Mathematics, 19.03.2020 23:16 abbeyj4737

The demand function for q units of a product at $p per unit is given by p(q + 3)2 = 100,000. Find the rate of change of quantity with respect to price when p = $40.

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Answer from: 7obadiah

-0.625 unit

Step-by-step explanation:

Given that:

p(q+3)^2 = 100, 000

where;

p = price

q = quantity

To find the rate of change of quantity (q) with respect to price (p) we go by the differentiation

$(q+3)^2\frac{dp}{dp} +p^2(q+3)\frac{dq}{dp}=0$

$(q+3)^2 +p^2(q+3)\frac{dq}{dp}=0$

$\frac{dq}{dp}=\frac{-(q+3)}{2p}$

when P =40

Then 4(q+3)² = 100, 000

(q+3)² = $\frac{100,000}{4}$

(q+3)² = 25,000

(q+3) = $\sqrt{2500}$

q+ 3 = 50

q = 50 -3

q = 47

NOW; $\frac{dq}{dp}=\frac{-(q+3)}{2p}$

$\frac{dq}{dp}=\frac{-(47+3)}{2*40}$

$\frac{dq}{dp}=\frac{-47-3}{2*40}$

$\frac{dq}{dp}=\frac{-50}{80}$

$\frac{dq}{dp}=-0.625$

Thus, the rate of change of quantity with respect to price when p = $40 is -0.625 unit.

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

Answer from: Quest

5/20 so 25%

step-by-step explanation:

Plz i only need the last question answerd

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The demand function for q units of a product at $p per unit is given by p(q + 3)2 = 100,000. Find th...

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