Answer:
1005
Step-by-step explanation:
If you just kept subtracting from 2580 then the next and then the next number you would get 1005
Answer:
A = 12 units ^2
Step-by-step explanation:
The area of the trapezoid is found by
A = 1/2 (b1+b2)h
b1 = 2
b2 = 4
h = 4
I found these by looking at the graph
A = 1/2(2+4) 4
A = 1/2(6*4)
A = 12 units ^2
-27 - (-3) = -27 + 3 = - 24
560 - 2(25 + 11) = 560 - 2(36) = 560 - 72 = 488
8y - x^2....x = -5, y = 4
8(4) - (-5)^2 =
32 + 5^2 =
32 + 25 =
57
The distances between the given pairs of points are:
- (-8, -2) and (6, -1); d = 14.04
- (-4, 5) and (4,0); d = 9.85
<h3>
How to find the distance between two points?</h3>
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √( (x₁ - x₂)^2 - (y₁ - y₂)^2)
1) The first pair of points is (-8, -2) and (6, -1), using the above formula we can see that the distance is:
d = √( (-8 - 6)^2 - (-2 +1)^2) = 14.04
2) The second pair is (-4, 5) and (4,0), and using the distance formula, we get:
d = √( (-4 - 5)^2 - (4 - 0)^2) = 9.85
If you want to learn more about the distance between points:
brainly.com/question/7243416
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Answer:
Using either method, we obtain: 
Step-by-step explanation:
a) By evaluating the integral:
![\frac{d}{dt} \int\limits^t_0 {\sqrt[8]{u^3} } \, du](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5Cint%5Climits%5Et_0%20%7B%5Csqrt%5B8%5D%7Bu%5E3%7D%20%7D%20%5C%2C%20du)
The integral itself can be evaluated by writing the root and exponent of the variable u as: ![\sqrt[8]{u^3} =u^{\frac{3}{8}](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bu%5E3%7D%20%3Du%5E%7B%5Cfrac%7B3%7D%7B8%7D)
Then, an antiderivative of this is: 
which evaluated between the limits of integration gives:

and now the derivative of this expression with respect to "t" is:

b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then

is continuous on [a,b], differentiable on (a,b) and 
Since this this function
is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:
