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2 years ago

Given cscx/cotx=sqrt2, find a numerical value of one trigonometric function of x.

Mathematics

2 answers:

Firlakuza [10]2 years ago

8 0

$\frac{csc (x)}{cot (x)} = \sqrt{2}$

⇒ $\frac{csc (x)}{1} * \frac{1}{cot (x)} = \sqrt{2}$

⇒ $\frac{1}{sin (x)} * \frac{sin(x)}{cos (x)} = \sqrt{2}$

⇒ $\frac{1}{cos (x)} = \sqrt{2}$ ; sin(x) ≠ 0, cos(x) ≠ 0

⇒ $\frac{cos (x)}{1} = \frac{1}{\sqrt{2}}$ ; sin(x) ≠ 0, cos(x) ≠ 0

⇒ $cos (x) = \frac{\sqrt{2}}{2}$

Use the Unit Circle to determine when $cos (x) = \frac{\sqrt{2}}{2}$

Answer: 45° and 315° $(\frac{\pi}{4} and \frac{7\pi }{4} )$

alex41 [277]2 years ago

5 0

Answer: secx= $\sqrt{2}$

Step-by-step explanation:

A on edge

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There are 250 wolves in a national park. the wolf population is increasing at a rate of 16% per year. write an exponential model

Helga [31]

$\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=250(1 + 0.16)^{t}\implies A=250(1.16)^t \\\\[-0.35em] ~\dotfill$

$A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &1000\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ 1000=250(1.16)^t\implies \cfrac{1000}{250}=1.16^t\implies 4=1.16^t \\\\\\ \log(4)=\log(1.16^t)\implies \log(4)=t\log(1.16) \\\\\\ \cfrac{\log(4)}{\log(1.16)}=t\implies \stackrel{\textit{about 9 years and 4 months}}{9.34\approx t}$

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1 year ago

What is the square root of four

xz_007 [3.2K]

Answer:

It is +2 or since (+2)*(+2 ) gives. If you think that it would be (-2) also then you are wrong because root of a positive rational number is always positive number.

Step-by-step explanation:

Let the square root of four be ‘k’.

Then we have

(4)^1/2=k

(Squaring both sides)

4=(k)^2

=>(k)^2–4=0

=>(k)^2-(2)^2=0

=>[k+2][k-2]=0 {since (a)^2-(b)^2=(a+b)(a-b)}

if product of two numbers is 0 then either of one must be zero.

If k+2=0 then k=-2

If k-2=0 then k=2

From here we got two answers but -2 should be omitted because when we square an equation we add “root extra”which means that when we square an equation one root is added.

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3 years ago

Clare used 25% less butter this month than last month when baking holiday treats. If she used 240 tablespoons of butter last mon

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Answer:

180 tablespoons

Step-by-step explanation:

240×.25=60

240-60=180

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