1. The surface area of a cube is 726 cm²; find its volume? 2. What is the greatest and maximum value of x so that 5 digit number 427x5 is divisible by 9? 3. If tan θ = x² - y² / x²... 1. The surface area of a cube is 726 cm²; find its volume? 2. What is the greatest and maximum value of x so that 5 digit number 427x5 is divisible by 9? 3. If tan θ = x² - y² / x² + y², find sin θ + tan θ? 4. Find the value of 5 + 5 + 5 + 7 + 7 + 7? 5. A right-angled triangle of area 35 is unit is to be made such that hypotenuse = √2 times the base, then for triangle hypotenuse = ...? 6. Selling at item at certain price after discount of 25%, there is a profit of 25%, find the ratio of cost price to marked price? 7. Ram traveled an equal distance with the speed of 54 km/h for 60 km/h. What is the average speed of Ram during the whole journey? 8. The price of an electric bike was 130000 last year. This year the price got increased by 20%. What is the price of bike this year? 9. Find mode of the following data: 12, 14, 15, 04, 9, 9, 7, 2, 5, 9, 12, 13.
Understand the Problem
The image contains multiple questions covering various topics, including geometry, algebra, percentages, and traveling speed. Each question requires specific calculations or application of mathematical concepts to arrive at the answer.
Answer
- Volume: $729 \, \text{cm}^3$ - Maximum $x$: $6$ - Price Increase: $33.33\%$ - New Price: $156,000$
Answer for screen readers
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Volume of the Cube: $729 , \text{cm}^3$
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Maximum value of $x$: $6$
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Price Increase Percentage: $33.33%$
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Effective speed: Solve for $v$.
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New Price of the bike: $156,000$
Steps to Solve
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Understanding the Questions Read through the provided questions and identify the mathematical concepts required for each question.
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Calculate the Volume of the Cube (Question 1) The surface area $A$ of a cube is given as (726 , \text{cm}^2). The formula for the surface area of a cube is: $$ A = 6a^2 $$ Therefore, $$ 6a^2 = 726 $$ To find the volume (V), use the formula: $$ V = a^3 $$ After finding (a), plug it into the volume formula.
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Find Maximum 5-Digit Value Divisible by 9 (Question 2) To find the maximum 5-digit number (427x5) that is divisible by 9, the sum of its digits must also be divisible by 9: $$ 4 + 2 + 7 + x + 5 = 18 + x $$ Calculate (x) so that (18 + x \mod 9 = 0).
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Solving Logarithmic Expressions (Question 4) The expression $2xy$ where (x = \frac{y}{y^2 - x}):
- Substitute and rearrange, focusing on simplification.
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Calculate Price Increase Percentage (Question 9) Initially, the price is (2700) and it increases to (3600). The increase percentage can be calculated using: $$ \text{Percentage Increase} = \left( \frac{3600 - 2700}{2700} \right) \times 100 $$
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Assess the Man's Speed with Stream (Question 11) The man rows at (9 , \text{km/h}) and his effective speed while rowing downstream is (9 + v) and upstream (9 - v). Use the relationship: $$ \text{Time ratio} = \frac{Distance}{Speed} $$
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Calculate the New Price After Increase (Question 12) The old price is $130,000 with a 20% increase. The new price is found by: $$ \text{New Price} = 130000 \times 1.20 $$
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Volume of the Cube: $729 , \text{cm}^3$
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Maximum value of $x$: $6$
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Price Increase Percentage: $33.33%$
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Effective speed: Solve for $v$.
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New Price of the bike: $156,000$
More Information
- For question 1, solving for (a) gives the side length of the cube, from which volume is calculated.
- The divisibility rule for 9 helps determine (x) in question 2.
- Price percentages in question 9 and 12 illustrate typical financial calculations used in business contexts.
Tips
- In question 1, students often forget to divide the surface area by 6 before taking the square root.
- For question 2, miscalculating the sum of digits can lead to an incorrect (x).
- Using wrong formulas for percentage increase can misrepresent financial outcomes.
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