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2 years ago

Find an exact value cos(19pi/12)

2 answers:

6 0

19 π / 12 = 19 * 180° / 12 = 285 °
cos ( 19 π / 12 ) = cos 285° = cos ( - 75° ) = cos 75°
cos 75° = cos ( 45° + 30° ) = cos 45° cos 30° - sin 45° sin 30° =
= ( √2 / 2 · √3/2 ) - ( √2 / 2 · 1/2 ) = √6/4 - √2/4 =
= ( √6 - √2 )/ 4

dmitriy555 [2]2 years ago

3 0

$cos\left ( \frac{9\pi}{12}\right )=\frac{\sqrt{2-\sqrt{3}}}{2}$

Step-by-step explanation:

We know that

cos 2x = 2cos²x - 1

So we have

$cosx=\sqrt{\frac{1+cos2x}{2}}$

Substituting $x=\frac{19\pi}{12}$

$cos\left ( \frac{19\pi}{12}\right )=\sqrt{\frac{1+cos2\left ( \frac{19\pi}{12}\right )}{2}}\\\\cos\left ( \frac{19\pi}{12}\right )=\sqrt{\frac{1+cos\left ( \frac{19\pi}{6}\right )}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{1+cos570}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{1-\frac{\sqrt{3}}{2}}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{2-\sqrt{3}}{4}}\\\\cos\left ( \frac{9\pi}{12}\right )=\frac{\sqrt{2-\sqrt{3}}}{2}$

$cos\left ( \frac{9\pi}{12}\right )=\frac{\sqrt{2-\sqrt{3}}}{2}$

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Katarina [22]

Answer:

$x=50.6cm$

Step-by-step explanation:

Triangle MAB is similar to triangle MNP

Since the triangles are similar, the corresponding ratios are in the same proportion.

Therefore we can write the relation;

$\frac{|MB|}{|MP|}=\frac{|MA|}{|MN|}$

$\frac{x}{72.6}=\frac{46.2-14}{46.2}$

This implies that;

$\frac{x}{72.6}=\frac{32.2}{46.2}$

We multiply both sides by 72.6 to get

$\frac{x}{72.6}\times 72.6=\frac{32.2}{46.2}\times72.6$

$\Rightarrow x=50.6$

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8 0

3 years ago

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MA_775_DIABLO [31]

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3 years ago

Can someone help me with system of equations?

umka21 [38]

#1)

Answer:

x=1 and y=12

Explanation:

y=5x+7

y=2x+10

This system should use substitution because the value of y is given in terms if x.

Substitution:

5x+7=2x+10

Solve:

3x=3

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Substitute x to solve for y by plugging x into one if the original equations(doesn’t matter which one is used).

y=5x+7

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#2)

Answer:

x=-8 and y=2

Explanation:

y=2x+18

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This system also uses substitution. The value of y us already given in terms if c in the first equations, so we will substitute in the second equation.

Substitute:

9(2x+18)=-2x+2

Solve:

18x+162=-2x+2

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Now that we have the value if x, plug it into one of the original equations(doesn’t matter which equation) and substitute to find y.

y=2x+18

Substitute:

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3 years ago

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I need help. Someone help please. (photo)

gayaneshka [121]

Answer:

Step-by-step explanation:

In order to solve all of these problems, you have to first create an equation. The typical format for an equation looks like this: y = mx + b

m is the slope and b is the y-intercept.

In order to create an equation, you have to find the slope and y-intercept of the function. You can find the slope using this expression: $\frac{y2-y1}{x2-x1}$ To find the y-intercept, you use a known point and the slope in the equation to solve for b.

Now that we know this, we can solve the problems.

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To create the equation, let's find the slope using points (1, 15) and (2, 30)

$\frac{30 - 15}{2 - 1}$ = 15/1 = 15

The equation now looks like this: h = 15w + b

Let's use the point (1, 15) from the table to find b

15 = 15(1) + b

15 = 15 + b

subtract 15 from both sides the isolate the b

0 = b

There is no y-intercept for this equation, so the equation looks like this:

h = 15w

1b. We know the equation is h = 15w, so all we have to do is input the 9 into the equation.

h = 15(9)

h = 135

2a. We'll use the points (1, 8) and (2, 16) to find the slope

$\frac{16 - 8}{2-1}$ = 8/1 = 8

The slope is 8.

Since it's impossible to sell any houses in 0 months, we already know that there is no y-intercept, so the equation looks like this:

h = 8m

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h = 8(15)

h = 120

3a. We'll use the points (1, 35) and (2, 70) to find the slope.

$\frac{70 - 35}{2 - 1}$ = 35/1 = 35

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c = 35m

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The slope is 8.

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4 0

3 years ago

Compute the fare without tip: 1 passenger, 9.5 miles. Round to nearest fifth of a mile when dividing.

vladimir1956 [14]

The fare without tip for the Metro Taxi is of 1 passenger and 9.5 miles is $27.83.

The given parameters:

Number of passenger = 1
Total distance = 9.5 miles
Cost of first 0.2 mile = $0.75
Cost of additional mile = $0.55
Cost of a passenger = $1.50

The fare without tip for the Metro Taxi is calculated as follows;

for the first 0.2 mile = $0.75
the remaining distance = 9.5 - 0.2 = 9.3 miles

$cost \ of \ distance = \$ 0.75 \ \ + \ \ \frac{\$ 0.55}{0.2 \ mile} \times 9.3 \ miles\\\\cost \ of \ distance = \$ 26.325$

Cost of 1 passenger = $1.50

The total cost is calculated as follows;

total cost = $1.50 + $26.325

total cost = $27.83

Thus, the fare without tip for the Metro Taxi is of 1 passenger and 9.5 miles is $27.83.

The complete question is below:

Compute the fare without tip: 1 passenger, 9.5 miles. Round to nearest fifth of a mile when dividing.

Metro Taxi: first 1/5 mi= $0.75, each additional 1/5 mi= $0.55, each additional passenger= $1.50.

Learn more about cost per miles here: brainly.com/question/2513267

8 0

2 years ago