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3 years ago

Coefficient x^2 in the expansion of (2+x)^5

1 answer:

7 0

Alright, expand the given equation:
(2+x) (2+x) (2+x) (2+x) (2+x)
Use FOIL method and distribution to solve
At the final answer, find the x^2 and the number that multiplies to it is the coefficient
I can't do the actually expansion for you, it would take a decently long time. You should be able to, its a good practice. Good luck!

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46/300

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3 years ago

Estimate the perimeter of the figure to the nearest tenth.

pantera1 [17]

Answer:

The Perimeter of the Figure to the nearest tenth is 18.7 units

Step-by-step explanation:

Please note I have attached an edited version of your sketch to aid my solution. Now this question can be solved in multiple ways. Here, we shall see one of them.

Looking at the original sketch, we can see that the figure is actually a combination of a Triangle (Figure 1 in my sketch) and a rectangle (Figure 2 in my sketch). So we can simply find the sides of a Triangle and the sides of a Rectangle and add them.

Perimeter on Figure 1:

The Perimeter of a Triangle is given by the Sum of the three sides as:

$A_{T}=a+b+c$

Perimeter on Figure 2:

The Perimeter of the Rectangle is given by:

$A_{R}=2(w+l)$

where here $w$ is the width and $l$ is the length of the rectangle.

Perimeter on Sketched Figure:

The perimeter of the total figure will be two sides of the triangle and the three sides of the rectangle (as the one adjacent between Fig. 1 and 2 can not be taken into account). Thus we need to find 5 different sides and add them together.

Now since the figure is on a graph paper, we can read of the size of some sides, thus the left side of the triangle is $a=3$ units and the base of the triangle is also $b=3$ units. Now to find the last unknown side we can take Pythagorian theorem, since our triangle is a Right triangle, (i.e. one angle is 90°).

Pythagoras states that the squared of the hypotenuse of a right triangle is equal to the sum of the squares of the other two legs of the triangle (where the hypotenuse side is always across the 90° angle. So here we can say that:

$h^2=a^2+b^2\\$

where $h$ is the hypotenuse and our unknown side. So plugging in values and solving for $h$ we have:

$h=\sqrt{a^2+b^2}\\ h=\sqrt{3^2+3^2}\\\\h=\sqrt{9+9}\\ h=\sqrt{18}\\ h=3\sqrt{2}$ units.

So from figure 1 we now have two known sides:

$a=3\\h=3\sqrt{2}$

Now lets find the other three sides from Figure 2. So here similarly we can read from the graph paper that the base of the rectangle (i.e. the width $w$ ) is $w=3$ and the lengths of the rectangle, are equal and also of the same length as the hypotenuse on the triangle steps. Thus from Figure 2 we have the three remaining sides as:

$w=3\\l=h=3\sqrt{2}$

So finally the Perimeter of the Sketched Total Figure will be the summation of all 5 sides as:

$\Pi_{figure}=a+h+w+l+l\\\Pi_{figure}=3+3\sqrt{2}+3+2(3\sqrt{2} )\\\Pi_{figure}= 6+9\sqrt{2} \\\Pi_{figure}=18.7$ units

(rounded to the nearest tenth)

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4 years ago