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1 year ago

11

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

2 answers:

vodomira [7]1 year 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]1 year 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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Jack is 27 years older than Susan. In 5 years he will be 4 times as old as she is. Find the present ages of jack and Susan

riadik2000 [5.3K]

X - Jack's age
y - Susan's age

Jack is 27 years older than Susan.
$x=y+27$

In 5 years he will be 4 times as old as she is.
$x+5=4(y+5)$

The system of equations:
$x=y+27 \\ x+5=4(y+5) \\ \\ \hbox{substitute y+27 for x in the 2nd equation:} \\ y+27+5=4(y+5) \\ y+32=4y+20 \\ y-4y=20-32 \\ -3y=-12 \\ y=\frac{-12}{-3} \\ y=4 \\ \\ x=y+27=4+27=31$

Jack is 31 years old and Susan is 4 years old.

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1 year ago

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Alik [6]

The answer is negative 5

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1 year ago

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How many marbles, each with a volume of 36 cubic centimeters, are needed to fill in a cylindrical vase with a radius of 6 centim

ANEK [815]

The volume of a cylinder can be found using the formula:

π r² h,

where r is the radius of the circular base and h is the height of the cylinder.

If we plug in the measurements of the cylinder, we get:

π (6²) (28)

When this is simplified, we get that the volume of the cylinder is:

1008π cubic cm

Thus, if each marble has a volume of 36π cubic cm, then to find how many marbles will fit into the vase we must divide the vases total volume by the volume of each marble.

1008π / 36π = 28

Therefore, the answer is D. 28 marbles

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1 year ago

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It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours. How long doe

lina2011 [118]

Answer:

Time taken by the un powered raft to cover this distance is T = 192.12 hr

Step-by-step explanation:

Let speed of boat = u $\frac{km}{hr}$

Speed of current = v $\frac{km}{hr}$

Let distance between A & B = 100 km

Time taken in downstream = 32 hours

$32 = \frac{100}{u +v}$

$u + v = \frac{100}{32}$

u + v = 3.125 ------ (1)

Time taken in upstream = 48 hours

$48 = \frac{100}{u -v}$

$u -v = \frac{100}{48}$

u - v = 2.084 ------- (2)

By solving equation (1) & (2)

u = 2.6045 $\frac{km}{hr}$

v = 0.5205 $\frac{km}{hr}$

Now the time taken by the un powered raft to cover this distance

$T = \frac{100}{v}$

Because un powered raft travel with the speed of the current.

$T = \frac{100}{0.5205}$

T = 192.12 hr

Therefore the time taken by the un powered raft to cover this distance is

T = 192.12 hr

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2 years ago

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1/4 of the roses are red, 1/3 of the remainder are yellow and the rest are pink. There are 24 more pink roses than red roses. Ho

Alika [10]

<h3>There are 96 roses altogether</h3>

<em><u>Solution:</u></em>

Let "x" be the number of roses

From given,

<em><u>1/4 of the roses are red</u></em>

$Red\ roses = \frac{1}{4} \times x\\\\Red\ roses = \frac{x}{4}$

<em><u>1/3 of the remainder are yellow</u></em>

$Remaining = x - \frac{x}{4}\\\\Remaining = \frac{3x}{4}$

Therefore,

$Yellow\ roses = \frac{1}{3} \times \frac{3x}{4}\\\\Yellow\ roses = \frac{x}{4}$

<em><u>Rest are pink</u></em>

$Remaining = \frac{3x}{4} - \frac{x}{4}\\\\Remaining = \frac{2x}{4}\\\\Remaining = \frac{x}{2}$

Therefore,

$Pink\ Roses = \frac{x}{2}$

There are 24 more pink roses than red roses

Therefore,

Number of pink roses = 24 + red roses

$\frac{x}{2} = 24 + \frac{x}{4}\\\\\frac{x}{2} - \frac{x}{4} = 24\\\\\frac{x}{4} = 24\\\\x = 24 \times 4\\\\x = 96$

Thus there are 96 roses altogether

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1 year ago