Find each measurement indicated.

c. If Biff is rational, and has no intention of winning the hot dog eating contest, what is the optimal number of hot dogs he wi

Afina-wow [57]

Answer:

8 units of Hot dog

Step-by-step explanation:

Total utility refers to the utility in which the is satisfaction after consuming the multiple units from a good or a service

As we can see from the attached figure that at the number of 8 hot dogs the total utility is maximum i.e 55

Therefore in the given case, the optimal number of hot dogs he will eat is 8 as at this point the total utility is more as compared to the other utilities

5 0

3 years ago

The height of a tree at time t is given by a twice-differentiable function H, where H(t) is measured in meters and t is measured

il63 [147K]

A) Use the mean value theorem.

$H'(6)\approx\dfrac{H(7)-H(5)}{7-5}=\dfrac{11-6}2=\dfrac52\text{ meters/year}$

Since $H(t)$ gives the tree's height in meters at time $t$ , the value of $H'(6)$ informs us how quickly the tree is growing exactly after 6 years have passed. (i.e. the instantaneous rate of change of the tree's height)

b) We use the mean value theorem again. Observe that $H(5)-H(3)=6-2=4$ , and that $5-3=2$ . By the MVT, there must be some $3$ such that

$H'(t)=\dfrac42=2$

c) The average height of the tree is given by the integral

$\displaystyle\frac1{10-2}\int_2^{10}H(t)\,\mathrm dt$

If you can remember the formula for the area of a trapezoid, then this is pretty easy to compute. With five data points, you end up with four trapezoids constructed by the four adjacent subintervals. The "bases" are given by the values of $H(t)$ at each pair of endpoints, and the "heights" are the lengths of the subintervals. For the integral itself, we get

$\dfrac{2+1.5}2(3-2)+\dfrac{6+2}2(5-3)+\dfrac{11+6}2(7-5)+\dfrac{15+11}2(10-7)=\dfrac{263}4$

So the average height of the tree (in meters) is

$\displaystyle\frac1{10-2}\int_2^{10}H(t)\,\mathrm dt\approx\frac{263}{32}$

d) When $G=50$ , the diameter of the base can be determined to be

$50=\dfrac{100x}{1+x}\implies x=1$

We're told that $\dfrac{\mathrm dx}{\mathrm dt}=0.03$ . $G$ is a function of $x$ which is in turn a function of $t$ , so when we differentiate, we use the chain rule:

$\dfrac{\mathrm dG}{\mathrm dt}=\dfrac{\mathrm dG}{\mathrm dx}\cdot\dfrac{\mathrm dx}{\mathrm dt}$

$\implies\dfrac{\mathrm dG}{\mathrm dt}=\dfrac{100}{(1+x)^2}\cdot\dfrac3{100}=\dfrac3{(1+x)^2}$

When the height of the tree is 50 meters, we found the diameter to be 1 meter, so at this point

$\dfrac{\mathrm dG}{\mathrm dt}=\dfrac34\text{ meters/year}$

4 0

3 years ago

Read 2 more answers

Hello can anyone help me

Scilla [17]

Answer:

Its a

Step-by-step explanation:

since its moving 2 units to the right its only moving in the x direction so you just add 2 to each value of x

5 0

3 years ago

:D PLZ HELP WITH MI MATH