Other Math Answers

A 28/32-inch hole must be enlarged to 58/64 inch to insert a bushing. How much wider than the original hole will the hole be?

You are throwing a party, and you need 2 bags of chips for every 20 guest how many bags of chips do you need?- Equivalent ratios

A particle is moving in the ~i - ~j plane with an acceleration of (1 - t)~ i+ t ~j where t is the time. The particle is projected from the point with an initial velocity of 3/2 ~i ms/1. Find the displacement of the particle at time t and the value of t when it is moving in the direction of motion.

What is the angle between its velocity and displacement at this time?

Let P and Q be points on the curve 𝑦=𝑥2−2𝑥 while x=2 and x=2+h respectively. Express the gradient of pq in terms of h and hence find the gradient of the curve 𝑦=𝑥2−2𝑥 at x= 2

i. find lim𝑥→2 𝑥^ 2−3𝑥 +2 / 𝑥 ^2−4

ii. Where are is the function 𝑓(𝑥) = 1 2𝑥 ^2−6𝑥+4 continuous?

iii. Given that given 𝑌 = tan−1 𝑥 show that 𝑑𝑦 /𝑑𝑥 = 1 1+𝑥 ^2 

iv. Prove using the first principle that the derivative of sin 𝑥 is cos 𝑥 and that the derivative of 𝑐𝑜𝑠𝑥 is – 𝑠𝑖𝑛x

v. Differentiate sin 𝑦 − 𝑥 2𝑦 3 − 𝑐𝑜𝑠𝑥 = 3y

vi. lim𝑥→1 𝑥^2+𝑥 3−5𝑥+3/ 𝑥^3+2𝑥^2+7𝑥+4

vii. lim𝑥→∞ 2𝑥/ 3𝑥^6+𝑥+4

a. An oil company bores a hole 120m deep. Estimate the cost of boring if the cost is k70 for drilling the first meter with an increase in cost of k3per meter for each succeeding meter.

b. An IPhone 12 pro who’s original Value was K32500 decreases in value by k85 per month. How long will it take before the Iphone’s value falls below k12500?

c. Given that 𝑢𝑖 = 5 + 2𝑖 𝑎𝑛𝑑 𝑣𝑖 = 2 − 5𝑖, find ∑⁵_i = 2𝑢𝑖 − 𝑣𝑖 And ∑⁵_i = 𝑢𝑖 (use the properties of the sigma notation)

d. Two competing companies, Tecno and Samsung produce mobile phones. Tecno starts production at 1000 phones per week and plans to increase output by 200 each week. Samsung start production with 500 phones per week and plans to increase output by 20% each week.

e. i). a. Calculate the weekly production in weeks 1; 5; 10; 15.

ii). Calculate the total production during the first 15 weeks for each firm 

a.. Differentiate the function 𝑦 = (3𝑥^2+2) ^2√6𝑥+2 / 𝑥 ^3+1

b. Let P and Q be points on the curve 𝑦 = 𝑥 2 − 2𝑥 while x = 2 and x = 2 + h respectively. Express the gradient of pq in terms of h and hence find the gradient of the curve 𝑦 = 𝑥 2 − 2𝑥 at x= 2

c. Find the gradient of the curve 𝑦 = 1/ 𝑥−1 at the point (2,1)

A straight line 𝑦 = −𝑥 + 4 cuts the parabola with equation 𝑦 = 16 − 𝑥 2 at the points A and B.

a) Find the coordinates of A and B

b) Calculate the distance between the points A and B

c) Find the equation of the tangents at A and B, and hence determine where the tangents meet.

d) The line µ is perpendicular to the line A at the point A and B meet. Give its equation

1) It is difficult to integrate geometry and visual literacy in the form of lines and shapes.

TRUE/FALSE

. The selling price for each item of a product is $50 and Total cost is given by

𝐶(𝑥) = 10𝑥 + 18,000

Where 𝑥 is the number of items.

a) Write revenue function.

b) Find 𝐶(100) and write a sentence that explains it’s meaning.

c) Find number of units that gives break-even point.

The total cost function for a product is

𝐶(𝑥) = 30𝑥 + 1200 and the total revenue is 

𝑅(𝑥) = 38𝑥 where 𝑥 is the number of units produced 

And sold. 

a) Find marginal cost. 

b) Find profit function. 

c) Find the number of units that gives break even. 

d) Find marginal profit and explain what it means.