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natta225 [31]
2 years ago
10

Which of the following pairs are complementary angles?

Mathematics
1 answer:
trasher [3.6K]2 years ago
7 0
It’s 2 since 20+70= 90

And complementary angles are two angles that sums up to 90 :)
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Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)
vfiekz [6]

Answer:

Step-by-step explanation:

given a point (x_0,y_0) the equation of a line with slope m that passes through the  given point is

y-y_0 = m(x-x_0) or equivalently

y = mx+(y_0-mx_0).

Recall that a line of the form y=mx+b, the y intercept is b and the x intercept is \frac{-b}{m}.

So, in our case, the y intercept is (y_0-mx_0) and the x  intercept is \frac{mx_0-y_0}{m}.

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph (x_0,\frac{1}{x_0}). Which means that y_0=\frac{1}{x_0}

The slope of the tangent line is given by the derivative of the function evaluated at x_0. Using the properties of derivatives, we get

y' = \frac{-1}{x^2}. So evaluated at x_0 we get m = \frac{-1}{x_0^2}

Replacing the values in our previous findings we get that the y intercept is

(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}

The x intercept is

\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0

The triangle in consideration has height \frac{2}{x_0} and base 2x_0. So the area is

\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0
3 years ago
A basketball player has made​ 70% of his foul shots during the season. If he shoots 3 foul shots in​ tonight's game, what is the
yulyashka [42]

Answer:

There is a 34.3% probability that he makes all of the​ shots.

Step-by-step explanation:

For each foul shot that he takes during the game, there are only two possible outcomes. Either he makes it, or he misses. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

n = 3, p = 0.7

What is the probability that he makes all of the​ shots?

This is P(X = 3).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{3,3}.(0.7)^{3}.(0.3)^{0} = 0.343

There is a 34.3% probability that he makes all of the​ shots.

7 0
3 years ago
The ratio of the length to the width to the height of an open rectangular tank is 10: 5: 8. The height is 18 feet longer than th
Svet_ta [14]

Answer:

hi

Step-by-step explanation:

how are you

4 0
2 years ago
Read 2 more answers
What is the recirpocal of 21/32
soldier1979 [14.2K]
The product of a number and its reciprocal would be equal to one

So just flip the numbers

=32/21
3 0
2 years ago
Which expression is equivalent to 8-(-8)
Aloiza [94]
What are the answer choices
8 0
3 years ago
Read 2 more answers
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