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2 years ago

Find the area of the polygon.

Mathematics

1 answer:

Anastaziya [24]2 years ago

5 0

Answer:

to find the area of a polygon

formula: area = 1/2 x perimeter x apothem

Step-by-step explanation:

Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.

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The sum of two numbers is 30. the first number is twice the second number. what are the numbers?

Fudgin [204]

Let the numbers be x and y.

by the first statement of the question, we get , x + y = 30.,,..(1)

by the second satement, we get , x = y+ y => x=2y... (2)

from equation (2), let us put the value of x in equation (1),
x + y = 30
=> 2y + y = 30
=> 3y = 30
=> y =30/3
=> y = 10

and x=2y => x = 2*10 = 20

in short, the numbers are 10 and 20

3 0

3 years ago

A bank converts US dollars to European Euros at a rate of $1.00 to 0.88

Naya [18.7K]

Answer:

$88

Step-by-step explanation:

100 euros, if multiplied by .88, will equal $88, which equals the USD.

7 0

2 years ago

Read 2 more answers

Andrea chai tea solve the equation 1/4(x+12)=2.What was his mistake

lara31 [8.8K]

Answer:

He was supposed to cross multiply the equation in the original equation. Step 2 was a wrong expression

Explanations:

The given equation is:

$\frac{1}{4}(x\text{ + 12) = 2}$

Cross multiply the equation, the equation becomes:

$x\text{ + 12 = 8}$

x = 8 - 12

x = -4

His mistake was in step 2, he did not properly expand the equation

The proper step was to cross multiply in step 2

3 0

8 months ago

Given that f(x) = x – 2 and g(x) = x2 + 3x – 4, find (f – g)(x). Question 1 options:A. (f – g)(x) = –x2 –2x + 2 B.(f – g)(x) = x

Katena32 [7]

Answer:

Step-by-step explanation:

$(f-g)(x)=f(x)-g(x)\\=(x-2)-(x^2+3x-4)\\=x-2-x^2-3x+4\\=-x^2-4x+2\\$

Therefore, answer is A.

3 0

2 years ago

Write out the first few terms of the Picard iteration scheme for each of the following initial value problems. Where possible, f

Artist 52 [7]

Given an ODE $x'=f(t,x)$ with initial condition $x(t_0)=x_0$ , the general process is to write the ODE as an integral equation,

$x(t)=x_0+\displaystyle\int_{t_0}^tf(u,x(u))\,\mathrm du$

By setting $x_0(t)=x_0$ for all $t$ , we get the following recurrence for $n\ge1$ .

$x_{n+1}(t)=x_0+\displaystyle\int_{t_0}^tf(u,x_n(u))\,\mathrm du$

From this we work towards finding a pattern for $x_n$ so that we can find a solution of the form $x=\lim\limits_{n\to\infty}x_n$ .

$\begin{cases}x'=x+2\\x(0)=2\end{cases}$

Write this as the integral equation,

$x_{n+1}=x(0)+\displaystyle\int_{t_0}^t(x_n(u)+2)\,\mathrm du$

First step:

$x_1=x(0)+\displaystyle\int_{t_0}^t(x_0(u)+2)\,\mathrm du$
$x_1=2\displaystyle\int_0^t\mathrm du$
$x_1=2t$

Second step:

$x_2=x(0)+\displaystyle\int_{t_0}^t(x_1(u)+2)\,\mathrm du$
$x_2=\displaystyle\int_0^t(2u+2)\,\mathrm du$
$x_2=t^2+2t$

Third step:

$x_3=x(0)+\displaystyle\int_{t_0}^t(x_2(u)+2)\,\mathrm du$
$x_3=\displaystyle\int_0^t(t^2+2t+2)\,\mathrm du$
$x_3=\dfrac13t^3+t^2+2t$

Fourth step:

$x_4=x(0)+\displaystyle\int_{t_0}^t(x_3(u)+2)\,\mathrm du$
$x_4=\displaystyle\int_0^t\left(\frac13u^3+u^2+2u+2\right)\,\mathrm du$
$x_4=\dfrac1{4\times3}t^4+\dfrac13t^3+t^2+2t$

You should already start seeing a pattern. Recall that

$e^t=\displaystyle\sum_{k=0}^\infty\frac{x^k}{k!}=1+t+\frac{t^2}2+\frac{t^3}{2\times3}+\frac{t^4}{2\times3\times4}+\cdots$

Multiplying this by 2 gives

$2e^t=2+2t+t^2+\dfrac{t^3}3+\dfrac{t^4}{4\times3}+\cdots$

which matches the solution we have for $x_4$ except for that first term. So subtracting that, we find a solution of

$x=2e^t-2$

with a domain of $t\in\mathbb R$ .

Hopefully this gives some insight on how to approach the other two problems.

6 0

3 years ago