Answer:
Demand is inelastic at p = 9 and therefore revenue will increase with
an increase in price.
Step-by-step explanation:
Given a demand function that gives <em>q</em> in terms of <em>p</em>, the elasticity of demand is
![E=|\frac{p}{q}\cdot \frac{dq}{dp} |](https://tex.z-dn.net/?f=E%3D%7C%5Cfrac%7Bp%7D%7Bq%7D%5Ccdot%20%5Cfrac%7Bdq%7D%7Bdp%7D%20%20%7C)
- If E < 1, we say demand is inelastic. In this case, raising prices increases revenue.
- If E > 1, we say demand is elastic. In this case, raising prices decreases revenue.
- If E = 1, we say demand is unitary.
We have the following demand equation
; p = 9
Applying the above definition of elasticity of demand we get:
![E(p)=\frac{p}{q}\cdot \frac{dq}{dp}](https://tex.z-dn.net/?f=E%28p%29%3D%5Cfrac%7Bp%7D%7Bq%7D%5Ccdot%20%5Cfrac%7Bdq%7D%7Bdp%7D)
where
- p = 9
- q =
![-\frac{3}{4}p+29](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B4%7Dp%2B29)
![\frac{dq}{dp}=\frac{d}{dp}(-\frac{3}{4}p+29)](https://tex.z-dn.net/?f=%5Cfrac%7Bdq%7D%7Bdp%7D%3D%5Cfrac%7Bd%7D%7Bdp%7D%28-%5Cfrac%7B3%7D%7B4%7Dp%2B29%29)
![\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{d}{dp}\left(\frac{3}{4}p\right)+\frac{d}{dp}\left(29\right)\\\\\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdp%7D%5Cleft%28-%5Cfrac%7B3%7D%7B4%7Dp%2B29%5Cright%29%3D-%5Cfrac%7Bd%7D%7Bdp%7D%5Cleft%28%5Cfrac%7B3%7D%7B4%7Dp%5Cright%29%2B%5Cfrac%7Bd%7D%7Bdp%7D%5Cleft%2829%5Cright%29%5C%5C%5C%5C%5Cfrac%7Bd%7D%7Bdp%7D%5Cleft%28-%5Cfrac%7B3%7D%7B4%7Dp%2B29%5Cright%29%3D-%5Cfrac%7B3%7D%7B4%7D)
Substituting the values
![E(9)=\frac{9}{-\frac{3}{4}(9)+29}\cdot -\frac{3}{4}\\\\E(9)=\frac{36}{89}\cdot -\frac{3}{4}\\\\E(9)=-\frac{27}{89}\approx -0.30337](https://tex.z-dn.net/?f=E%289%29%3D%5Cfrac%7B9%7D%7B-%5Cfrac%7B3%7D%7B4%7D%289%29%2B29%7D%5Ccdot%20-%5Cfrac%7B3%7D%7B4%7D%5C%5C%5C%5CE%289%29%3D%5Cfrac%7B36%7D%7B89%7D%5Ccdot%20-%5Cfrac%7B3%7D%7B4%7D%5C%5C%5C%5CE%289%29%3D-%5Cfrac%7B27%7D%7B89%7D%5Capprox%20-0.30337)
![|E(9)|=|\frac{27}{89}| < 1](https://tex.z-dn.net/?f=%7CE%289%29%7C%3D%7C%5Cfrac%7B27%7D%7B89%7D%7C%20%3C%201)
Demand is inelastic at p = 9 and therefore revenue will increase with an increase in price.
3.5 pound = 3 5/10 pounds = 3 1/2 pounds
Now, 1 pound = 16 ounces, so 1/2 pound = 16*1/2 = 8 oz
<span>So the answer is 3 pounds and 8 oz.</span>
The answer to this equation is 2x/x+7 or 2x over x+7
1+68
2+67
3+66
4+65
5+64
6+63
7+62
8+61
9+60
Ok, so if he walks 4 miles per 64 minutes, or 4 miles/64 min which will
reduce to 1 mile/ 16 min, then the numbers of miles he walks in a given
number of minutes would be
1/16 * number of minutes
The question states we represent miles with y and number of minutes with x, so...
y = 1/16x
So let's check it...
How many miles (y) in 64 minutes (x)
y = 1/16x
y = 1/16 * 64
y = 64/16 = 4 miles
Yep! It checks!