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ddd [48]

3 years ago

"absmiddle" class="latex-formula">

Mathematics

2 answers:

vivado [14]3 years ago

8 0

Answer:

i

Step-by-step explanation:

Simplify the following:

sqrt(-1)

By definition, sqrt(-1) = i:

Answer: i

tiny-mole [99]3 years ago

4 0

I. .....,,,,,,...........,,,??,.

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Simplify the expression. (2x)(3x)

Maksim231197 [3]

Answer:

6x²

Step-by-step explanation:

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16 to the power of 1/2

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“8” is your answer!!

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How does recipe conversion factors work? For example, if I have a soup that is originally 24 servings and has 16 oz of fish, and

Neporo4naja [7]

You have to find the unit rate, which in this case means the amount of fish you need per serving of soup.

If 16 oz of fish makes 24 servings, then 16/24 oz = 2/3 oz makes 1 serving.

Now multiply both quantities by 10, so that 10 servings require 20/3 oz ≈ 6.67 oz of fish.

A more direct way to do this is to solve for x in the following equation:

(16 oz fish) / (24 servings) = (x oz fish) / (10 servings)

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x = 10 • 16 / 24 = 20/3

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3 years ago

Derive these identities using the addition or subtraction formulas for sine or cosine: sinacosb=(sin(a+b)+sin(a-b))/2

Sergeu [11.5K]

Answer:

The work is in the explanation.

Step-by-step explanation:

The sine addition identity is:

$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$ .

The sine difference identity is:

$\sin(a-b)=\sin(a)\cos(b)-\cos(a)\sin(a)$ .

The cosine addition identity is:

$\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$ .

The cosine difference identity is:

$\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)$ .

We need to find a way to put some or all of these together to get:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$ .

So I do notice on the right hand side the $\sin(a+b)$ and the $\sin(a-b)$ .

Let's start there then.

There is a plus sign in between them so let's add those together:

$\sin(a+b)+\sin(a-b)$

$=[\sin(a+b)]+[\sin(a-b)]$

$=[\sin(a)\cos(b)+\cos(a)\sin(b)]+[\sin(a)\cos(b)-\cos(a)\sin(b)]$

There are two pairs of like terms. I will gather them together so you can see it more clearly:

$=[\sin(a)\cos(b)+\sin(a)\cos(b)]+[\cos(a)\sin(b)-\cos(a)\sin(b)]$

$=2\sin(a)\cos(b)+0$

$=2\sin(a)\cos(b)$

So this implies:

$\sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)$

Divide both sides by 2:

$\frac{\sin(a+b)+\sin(a-b)}{2}=\sin(a)\cos(b)$

By the symmetric property we can write:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$

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3 years ago

A medical clinic is reducing the number of incoming patients by giving vaccines before flu season. During week 5 of flu season,

8_murik_8 [283]

Answer:

$f(x) = -6x +120$

Step-by-step explanation:

Let's call y the number of patients treated each week

Let's call x the week number.

If the reduction in the number of patients each week is linear then the equation that models this situation will have the following form:

$y = mx + b$

Where m is the slope of the equation and b is the intercept with the x-axis.

If we know two points on the line then we can find the values of m and b.

We know that During week 5 of flu season, the clinic saw 90 patients, then we have the point:

(5, 90)

We know that In week 10 of flu season, the clinic saw 60 patients, then we have the point:

(10, 60).

Then we can find m and b using the followings formulas:

$m=\frac{y_2-y_1}{x_2-x_1}$ and $b=y_1-mx_1$

In this case: $(x_1, y_1) = (5, 90)$ and $(x_2, y_2) = (10, 60)$

Then:

$m=\frac{60-90}{10-5}$

$m=-6$

And

$b=90-(-6)(5)$

$b=120$

Finally the function that shows the number of patients seen each week at the clinic is:

$f(x) = -6x +120$

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