Answer:
Option B
Step-by-step explanation:
Let the point O is the origin.
Then the coordinates of the vertices A,B and C will be,
A → (-12, -8)
B → (-8, 0)
C → (-6, -4)
Rule for the dilation of a point (x, y) by scale factor 'k' about the origin is,
(x, y) → (kx, ky)
By this rule, coordinates of the vertices of the image triangle will be,
If k = ,
A(-12, -8) → A'(-6, -4)
B(-8, 0) → B'(-4, 0)
C(-6, -4) → C'(-3, -2)
From the given options,
Option B is the answer.
Given:
The two functions are:
To find:
The statement that best compares the graph of g(x) with the graph of f(x).
Solution:
The horizontal stretch is defined as:
...(i)
If , the function f(x) is horizontally stretched by factor
.
If , the function f(x) is horizontally compressed by factor
.
We have,
Using these functions, we get
...(ii)
On comparing (i) and (ii), we get
Since , the function f(x) is horizontally stretched by factor
.
Hence, the correct option is D.
Answer:
2758 Nm
Step-by-step explanation
Work done usually depends on two things force applied and distance travelled due to applied force. In this current scenario, the force is being applied at an angle so we will have to find a component of force in the direction of the movement.
We usually find component using cos θ.
Here θ is 40°
Now, the modified equation becomes,
Work Done = Force * Distance * Component of force along the direction of distance
∴ Work = 30 N * 120 m * Cos 40°
⇒Work = 30 * 120 * 0.766
⇒Work = 2757.6 Nm
Rounding to the nearest whole number.
∴ The work done by force is 2758 Nm which is option B
