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Questions and Answers
In the parallelogram with sides 7 and 13, if one interior angle is 75°, what is the length of the longer diagonal?
In the parallelogram with sides 7 and 13, if one interior angle is 75°, what is the length of the longer diagonal?
If the area of triangle DEF is 90 mm^2, DE = 11 mm, and angle D = 60°, what is the length of side EF?
If the area of triangle DEF is 90 mm^2, DE = 11 mm, and angle D = 60°, what is the length of side EF?
If the fourth term of a geometric progression is 1.5 and the eighth term is 24, what is the fourteenth term?
If the fourth term of a geometric progression is 1.5 and the eighth term is 24, what is the fourteenth term?
If log P - log Q = log (P/Q), what is the value of log P/log Q?
If log P - log Q = log (P/Q), what is the value of log P/log Q?
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In triangle ABC, if two sides are 60m and 80m long, and the area is 2,175m^2, what is the length of the third side?
In triangle ABC, if two sides are 60m and 80m long, and the area is 2,175m^2, what is the length of the third side?
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What is the distance from the origin to the line 8x - 5y - 12 = 0?
What is the distance from the origin to the line 8x - 5y - 12 = 0?
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What are the coordinates of the center of the circle x^2 + y^2 - 10x - 10y + 25 = 0?
What are the coordinates of the center of the circle x^2 + y^2 - 10x - 10y + 25 = 0?
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If the difference between two numbers is 4 and the difference of their squares is 56, what is the sum of the numbers?
If the difference between two numbers is 4 and the difference of their squares is 56, what is the sum of the numbers?
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A polygon has 54 diagonals. What is the sum of its interior angles?
A polygon has 54 diagonals. What is the sum of its interior angles?
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A car starts with an initial velocity of 3600 m/s and decelerates at 450 m/min. How far does it travel before reaching 3000 m/s?
A car starts with an initial velocity of 3600 m/s and decelerates at 450 m/min. How far does it travel before reaching 3000 m/s?
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Evaluate the indefinite integral $\int \frac{dx}{5 - 2x}$
Evaluate the indefinite integral $\int \frac{dx}{5 - 2x}$
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What is the value of $x$ in the equation $x^x = 256$?
What is the value of $x$ in the equation $x^x = 256$?
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When dividing the number 80 into two parts, what are the values of $x$ and $y$ that maximize the product of one part and the cube of the other?
When dividing the number 80 into two parts, what are the values of $x$ and $y$ that maximize the product of one part and the cube of the other?
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Water is flowing into a cylindrical tank at a rate of 0.50 m/s. If the radius of the tank is 0.75 m, how fast is the liquid rising?
Water is flowing into a cylindrical tank at a rate of 0.50 m/s. If the radius of the tank is 0.75 m, how fast is the liquid rising?
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What is the radius of curvature of the function $y = 3x^2 - 6x + 25$ at $x = 2$?
What is the radius of curvature of the function $y = 3x^2 - 6x + 25$ at $x = 2$?
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Find the y-intercept of a line with slope $\frac{4}{3}$ and passing through the point $(-3, 2)$.
Find the y-intercept of a line with slope $\frac{4}{3}$ and passing through the point $(-3, 2)$.
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Find the area bounded by the curve $x^2 - 4x + 12y - 20 = 0$ and the x-axis between $x = 1$ and $x = 2$.
Find the area bounded by the curve $x^2 - 4x + 12y - 20 = 0$ and the x-axis between $x = 1$ and $x = 2$.
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Study Notes
Geometry and Measurement
- A parallelogram has sides of 7 and 13, and one of its interior angles is 75⁰; the measurement of its longer diagonal is 15.29.
Triangles
- In triangle DEF, DE = 11 mm, ∠D = 60⁰, and the area is 90 mm²; the measurement of side EF is 18.90.
Quadrilaterals
- The given quadrilateral is a rhombus with interior angles congruent to each other.
Geometric Progression
- In a geometric progression, the fourth term is 1.5, and the eighth term is 24; the 14th term is 768.
Logarithms
- Log P – Log Q is equal to Log P/Q.
Triangle Properties
- In triangle ABC, two sides are 60m and 80m long, and the area is 2,175m²; the third side is 72.10 m.
Time and Clocks
- Ben leaves his office between 1 pm and 2 pm, and after 4-5 hours, he arrives at a time when the hands of the clock are interchanged; he arrives at 1:25.59 pm.
Dilution of Mixture
- A factory produces 95% alcohol per volume; to dilute it to 50% for safe distribution, 5.26 cubic meters of water must be added to 10 cubic meters of mixture.
Ladder and Wall
- A 7m ladder leans against a vertical wall 6m high; the top of the ladder slides downward at 0.5 m/s when the lower end is sliding at 0.5 m/s.
Distances and Lines
- The distance from the origin to the line 8x – 5y – 12 = 0 is 12.83.
Equations and Curves
- The center of the equation x² + y² – 10x – 10y + 25 = 0 is (5, 5).
Number Systems
- The difference of two numbers is 4, and the difference of their squares is equal to 56; the sum of the numbers is 26.
Polygon Angles
- A polygon has a total of 54 diagonals; the sum of its interior angles is 900.
Motion and Velocity
- A car moves at an initial velocity of 3600 m/s and decelerates at 450 m/min²; the distance traveled by the car until it reaches a velocity of 3000 m/s is 264 km.
Integration
- The integral of dx / (5 – 2x) is –(1/2) ln(5 – 2x) + c.
Trigonometry
- The integral of cos(73x) dx with a limit from x = 0 to x = π/6 is 0.148.
Algebraic Equations
- The equation x² = 256 has a solution of x = 4.
Optimization
- The numbers 80 can be divided into two parts so that the product of one part and the cube of the other is at maximum; the parts are x = 20, y = 60.
Cylindrical Tank
- Water flows into a cylindrical tank at a rate of 0.50 m³/sec; the liquid rises at a rate of 0.95 m/s.
Radius of Curvature
- The radius of curvature of the function y = 3x² – 6x + 25 at x = 2 is 3.1.
Lines and Intercepts
- The y-intercept of a line with slope = 4/3 and passing through (-3, 2) is 3.
Area Bounded by Curves
- The area bounded by the curve x² – 4x + 12y – 20 = 0 and the x-axis between x = 1 and x = 2 is 2.11.
Simplification of Expressions
- The integral of e⁷xdx is (1/7)e⁷x + C.
Normal and Tangent Lines
- The equation of the line normal to the curve f(x) = x³ – 1 at (2, 7) is x – 12y + 82 = 0.
Circumference and Area
- The equation of the line tangent to the curve x² + y² = 25 at (4, 3) is 4x + 3y – 25 = 0.
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Description
Test your knowledge on computing the distance from the origin to a given line. Avoid erasures and cheating while solving the problems. Choose the correct answer and shade it on the answer sheet provided.
