What is the length of a in this triangle? A=x B=35 C=37 find C

Verify the identitiy:

Advocard [28]

Answer:

$\frac{sinx}{1-cos x}$ = $cosecx$ + $cot x$

Step-by-step explanation:

To verify the identity:

sinx/1-cosx = cscx + cotx

we will follow the steps below;

We will take just the left-hand side and work it out to see if it is equal to the right-hand side

sinx/1-cosx

Multiply the numerator and denominator by 1 + cosx

That is;

$\frac{sinx}{1-cos x}$ = $\frac{sinx(1+cosx)}{(1-cosx)(1+cosx)}$

open the parenthesis on the right-hand side of the equation at the numerator and the denominator

sinx(1+cosx) = sinx + sinx cosx

(1-cosx)(1+cosx) = 1 - cos²x

Hence

$\frac{sinx(1+cosx)}{(1-cosx)(1+cosx)}$ = $\frac{sinx + sinx cosx}{1-cos^{2}x }$

But 1- cos²x = sin²x

Hence we will replace 1- cos²x by sin²x

$\frac{sinx}{1-cos x}$ = $\frac{sinx(1+cosx)}{(1-cosx)(1+cosx)}$ = $\frac{sinx + sinx cosx}{1-cos^{2}x }$ = $\frac{sinx+sinxcosx}{sin^{2}x }$

= $\frac{sinx}{sin^{2}x }$ + $\frac{sinxcosx}{sin^{2}x }$

= $\frac{1}{sinx}$ + $\frac{cosx}{sinx}$

= $cosecx$ + $cot x$

$\frac{sinx}{1-cos x}$ = $cosecx$ + $cot x$

Note that;

$\frac{1}{sinx}$ = $cosecx$

$\frac{cosx}{sinx}$ = $cot x$

6 0

3 years ago

Find the domain of the function y = 3 tan(23x)

solmaris [256]

Answer:

$\mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

In other words, the $x$ in $f(x) = 3\, \tan(23\, x)$ could be any real number as long as $x \ne \displaystyle \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right)$ for all integer $k$ (including negative integers.)

Step-by-step explanation:

The tangent function $y = \tan(x)$ has a real value for real inputs $x$ as long as the input $x \ne \displaystyle k\, \pi + \frac{\pi}{2}$ for all integer $k$ .

Hence, the domain of the original tangent function is $\mathbb{R} \backslash \displaystyle \left\lbrace \left. \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

On the other hand, in the function $f(x) = 3\, \tan(23\, x)$ , the input to the tangent function is replaced with $(23\, x)$ .

The transformed tangent function $\tan(23\, x)$ would have a real value as long as its input $(23\, x)$ ensures that $23\, x\ne \displaystyle k\, \pi + \frac{\pi}{2}$ for all integer $k$ .

In other words, $\tan(23\, x)$ would have a real value as long as $x\ne \displaystyle \frac{1}{23} \, \left(k\, \pi + \frac{\pi}{2}\right)$ .

Accordingly, the domain of $f(x) = 3\, \tan(23\, x)$ would be $\mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

4 0

1 year ago

Which number line shows the solution to −6 − (−2)? A number line is shown from negative 10 to 0 to positive 10. There are increm

VARVARA [1.3K]

Answer:

The correct option is A) A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 4 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.

Step-by-step explanation:

Consider the provided expression.

−6 − (−2)

Open the parentheses and change the sign.

−6 − (−2)

−6 + 2

Subtract the numbers.

−4

Now draw this on number line.

First draw a number line is shown from −10 to 0 to 10. with scale of 2 unit on either side of the number line. Draw an arrow pointing from 0 to −6 Which show −6. Above this, another arrow pointing from −6 to −4 which shows −6 − (−2) = −4. A vertical bar is shown at the tip of the arrowhead of the top arrow.

The required number line is shown in the figure 1.

Hence, the correct option is A) A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 4 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.

4 0

2 years ago

There are 220 students in the seventh grade, and 10% are in the Environmental Club. How many students are in the Environmental C

siniylev [52]

Answer:

22 students are in the environmental club

Step-by-step explanation:

220 / 10 = 22

7 0

2 years ago

genetic experiment with peas resulted in one sample of offspring that consisted of green peas and yellow peas. a. Construct a %

Andreas93 [3]

Complete Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 164 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

Answer:

The 95% confidence interval is $0.2392 < p < 0.3108$