Take Class 10 Tuition from the Best Tutors
Search in
Answered on 18 Apr Learn Sphere
Nazia Khanum
Calculating the Longest Pole Length for a Room
Introduction: In this scenario, we aim to determine the longest possible length of a pole that can fit inside a room with given dimensions.
Given Dimensions:
Approach: To find the longest pole that can fit inside the room without sticking out, we need to consider the diagonal length of the room.
Calculations:
Diagonal Length of the Room (d):
=225
Longest Pole Length:
Conclusion: Hence, the longest pole that can be put in a room with dimensions l=10l=10 cm, b=10b=10 cm, and h=5h=5 cm is 15 cm.
Answered on 18 Apr Learn Real Numbers
Nazia Khanum
Locating √3 on the Number Line
Introduction Locating √3 on the number line is an essential concept in mathematics, particularly in understanding irrational numbers and their placement in relation to rational numbers.
Understanding √3 √3 represents the square root of 3, which is an irrational number. An irrational number cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal expansion.
Steps to Locate √3 on the Number Line
Identify Nearby Perfect Squares:
Estimation:
Plotting √3 on the Number Line:
Final Position:
Conclusion Locating √3 on the number line involves understanding its position between perfect squares and accurately plotting its approximate value. This skill is fundamental for comprehending the continuum of real numbers and their relationships.
Answered on 18 Apr Learn Real Numbers
Nazia Khanum
Are the square roots of all positive integers irrational?
Introduction: The question probes into the nature of square roots of positive integers, whether they are exclusively irrational or if there are exceptions.
Explanation: The statement that the square roots of all positive integers are irrational is false. While there are indeed many examples of square roots that are irrational, there are also instances where the square root of a positive integer results in a rational number.
Example:
Explanation of the Example:
Conclusion: In conclusion, not all square roots of positive integers are irrational. The square root of 4, for instance, is a rational number, demonstrating that exceptions exist to the notion that all such roots are irrational.
Take Class 10 Tuition from the Best Tutors
Answered on 18 Apr Learn Real Numbers
Nazia Khanum
Decimal Expansions of Fractions
1. Decimal Expansion of 10/3:
Calculation:
Decimal Expansion:
2. Decimal Expansion of 7/8:
Calculation:
Decimal Expansion:
3. Decimal Expansion of 1/7:
Calculation:
Decimal Expansion:
Conclusion:
Answered on 18 Apr Learn Linear equations in 2 variables
Nazia Khanum
Finding Solutions of Line AB Equation
Given Information:
Procedure:
1. Identify Points on Line AB:
2. Determine Coordinates:
3. Substitute Coordinates:
4. Verify Solutions:
Example:
Conclusion:
Answered on 18 Apr Learn Linear equations in 2 variables
Nazia Khanum
Let's denote:
The total fare can be calculated as the sum of the initial fare and the fare for the subsequent distance.
So, the equation can be expressed as:
y=10+6(x−1)y=10+6(x−1)
Where:
Now, let's substitute x=15x=15 into the equation to find the total fare for a 15 km journey.
y=10+6(15−1)y=10+6(15−1) y=10+6(14)y=10+6(14) y=10+84y=10+84 y=94y=94
The total fare for a 15 km journey would be Rs. 94.
Take Class 10 Tuition from the Best Tutors
Answered on 18 Apr Learn Linear equations in 2 variables
Nazia Khanum
Problem Analysis:
Given the equation 2x−y=p2x−y=p and a solution point (1,−2)(1,−2), we need to find the value of pp.
Solution:
Step 1: Substitute the Given Solution into the Equation
Substitute the coordinates of the given solution point (1,−2)(1,−2) into the equation:
2(1)−(−2)=p2(1)−(−2)=p
Step 2: Solve for pp
2+2=p2+2=p 4=p4=p
Step 3: Final Result
p=4p=4
Conclusion:
The value of pp for the equation 2x−y=p2x−y=p when the point (1,−2)(1,−2) is a solution is 44.
Answered on 18 Apr Learn Linear equations in 2 variables
Nazia Khanum
Graph of the Equation x - y = 4
Graphing the Equation:
To draw the graph of the equation x−y=4x−y=4, we'll first rewrite it in slope-intercept form, which is y=mx+by=mx+b, where mm is the slope and bb is the y-intercept.
Given equation: x−y=4x−y=4
Rewriting in slope-intercept form:
y=x−4y=x−4
Now, let's plot the graph using this equation.
Plotting the Graph:
Find y-intercept:
Set x=0x=0 in the equation y=x−4y=x−4
y=0−4y=0−4
y=−4y=−4
So, the y-intercept is at the point (0,−4)(0,−4).
Find x-intercept:
To find the x-intercept, set y=0y=0 in the equation y=x−4y=x−4.
0=x−40=x−4
x=4x=4
So, the x-intercept is at the point (4,0)(4,0).
Drawing the Graph:
Now, plot the points (0,−4)(0,−4) and (4,0)(4,0) on the Cartesian plane and draw a straight line passing through these points. This line represents the graph of the equation x−y=4x−y=4.
Intersecting with the x-axis:
To find where the graph line meets the x-axis, we need to find the point where y=0y=0.
Substitute y=0y=0 into the equation x−y=4x−y=4:
x−0=4x−0=4
x=4x=4
So, when the graph line meets the x-axis, the coordinates of the point are (4,0)(4,0).
Answered on 18 Apr Learn Linear equations in 2 variables
Nazia Khanum
Graphing the Equation x + 2y = 6
To graph the equation x+2y=6x+2y=6, we'll first rewrite it in slope-intercept form (y=mx+by=mx+b):
x+2y=6x+2y=6 2y=−x+62y=−x+6 y=−12x+3y=−21x+3
Plotting the Graph
To plot the graph, we'll identify two points and draw a line through them:
Intercept Method:
Slope Method: From the slope-intercept form y=−12x+3y=−21x+3, the slope is -1/2, meaning the line decreases by 1 unit in the y-direction for every 2 units in the x-direction.
Plotting the Points and Drawing the Line
Using the intercepts and the slope, we plot the points (0, 3) and (-6, 0), then draw a line through them.
Finding the Value of x when y = -3
Given y=−3y=−3, we substitute this value into the equation y=−12x+3y=−21x+3 and solve for x:
−3=−12x+3−3=−21x+3 −12x=−3−3−21x=−3−3 −12x=−6−21x=−6 x=−6×(−2)x=−6×(−2) x=12x=12
Conclusion
Take Class 10 Tuition from the Best Tutors
Answered on 18 Apr Learn Polynomials
Nazia Khanum
Perimeter Calculation for Rectangle with Given Area
Given Information:
Step 1: Determine the Dimensions
To calculate the perimeter of a rectangle, we need to know its length and width. We can find these dimensions using the area provided.
Step 2: Factorize the Area
Factorize the given quadratic expression 25x2−35x+1225x2−35x+12 to find its factors, which represent the possible lengths and widths of the rectangle.
Step 3: Use Factorization to Find Dimensions
Once the quadratic expression is factorized, identify the pairs of factors that, when multiplied, give the area of the rectangle. These pairs represent possible lengths and widths.
Step 4: Calculate Perimeter
With the length and width of the rectangle known, calculate the perimeter using the formula:
Perimeter=2×(Length+Width)Perimeter=2×(Length+Width)
Step 5: Finalize
Plug in the values of length and width into the perimeter formula to obtain the final result.
Let's proceed with these steps to find the perimeter.
UrbanPro.com helps you to connect with the best Class 10 Tuition in India. Post Your Requirement today and get connected.
Ask a Question
The best tutors for Class 10 Tuition Classes are on UrbanPro
The best Tutors for Class 10 Tuition Classes are on UrbanPro