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2 years ago

Show me steps for 1,166 divided by 53

Mathematics

2 answers:

sukhopar [10]2 years ago

4 0

You do 53 can go into 66 1 time so put

nikdorinn [45]2 years ago

4 0

1.set up the long divison
53 divided by 1166
2. calculate 116 divided by 53 which is 2 with a remainder of 10
3. bring down 6, so that 106 is large enough to be divided by 53
4. calculate 106 divided by 53 which is 2
5.therefore 1166 divided by 53 is 22

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Which function is the same as y = 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2? y = 3 sine (2 (x startfraction p

kirza4 [7]

The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

<h3>How to convert sine of an angle to some angle of cosine?</h3>

We can use the fact that:

$\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)$

to convert the sine to cosine.

<h3>Which trigonometric functions are positive in which quadrant?</h3>

In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
In second quadrant(π/2 < θ < π), only sin and cosec are positive.
In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.

(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)

Here, the given function is:

$y= 3\cos(2(x + \pi/2)) - 2$

The options are:

$y= 3\sin(2(x + \pi/4)) - 2$
$y= -3\sin(2(x + \pi/4)) - 2$
$y= 3\cos(2(x + \pi/4)) - 2$
$y= -3\cos(2(x + \pi/2)) - 2$

Checking all the options one by one:

Option 1: $y= 3\sin(2(x + \pi/4)) - 2$

$y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2$

(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.

Option 2: $y= -3\sin(2(x + \pi/4)) - 2$

This option if would be true, then from option 1 and this option, we'd get:
$-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0$

which isn't true for all values of x.

Thus, this option is not same as the given function.

Option 3: $y= 3\cos(2(x + \pi/4)) - 2$

The given function is $y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2$

This option's function simplifies as:

$y= 3\cos(2(x + \pi/4)) - 2 = 3\cos(2x + \pi/2) -2 = -3\sin(2x) - 2$

Thus, this option isn't true since $\sin(2x) \neq \cos(2x)$ always (they are equal for some values of x but not for all).

Option 4: $y= -3\cos(2(x + \pi/2)) - 2$

The given function simplifies to: $y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2$

The given option simplifies to:

$y= -3\cos(2(x + \pi/2)) - 2 = -3\cos(2x + \pi ) -2\\y = 3\cos(2x) -2$

Thus, this function is not same as the given function.

Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

Learn more about sine to cosine conversion here:

brainly.com/question/1421592

4 0

1 year ago

Read 2 more answers

A bowling alley charges $2.50 per game plus $4 to rent shoes. A second bowling alley charges $4 per game plus $1 to rent shoes.

adelina 88 [10]

Answer:

The person would have to play 2 games for the two bowling alleys to cost the same amount

Step-by-step explanation:

Assume that the number of games that makes the two costs equal is x

∵ A bowling alley charges $2.50 per game plus $4 to rent shoes

∵ The number of games is x

∴ The cost = 2.50x + 4

∵ A second bowling alley charges $4 per game plus $1 to rent shoes

∵ The number of games is x

∴ The cost = 4x + 1

∵ They have the same cost

→ Equate the 2 expressions above

∴ 4x + 1 = 2.50x + 4

→ Subtract 2.50x from both sides

∵ 4x - 2.50x + 1 = 2.50x - 2.50x + 4

∴ 1.50x + 1 = 4

→ Subtract 1 from both sides

∵ 1.50x + 1 - 1 = 4 - 1

∴ 1.50x = 3

→ Divide both sides by 1.50

∴ x = 2

∴ The person would have to play 2 games for the two bowling alleys to

cost the same amount

7 0

1 year ago

Algebra 2 - Grade 11

saveliy_v [14]

Answer:

for the first equation

f(-3) = 34

f(4) = 6

for the 2nd equation

f(-3) = -56

f(4) ÷ 70

Step-by-step explanation:

my work is attached in a picture.

all you do is substitute each x value into each equation

8 0

2 years ago

A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a stand

Art [367]

Answer:

b. Mean = 1.6 years, standard deviation - 0.92 years, shape: approximately Normal.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of normal Variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a standard deviation of 4.2 years. Sample of 35:

This means that:

$\mu_G = 15$