2/3n + 5 > 12
2/3n > 12 - 5
2/3n > 7
n > 7 * 3/2
n > 21/2 or 10 1/2
Answer:
6.68, 13.37, 14.95
Step-by-step explanation:
One of the legs is twice as long as the other.
b = 2a
The perimeter is 35.
35 = a + b + c
The triangle is a right triangle.
c² = a² + b²
Three equations, three variables. Start by plugging the first equation into the second and solving for c.
35 = a + 2a + c
c = 35 − 3a
Now plug this and the first equation into the Pythagorean theorem:
(35 − 3a)² = a² + (2a)²
1225 − 210a + 9a² = a² + 4a²
1225 − 210a + 4a² = 0
Solve with quadratic formula:
a = [ -(-210) ± √((-210)² − 4(4)(1225)) ] / 2(4)
a = (210 ± √24500) / 8
a ≈ 6.68 or 45.82
Since the perimeter is 35, a = 6.68. Therefore, the other sides are:
b ≈ 13.37
c ≈ 14.95
By definition we have that the average rate of change is given by:
AVR = (f (x2) - f (x1)) / (x2 - x1)
Substituting the values we have:
AVR = (204 - (-6)) / (10 - 0)
Rewriting we have:
AVR = (204 + 6) / (10 - 0)
AVR = 210/10
AVR = 21
Answer:
the average rate of change for f (x) from x = 0 to x = 10 is:
AVR = 21
a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is
b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so
c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so
Then by linearity, we have
This is so easy. You should try before posting a question on this site. No offense.
Having said that im still here to help :)
10. 4,2 -3,5
11. Sorry dont know this one
12. Plot a point at -3,-4 label is Resturant
13. Plot a point at 0,-3 label it Beth
I will only post these ones, The others are extremely simple.
