You have to know that the graph of the arctangent function is a flat S-shaped curve that goes through (0, 0) and has asymptotes at ±π/2. The factor of 2 that multiplies it here expands it vertically so the asymptotes are at ±π. The +3 added to the x causes it to be shifted to the left by 3 units.
Each numbered angle equals 37°.
Answer:
44.1 x 10^-2
Step-by-step explanation:
Since one grain
= 7 x 10^-5
6300kg = 7 x 10^-5 x 6300
Put 6300 in standard form
7 x 10^-5 x 6.3 x 10^3
Multiply the whole numbers and add the exponents
7 x 6.3 x 10^-5 + 3
44.1 x 10^-2
There are 44.1 x 10^-2 grains of sand in 6300kg
Answer:
Example:
A bag contains 3 black balls and 5 white balls. Paul picks a ball at random from the bag and replaces it back in the bag. He mixes the balls in the bag and then picks another ball at random from the bag.
a) Construct a probability tree of the problem.
b) Calculate the probability that Paul picks:
i) two black balls
ii) a black ball in his second draw
Solution:
tree diagram
a) Check that the probabilities in the last column add up to 1.
b) i) To find the probability of getting two black balls, first locate the B branch and then follow the second B branch. Since these are independent events we can multiply the probability of each branch.
ii) There are two outcomes where the second ball can be black.
Either (B, B) or (W, B)
From the probability tree diagram, we get:
P(second ball black)
= P(B, B) or P(W, B)
= P(B, B) + P(W, B)
Answer:
Result:
Step-by-step explanation:
Given
The parallelogram DEFG
DE = 6x-12
FG = 2x+36
EF = 4y
DG = 6y-42
We know that the opposite sides of a parallelogram are equal.
As DE and FG are opposite sides, so
DE = FG
substituting DE = 6x-12 and FG = 2x+36 in the equation
6x-12 = 2x+36
6x-2x = 36+12
simplifying
4x = 48
dividing both sides by 4
4x/4 = 48/4
x = 12
Therefore,
The value of x = 12
Also, EF and DG are opposite sides, so
EF = DG
substituting EF = 4y and DG = 6y-42 in the equation
4y = 6y-42
switching sides
6y-42 = 4y
6y-4y = 42
2y = 42
dividing both sides by 2
2y/2 = 42/2
y = 21
Therefore,
The value of y = 21
Result:
