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3 years ago

Marco wrote the equation below.

Mathematics

1 answer:

vova2212 [387]3 years ago

6 0

Answer:

It is true, because the cosine function has a period of 2π

Step-by-step explanation:

Since, the period of the cos function is 360° ( or 2π radians ), it holds the property of:

$Cos(\theta)=Cos(2\pi +\theta)$

Taking $\theta$ as $-\frac{\pi}{2}$ , $(2\pi + \theta)$ is equal to $2\pi + (-\frac{\pi}{2})\\=2\pi - \frac{\pi}{2}\\=\frac{4\pi-\pi}{2}\\=\frac{3\pi}{2}$

The equation is true!

<u>Note:</u> The cos function is even function

Hence, the equation is true, because the cosine function has a period of 2π, NOT because the cosine function is ODD, which it is not!!

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2 years ago

Question 30 The Royal Fruit Company produces two types of fruit drinks. The first type is pure fruit juice, and the second type

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The answer is below

Step-by-step explanation:

The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 85% pure fruit juice?

Answer: Let x be the number of pints of the first fruit juice (i.e 65%) and y be the number of pints of the second fruit juice (i.e 90%).

Since the total number of pints to make the 85% pure fruit juice is 80, it can be represented using the equation:

x + y = 80 . . . 1)

Also, x pints of the first juice = 0.65x, y pints of the second juice = 0.9y and 80 pints of the mixture to be produced = 80(0.85) = 68. Therefore:

0.65x + 0.9y = 68 . . . 2)

We have to solve equation 1 and 2 simultaneously, first multiply equation 1 by 0.65 to get equation 3:

0.65x + 0.65y = 52 . . . 3)

Subtract equation 3 from 2 and solve for y:

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y = 16/0.25 = 64

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3 years ago

A van and a bicycle move towards each other. The speed of the van is 80 km per hour, and the speed of the bike is 20 km per hour

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-- :

Bike > ________300km_________< Van

20km/h 80km/h

In one hour, the bike will have moved 20km and the van would have moved 80km.

The distance between them was 300km. But the bike moved 20km and the van moved 80km, since its been one hour. Which means the distance between them is less.

300km-(20km+80km) = 200km

So now the distance between them is 200km.

Now another hour passes. The distance between them was 200km. But the bike moved 20km and the van moved 80km, since its been one hour. Which means the distance between them is less.

200km-(20km+80km) = 100km

So now the distance between them is 100km

Now another hour passes. The distance between them was 100km. But the bike moved 20km and the van moved 80km, since its been one hour. Which means the distance between them is less.

100km-(20km+80km) = 0km

So now the distance between them is 0km, which means they have met. If we count, it took them 3 hours.

Step 1)

Add both speeds. 20km+80km=100km

Step 2)

Total distance between them = 300km

So do 300km/100km = 3hours.

______

The solution is: .

————

Hope this helped!

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3 years ago