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3 years ago

Given that AC and BD are chords, apply the Intersecting Chord Theorem to set up an equation and solve for x.

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

8 0

Answer:

The value of x = 3 units

Step-by-step explanation:

Here, AC = 3 ,( 5x - 3)

BD = x , (x +9)

INTERSECTING CHORD THEOREM

It states that the products of the lengths of the line segments on each chord are equal.

Applying the theorem here, we get

$3( 5x - 3 ) = x (x +9)\\\implies 3(5x) - 3(3) = x(x) + 9 (x)\\or, 15x - 9= x^2 + 9x\\\implies x^2 + 9x - 15 x + 9 = 0\\or, x^2 -6x + 9 = 0$

Simplifying for the value of x , we get

$x^2 -6x + 9 = 0 \implies x^2 - 3x - 3x + 9 = 0\\x(x-3) -3(x -3) =0\\or, (x-3)(x-3) = 0$

or, x = 3

Hence, the value of x = 3 units

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A force of 12 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching i

sattari [20]

Answer:

Work done in stretching the spring = 7.56 lb-ft.

Step-by-step explanation:

Normal length of the spring = 8 in or $\frac{8}{12}$ ft

= $\frac{2}{3}$ ft

If the spring has been stretched to 11 inch then the stretched length of the spring is = 11 in

= $\frac{11}{12}$ ft

Force applied to stretch the spring = 12 lb

By Hook's law,

F = kx [where k is the spring constant and x = length by which the spring is stretched]

12 = k( $\frac{2}{3}$ )

k = 18

Work done (W) to stretch the spring by $\frac{11}{12}$ ft will be

W = $\int\limits^\frac{11}{12} _0 {kx} \, dx$

= $\int\limits^\frac{11}{12} _0 {(18x)} \, dx$

= $18[\frac{x^{2}}{2}]^{\frac{11}{12}}_0$

= 9( $\frac{11}{12}$ )²

= 7.56 lb-ft

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3 years ago

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3 years ago

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3 years ago

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3 years ago

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The figure below shows the net of a triangular pyramid. The given height is rounded to the nearest hundredth. If all the triangl

Nataly [62]

Answer: 43.3 square inches

Step-by-step explanation:

Formula for Triangle: A = bh/2

Key:

* = multiple

/ = divide

Fill in the formula with what you know:

A = bh/2

A = 5 * 4.33 / 2

A= 21.65 / 2 = 10.825 square inches

However, 10.825 is not our answer. 10.825 is the area of only one triangle. Since all four of the triangles are congruent (or the same) we can:

Add: 10.825 + 10.825 + 10.825 + 10.825 = 43.3 square inches

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Thus, the surface area of the pyramid is 43.3 square inches.

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3 years ago