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3 years ago

Find the distance between the pair of points. Round your answer to the nearest tenth if necessary.

Mathematics

1 answer:

Kaylis [27]3 years ago

6 0

Answer:

The distance between the pair of points is 12.0 (to the nearest tenth)

Step-by-step explanation:

The distance between a pair of points in a coordinate system is found by the formula:

d = $\sqrt({x_2-x_1)^2+(y_2-y_1)^2}$

where, the points are:

$(x_1,y_1)\ and\ (x_2,y_2)$

From the graph,

$(x_1,y_1)=(-6,-2)\\(x_2,y_2)=(2,7)$

Substitute the points into the formula:

$d=\sqrt{(2-(-6)^2+(7-(-2)^2} \\d=\sqrt{(2+6)^2+(7+2)^2} \\d=\sqrt{8^2+9^2} \\d=\sqrt{64+81} \\d=\sqrt{145} \\\d=12.0$

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Find the volume of the composite figure to the nearest tenth. Use 3.14 for pi.

Vilka [71]

Given:

In the given fig,

The radius of the cylinder = 15 ft

The height of the cylinder = 26 ft

The height of the cone = 21 ft

The radius of the cone = 15 ft

To find the volume of the cone, the volume of the cylinder and the composite figure.

Formula

The volume of the given composite fig is

$V = V_{1} +V_{2}$

where, $V_{1}$ be the volume of the cone.

$V_{2}$ be the volume of the cylinder.

$V_{1} = \frac{1}{3} \pi r^{2} h$ , r be the radius and h be the height.

$V_{2} = \pi r^{2} h$ , r be the radius and h be the height.

Now,

Putting, r = 15, h = 21 and π = 3.14 we get,

$V_{1} = \frac{1}{3} (3.14)(15^{2} )(21)$ cube ft

$V_{1} = 4945.5$ cube ft

Again,

Putting,

$V_{2} = (3.14)(15^{2} )(26)$ cube ft

$V_{2} = 18369$ cube ft

Therefore, the volume of the composite fig = (4945.5+18369) cube ft = 23314.5 cube ft

Hence,

a) The volume of the cone is 4945.5 cube ft.

b) The volume of the cylinder is 18369 cube ft.

c) The volume of the composite figure is 23314.5 cube ft.

3 0

3 years ago

Write the following decimal number in its equivalent fraction form.

Alecsey [184]

Answer:

-0.6666.... = - $\frac{2}{3}$

Step-by-step explanation:

Repeating decimals can be written as either 0.6666..., or as 0.6 with a small line over the top of the 6 to indicate it repeats. Repeating fractions are not put into fractions in the traditional way. If we had the terminating decimal 0.4, then we know to put the 4 over 10 and reduce:

$\frac{4}{10}=\frac{2}{5}$

However, with repeating decimals, instead of putting the number of the decimal over a value of 10, we put it over a value of 9. So, for the equivalent fraction form of -0.6 (repeating) we would get:

$\frac{6}{9}=-\frac{2}{3}$