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3 years ago

Given this unit circle

Mathematics

1 answer:

Sloan [31]3 years ago

7 0

Answer:

x = cos 135° = - (√2) / 2

Step-by-step explanation:

x = cos 135° = - √2/2

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Papessa [141]

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3 years ago

Solve the problem.A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course. At that t

Mice21 [21]

Given:

A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course.

The distance between plan and mountain is 10 km.

A short time later, the bearing to the mountain becomes 45°.

Here NM is the distance between the plane from the mountain when the second bearing is taken.

We need to find the measure of NM.

$We\text{ know that }\angle INM\text{ and }\angle\text{XNM are supplementary angles.}$

The sum of the supplementary angles is 180 degrees.

$\angle INM+\angle XNM=180^o$ $\text{Substitute }\angle XNM=45^o\text{ in the equation.}$

$\angle INM+45^o=180^o$

$\angle INM=180^o-45^o$

$\angle INM=135^o$

We know that the sum of all three angles of the triangle is 180 degrees.

$\angle INM+\angle NIM+\angle INM=180^o$ $\text{Substitute }\angle INM=135^o\text{ and }\angle NIM=35^o\text{ in the equation.}$

$135^o+35^o+\angle INM=180^o$

$170^o+\angle INM=180^o$

$\angle INM=180^o-170^o$

$\angle INM=10^o$

Consider the sine law.

$\frac{\sin N}{IM}=\frac{\sin M}{IN}=\frac{\sin I}{NM}$

Take the equation to find the measure of NM.

$\frac{\sin N}{IM}=\frac{\sin I}{NM}$ $\text{Substitute }\angle N=135^o,\angle I=35^o,\text{ and IM=10 in the equation.}$

$\frac{\sin 135^o}{10}=\frac{\sin35^o}{NM}$

$NM=\frac{\sin 35^o}{\sin 135^o}\times10$ $NM=8.11$

Hence the measure of NM is 8.1 km.

The plane is 8.1 km far from the mountain when the second bearing is taken.

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1 year ago

Write the slope-intercept of the equation of the line through the given point with the given slope.

ch4aika [34]

Answer:

-5 = 2(-1) + b

Step-by-step explanation:

the slope-intercept form is writing as y = mx +b

3 0

3 years ago

Read 2 more answers

How would you come up with 2.5 from 2 1/2 hours in fraction and how would you come up with 4.5 from 414 in hours and fractions

Morgarella [4.7K]

The clock breaks down to a different number sequence 2 B .5 it would be half past the hour 15 minutes past the hour would be 1 / 4 or .25

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3 years ago

Using an infinite geometric series for the repeating decimal 0.551¯¯¯¯¯¯¯¯, with ratio 11000, find integers a and b so that 0.55

irga5000 [103]

Answer:

Sum = 551/999

Where a = 551 and b = 999

The two integers are 551 and 999

Step-by-step explanation:

Given

Decimal = 0.551

Ratio = 1/1000

By repeating the decimal, we can write;

0.551 -bar = 0.551551551.....

0.551551551..... = 0.551 + 0.000551 + 0.000000551 + ....

= 551/1000 + 551/1000000 + 551/1000000000 + ......

= 551/10³ + 551/10^6 + 551/10^9 + .....

= n=0 Σ∝(551/10³)(1/10³)^n

Hence, the infinite geometrc series is Σ(551/10³)(1/10³)^n for n = 0 to

∝

Given the ratio of 1/1000

Let r = 1/1000

r = 1/10³

a = 551/10³

The sum is defined as follows;

a/(1-r)

Sum = 551/10³ / (1 - 1/10³)

Sum = 551/1000 ÷ 999/1000

Sum = 551/999

So, a/b = 551/999

Where a = 551 and b = 999

The two integers are 551 and 999

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3 years ago