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nasty-shy [4]
2 years ago
9

On a number line, point D is at -3, and point E is at 6. The point F lies on DE. The ratio of DF to FE is 2:3. Where does point

F lie on the number line?
Mathematics
1 answer:
expeople1 [14]2 years ago
5 0

Answer: point F is at <u>   0.6   </u> on the number line

=============================================================

Explanation:

The ratio 2:3 scales up to 2x:3x for some positive real number x.

This means the distance from D to F is 2x units, and the distance from F to E is 3x units. Combine those two smaller distances to get 2x+3x = 5x to represent the full distance from D to E.

D is at -3 and E is at 6. This is a distance of 9 units since |-3-6| = |-9| = 9

Set this equal to the 5x from earlier and solve

5x = 9

x = 9/5

x = 1.8

This leads to 2x = 2*1.8 = 3.6

Therefore, we'll move 3.6 units from -3 to -3+3.6 = 0.6 which is the location of point F on the number line.

Notice that from 0.6 to 6 is 5.4 units and that 3x = 3*1.8 = 5.4 matches up to help confirm the answer.

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Find the area of the largest square contained by a circle of radius r = 1cm. Explain your answer and justify that it is correct.
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Answer:

2 square cm

Step-by-step explanation:

Given :

A square is inscribed in a circle whose radius is r = 1 cm

Therefore, the diameter of the circle is 2 r = 2 x 1

                                                                      = 2 cm.

So the diagonal of the square is 2r.

Using the Pythagoras theorem, we find each of the side of the triangle is $r \sqrt 2$.

Therefore, the area of the square is given by $\text{(side)}^2$

                                                                         = $(r\sqrt 2)^2$

                                                                         $= 2 r^2$

                                                                         $= 2 (1)^2$

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Hence the area of the largest square that is contained by a circle of radius 1 cm is 2 cm square.

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3 years ago
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