Answer:
The system has zero solutions.
Answer:
Bailey: 16%
Coco: 28%
Ginger: 32%
Ruby: 24%
<em>I hope this helps!</em>
The maximum height is 9.0 feet and the time to hit the ground is 4.5 seconds
<h3>How to determine the maximum height?</h3>
The function is given as:
f(x) = -0.6x^2 + 2.7x + 6
Differentiate
f'(x) = -1.2x + 2.7
Set to 0
-1.2x + 2.7 = 0
Subtract 2.7 from both sides
-1.2x = -2.7
Divide both sides by -1.2
x = 2.25
Substitute x = 2.25 in f(x) = -0.6x^2 + 2.7x + 6
f(2.25) = -0.6(2.25)^2 + 2.7(2.25) + 6
Evaluate
f(2.25) = 9.0
Hence, the maximum height is 9.0 feet
<h3>How to determine the time to hit the ground?</h3>
The time to hit the ground is twice the time to reach the maximum height.
In (a), we have:
x = 2.25
So, we have:
Time = 2 * 2.25
Evaluate
Time = 4.5
Hence, the time to hit the ground is 4.5 seconds
Read more about quadratic functions at:
brainly.com/question/1214333
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Answer:
Step-by-step explanation:
cos²<em>x</em> = 1-sin²<em>x</em> = 1-(5/13)² = 144/169
cos<em>x</em> = √(144/169) = 12/13
tan<em>x</em> = sin<em>x</em>/cos<em>x </em>= (5/13)/(12/13) = (5/13)×(13/12) = 5/12
Answer:
0
Step-by-step explanation:
First we need to find the value of constant k in equation. To find k we use the formula:
![\int\limits^{100}_0 {ke^{-0.01x}} \, dx =1\\Integrating:\\k\int\limits^{100}_0 {e^{-0.01x}} \, dx =1\\\frac{k}{-0.01}[e^{-0.01x}]_0^{100}=1\\-100k [e^{-0.01x}]_0^{100}=1\\-100k[e^{-0.01*100}-e^{-100*0}]=1\\-100k[e^{-1}-e^0]=1\\-100k(-0.632)=1\\63.2k = 1\\k=0.0158](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B100%7D_0%20%7Bke%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%3D1%5C%5CIntegrating%3A%5C%5Ck%5Cint%5Climits%5E%7B100%7D_0%20%7Be%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%3D1%5C%5C%5Cfrac%7Bk%7D%7B-0.01%7D%5Be%5E%7B-0.01x%7D%5D_0%5E%7B100%7D%3D1%5C%5C-100k%20%5Be%5E%7B-0.01x%7D%5D_0%5E%7B100%7D%3D1%5C%5C-100k%5Be%5E%7B-0.01%2A100%7D-e%5E%7B-100%2A0%7D%5D%3D1%5C%5C-100k%5Be%5E%7B-1%7D-e%5E0%5D%3D1%5C%5C-100k%28-0.632%29%3D1%5C%5C63.2k%20%3D%201%5C%5Ck%3D0.0158)
the probability that a person age 20 will live for at least 20 more years = P(40 ≤ x <∞).
The person would live for at least 40 years
Therefore:
P(40 ≤ x <∞) =
![\int\limits^{\infty}_{40} 0.0158e^{-0.01x}} \, dx \\Integrating:\\0.0158\int\limits^{\infty}_{40} {e^{-0.01x}} \, dx =\frac{0.0158}{-0.01}[e^{-0.01x}]_{40}^{\infty}\\=-1.58 [e^{-0.01x}]_{40}^{\infty}=-1.58[e^{-\infty}-e^{-100*40}]\\=-1.58[e^{-\infty}-e^{-4000}]=-1.58(0-0)=0](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B40%7D%200.0158e%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%5C%5CIntegrating%3A%5C%5C0.0158%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B40%7D%20%7Be%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%3D%5Cfrac%7B0.0158%7D%7B-0.01%7D%5Be%5E%7B-0.01x%7D%5D_%7B40%7D%5E%7B%5Cinfty%7D%5C%5C%3D-1.58%20%5Be%5E%7B-0.01x%7D%5D_%7B40%7D%5E%7B%5Cinfty%7D%3D-1.58%5Be%5E%7B-%5Cinfty%7D-e%5E%7B-100%2A40%7D%5D%5C%5C%3D-1.58%5Be%5E%7B-%5Cinfty%7D-e%5E%7B-4000%7D%5D%3D-1.58%280-0%29%3D0)