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2 years ago

11

___ cosb =1/2 sin(a+b)+sin(a-b)?

2 answers:

vodomira [7]2 years ago

8 0

Answer:

That would be sina.

Step-by-step explanation:

sin(a+b) = sinacosb + cosasinb

sin(a-b) = sinacosb - cosasinb

Adding we get sin(a+b) + sin(a-b) = 2sinaccosb

so sinacosb = 1/2sin(a+b) + sin(a-b)

dem82 [27]2 years ago

6 0

Answer:

sina

Step-by-step explanation:

We have

sin(a+b) = sina cosb + cosa sinb ---------------------eqn 1

sin(a-b) = sina cosb - cosa sinb ---------------------eqn 2

eqn 1 + eqn 2

sin(a+b) + sin(a-b) = sina cosb + cosa sinb + sina cosb - cosa sinb

sin(a+b) + sin(a-b) = 2sina cosb

$sina\times cosb =\frac{1}{2}(sin(a+b) + sin(a-b))$

So answer is sina

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If each lap in a pool is 100 meters long, how many laps equal one mile? Round to the nearest tenth. (Hint: 1 foot ≈0.3048 meter)

aalyn [17]

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2 years ago

A car traveled at a constant speed. The graph shows how far the car traveled, in miles, during a given amount of time, in hours.

snow_tiger [21]

Answer:

Step-by-step explanation:

A car traveled at a constant speed as shown in the graph.

Distance traveled is on the y-axis and duration of travel on the x-axis.

Point A(3.5, 210) shows,

Distance traveled = 210 miles

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So the point (3.5, 210) shows the distance traveled by the car in 3.5 hours is 210 miles.

Slope of the line = speed of the car = $\frac{\text{Distance traveled}}{\text{Time}}$

= $\frac{210}{3.5}$

= 60 mph

Now we will find the speed of the car at another point B(1, 60).

If the speed of car is same as the point B as of point A, point B will lie on the graph.

Speed of the car at B(1, 60) = $\frac{\text{Distance traveled}}{\text{Time}}$

= $\frac{60}{1}$

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Hence, we can say that point B(1, 60) lies on the graph.

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1 year ago

After calculating the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum

Svetlanka [38]

Answer: 40000

Step-by-step explanation:

The formula to find the sample size is given by :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$ , where p is the prior estimate of the population proportion.

Here we can see that the sample size is inversely proportion withe square of margin of error.

i.e. $n\ \alpha\ \dfrac{1}{E^2}$

By the equation inverse variation, we have

$n_1E_1^2=n_2E_2^2$

Given : $E_1=0.05$ $n_1=1000$

$E_2=0.025$

Then, we have

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Hence, the sample size will now have to be 4000.

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1 year ago