Answer:
Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f. A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f brainliest ?
The answer is 5. You are basically adding a 2 to the 3 which means you’ll get 5
<h3>
Answer: Choice B. 5*sqrt(10)</h3>
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Explanation:
It helps to add point labels. Let's place point A at the very top point of the triangle. Then point B will be at the 90 degree angle. Point C is the far left point. Lastly, point D is on segment BC such that DC = 3.
Since BC = 8 and CA = 17, we can use the pythagorean theorem to get...
(AB)^2 + (BC)^2 = (AC)^2
(AB)^2 + (8)^2 = (17)^2
(AB)^2 + 64 = 289
(AB)^2 = 289-64
(AB)^2 = 225
AB = sqrt(225)
AB = 15
Now focus on triangle ABD and apply the pythagorean theorem again to find side AD
(AB)^2 + (BD)^2 = (AD)^2
AD = sqrt( (AB)^2 + (BD)^2 )
AD = sqrt( (AB)^2 + (BC-CD)^2 )
AD = sqrt( (15)^2 + (8-3)^2 )
AD = sqrt(250)
AD = sqrt(25*10)
AD = sqrt(25)*sqrt(10)
AD = 5*sqrt(10) .... answer is choice B
Answer:
$7812.5million
$7812.5million
Step-by-step explanation:
From the question, the demand quantity <em>D(x) is 410-x </em> and the supply quantity <em>S(x)=160+x.</em> We determine the equilibrium quantity by equating the Demand quantity and the Supply quantity i.e
<em>D(x)=S(x). </em>
<em>
</em>
Hence the equilibrium quantity is 125.
Next we determine the equilibrium price. This can be obtain by just substituting the equilibrium quantity into either the demand quantity or the supply quantity. I prefer using the Demand quantity.
Equilibrium price=
.
Next we write the expression for the Consumer Surplus
![CS=\int\limits^q_0 {D(x)} \, dx -pq](https://tex.z-dn.net/?f=CS%3D%5Cint%5Climits%5Eq_0%20%7BD%28x%29%7D%20%5C%2C%20dx%20-pq)
where <em>p</em> and <em>q </em> are the equilibrium price and equilibrium quantity respectively.
By substituting values we have
![CS=\int\limits^q_0 {(410-x)} \, dx (285)(125)\\](https://tex.z-dn.net/?f=CS%3D%5Cint%5Climits%5Eq_0%20%7B%28410-x%29%7D%20%5C%2C%20dx%20%28285%29%28125%29%5C%5C)
![CS=/410x-\frac{x^{2} }{2} /^{125}_{0} \\](https://tex.z-dn.net/?f=CS%3D%2F410x-%5Cfrac%7Bx%5E%7B2%7D%20%7D%7B2%7D%20%2F%5E%7B125%7D_%7B0%7D%20%5C%5C)
By carrying out simple arithmetic we arrive at
.
To determine the producer surplus, we use the expression below
![PS=pq-\int\limits^q_0 {S(x)} \,dx\\](https://tex.z-dn.net/?f=PS%3Dpq-%5Cint%5Climits%5Eq_0%20%7BS%28x%29%7D%20%5C%2Cdx%5C%5C)
Hence if we substitute values we arrive at
.
By simply simplification we arrive at
![PS=(285)(125)-(20000+7812.5)\\PS=35625-27812.5\\PS=$7812.5million](https://tex.z-dn.net/?f=PS%3D%28285%29%28125%29-%2820000%2B7812.5%29%5C%5CPS%3D35625-27812.5%5C%5CPS%3D%247812.5million)