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olasank [31]
3 years ago
7

Please help! 20 points! Calculate the average rate of change for the given function, from x = 1 to x = 4.

Mathematics
1 answer:
zvonat [6]3 years ago
4 0

Answer:

4) 2

Step-by-step explanation:

(4-0) / (1-(-1)) = 4/2 = 2

(10-4) / (4-1) = 6/3 = 2

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3 years ago
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What is 1/20 written as a decimal?
Black_prince [1.1K]

Answer:

0.05

Step-by-step explanation:

divide 100 by 20

6 0
3 years ago
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
The large rectangle shown here is 3cm by 5 cm. What is a direct way to determine the area of the rectangle in square centimeters
dlinn [17]

Answer:

Place the squares on the rectangle.

Step-by-step explanation:

Hello!

The area of the 1cm by 1cm square is 1 square cm.

We can solve for the area by placing multiple of those squares in the larger rectangle.

If we place it, we get 15 placed squares, with a total area of 15 square cm. This relies on the meaning of area, as we are simply measuring the number of square cm taken up by the object.

We would place 3 rows of 5 squares, representing a height of 3 cm (side length of 3 squares), and a length of 5 cm (side length go 4 squares).

This also proves the area formula A = L * W, as we multiple the side lengths to find the number of square units.

8 0
2 years ago
The coordinates of three vertices of square ABCD are A(−212,112),B(−212,−3), and C(2,112).
Lady_Fox [76]

Answer:

<em>P=760</em>

Step-by-step explanation:

Three of the coordinates of the square ABCD are A(-212,112) B(-212,-3) C(2,112). The image below shows the square is not ABCD but ABDC. In fact, this is not a square, as we'll prove later.

Note the x-coordinate of A and B are the same. It means this side is parallel to the y-axis. Also, the y-coordinate of A and C are the same, meaning this side is parallel to the x-axis. The missing point D should have the same x-coordinate as C and y-coordinate as B, i.e. D=(2,-3).

This shape has sides that are parallel to both axes.

To calculate the perimeter we find the length of two sides.

The distance from A to B is the difference between their y-axis:

w=112-(-3)=115

The distance from A to C is the difference between their x-axis:

l=2-(-212)=215

It's evident this is not a square but a rectangle. The perimeter is

P=2w+2l=330+430

P=760

7 0
3 years ago
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