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slega [8]
3 years ago
14

Which point is an x intercept of the graphic of the quadratic function f(x) = (x+6) (x-3)

Mathematics
1 answer:
IceJOKER [234]3 years ago
8 0

Answer:

x intercepts: (-6, 0), (3,0)

Step-by-step explanation:

x intercept  when f(x) = 0

so

(x+6)(x-3) = 0

x + 6 = 0; x = -6

x - 3 = 0; x = 3

x intercepts: (-6, 0), (3,0)

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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
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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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