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3 years ago

Two possible solutions of are -7 and 1. Which statement is true?

Mathematics

1 answer:

quester [9]3 years ago

4 0

We can plug those values into the equation, and if the answer is incorrect, we'll know if either one is extraneous.

√11 - 2(-7) = √(-7)^2 + 4(-7) + 4

√25 = √25

5 = 5

The first solution, -7, makes the equation true, and so it is not extraneous.

√11 - 2(1) = √(1)^2 + 4(1) + 4

√9 = √9

3 = 3

The second solution, 1, makes the equation true, and so it is also not extraneous.

<h3>The correct option is D, neither solution is extraneous. </h3>

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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,

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

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

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

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

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

$\Rightarrow-r^3= -27$

⇒r= 3

The internal radius of the sphere is = 3 cm.

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

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