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3 years ago

What is the perimeter?

Mathematics

1 answer:

Harlamova29_29 [7]3 years ago

5 0

Answer:

Step-by-step explanation:

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Mailani has 184 folders that she plays evenly into seven piles how folders were placed in to the last pile

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Marcus baked a loaf of banana bread for a party he cut the loaf into equal size pieces at the end of the party there were six pi

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Step-by-step explanation:

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2 years ago

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Evaluate the definite integrals using properties of the definite integral and the fact that

anygoal [31]

I gather that the given functions satisfy the following definite integral relations:

$\displaystyle \int_{-1}^4 f(x) = -6$

$\displaystyle \int_4^5 f(x) = 10$

$\displaystyle \int_4^5 g(x) =5$

a) By linearity of the integral operator, we have

$\displaystyle \int_{-1}^4 10 f(x) \, dx = 10 \int_{-1}^4 f(x) \, dx = 10 \times (-6) = \boxed{-60}$

b) The integral over an interval is equal to the sum of integrals over a partition of that interval. In this case, the interval [-1, 5] can be written as the interval union [-1, 4] U [4, 5], so that

$\displaystyle \int_{-1}^5 f(x) \, dx = \int_{-1}^4 f(x) \, dx + \int_4^5 f(x) \, dx = -6 + 10 = \boxed{4}$

c) By linearity,

$\displaystyle \int_4^5 (f(x) - g(x)) \, dx = \int_4^5 f(x) \, dx - \int_4^5 g(x) \, dx = 10 - 5 = \boxed{5}$

d) By linearity,

$\displaystyle \int_4^5 (4f(x) + 5g(x)) \, dx = 4 \int_4^5 f(x) \, dx + 5 \int_4^5 g(x) \, dx = 4\times10 + 5\times5 = \boxed{65}$

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2 years ago

Find the perimeter of parallelogram ABCD with vertices A(–2, 6), B(1, 2), C(–2, –2), and D(1, –6).

slamgirl [31]

Answer:

The perimeter = 26 unites

Step-by-step explanation:

* Lets revise some facts of parallelogram

- Every two opposite sides are parallel and equal

- Every two opposite angles are equal

- Every two adjacent angles are supplementary

- Th two diagonals bisects each other

- The perimeter = 2(S1 + S2)

* Now lets solve the problem

- ABCD is a parallelogram, where

A = (-2 , 6) , B = (1 , 2) , C = (-2 , -2) , D = (1 , -6)

- To find the perimeter we need the length of AB and BD

- The rule of the distance between two point is

d = √[(x2 - x1)² + (y2 - y1)²]

* Lets find AB

∵ AB = √[1 - -2)² + (2 - 6)²] = √[(3²) + (-4)²]

∴ AB = √25 = 5

* Lets find BD

∵ BD = √[(1 - 1)² + (-6 - 2)² = √[(0)² + (-8)²]

∴ BD = √64 = 8

* Lets find the perimeter

∵ The perimeter = 2 (5 + 8) = 26 unites

8 0

3 years ago

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