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3 years ago

Based on Pythagorean identities, which Equation is true?

Mathematics

2 answers:

Pavel [41]3 years ago

8 0

The answer is cot² ∅ - csc² ∅ = -1

Referring to Pythagorean identities:
sin² ∅ + cos² ∅ = 1
1+cot² ∅ = csc² ∅
tan² ∅ + 1 = sec² ∅

1+cot² ∅ = csc² ∅
⇒ transposing 1 and csc² ∅ we will have now
cot² ∅ - csc² ∅ = -1

lara [203]3 years ago

4 0

Answer: The answer is D.

Step-by-step explanation:

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Write (1/3i)-(-6+2/3i) as a complex number in standard form

Eddi Din [679]

Answer:

$6+\frac{i}{3}$

Step-by-step explanation:

$\frac{1}{3\imath}-(-6+\frac{2}{3\imath})$

$\frac{1}{3\imath}+6-\frac{2}{3\imath}$

taking like terms together

$\frac{1}{3\imath}-\frac{2}{3\imath}+6$

taking LCM

$\frac{1-2}{3\imath}+6$

$\frac{-1}{3\imath}+6$

taking LCM

$\frac{-1+18\imath}{3\imath}$

splitting the term

$\frac{-1+18\imath}{3\imath}$

splitting the term

$-\frac{1}{3\imath}+\frac{18\imath}{3\imath}$

$-\frac{1\times3\imath}{3\imath \times \imath}+6$

$-\frac{i}{3\imath^2}+6$

we know that

$\imath^2=-1$

putting this value in above equation

$\frac{\imath}{3}+6$

7 0

3 years ago

a stock was selling at $120 per share. a month later, it was selling at $150 per share. what is the percent increase?

goldfiish [28.3K]

Answer:

25%

Step-by-step explanation:

The formula to find percent increase is $100 * \frac{final-initial}{|initial|}$ . We're given the initial value as 120 and the final value as 150.

$100*\frac{150-120}{|120|}$
$100*\frac{30}{120}$
$100*\frac{1}{4}$
$100/4$
$25$

Therefore, the percent increase is 25%.

4 0

2 years ago

Determine the area of the composite figure to the nearest whole number

Nimfa-mama [501]

Check the picture below.

so, let's notice, is really just a 2x20 rectangle with a quarter of a semicircle with a radius of 11.

$\bf \stackrel{\textit{area of a circle}}{A=\pi r^2}~~ \implies A=\pi 11^2\implies A=121\pi \implies \stackrel{\textit{one quarter of that}}{\boxed{A=\cfrac{121\pi }{4}}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\underline{\textit{area of the figure}}}{\stackrel{\textit{rectangle's area}}{(2\cdot 20)}+\stackrel{\textit{circle's quart's area}}{\cfrac{121\pi }{4}}\qquad \approx \qquad 135.03\implies \stackrel{\textit{rounded up}}{135}}$