A rectangular garden has a length that is modeled by the expression 2x - 7 and a width of 3x^2+4x.
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Answer:
m+n = 337
Step-by-step explanation:
Lets start from the first triangle, It is given to be as 30-60-90.
The hypotenous of first rectangle be 2x, then other sides are by default x and
, using laws of trigonometry.
(sin(30) = 0.5 and cos(30) = )
The perimeter of first triangle is ,
=
Now, for second triangle, the longer leg is 2x, and similarly again,
other 2 sides are .
Again the perimeter of triangle comes out as,
=
Thus, the repeating pattern is identified. The consecutive perimeters differ by, multiplying by factor
Thus, we can say that perimeter of 4th triangle is,
= , where X is the repeating constant.
And of 12th triangle is,
= ,
Evaluating the above ratio, we get,
=
Thus, m =256 and n=81.
Thus, m+n = 256+81 = 337.
If the third term of the aritmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.
Given the third term of the aritmetic sequence is 126 and sixty fourth term is 3725.
We are required to find the first term of the arithmetic sequence.
Arithmetic sequence is a series in which all the terms have equal difference.
Nth term of an AP=a+(n-1)d
=a+(3-1)d
126=a+2d--------1
=a+(64-1)d
3725=a+63d------2
Subtract second equation from first equation.
a+2d-a-63d=126-3725
-61d=-3599
d=59
Put the value of d in 1 to get the value of a.
a+2d=126
a+2*59=126
a+118=126
a=126-118
a=8
=a+(1-1)d
=8+0*59
=8
Hence if the third term of the arithmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.
Learn more about arithmetic progression at brainly.com/question/6561461
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