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2 years ago

Explanation on How to answer what is the density of an object that has a mass of 73,430 and the volume of 7 m3

Mathematics

1 answer:

scZoUnD [109]2 years ago

7 0

Answer:

Density = 10,490 g/m³

Step-by-step explanation:

Density = mass ÷ volume

here mass = 73,430 g

volume = 7 m³

density = 73,430 ÷ 7

= 10490 g/m³

Density = 10,490 g/m³

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Which expression represents the distance between point (0, a) and point (a, 0) on a coordinate grid?

o-na [289]

Answer:

$\sqrt{2} a$

Step-by-step explanation:

The distance between point (x1,y1) and (x2,y2) on a coordinate plane is given by expression $\sqrt{(x1-x2)^2+(y1-y2)^2}$

In the problem given coordinate points are

(0, a) and (a, 0).

Thus, distance between these points are given by

$distance = \sqrt{(x1-x2)^2+(y1-y2)^2}\\=>distance = \sqrt{(0-a)^2+(a-0)^2}\\=>distance = \sqrt{(a)^2+(a)^2}\\\\=>distance = \sqrt{2a^2}\\=>distance = \sqrt{2} a$

Thus , expression $\sqrt{2} a$ gives the distance between point (0, a) and point (a, 0) on a coordinate grid.

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3 years ago

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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.

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3 years ago

If events A and B are independent, find P(A|B)

almond37 [142]

Read the introductory paragraph and answer the question in complete sentences.

The community comes alive at night! Schools that once were dark in the evening are now alive with lights and people. The people are adults and the lights are on and the school buildings are open because adults are enrolled in community education classes.

What do you believe the subject will be?

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3 years ago

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Sophia exchanged 1000 U.S. dollars for the South African currency which is called the rand. The exchange rate was 8.05 rand to 1

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Answer:

Sophia gets 7,150

Step-by-step explanation:

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2 years ago

Carla is going to arrange her 4 books on a shelf: Algebra, Trigonometry, Geometry and Calculus. How many different possible arra

PilotLPTM [1.2K]

Arranging of books is an illustration of permutation and combination

There are 24 different possible arrangements she can make

<h3>How to calculate the number of arrangement</h3>

The number of books is given as:

n = 4

Take the factorial of both sides

n! = 4!

Evaluate

n! = 4 * 3 * 2 * 1

n! = 24

Hence, there are 24 different possible arrangements she can make

Read more about permutation and combination at:

brainly.com/question/1216161

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2 years ago