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3 years ago

8

Ke Shawn is placing a right triangle in the coordinate plane. He knows that the longer leg is twice the length of the shorter le

g. He places the longer leg on the x-axis.
What coordinates should he assign to the third vertex of the triangle?

2 answers:

Artist 52 [7]3 years ago

7 0

the 3rd vertex is on the x axis line which means Y =0

since the longer leg is twice as long as the shorter leg and the length of the shorter leg is a, then twice the length would be 2a ( 2 times a)

so the 3rd vertex is (2a,0)

Nutka1998 [239]3 years ago

5 0

Answer:

The third vertex of triangle is (2a,0)

Step-by-step explanation:

We are given the following information in the question:

A right angled triangle such the longer side is twice the length of the shorter side.

We have to find the coordinate of the third vertex of triangle.

Let A(0,a), B(0,0), C(x,0)

Distance between two points with coordinate $(x_1,y_1), (x_2,y_2)$ is given by:

$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

Now, we are given that the longer side is twice the length of the shorter side.

Thus, we can write:

$AC = 2AB\\\sqrt{(x-0)^2 + (0-0)^2}= 2\sqrt{(0-0)^2 + (a-0)^2}\\\pm x = \pm 2a\\\text{Since the point lies on the positive side of x-axis}\\x = 2a$

The third vertex of triangle is (2a,0)

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In an arithmetic sequence, a_17 = -40 and a_28 = -73. Please explain how to use this information to write a recursive formula fo

Vinvika [58]

An arithmetic sequence

$a_1,a_2,a_3,\ldots,a_n,\ldots$

is one in which consecutive terms of the sequence differ by a fixed number, call it <em>d</em>. This means that, given the first term $a_1$ , we can build the sequence by simply adding <em>d</em> :

$a_2=a_1+d$

$a_3=a_2+d$

$a_4=a_3+d$

and so on, the general pattern governed by the recursive rule,

$a_n=a_{n-1}+d$

We can exploit this rule in order to write any term of the sequence in terms of the first one. For example,

$a_3=a_2+d=(a_1+d)+d=a_1+2d$

$a_4=a_3+d=(a_1+2d)+d=a_1+3d$

and so on up to

$a_n=a_1+(n-1)d$

In this case, we're not given the first term right away, but the 17th. But this isn't a problem; we can use the same exploit to get

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$a_{20}=a_{17}+3d$

and so on, up to the next term we know,

$a_{28}=a_{17}+11d=-40+11d$

(Notice how the subscript of <em>a</em> on the right and the coefficient of <em>d</em> add up to the subscript of <em>a</em> on the left.)

The 28th term is -73, so we can solve for <em>d</em> :

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To get the first term of the sequence, we use the rule found above and either of the known values of the sequence. For instance,

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3 years ago

Suppose the voltage in an electrical circuit varies with time according to the formula V(t) = 40 sin(t) for t in the interval [0

grigory [225]

The numerical value of the mean voltage is 25.47 V

To find the numerical value of the mean voltage, V of V(t) = 40 sin(t), we integrate V(t) with respect to t over the interval [0.π]

So,

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V ≅ 25.47 V

So, the numerical value of the mean voltage is 25.47 V

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almond37 [142]

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Bezzdna [24]

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2 years ago