Irrational numbers are numbers that cannot be expressed in fractions
Answer:
an = 2(−4)^(n − 1); all integers where n ≥ 1
Step-by-step explanation:
The equation has the form ...
an = a1(r)^(n-1) . . . . . where a1 is the first term and r is the common ratio.
The first term is given as 2, and the ratio will be the ratio of the first two terms:
r = (-8)/(2) = -4
Terms are numbered starting with n=1, so the formula is ...
an = 2(-4)^(n-1) for n≥1
Answer: the distance from the bottom of the ladder to the base of the building is 12 feet.
Step-by-step explanation:
The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.
The length of the ladder represents the hypotenuse of the right angle triangle.
The distance from the ground to the point where the ladder touches the wall of the building represents the opposite side
Therefore, to determine the distance from the bottom of the ladder to the base of the building, x, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
37² = 35² + x²
1369 = x² + 1225
x² = 1369 - 1225 = 144
x = √144 = 12 feet
Answer:
8
Step-by-step explanation:
first, 70-79 have 3 students
then 80-89 have 5 students
Answer:
a) 
b) 14650
Step-by-step explanation:
First let's find out how much the population increased during those 4 years.
In 1992 it was 1000.
In 1996 it was 4900.
. During 4 years, the population increased by 3900.
Therefore during 1 year, the population increased by 
Since it's linear, we can write it using the general equation for a straight line, which is 
.
We've already found m, which is the slope of the line (975).
The question asks us to write it in the form: 
. where P is the population and t is the time in years since 1990.
We can sub some values into this formula to work out the constant, c.
Let's put in the values for 1992. Population is 1000 and the time in years after 1990 is 2 (since 1992 - 1990 = 2)..
Therefore:
Re-arrange to get: 
Therefore, we have our formula now.
Now for the second part of the question, population of moose in 2006. We need to work out how many years apart 1990 and 2006 are which we can calculate by doing 
.
Now let's put this into our formula.
