Which of the following are mathematical sentences? Check all that apply.

Mathematics

1 answer:

babymother [125]3 years ago

5 0

The following that are mathematical sentences are b,c

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Given that cos(theta) = 8/17 and that theta lies in Quadrant IV, what is the exact value of sin 2(theta)?

Deffense [45]

Answer: $-\frac{240}{289}$

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Explanation:

Use the pythagorean trig identity $\sin^2(\theta)+\cos^2(\theta) = 1$ and plug in the fact that $\cos(\theta) = \frac{8}{17}\\\\$

Isolating sine leads to $\sin(\theta) = -\frac{15}{17}\\\\$ . I'm skipping the steps here, but let me know if you need to see them.

The result is negative because we're in quadrant 4, when y < 0 so it's when sine is negative.

Therefore,

$\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\\\\sin(2\theta) = 2*\left(-\frac{15}{17}\right)*\left(\frac{8}{17}\right)\\\\\sin(2\theta) = -\frac{240}{289}\\\\$

6 0

1 year ago

Need to find the sum of 50

Bumek [7]

Answer:

4600

Step-by-step explanation:

This is an arithmetic sequence with common difference d between consecutive terms.

d = - 2 - (- 6) = 2 - (- 2) = 6 - 2 = 4

The sum to n terms of an arithmetic sequence is

$S_{n}$ = $\frac{n}{2}$ [ 2a + (n - 1)d ]

where a is the first term

here a = - 6, d= 4 and n = 50, hence

$S_{50}$ = $\frac{50}{2}$ [ (2 × - 6) + (49 × 4) ]

= 25 ( - 12 + 196 )

= 25 × 184

= 4600

6 0

3 years ago

Uhh solve the question? i hope i find some haikyuu stans out there✌️

musickatia [10]

Answer and Step-by-step explanation:

$(\frac{1.25 - x}{1.25x} ) * 100\\\\\\(\frac{1.25}{1.25x} - \frac{x}{1.25x} ) * 100\\\\(\frac{1}{x} - \frac{1}{1.25} ) * 100\\\\\frac{100}{x} - 80\\\\\\$