3 years ago

Help pleaseeee attachment below

1 answer:

8 0

Graph the step function on paper and you will see that the maximum y-value is 5. Thus the only possible answer is B.

f(x) ≤ 5

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Colt1911 [192]

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3 years ago

Find the length of the curve x=e^t e^{-t},\;\;y=5-2t,\;\;0 \le t \le 3.

Oksana_A [137]

$\begin{cases}x(t)=e^t+e^{-t}\\y(t)=5-2t\end{cases}\implies\begin{cases}x'(t)=e^t-e^{-t}\\y'(t)=-2\end{cases}$

The length of the curve is given by the integral

$\displaystyle\int_0^3\sqrt{(e^t-e^{-t})^2+(-2)^2}\,\mathrm dt$

Expand and rewrite the integrand:

$(e^t-e^{-t})^2+(-2)^2=e^{2t}+2+e^{-2t}$
$=e^{-2t}(e^{4t}+2e^{2t}+1)$
$=e^{-2t}(e^{2t}+1)^2$
$\implies\sqrt{(e^t-e^{-t})^2+(-2)^2}=\dfrac{e^{2t}+1}{e^t}$

Now the integral is

$\displaystyle\int_0^3\dfrac{e^{2t}+1}{e^t}\,\mathrm dt=\int_0^3(e^t+e^{-t})\,\mathrm dt$
$=2\displaystyle\int_0^3\cosh t\,\mathrm dt$
$=2\sinh t\bigg|_{t=0}^{t=3}$
$=2\sinh 3$

7 0

3 years ago

Ramona went to a theme park during spring break. She was there for 9 hours and rode 18 rides. At what rate did Ramona ride rides

LenaWriter [7]

Answer:

2 rides per hour

Step-by-step explanation:

she rode 18 rides in 9 hours

therefore rate at which she rides = 18/9 = 2

4 0

3 years ago

Plzzzzz help me..write a word sentence for the equation 4 1/3 + q =5 1/6

quester [9]

Four and one third plus q equals five and one sixth

5 0

4 years ago

Which is the best estimate of x based on rounding the constants and coefficients in the equation to the nearest integer? 6.2x+1.

DerKrebs [107]

<span>6.2x+1.2=8.9
</span>estimate<span>
6x + 1 = 9
6x = 8
x = 8/6
x = 1.33

answer
x = 1.33</span>

7 0

3 years ago