Answer:
a) V_avg = 32 ft/s
b) V_avg = -30 ft/s
c) See explanation
Step-by-step explanation:
Given:
- The displacement function is given:
S(t) = -16t^2 + 64t + 80
Find:
a. Find the balls average velocity between the time it was thrown and 2 seconds later
b. Find the ball’s average velocity between 2 and 4 seconds after it was thrown
c. What do the signs in your answers to parts (a) and (b) mean in terms of the direction of the ball’s motion?
Solution:
- The average velocity of an object is the displacement over time, and it is expressed as follows:
V_avg = ( S_2 - S_1 ) / dt
- Evaluate S(2), S(0), and S(4):
S(2) = -16*2^2 +64*2 +80
S(2) = 144 ft
S(0) = -16*0^2 +64*0 +80
S(0) = 80 ft
S(4) = -16*4^2 +64*4 +80
S(4) = 80 ft
- For part a. Compute V_avg:
V_avg = ( S(2) - S(0) ) / 2
V_avg = (144 - 80) / 2
V_avg = 32 ft/s
- For part b. Compute V_avg:
V_avg = ( S(4) - S(2) ) / 2
V_avg = (80 - 140) / 2
V_avg = -30 ft/s
- We see that the signs of the Velocity have changed. The coordinate axis up against gravity was chosen to positive. While a negative access is in favor of the gravity. Hence, from the signs we can see that the ball is going down towards ground in motion from t = 2 s to t = 4 s.
Answer:
The ratio of the areas will be will be 1 : 9
Step-by-step explanation:
The linear scale factor represents a ratio that is used to multiply the dimensions of objects so that accurate geometries can be transferred between real-life and paper.
The linear scale factor is quite different from the area scale factor but related to it in the following way:
The area factor can be obtained by squaring the linear scale factor.
This is Area factor = (Linear scale factor) ^2.
Linear scale factor = (1:3)
Area factor = 
Area factor will be 1: 9
Thus, when the linear scale factor is 1:3 the area factor will be 1 : 9
Answer: C the set of all integers, the set of all rational numbers, and the set of all real numbers
Step-by-step explanation: The value of square root of 9 is ±3. This means that there two answers to square root of 9: 3 and -3.
As far as 3 is concerned, it is one of the elements of the natural number set. It is already known that natural numbers are also whole numbers, also integers, also rational numbers, and also real numbers.
As far as -3 is concerned, it is not a natural number since the set of natural numbers does not contain negative numbers. -3 is an integer. Which means that -3 is also a rational number and also a real number.
After identifying the common sets and taking the intersection of both the above classifications, it yields the set of all integers, the set of all rational numbers, and the set of all real numbers
Hopes this helps bro
We need to solve the following system by substituition:
To solve by substituition means that we need to isolate one variable in one of the equations and replace one expression with the other. This is done below:
Then we need to replace the value of "x" in any of the two equations.
The solution is (-3,-5).
