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2 years ago

Please help me with this math question. Thank You so much

Mathematics

2 answers:

lisabon 2012 [21]2 years ago

8 0

Answer:

1/32

Step-by-step explanation:

1/4 divided by 8 equals 1/32 using calculator. No explanation really... Brainliest?

Dennis_Churaev [7]2 years ago

4 0

Answer:

1) 1/32

Step-by-step explanation:

1/4 = 0.25

0.25/8 = 0.03125

turn 0.03125 into a fraction and get = 1/32

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For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

$1-cos(\theta)=sin^{2}(\theta)$

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

$sin^{2}(\theta)=1-cos^{2}(\theta)$

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

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

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

7 0

2 years ago

A set of a thousand numbers has a mean of zero.

Alona [7]

We want to find the mean of two elements in a set, given that we know the other elements of the set and the mean of the whole set.

The answer is: -490

-----------------------------

For a set with N elements {x₁, x₂, ..., xₙ} the mean is given by:

$M = \frac{x_1 + x_2 + ... + x_n}{N}$

Here we know that:

The mean of the set is 0.
The set has 1000 elements.
998 of these elements are ones, the other two are A and B.

We want to find the mean of the values of A and B.

First, we can start by writing the equation for the mean:

$\frac{1 + 1 + 1 + ... A + B}{1000} = 0$

We can rewrite this as:

$1 + 1 + 1 +... + A + B = 0$

And we have 998 ones, then:

$1 + 1 + 1 +... + A + B = 998 + A + B = 0\\\\B = - 998 - A$

Now we have B isolated.

With this, the mean of A and B can be written as:

$\frac{A + B}{2} = \frac{A - 980 - A}{2} = -490$

So we can conclude that the mean of the other two numbers is -490.

If you want to learn more, you can read:

brainly.com/question/22871228

5 0

2 years ago

Set B is defined as B={x|x is an integer}. Name two elements of B.

jenyasd209 [6]

By definition we have an integer number given by:
An integer is an element of the numeric set that contains the natural numbers {N} = {1,2,3,4, ...}, its opposite and zero.
On the number line we find the negative numbers to the left of the zero and to its right the positive numbers.
We have then, according to the definition, that the following are whole numbers:
-527, 1
Answer:
B = {x | x is an integer}
-527 ∈ B
1 ∈ B
option D

7 0

3 years ago

Read 2 more answers

the smaller rectangle is a 1/4 scale drawing of the original figure. Use the drop-down menus to show the missing dimensions of t

mihalych1998 [28]

Answer:the answer is 363

Step-by-step explanation:

4 0

3 years ago

The table shows information about the population of a city.

anastassius [24]

Answer:

ok thank you

Step-by-step explanation:

7 0

2 years ago