Answer:
7/10 pi (radians)
Step-by-step explanation:
The formula for sector area is (angle * r^2)/2
140pi = angle*r^2/2
multiply both sides by 2
280pi = angle * r^2
r = 20 cm (substitute)
280pi = angle * (20)^2
280pi = angle * 400
Divide both sides by 400
7/10 pi = angle
Answer: The sum that will be the upper limit of this population is 1280.
Step-by-step explanation:
Since we have given that
Initial population a₁ = 960
Common ratio =
So, We have to write the sum in sigma notation:
Since
so, the sum is convergent, then,
Hence, the sum that will be the upper limit of this population is 1280.
It's useful to divide out the GCF first because it makes factoring easier as the coefficients are smaller requiring less steps.
Example where you don't factor GCF first...
4*-32 = -128
numerous factor pairs for 128 ... takes time to find the correct one
right factor pair is 16,-8
substitute for 8x
4x² + 16x - 8x - 32 = 0
group then factor
4x(x+4) - 8(x+4) = 0
group again
(4x-8)(x+4) = 0
Example of factoring GCF first
4x² + 8x - 32 = 0
4 is GCF
x² + 2x - 8 = 0
factor
(x+4)(x-2) = 0
Solving for x gives the same answer just less steps and simpler math when you factor GCF first.
Answer:
The correct answer is the linear model would be y = 500x - 390 where x is the number of swords sold in a month and y is the net monthly profit; B. 4.96 ≈ 5 swords monthly.
Step-by-step explanation:
Let x number of swords are sold per month.
Cost price of the swords per month is $ 195x.
Fixed cost to maintain the website per month is $390.
Total cost incurred per month is $ (195x + 390).
Selling price per katana is $695.
Total selling price of x swords per month is $695x.
Therefore, Net monthly profit y =695x - (195x + 390)
⇒ y = 695x - 195x - 390
⇒ y = 500x - 390
Thus the linear model would look like y = 500x - 390 where x is the number of swords sold in a month and y is the net monthly profit.
B. Now, given monthly profit y = $2090.
Thus the number of swords needed to be sold is
2090 = 500x - 390
⇒ 2480 = 500x
⇒ x = 4.96
A minimum of 5 swords need to be sold to get a monthly profit of more than $2090.
Given :
We know the identity
We use this property to simplify the left hand side
So
we know ,
when then
For
Add on both sides
Finally we add 2npi for general solution
So options C and D are correct