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2 years ago

The ratio of cats to dogs at a local pet shelter is 5 to 3. If there are 60 cats in the shelter, which of

Mathematics

1 answer:

andre [41]2 years ago

6 0

Answer:

Step-by-step explanation:

cats : dogs

5 : 3

Since you are looking for dogs it is :-

$\frac{dogs}{cats}$ × 60 cats (the number of cats).

$\frac{3}{5}$ × 60 cats = 36 dogs.

∴ There are 36 dogs.

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Express 194720 in standard form correct to 3 significant figures<br>

ELEN [110]

Answer:

1.95 x 10^5

Step-by-step explanation:

First look at the 4th digit in the number 194720 as the the question said to round to 3 significant figures. If the 4th digit is more than 5, then add 1 to the third digit which results in 195000. Now the question also said to express in standard form. Look for the first non-digit number in 195000. After 1 put a decimal point and remove all the zeros after the point which results in 1.95. Now count how many digits you moved to the left which comes as 5. Write the answer as 1.95 x 10^5.

Hope you can understand this!!

3 0

2 years ago

1. Six units to the left of 3

trapecia [35]

Answer:

six uniys to left of 3 is= +2,+1,0,-1-2-3

three unit right of 15is= +16,+17, +18

Eight unit to the left of =-4,-5,-6,-8,-9,-10,-11,-12

seven units ti right of -5=-3,-2,-1,0+1,+2,+3,+4

8 0

2 years ago

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:
$-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0$