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3 years ago

Someone please let me know the answer

Mathematics

1 answer:

erastova [34]3 years ago

3 0

Answer:

The answer is 30°

Step-by-step explanation:

$when \: \: \sqrt{3} \sin( \alpha ) - \cos( \alpha ) = 0 \\ \sqrt{3} \sin( \alpha ) = \cos( \alpha ) \\ multiply \: by \: \frac{1}{ \sqrt{3} \cos( \alpha ) } \\ then \\ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = \frac{1}{ \sqrt{3} } \\ \tan( \alpha ) = \frac{1}{ \sqrt{3} } \\ then \: \alpha = 30$

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Find the area of the polygon defined by the coordinates (0,-5),(-5,0),(-15,-20),and(-20,-15)

alekssr [168]

Area of the polygon defined by the given points is 62.5 sq units

Step-by-step explanation:

Step 1 :

Let P be the point (-5,0) Q = (0,-5), R = (-15,-20) and S = (20,-15)

We have to to find the area of the polygon PQRS

Step 2 :

The area of polygon given the vertices (x $(x_{1} ,y_{1} ), (x_{2} ,y_{2}) ... (x_{n} ,y_{n} )$ is given by

Area = mod ( $(x_{1} y_{2} - y_{1}x_{2}) + (x_{2} y_{3} - y_{2}x_{3}) + ... (x_{n} y_{1} - y_{n}x_{1})$ ) ÷ 2

Where $x_{n}$ is the vertex n's x coordinate , $y_{n}$ is the vertex n's y coordinate

Substituting the corresponding values ,

Area of PQRS = mod ( (25 - 0)+ (0-75) +(300-300) +( 0-75) ) ÷ 2

= mod (25-75+0-75) ÷ 2

= mod (-125) ÷ 2 = 125 ÷ 2 = 62.5 sq units

Step 3 :

Answer :

Area of the polygon defined by the given points is 62.5 sq units

4 0

3 years ago

Can anybody show me how to do this half angle identity problem STEP BY STEP? I always seem to be missing something

klio [65]

Answer: $\bold{-\dfrac{7\sqrt2}{10}}$

<u>Step-by-step explanation:</u>

It is given that θ is between 270° and 360°, which means that θ is located in Quadrant IV ⇒ (x > 0, y < 0). Furthermore, the half-angle will be between 135° and 180°, which means the half-angle is in Quadrant II ⇒ $cos\ \dfrac{\theta}{2}$

It is given that sin θ = $-\dfrac{7}{25}$ ⇒ y = -7 & hyp = 25

Use Pythagorean Theorem to find "x":

x² + y² = hyp²

x² + (-7)² = 25²

x² + 49 = 625

x² = 576

x = 24

Use the "x" and "hyp" values to find cos θ:

$cos\ \theta=\dfrac{x}{hyp}=\dfrac{24}{25}$

Lastly, input cos θ into the half angle formula:

$cos\bigg(\dfrac{\theta}{2}\bigg)=\pm \sqrt{\dfrac{1+cos\ \theta}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{1+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{25}{25}+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{49}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{49}{50}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\.\qquad \quad =\pm \dfrac{7\sqrt2}{10}$

Reminder: We previously determined that the half-angle will be negative.

6 0

2 years ago

An online retailer collects 7% sales tax. If the sub total of the purchase is $76.00, then how much is collected for sales tax?

jok3333 [9.3K]

The collected tax on purchase of $76.00 is $5.32

Further explanation:

The sales tax is calculated on the total sales by the formula

$Tax = total * \frac{7}{100}$

Given

Total purchase = $76.00

Percentage of tax = 7%

So,

Putting the values in the formula

$Tax\ amount = 76.00 * \frac{7}{100}\\= 5.32$

So, the collected tax on purchase of $76.00 is $5.32

Keywords: Tax, tax calculation

Learn more about tax calculation at:

#LearnwithBrainly

3 0

3 years ago

ASAP! I'll mark you as Branliest! Gina plotted the points (-3,4), (4,4), (-3,-2), and (4,-2), on the coordinate plane.

neonofarm [45]

Answer:

the reson why is becuase the length and width are equal

Step-by-step explanation:

8 0

3 years ago

What is M<3. PLEASE HELPPP

melamori03 [73]

Answer:

105 degrees

Step-by-step explanation:

The angle of a straight line is 180 degrees. Since we need to find the angle for 3, it is 180-75 which is 105 degrees.

4 0

3 years ago

Someone please let me know the answer ​

Someone please let me know the answer