Someone helppppp pleaseeeeeee

Root 3 cosec140° - sec140°=4 prove that

Lorico [155]

Answer:

Step-by-step explanation:

We are to show that $\sqrt{3} cosec140^{0} - sec140^{0} = 4\\$

Proof:

From trigonometry identity;

$cosec \theta = \frac{1}{sin\theta} \\sec\theta = \frac{1}{cos\theta}$

$\sqrt{3} cosec140^{0} - sec140^{0} \\= \frac{\sqrt{3} }{sin140} - \frac{1}{cos140} \\= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\$

From trigonometry, 2sinAcosA = Sin2A

$= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\\\= \frac{\sqrt{3}cos140-sin140 }{sin280/2}\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{2sin280}\\\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{sin280}\\since sin420 = \sqrt{3}/2 \ and \ cos420 = 1/2 \\ then\\\frac{4(sin420cos140-cos420sin140) }{sin280}$

Also note that sin(B-C) = sinBcosC - cosBsinC

sin420cos140 - cos420sin140 = sin(420-140)

The resulting equation becomes;

$\frac{4(sin(420-140)) }{sin280}$

= $\frac{4sin280}{sin280}\\ = 4 \ Proved!$

3 0

3 years ago

The manufacturing of a ball bearing is normally distributed with a mean diameter of 22 millimeters and a standard deviation of .

Misha Larkins [42]

Answer:

0.1507 or 15.07%.

Step-by-step explanation:

We have been given that the manufacturing of a ball bearing is normally distributed with a mean diameter of 22 millimeters and a standard deviation of .016 millimeters. To be acceptable the diameter needs to be between 21.97 and 22.03 millimeters.

First of all, we will find z-scores for data points using z-score formula.

$z=\frac{x-\mu}{\sigma}$ , where,

z = z-score,

x = Sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

$z=\frac{21.97-22}{0.016}$

$z=\frac{-0.03}{0.016}$

$z=-0.1875$

Let us find z-score of data point 22.03.

$z=\frac{22.03-22}{0.016}$

$z=\frac{0.03}{0.016}$

$z=0.1875$

Using probability formula $P(a$ , we will get:

$P(-0.1875$

Therefore, the probability that a randomly selected ball bearing will be acceptable is 0.1507 or 15.07%.

6 0

3 years ago

Austin invested $60,000 in an account paying an interest rate of 4.7% compounded

pantera1 [17]

Answer:

100300

Step-by-step explanation:

4 0

3 years ago

12 whites 4 blacks 3 blue 1 red. Find each experimental probability as a fraction? 1.)p(white)

Dafna1 [17]

Experimental probability is if an experiment was actually run. If those values are the result of an experiment, then the probability is desired value (white) over total possibilities.

$\frac{12}{20} = \frac{3}{5}$ or 0.6

5 0

3 years ago

X^2-4x+1=0 . RESOLVE PLS

Mkey [24]

$x^2-4x+1=0\\ x^2-4x+4-3=0\\ (x-2)^2=3\\ x-2=\sqrt 3\vee x-2=-\sqrt3\\ x=2+\sqrt 3\vee x=2-\sqrt3$

4 0

3 years ago