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zmey [24]
3 years ago
14

Pierre uses 30 grams of chocolate to make

Mathematics
1 answer:
Travka [436]3 years ago
3 0

Pierre can make 3 liters of chocolate sauce from 450 grams of chocolate.

Step-by-step explanation:

Given,

Chocolate used to make 200 ml of chocolate sauce = 30 grams

Ratio of chocolate to milliliters of chocolate sauce = 30:200

Let,

x be the milliliters of sauce made from 450 grams of chocolate

Ratio of chocolate to ml of sauce = x:450

Using proportion;

Ratio of chocolate to ml of sauce:: ratio of chocolate to ml of sauce

30:200::450:x

Product of extreme = Product of mean

30*x=200*450\\30x=90000

Dividing both sides by 30

\frac{30x}{30}=\frac{90000}{30}\\x=3000

450 grams of chocolate will make 3000 milliliters of chocolate sauce.

We will convert this in liters.

1 liter = 1000 ml

3000 ml = \frac{3000}{1000} = 3 liters

Pierre can make 3 liters of chocolate sauce from 450 grams of chocolate.

Keywords: ratio, proportion

Learn more about proportion at:

  • brainly.com/question/1414350
  • brainly.com/question/1418853

#LearnwithBrainly

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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:

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

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Answer:

  see below

Step-by-step explanation:

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The exponents of z have the right values in choices B and D, but the ratio of constants only matches in choice D. Looking at the rest of choice D, we see that we can factor 6w²z² from both numerator and denominator, then factor 2 from the remaining numerator to make it match the desired form.

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kvasek [131]

Answer:

EG = 2 units

Step-by-step explanation:

Given that line q bisects EG at T , then

ET = TG  ( substitute values )

\frac{1}{3} x = x - 2 ( multiply through by 3 to clear the fraction )

x = 3x - 6 ( subtract x from both sides )

0 = 2x - 6 ( add 6 to both sides )

6 = 2x ( divide both sides by 2 )

3 = x

Then

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TG = x - 2 = 3 - 2 = 1

Thus

EG = ET + TG = 1 + 1 = 2 units

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Answer:

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Step-by-step explanation:

Given:

A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches.

Now, to find the ratio of the area of the school banner to the area of the sign.

Dimensions of school banner :

Length = 54 inches.

Width = 36 inches.

Dimension of school sign:

Length = 17 inches.

So, to we find the width of sign by using cross multiplication method:

Let the width be x.

So, 54 is equivalent to 36.

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Thus, the width of sign = 11.33 inches.

Now, to get the ratio of the area of the school banner to the area of the sign:

Area of the school banner : Area of the school sign.

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Therefore, the ratio of the area of the school banner to the area of the sign is 1944 cubic inches : 192.61 cubic inches.

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