Podcast
Questions and Answers
What is the current through a resistor when a voltage of 52 volts is applied?
What is the current through a resistor when a voltage of 52 volts is applied?
If X and Y are inversely proportional and X = 15,000 when Y = 162,500, what is X when Y = 328,400?
If X and Y are inversely proportional and X = 15,000 when Y = 162,500, what is X when Y = 328,400?
What is the smallest integer among seven consecutive integers that sum to zero?
What is the smallest integer among seven consecutive integers that sum to zero?
What is the area of a park if the map area is 500 $mm^{2}$ and the scale is 1 to 40,000?
What is the area of a park if the map area is 500 $mm^{2}$ and the scale is 1 to 40,000?
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What is the curved surface area of a spherical segment with bases 100 cm and 140 cm apart?
What is the curved surface area of a spherical segment with bases 100 cm and 140 cm apart?
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Evaluate the integral $\int \csc x \cot x ,dx$. What is the result?
Evaluate the integral $\int \csc x \cot x ,dx$. What is the result?
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What is the general solution of the differential equation $y + 3y - 4y = 0$?
What is the general solution of the differential equation $y + 3y - 4y = 0$?
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What is the largest integer among three distinct positive integers whose sum is 15 and product is 45?
What is the largest integer among three distinct positive integers whose sum is 15 and product is 45?
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Study Notes
Inverse Proportionality
- X and Y are inversely proportional if their product is constant.
- If X = 15,000 when Y = 162,500, find X when Y = 328,400.
- (X1)(Y1) = (X2)(Y2)
- (15000)(162500) = (X2)(328400)
- X2 = 7,422.35
Consecutive Integers
- The sum of seven consecutive integers is zero.
- Find the smallest integer.
- The smallest integer is -4.
Three Distinct Positive Integers
- The sum and product of three distinct positive integers are 15 and 45 respectively.
- Find the largest integer.
- The largest integer is 9.
Spherical Segment Curved Surface Area
- Find the curved surface area of a spherical segment.
- The diameters of the bases are 100 cm and 140 cm, and they are 25 cm apart.
- The curved surface area is 11,673.43 cm².
Map Scale
- The area of a park on a map is 500 mm²; the scale is 1:40,000.
- Determine the true area in hectares.
- The true area is 80 hectares.
Integral Evaluation
- Evaluate the integral ∫cscx cotx dx.
- The result is -cscx + C.
Differential Equation
- Find the general solution for y + 3y − 4y = 0.
- The solution is y = C₁e⁴ˣ + C₂e⁻ˣ
Ohm's Law
- Ohm's law states that the current in a resistor is proportional to the voltage.
- If 30 volts yields 2.4 x 10⁻³ amperes, find the constant of proportionality
- The constant of proportionality is 8 x 10⁻⁵.
- If voltage is 52 volts, the current is 4.16x10⁻³ amperes.
Linear Equation
- Find the value of x-y from 3x - 5y = 14; 6x - 3y = 21
- The value of x - y is 4.
Solving for x
- Solve for x if 48¹/₄ = 4 x ³/₂
- x = 2
Solving for x & y
- The equations are axb = 8, axc=3, bxc =6
- The value of x/y is 3/2
Non-zero solution
- Find the non-zero solution to 3x² - 30x = 0
- The non-zero solution is 10.
Possible Line Length
- A line is divided into 10 equal parts.
- The measure of each part is a prime integer.
- Find the possible length of the line.
- The possible length is 150.
Hat Problem
- Mano's hat count is four more than Alex's hat and one half that amount of Miguel's.
- The total number of hats is 24.
- Find Miguel's hats.
- Miguel has 16 hats.
Ratio of Portions
- The shipment of items is divided into two portions.
- The difference is half the average of the two portions.
- The ratio of the larger to smaller portion is 7/3.
Musical Trio
- A group of musicians includes three drummers, four pianists, and five guitarists.
- Find the number of ways to form a trio with 1 drummer, 1 pianist, and 1 guitarist.
- There are 60 ways to assemble the trio.
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Description
Test your understanding of various mathematics topics including inverse proportionality, sums of integers, product of integers, spherical segments, and integral evaluation. This quiz covers real-world applications and theoretical calculations. Assess your knowledge and problem-solving skills in these areas.
