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2 years ago

Find all solutions to the equation in the interval [0, 2pi). COS X = sin 2x

Mathematics

1 answer:

Lera25 [3.4K]2 years ago

6 0

Answer:

Step-by-step explanation:

cos x=sin 2x

sin 2x-cos x=0

2 sin x cos x-cos x=0

cos x(2 sin x-1)=0

either cos x=0

$x=\frac{\pi }{2},\frac{3\pi }{2}$

2 sin x-1=0

$sin x=\frac{1}{2} =sin (\frac{\pi }{6}),sin(\pi -\frac{\pi }{6} )\\x=\frac{\pi }{6} ,\frac{5 \pi }{6}$

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How many different ways are there to choose a subset of the set {1,2,3,4,5,6} so that the product of the members of the subset i

zvonat [6]

You have to pick at least one even factor from the set to make an even product.

There are 3 even numbers to choose from, and we can pick up to 3 additional odd numbers.

For example, if we pick out 1 even number and 2 odd numbers, this can be done in

$\dbinom 31 \dbinom 32 = 3\cdot3 = 9$

ways. If we pick out 3 even numbers and 0 odd numbers, this can be done in

$\dbinom 33 \dbinom 30 = 1\cdot1 = 1$

way.

The total count is then the sum of all possible selections with at least 1 even number and between 0 and 3 odd numbers.

$\displaystyle \sum_{e=1}^3 \binom 3e \sum_{o=0}^3 \binom 3o = 2^3 \sum_{e=1}^3 \binom3e = 8 \left(\sum_{e=0}^3 \binom3e - \binom30\right) = 8(2^3 - 1) = \boxed{56}$

where we use the binomial identity

$\displaystyle \sum_{k=0}^n \binom nk = \sum_{k=0}^n \binom nk 1^{n-k} 1^k = (1+1)^n = 2^n$

3 0

1 year ago

For a map a scale of 2 inches to 70 miles is used. If the distance on the map measures 1.8 inches what is the actual distance

asambeis [7]

Answer:

63 miles

Step-by-step explanation:

2/70 = 1.8/x Cross multiply

2x = 70 * 1.8 Combine

2x = 126 Divide by 2

x = 126/2

x = 63

The actual distance is 63 miles.

3 0

2 years ago

-10(n+30)=1/2(24-14n)

Pavel [41]

N = -104 is the correct answer

6 0

2 years ago

Before going to school, Eudora ran from her home to a secret laboratory at an average speed of 12 km. Since she was running late

Brrunno [24]

Answer:

Eudora spent 0.5 hours in running and 1.5 hours flying using her jet-pack.

Step-by-step explanation:

Let x represent time spent in running.

We have been given that the entire trip took 2 hours, so time spent in flying the jet-packs would be $2-x$ .

We know that distance is equal to speed times time.

$\text{Distance}=\text{Speed}\times\text{Time}$

Eudora ran from her home to a secret laboratory at an average speed of 12 km, so distance traveled by running would be $12x$ .

Eudora took one of her jet-packs and flew to her school at an average speed of 76 km, so distance covered by jet-packs would be $76(2-x)$ .

We are told that Eudora traveled a total distance of 120 km. We can represent this information in an equation as:

$12x+76(2-x)=120$

$12x+152-76x=120$

Combine like terms:

$-64x+152=120$

$-64x+152-152=120-152$

$-64x=-32$

Divide both sides by $-64$ :

$\frac{-64x}{-64}=\frac{-32}{-64}$

$x=0.5$

Therefore, Eudora spent 0.5 hours in running.

Upon substituting $x=0.5$ in expression for time spent in flying jet-packs, we will get:

$2-x\Rightarrow 2-0.5=1.5$

Therefore, Eudora spent 1.5 hours flying using her jet-pack.

7 0

2 years ago

Do you mean 15-n=11 1/2

svetlana [45]

i think youre on the wrong thing

3 0

2 years ago

Find all solutions to the equation in the interval [0, 2pi). COS X = sin 2x​

Find all solutions to the equation in the interval [0, 2pi). COS X = sin 2x