-min%7D%7B2%7D%3D%5Cfrac%7B17-1%7D%7B2%7D%3D%5Cfrac%7B16%7D%7B2%7D%3D8%5C%5C%5C%5CPeriod%3D%5Cfrac%7B2%5Cpi%7D%7BB%7D%5C%5C%5C%5C20%3D%5Cfrac%7B2%5Cpi%7D%7BB%7D%5C%5C%5C%5CB%3D%5Cfrac%7B2%5Cpi%7D%7B20%7D%5C%5C%5C%5CB%3D%5Cfrac%7B%5Cpi%7D%7B10%7D%5C%5C%5C%5C)
Calculating the phase shift:
for
function:
for
function:
Calculating the vertical shift:
![\to D=\frac{max+ min }{2}=\frac{17+ 1}{2}=\frac{18}{2}=9\\\\y=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\y=8 \cos \{ \frac{\pi}{10}(t-10)\} +9\\\\](https://tex.z-dn.net/?f=%5Cto%20D%3D%5Cfrac%7Bmax%2B%20min%20%7D%7B2%7D%3D%5Cfrac%7B17%2B%201%7D%7B2%7D%3D%5Cfrac%7B18%7D%7B2%7D%3D9%5C%5C%5C%5Cy%3D8%20%5Csin%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%5C%7D%20%2B9%5C%5C%5C%5Cy%3D8%20%5Ccos%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-10%29%5C%7D%20%2B9%5C%5C%5C%5C)
For point b:
![y> 12\ m\\\\12=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\12-9=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\3=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\\frac{3}{8}=\sin \{ \frac{\pi}{10}(t-5)\} \\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (0.38439677)=(t-5) \\\\1.22357+5=t \\\\t=6.22357\ second\\\\t=6.22\ second\\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (2.7571961)=(t-5) \\\\t=8.7764+5\\\\t=13.78\ second\\\\t_2-t_1=13.7764-6.22357= 7.55283\approx 7.55\ second \\\\](https://tex.z-dn.net/?f=y%3E%2012%5C%20m%5C%5C%5C%5C12%3D8%20%5Csin%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%5C%7D%20%2B9%5C%5C%5C%5C12-9%3D8%20%5Csin%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%5C%7D%20%5C%5C%5C%5C3%3D8%20%5Csin%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%5C%7D%20%5C%5C%5C%5C%5Cfrac%7B3%7D%7B8%7D%3D%5Csin%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%5C%7D%20%5C%5C%5C%5C%5Csin%5E%7B-1%7D%5Cfrac%7B3%7D%7B8%7D%3D%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%20%5C%5C%5C%5C%5Cfrac%7B%5Cpi%7D%7B10%7D%20%280.38439677%29%3D%28t-5%29%20%5C%5C%5C%5C1.22357%2B5%3Dt%20%5C%5C%5C%5Ct%3D6.22357%5C%20second%5C%5C%5C%5Ct%3D6.22%5C%20second%5C%5C%5C%5C%5Csin%5E%7B-1%7D%5Cfrac%7B3%7D%7B8%7D%3D%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%20%5C%5C%5C%5C%5Cfrac%7B%5Cpi%7D%7B10%7D%20%282.7571961%29%3D%28t-5%29%20%5C%5C%5C%5Ct%3D8.7764%2B5%5C%5C%5C%5Ct%3D13.78%5C%20second%5C%5C%5C%5Ct_2-t_1%3D13.7764-6.22357%3D%207.55283%5Capprox%207.55%5C%20second%20%5C%5C%5C%5C)
Learn more:
Rotation: brainly.in/question/39626227
The domain of the function is given by (–∞, –3) ∪ (–3, 2) ∪ (2, ∞)
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The function is given by:
![g(x) = \frac{x^2 + 3x}{x^2 + x - 6}, x < 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7Bx%5E2%20%2B%203x%7D%7Bx%5E2%20%2B%20x%20-%206%7D%2C%20x%20%3C%203)
![g(x) = \log_{2}{x + 5}, x \geq 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Clog_%7B2%7D%7Bx%20%2B%205%7D%2C%20x%20%5Cgeq%203)
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- For the second definition, the restriction is that x + 5 has to be positive. Since the definition is only valid for
, this will <u>always be true.</u> - In the second definition, the denominator cannot be zero, thus the <u>zeros of the denominator will be outside the domain.</u>
These zeros are found using Bhaskara, we have the quadratic function
, thus the coefficients are
.
![\Delta = b^2 - 4ac = (1)^2 - 4(1)(-6) = 25](https://tex.z-dn.net/?f=%5CDelta%20%3D%20b%5E2%20-%204ac%20%3D%20%281%29%5E2%20-%204%281%29%28-6%29%20%3D%2025)
![x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-1 + 5}{2} = 2](https://tex.z-dn.net/?f=x_1%20%3D%20%5Cfrac%7B-b%20%2B%20%5Csqrt%7B%5CDelta%7D%7D%7B2a%7D%20%3D%20%5Cfrac%7B-1%20%2B%205%7D%7B2%7D%20%3D%202)
![x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{-1 - 5}{2} = -3](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cfrac%7B-b%20-%20%5Csqrt%7B%5CDelta%7D%7D%7B2a%7D%20%3D%20%5Cfrac%7B-1%20-%205%7D%7B2%7D%20%3D%20-3)
Thus, <u>x = 2 and x = -3 are outside the</u> domain, which is given by:
(–∞, –3) ∪ (–3, 2) ∪ (2, ∞)
A similar problem is given at brainly.com/question/13136492
Tierra's equation: 1.05 x 100 = 105. She will have $105 in her savings account
Cameron's equation. 100 + 0.005 x 100 = 100.5. She will have $100.5 in her savings account.
Justice's equation: 100 x 1.005 = 100.5. She will have $100.5 in her savings account.
The account either has $105.00 or $100.50.
Answer:
-8 < x, the answer is B
Step-by-step explanation:
Since its starting from -8 and your going to the greater side of the numberline teh variable will be greater than -8, whenever the circle is filled it just means greater than or equal to depending on which side its going. If its filled in, it means that its greater than or equal to or less than or equal to depending on which side its going towards.
Reminder:
<--------------- Negative side/Lower -----------------------> Positive side/Greater