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3 years ago

Use elimination to solve the following system.

Mathematics

2 answers:

Volgvan3 years ago

4 0

Answer:

A (0, 10)

Step-by-step explanation:

lilavasa [31]3 years ago

3 0

Answer:

D its

Step-by-step explanation:

Since x+y = 10-----(1)

And 3x+3y = 30----(2)

We can see from (2) that 3(x+y) =30;

Also same as saying x+y = 30/3 which is equivalent to x+y = 10.

So in this case we have many possible values

x = 0, y = 10 and vice versa

x = 1, y = 9 and vice versa

x = 2, y = 8 and so on

So the question has a lot of solutions

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3 years ago

A solid right circular cone of diameter 14cm and height 8cm is melted to form a hollow sphere. If the external diameter of the s

Pani-rosa [81]

Answer:

The internal diameter of the sphere is 6 cm.

Step-by-step explanation:

Given that, a solid right circular cone of diameter 14 cm and height 8 cm.

The radius of the cone is $=\frac{diameter}{2}$

$=\frac{14}{2} \ cm$

= 7 cm.

The volume of the cone is $= \frac13 \pi r^2 h$

$=(\frac1 3\times \pi \times 7^2\times 8) \ cm^3$

$=\frac{392}{3}\pi \ cm^3$

Let the internal radius of the sphere be r.

The external diameter of the sphere is = 10 cm

The external radius of the sphere is(R) = 5 cm

The volume of the sphere is $= \frac43 \pi(R^3-r^3)$

$=\frac43 \pi (5^3-r^3) \ cm^3$

The sphere is formed by the solid right circular cone.

∴The volume of the sphere = The volume of the cone

According to the problem,

$\frac43 \pi (5^3-r^3) =\frac{392}{3}\pi$

$\Rightarrow 4(5^3-r^3)= 392$

$\Rightarrow 5^3-r^3=\frac{392}{4}$

$\Rightarrow 5^3-r^3=98$

$\Rightarrow -r^3=98-125$

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⇒r= 3

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The internal diameter of the given sphere is = (2×3) cm =6 cm.

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