Answer: 1106.13 (2 decimal places)
Step-by-step explanation:
To work out the area of this composite shape you would have to put the two semi circles together to form a circle and work out the area of the circle (they have provided the radius which is 11in), then work out the area of the rectangle separately.
The formula for the area of a circle is πr^2 (pi x radius squared).
So when you put the numbers in the formula the area is πx11^2=380.1327111
Then to work out the area of the rectangle you would do base x height.
The height of the rectangle is the same as the diameter of the circle (the diameter is double the radius of a circle) which is 22in.
To find the area of the rectangle you do 22x33=726
So then to find the area of the whole shape you would have to add the area of the circle and the rectangle together.
726+380.1327111=1106.13 (2 decimal places).
You did it right (almost, I got 21 instead of 19) but didn't finish. You need to show your discriminant is never negative.
x² + (p+1)x = 5-2p
x² + (p+1)x +(2p-5) =0
Real roots mean a positive (or at least non-negative) discriminant:
D = b² - 4ac = (p+1)² - 4(1)(2p - 5) = p² + 2p + 1 - 8p + 20
D = p² - 6p + 21
It's not totally obvious that D>0; we prove that by completing the square by noting
(p-3)² = p² - 6p + 9
so
p² - 6p = (p-3)² - 9.
D = p² - 6p + 21
D = (p-3)² - 9 + 21
D = (p-3)² + 12
Now we clearly see D>0 always because the squared term can't be negative, so D is always at least 12. We always get two distinct real roots.
What you do is turn them in to improper fractions
you will have 15/4 times 12/5 then multiply
you would get 180/20 and you simplify it to get
9/1 witch = 9
It is answer #1 the depandent variable is distance, y=25x, the dragonfly will travel 600 miles
