What is the range and domain of the function p(t)=-8t+100

Mathematics

1 answer:

Aleks [24]3 years ago

5 0

Answer:

Real numbers for both

Step-by-step explanation:

The domain of a function is the set of values that the unknown t can adopt. For this function, t can be any real number as there are no restrictions for the t. Ir can be any positive number, 0, negative numbers, fractions, irrational numbers, whatever number you like.

The range of a function is the values that p(t) adopt when we replace the t value with any number. Here, again, it range is all real numbers. If you want p(t) to be positive it is possible, negative is possible, 0 is possible, and so on. If you like, you can verify it by replacing the numbers you like.

Something to know is that linear polynomial functions ALWAYS have their domains and ranges in real numbers.

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slamgirl [31]

Answer:

cos(θ) = 3/5

Step-by-step explanation:

We can think of this situation as a triangle rectangle (you can see it in the image below).

Here, we have a triangle rectangle with an angle θ, such that the adjacent cathetus to θ is 3 units long, and the cathetus opposite to θ is 4 units long.

Here we want to find cos(θ).

You should remember:

cos(θ) = (adjacent cathetus)/(hypotenuse)

We already know that the adjacent cathetus is equal to 3.

And for the hypotenuse, we can use the Pythagorean's theorem, which says that the sum of the squares of the cathetus is equal to the square of the hypotenuse, this is:

3^2 + 4^2 = H^2

We can solve this for H, to get:

H = √( 3^2 + 4^2) = √(9 + 16) = √25 = 5

The hypotenuse is 5 units long.

Then we have:

cos(θ) = (adjacent cathetus)/(hypotenuse)

cos(θ) = 3/5