Type the correct answer in the box. If necessary, use / for the fraction bar and simplify the fraction. cos(75°)cos(15°) =

Mathematics

2 answers:

diamong [38]3 years ago

5 0

Answer:

1/4

Step-by-step explanation:

using the product-to sum formulas, this is

1/2 (cos(75+15) + cos(75-15))

Vikki [24]3 years ago

3 0

Answer:

1/4

Step-by-step explanation:

PLATO USER

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Which rays form the sides of IHG

blagie [28]

Answer:

A and C

Step-by-step explanation:

When talking about a ray, the end of the arrow must start at the letter representing the endpoint and the head must be near where the arrow passes through.

In this case, the endpoint is H of both rays, so the end of the arrow has the letter H under it, which leaves only A and C, but let's go further. The head has to be above the nearest point it passes through, and in this case, the left ray passes through I, which makes one of the rays. So the left ray is written as HI with the arrow facing right. The second one, following the guidelines above, has to be HG, with the arrow facing right. Both of these are seen in choices A and C, meaning those are your answers.

Hoped this helps and vote Brainliest, Thx :)

8 0

3 years ago

The quantity, Q, of a drug in the blood stream begins with 250 mg and decays to one-fifth its value over every 90 minute period.

Mazyrski [523]

Answer:

$a=250 \, mg\\\\b=5\\\\T= 90'$

Step-by-step explanation:

We have that $Q(t) = a\cdot b^{-\frac{t}{T}} \\$

Where t is the time (in minutes) and for the sake of dimensional consistency, let's assume that T is also in minutes, b is an adimensional number, and a is in mg. So we will have Q in mg as a consequence.

We now want to find out what values these constants might take. Let's see what happens when $t=0$ , that is, just as we start. At that point, we have that the amount of drug in the bloodstream must be equal to 250mg, thus:

$Q(0)= a\cdot b ^{-\frac{0}{T} }=250\,mg\\Q(0)= a=250\,mg$

We have found the constant $a$ ! It is the initial amount of drug! we have made use of the fact that any number raised to the 0th power is equal to one.

Now, we know that every 90 minutes, the amount of drug decreases to one fifth of its former value. How do we put this in mathematical form? Like so:

$Q(t+90')=Q(t)/5$

That is, 90 minutes after time t the amount of drug will be one fifth of the amount of drug at time t. Let's expand the last equation:

$Q(t+90')=Q(t)/5\\\\a\cdot b^{-\frac{t+90'}{T} }=a\cdot b^{-\frac{t}{T} }/5\\\\ b^{-\frac{t+90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{t}{T} }b^{-\frac{90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{90'}{T} }=\frac{1}{5}$

Now the last expression isn't enough to determine both T and b, but that also means that we have some freedom in how we choose them. What seems most simple is to pick $T=90'$ and thus we will get: