We are given: 8 tan x = 15. Step 1: Solve for tan x Rearrange the equation to solve for tan x: tan x = 15/8. Step 2: Express sin x and cos x in terms of tan x Using the identity tan x = sin x / cos x, we can write: sin x = 15k and cos x = 8k, where k is a positive constant such that sin²x + cos²x =Read more
We are given:
8 tan x = 15.
Step 1: Solve for tan x
Rearrange the equation to solve for tan x:
tan x = 15/8.
Step 2: Express sin x and cos x in terms of tan x
Using the identity tan x = sin x / cos x, we can write:
sin x = 15k and cos x = 8k,
where k is a positive constant such that sin²x + cos²x = 1 (Pythagorean identity).
Substitute sin x = 15k and cos x = 8k into the identity:
(15k)² + (8k)² = 1
225k² + 64k² = 1
289k² = 1
k² = 1/289
k = √(1/289)
k = 1/17.
Thus:
sin x = 15k = 15/17,
cos x = 8k = 8/17.
Step 3: Find sin x – cos x
Now, calculate sin x – cos x:
sin x – cos x = (15/17) – (8/17)
= (15 – 8)/17
= 7/17.
Step 4: Final Answer
The value of sin x – cos x is 7/17.
The correct answer is:
d) 7/17
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
Finding the Distance of a Point from the x-Axis We are given a point P(2,3) and need to find its distance from the x-axis. Step 1: Understanding Distance from the x-Axis The x-axis is the horizontal axis in the Cartesian plane. The distance of any point (x, y) from the x-axis is simply the absoluteRead more
Finding the Distance of a Point from the x-Axis
We are given a point P(2,3) and need to find its distance from the x-axis.
Step 1: Understanding Distance from the x-Axis
The x-axis is the horizontal axis in the Cartesian plane.
The distance of any point (x, y) from the x-axis is simply the absolute value of its y-coordinate.
This is because the x-axis is located at y=0, and the vertical distance from any point to this axis is determined by how far its y-value is from zero.
Step 2: Applying the Formula
For a point (x,y), the distance from the x-axis is given by:
Distance = |y|
For point P(2, 3), we substitute y = 3:
Distance = |3| = 3
Step 3: Final Answer
Thus, the distance of point P(2,3) from the x-axis is 3.
Correct Option: (b) 3
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
To determine the type of quadrilateral formed by the points A(9, 0), B(9, 6), C(-9, 6), and D(-9, 0), we will analyze the properties of the sides and angles using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²) ### StepRead more
To determine the type of quadrilateral formed by the points A(9, 0), B(9, 6), C(-9, 6), and D(-9, 0), we will analyze the properties of the sides and angles using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ – x₁)² + (y₂ – y₁)²)
### Step 1: Calculate the lengths of all sides
1. Length of AB:
AB = √((9 – 9)² + (6 – 0)²)
= √(0² + 6²)
= √36
= 6
4. Length of DA:
DA = √((9 – (-9))² + (0 – 0)²)
= √((9 + 9)² + 0²)
= √324
= 18
Step 2: Analyze the side lengths
From the calculations:
– AB = CD = 6 (opposite sides are equal)
– BC = DA = 18 (opposite sides are equal)
Thus, the quadrilateral has opposite sides that are equal in length.
Step 3: Check if the angles are right angles
To confirm whether the angles are right angles, we calculate the slopes of adjacent sides and check if their product is -1 (indicating perpendicularity).
1. Slope of AB:
Slope of AB = (6 – 0) / (9 – 9) = undefined (vertical line)
2. Slope of BC:
Slope of BC = (6 – 6) / (-9 – 9) = 0 (horizontal line)
3. Slope of CD:
Slope of CD = (0 – 6) / (-9 – (-9)) = undefined (vertical line)
4. Slope of DA:
Slope of DA = (0 – 0) / (9 – (-9)) = 0 (horizontal line)
Since the slopes of adjacent sides (e.g., AB and BC, or BC and CD) indicate perpendicularity (one is vertical and the other is horizontal), all angles are right angles.
Step 4: Conclusion
The quadrilateral has opposite sides equal and all angles are right angles. Therefore, it is a **rectangle**.
The correct answer is:
b) rectangle
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
To find the ratio in which the x-axis divides the line segment joining the points (2, -3) and (5, 6), we use the section formula. The x-axis has the equation y = 0, so the point of division lies on the x-axis, meaning its y-coordinate is 0. Step 1: Section formula The section formula states that ifRead more
To find the ratio in which the x-axis divides the line segment joining the points (2, -3) and (5, 6), we use the section formula. The x-axis has the equation y = 0, so the point of division lies on the x-axis, meaning its y-coordinate is 0.
Step 1: Section formula
The section formula states that if a point (x, y) divides the line segment joining two points (x₁, y₁) and (x₂, y₂) in the ratio m:n, then:
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
Here, the given points are:
(x₁, y₁) = (2, -3)
(x₂, y₂) = (5, 6)
Let the ratio be m:n. Since the point of division lies on the x-axis, its y-coordinate is 0. Using the y-coordinate formula:
y = (my₂ + ny₁) / (m + n)
Substitute y = 0, y₁ = -3, and y₂ = 6:
0 = (m(6) + n(-3)) / (m + n)
Simplify:
0 = (6m – 3n) / (m + n)
Multiply through by (m + n) (which is nonzero):
6m – 3n = 0
Rearrange to solve for the ratio m:n:
6m = 3n
m/n = 3/6
m/n = 1/2
Thus, the ratio is 1:2.
Step 2: Verify the solution
The x-axis divides the line segment in the ratio 1:2. To confirm, substitute m = 1 and n = 2 into the section formula for the y-coordinate:
y = (my₂ + ny₁) / (m + n)
y = (1(6) + 2(-3)) / (1 + 2)
y = (6 – 6) / 3
y = 0
This confirms that the point of division lies on the x-axis.
The correct answer is:
a) 1:2
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
The distance of a point (x, y) from the x-axis is given by the absolute value of its y-coordinate. This is because the x-axis is the horizontal line where y = 0, and the vertical distance between the point and the x-axis depends only on the y-coordinate. Given the point (-1, 7), the y-coordinate isRead more
The distance of a point (x, y) from the x-axis is given by the absolute value of its y-coordinate. This is because the x-axis is the horizontal line where y = 0, and the vertical distance between the point and the x-axis depends only on the y-coordinate.
Given the point (-1, 7), the y-coordinate is 7. The distance from the x-axis is:
Distance = |y| = |7| = 7 units
Thus, the distance of the point (-1, 7) from the x-axis is 7 units.
The correct answer is:
b) 7
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
If 8 tan x = 15, then sin x – cos x is equal to
We are given: 8 tan x = 15. Step 1: Solve for tan x Rearrange the equation to solve for tan x: tan x = 15/8. Step 2: Express sin x and cos x in terms of tan x Using the identity tan x = sin x / cos x, we can write: sin x = 15k and cos x = 8k, where k is a positive constant such that sin²x + cos²x =Read more
We are given:
8 tan x = 15.
Step 1: Solve for tan x
Rearrange the equation to solve for tan x:
tan x = 15/8.
Step 2: Express sin x and cos x in terms of tan x
Using the identity tan x = sin x / cos x, we can write:
sin x = 15k and cos x = 8k,
where k is a positive constant such that sin²x + cos²x = 1 (Pythagorean identity).
Substitute sin x = 15k and cos x = 8k into the identity:
(15k)² + (8k)² = 1
225k² + 64k² = 1
289k² = 1
k² = 1/289
k = √(1/289)
k = 1/17.
Thus:
sin x = 15k = 15/17,
cos x = 8k = 8/17.
Step 3: Find sin x – cos x
Now, calculate sin x – cos x:
sin x – cos x = (15/17) – (8/17)
= (15 – 8)/17
= 7/17.
Step 4: Final Answer
The value of sin x – cos x is 7/17.
The correct answer is:
d) 7/17
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-8/
The distance of the point P(2, 3) from the x- axis is
Finding the Distance of a Point from the x-Axis We are given a point P(2,3) and need to find its distance from the x-axis. Step 1: Understanding Distance from the x-Axis The x-axis is the horizontal axis in the Cartesian plane. The distance of any point (x, y) from the x-axis is simply the absoluteRead more
Finding the Distance of a Point from the x-Axis
We are given a point P(2,3) and need to find its distance from the x-axis.
Step 1: Understanding Distance from the x-Axis
The x-axis is the horizontal axis in the Cartesian plane.
The distance of any point (x, y) from the x-axis is simply the absolute value of its y-coordinate.
This is because the x-axis is located at y=0, and the vertical distance from any point to this axis is determined by how far its y-value is from zero.
Step 2: Applying the Formula
For a point (x,y), the distance from the x-axis is given by:
Distance = |y|
For point P(2, 3), we substitute y = 3:
Distance = |3| = 3
Step 3: Final Answer
Thus, the distance of point P(2,3) from the x-axis is 3.
Correct Option: (b) 3
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-7/
The points A (9, 0), B (9, 6), C(-9, 6) and D(-9, 0) are the vertices of a
To determine the type of quadrilateral formed by the points A(9, 0), B(9, 6), C(-9, 6), and D(-9, 0), we will analyze the properties of the sides and angles using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²) ### StepRead more
To determine the type of quadrilateral formed by the points A(9, 0), B(9, 6), C(-9, 6), and D(-9, 0), we will analyze the properties of the sides and angles using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ – x₁)² + (y₂ – y₁)²)
### Step 1: Calculate the lengths of all sides
1. Length of AB:
AB = √((9 – 9)² + (6 – 0)²)
= √(0² + 6²)
= √36
= 6
2. Length of BC:
BC = √((-9 – 9)² + (6 – 6)²)
= √((-18)² + 0²)
= √324
= 18
3. Length of CD:
CD = √((-9 – (-9))² + (0 – 6)²)
= √(0² + (-6)²)
= √36
= 6
4. Length of DA:
DA = √((9 – (-9))² + (0 – 0)²)
= √((9 + 9)² + 0²)
= √324
= 18
Step 2: Analyze the side lengths
From the calculations:
– AB = CD = 6 (opposite sides are equal)
– BC = DA = 18 (opposite sides are equal)
Thus, the quadrilateral has opposite sides that are equal in length.
Step 3: Check if the angles are right angles
To confirm whether the angles are right angles, we calculate the slopes of adjacent sides and check if their product is -1 (indicating perpendicularity).
1. Slope of AB:
Slope of AB = (6 – 0) / (9 – 9) = undefined (vertical line)
2. Slope of BC:
Slope of BC = (6 – 6) / (-9 – 9) = 0 (horizontal line)
3. Slope of CD:
Slope of CD = (0 – 6) / (-9 – (-9)) = undefined (vertical line)
4. Slope of DA:
Slope of DA = (0 – 0) / (9 – (-9)) = 0 (horizontal line)
Since the slopes of adjacent sides (e.g., AB and BC, or BC and CD) indicate perpendicularity (one is vertical and the other is horizontal), all angles are right angles.
Step 4: Conclusion
The quadrilateral has opposite sides equal and all angles are right angles. Therefore, it is a **rectangle**.
The correct answer is:
b) rectangle
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-7/
Find the ratio in which the line segment joining (2, -3) and (5, 6) is divided by x-axis
To find the ratio in which the x-axis divides the line segment joining the points (2, -3) and (5, 6), we use the section formula. The x-axis has the equation y = 0, so the point of division lies on the x-axis, meaning its y-coordinate is 0. Step 1: Section formula The section formula states that ifRead more
To find the ratio in which the x-axis divides the line segment joining the points (2, -3) and (5, 6), we use the section formula. The x-axis has the equation y = 0, so the point of division lies on the x-axis, meaning its y-coordinate is 0.
Step 1: Section formula
The section formula states that if a point (x, y) divides the line segment joining two points (x₁, y₁) and (x₂, y₂) in the ratio m:n, then:
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
Here, the given points are:
(x₁, y₁) = (2, -3)
(x₂, y₂) = (5, 6)
Let the ratio be m:n. Since the point of division lies on the x-axis, its y-coordinate is 0. Using the y-coordinate formula:
y = (my₂ + ny₁) / (m + n)
Substitute y = 0, y₁ = -3, and y₂ = 6:
0 = (m(6) + n(-3)) / (m + n)
Simplify:
0 = (6m – 3n) / (m + n)
Multiply through by (m + n) (which is nonzero):
6m – 3n = 0
Rearrange to solve for the ratio m:n:
6m = 3n
m/n = 3/6
m/n = 1/2
Thus, the ratio is 1:2.
Step 2: Verify the solution
The x-axis divides the line segment in the ratio 1:2. To confirm, substitute m = 1 and n = 2 into the section formula for the y-coordinate:
y = (my₂ + ny₁) / (m + n)
y = (1(6) + 2(-3)) / (1 + 2)
y = (6 – 6) / 3
y = 0
This confirms that the point of division lies on the x-axis.
The correct answer is:
a) 1:2
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-7/
The distance of the point (-1, 7) from x axis is
The distance of a point (x, y) from the x-axis is given by the absolute value of its y-coordinate. This is because the x-axis is the horizontal line where y = 0, and the vertical distance between the point and the x-axis depends only on the y-coordinate. Given the point (-1, 7), the y-coordinate isRead more
The distance of a point (x, y) from the x-axis is given by the absolute value of its y-coordinate. This is because the x-axis is the horizontal line where y = 0, and the vertical distance between the point and the x-axis depends only on the y-coordinate.
Given the point (-1, 7), the y-coordinate is 7. The distance from the x-axis is:
Distance = |y| = |7| = 7 units
Thus, the distance of the point (-1, 7) from the x-axis is 7 units.
The correct answer is:
b) 7
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-7/