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Let 𝑃 be the midpoint of the line segment joining the points 𝐴(π‘Ž + 𝑏, 𝑏) and 𝐡(π‘Ž βˆ’ 𝑏, π‘Ž + 𝑏). Find the slope of the line passing through 𝑃 and 𝑄 (𝑏, βˆ’π‘Ž/2) .


Prove that the conic passing through the points of intersection of two rectangular hyperbolas is also a rectangular hyperbola.


10. The Bok Chicken Factory is trying to figure out how to minimize the cost of producing 1200 units of chicken parts. The production function is q = 100L0.5 K0.5. The wage rate is birr 9 per hour and the rental rate on capital is birr 4 per machine hour



A.B. Find the maximum output that can be produced for a total cost of birr 720.

(DΒ² βˆ’ 3DD + 2DΒ²)z = eΒ²x+Β³y +sin(x-2y)

Β 2NH3 Using the equation above answer the following question given for items 39 to 44 that has 2.7 moles of N_2 and 8.9 moles of H_2 used. The actual yield after the production is 89.43 g. (Note: atomic number N= 14.007, H= 1.008)


Β A monopolist always faces a demand curve that is

a. perfectly inelastic.

b. perfectly elastic.

c. unit elastic.

d. the same as the market demand curve.



what will be the final volume of the weather balloons if the pressure increases at 100 kpa *


For Items 1-3 consider the problem, A weather balloon with a volume of 2000L at a pressure of 96.3 kPa rises to an altitude of 1000m, where the atmospheric pressure is measured to be 60.8kPa. Assuming there is no change in the temperature or the amount of gas, calculate the weather balloon’s final volume

take 10 integer inputs from user and print the following:


01:postive number


02:negative number


03:odd numbers


04:even numbers all through arra

The pistons in an automobile engine move up and down in the cylinders. If t is in milliseconds, the distance from the top of the piston to the top of the cylinder is given in centimeters by D=7+6 sin (4m)




(a) identify the amplitude, period and frequency of function




(b) Find the largest and the smallest clearance between the piston and the top of the cylinder.

Positron emission from 11C, 11 6C Β‘ 11 5B + 0 + 1e, occurs with release of 2.87 * 1011 J per mole of 11C. What is the mass change per mole of 11C in this nuclear reaction? The masses of 11B and 11C are 11.009305 and 11.011434 amu, respectively


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