Find rates of change until you find a constant.
dy/dx=1,2,3,4,5,6
d2y/dx2=1,1,1,1,1
So the acceleration, d2y/d2x, is constant. This means that this is a quadratic sequence of the form a(n)=an^2+bn+c. So we can set up a system of equations to solve for the values of a,b, and c. Using the first three points, (1,1), (2,2), and (3,4) we have:
9a+3b+c=4, 4a+2b+c=2, and a+b+c=1 getting the differences...
5a+b=2 and 3a+b=1 and getting this difference...
2a=1, so a=1/2 making 5a+b=2 become:
2.5+b=2, so b=-1/2, making a+b+c=1 become:
1/2-1/2+c=1, so c=1 so the rule is:
a(n)=0.5x^2-0.5x+1 or if you prefer to not have decimals
a(n)=(x^2-x+2)/2
Answer:
An exponential
Step-by-step explanation:
The second one is ratio
Answer:
a) Triangle.
b) Triangle.
c) The area is 110 cm.
Step-by-step explanation:
The shape is given because it is a cross section of a Pyramid which we can see shaded in grey.
The area is given by the base times hight devided by 2. So 10cm * 22cm/2= 110cm.
Hope this helped ;)
Answer:
The radius is growing at the rate of 0.09 centimeter per second at the instant it pops.
Step-by-step explanation:
We are given the following information in the question:
A spherical balloon is designed to pop at the instant its radius has reached 3 centimeters.
The balloon is filled with helium at a rate of 10 cubic centimeters per second .
We have to find fast the radius is growing at the instant it pops.
Volume of spherical balloons =
Differentiating, we get,
Putting the values, we get,
The radius is growing at the rate of 0.09 centimeter per second at the instant it pops.
Answer:
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