C is the correct answer! :)
Answer:
D, 5/13
Step-by-step explanation:
The cosine of an angle is the adjacent side over the hypotenuse. In this case, that is 5/13. Hope this helps!
The height that a ball reaches at a certain time t is given by the equation,
h = 2 - 15t + 5t²
We are asked to compute for the values of t that would allow the ball to reach a height of 7 meters.
Substitute the 7 to the equation,
7 = 2 - 15t + 5t²
Transposing,
5t² - 15t - 7 + 2 = 0
Simplifying,
5t² - 15t - 5 = 0
Divide the equation by 5,
t² - 3t - 1 = 0
The values of t can be calculated through the quadratic formula,
t = (-b +/- sqrt(b² - 4ac))/2a
Substituting,
t = (3 +/-sqrt (9 - 4(-1)) / 2(1)
t = 3.3 or t = -0.30
Since, we cannot have t as a negative number hence, our final answer is:
<em> t = 3.3 s</em>
Answer:
12.9
Step-by-step explanation:
30400=
30400=
\,\,22000e^{0.025t}
22000e
0.025t
Plug in
\frac{30400}{22000}=
22000
30400
=
\,\,\frac{22000e^{0.025t}}{22000}
22000
22000e
0.025t
Divide by 22000
1.3818182=
1.3818182=
\,\,e^{0.025t}
e
0.025t
\ln\left(1.3818182\right)=
ln(1.3818182)=
\,\,\ln\left(e^{0.025t}\right)
ln(e
0.025t
)
Take the natural log of both sides
\ln\left(1.3818182\right)=
ln(1.3818182)=
\,\,0.025t
0.025t
ln cancels the e
\frac{\ln\left(1.3818182\right)}{0.025}=
0.025
ln(1.3818182)
=
\,\,\frac{0.025t}{0.025}
0.025
0.025t
Divide by 0.025
12.9360062=
12.9360062=t
t = 12.9
12.9
