Answer:
p = 5/7
Step-by-step explanation:
The given function is:
for -4 ≦ x < 1
for 1 ≦ x ≦ 5
Part a)
A continuous function has no breaks, jumps or holes in it. So, in order for g(x) to be continuous, the point where g(x) stops during the first interval -4 ≦ x < 1 must be equal to the point where g(x) starts in the second interval 1 ≦ x ≦ 5
The point where, g(x) stops during the first interval is at x = 1, which will be:
The point where g(x) starts during the second interval is:
For the function to be continuous, these two points must be equal. Setting them equal, we get:
3 = 7p - 2
3 + 2 = 7p
p = 
Thus the value of p for which g(x) will be continuous is .
Part b)
We have to find p by setting the two pieces equal to each other. So, we get the equation as:
Substituting the point identified in part (a) i.e. x=1, we get:
This value agrees with the answer found in previous part.
Answer:
4
Step-by-step explanation:
The distance of the robot from the charging base is gotten as; 62 cm
<h3>How to use Cosine Rule?</h3>
From the image attached showing the movement of Kapil's robot, we can use cosine rule to find the value of h which is the distance of the robot from the charging base.
The distance of the robot from the charging base is gotten by;
h = x² + b² - 2xb cos 60
h = 50² + 70² - 2*50*70 * 0.5
h = 62 cm
Read more about Cosine Rule at; brainly.com/question/4372174
#SPJ1
Answer:
1/2
Step-by-step explanation:
Simple probability is a ratio of the number of ways the thing we want to happen can to the total possible outcomes.
(For example, we flip a coin and want heads, but it can land on heads or tails. Our probability of getting heads is 1/2, one way to get heads over the 2 possible outcomes)
So for this problem, there's 20 possible things that CAN happen (3 + 7 + 10) and 10 ways we get what we want (a green marble).
Our probability of getting a green marble is 
, which simplifies to 
Answer:
<u>3</u> * <u>3</u>
4 1
Step-by-step explanation:
To convert division problems with fraction into multiplication problems use the KCF rule
- Keep the 1st Fraction the same
- Change the division sign to a multiplication sign
- Flip the fraction (reciprocal)
