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salantis [7]
3 years ago
12

Look down below for question

Mathematics
1 answer:
Rainbow [258]3 years ago
3 0
The maximum amount of time the skier is in the air would be the time to "fall" the 50 meters. 

distance = 1/2 a t^2

50 = 1/2 (9.8) t^2

t= 3.2 seconds
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How to turn 2.96 into a mixed number
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First, isolate the decimal. second, put it over the correct denominator based on the decimal place:   96/100.  Next, divide by a number that goes into both 96 and 100. 4 works.... 24/25. And that is your answer, after you add the original 2 back: 2 \frac{24}{25}
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Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =
irga5000 [103]

Answer:  The required solution is y=50e^{0.1386t}.

Step-by-step explanation:

We are given to solve the following differential equation :

\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

\dfrac{dy}{y}=kdt.

Integrating both sides, we get

\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]

Also, the conditions are

y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50

and

y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.

Thus, the required solution is y=50e^{0.1386t}.

8 0
3 years ago
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(9x + 7)(4x + 1)(3x + 4) = 0<br> 1 root<br> 3 roots<br> 4 roots<br> 9 roots
asambeis [7]

Answer:

3 roots

Step-by-step explanation:

(9x+7)(4x+1)(3x+4)=0

x=-7/9 or - 1/4 or - 4/3

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2 years ago
Find all the real cube roots of 0.000064
prohojiy [21]
\sqrt[3]{0.000064}=  \sqrt[3]{ \frac{64}{1,000,000} }= \sqrt[3]{ \frac{4^3}{100^3} }=  \sqrt[3]{ (\frac{4}{100})^3 }= \frac{4}{100}=0.04
6 0
3 years ago
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