Why are there two sine ratios, two cosine rations, and two tangent ratios for any right triangle?

1 answer:

5 0

You could take it from either of the non-right angles.
To one angle, which side is opposite and which is adjacent is different than to the other angle. This is also why sin(x) = cos(90-x) and cos(x) = sin(90-x).

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The area of one field is 16 acres, and the area of the second field is 1 1/4 times bigger. A barn of wheat on the first field ma

gregori [183]

Answer: 23.89 thousands of pounds is more wheat that was gathered from the second field than from the first field.

Step-by-step explanation:

Since we have given that

the area of one field = 16 acres

Area of second field is given by

$1\frac{1}{4}\times 16\\\\=\frac{5}{4}\times 16\\\\=5\times 4\\\\=20\ acres$

A barn of wheat on the first field makes up

$3\frac{7}{12}\times 16\\\\=\frac{43}{12}\times 16\\\\=57.33\text{ thousands of pounds.}$

A barn of wheat on the second field makes up

$1\frac{2}{15}\times 20\\\\=\frac{43}{12}\times \frac{17}{15}\times 20\\\\=81.22\text{ thousands of pounds }$

Now,

$81.22-57.33=23.89$

Hence, 23.89 thousands of pounds is more wheat that was gathered from the second field than from the first field.

7 0

3 years ago

Find the sum of the first 20 terms of the arithmetic sequence 4, -4, -12, -20

Vsevolod [243]

Answer:

The sum of the first 20 terms is -1440.

Step-by-step explanation:

We want to find the sum of the first 20 terms of the arithmetic sequence:

4, -4, -12, -20...

The sum of an arithmetic sequence is given by:

$\displaystyle S=\frac{k}{2}(a+x_k)$

Where k is the number of terms, a is the initial term, and x_k is the last term.

Since we want to find the sum of the first 20 terms, k = 20.

Our initial term a is 4.

Our last term is also the 20th term as we want the sum of the first 20 terms.

To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:

$x_n=a+d(n-1)$

Where a is the initial term, d is the common difference, and n is the nth term.

Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:

$x_n=4-8(n-1)$