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jarptica [38.1K]
3 years ago
15

The original price of a mountain bike was reduced by $125. If p = the mountain bike's original price in dollars, which algebraic

expression represents the reduced price?
Mathematics
2 answers:
wel3 years ago
7 0

Answer:

r = p-125

Where p = the mountain bike's original price in dollars

r is the reduced amount  in dollars

Step-by-step explanation:

Given : The original price of a mountain bike was reduced by $125.

To Find: If p = the mountain bike's original price in dollars, which algebraic expression represents the reduced price?

Solution:

Let the original price be p

Let the reduced price be r

Now we are given that The original price of a mountain bike was reduced by $125.

So, the reduced amount = Original price - 125

So, equation becomes : r = p-125

AlladinOne [14]3 years ago
5 0
Let the original price of the bike be x
Therefore,
          x= p - $125
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Answer:

a)  see below

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c)  18°. Yes contents will remain. No, handle will not rest on the ground.

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Step-by-step explanation:

<u>Part a</u>

A chord is a <u>line segment</u> with endpoints on the <u>circumference</u> of the circle.  

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Therefore, the spokes passing through the center of the wheel are congruent chords.

The spokes on the wheel represent the radii of the circle.  Spokes on a wheel are usually evenly spaced, therefore the congruent central angles are the angles formed when two spokes meet at the center of the wheel.

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The <u>tangent</u> of a circle is always <u>perpendicular</u> to the <u>radius</u>.

The tangent to the wheel touches the wheel at point B on the diagram.  The radius is at a right angle to this tangent.  Therefore, we can model this as a right triangle and use the <u>tan trigonometric ratio</u> to calculate the radius of the wheel (see attached diagram 1).

\sf \tan(\theta)=\dfrac{O}{A}

where:

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  • O is the side opposite the angle
  • A is the side adjacent the angle

Given:

  • \theta = 20°
  • O = radius (r)
  • A = 45 in

Substituting the given values into the tan trig ratio:

\implies \sf \tan(20^{\circ})=\dfrac{r}{45}

\implies \sf r=45\tan(20^{\circ})

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Therefore, the radius is 16.4 in (1 d.p.).

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The measure of an angle formed by a secant and a tangent from a point outside the circle is <u>half the difference</u> of the measures of the <u>intercepted arcs</u>.

If the measure of the arc AB was changed to 72°, then the other intercepted arc would be 180° - 72° = 108° (since AC is the diameter).

\implies \sf new\: angle=\dfrac{108^{\circ}-72^{\circ}}{2}=18^{\circ}

As the handle of the cart needs to be no more than 20° with the ground for the contents not to spill out, the contents will remain in the handcart at an angle of 18°.

The handle will not rest of the ground (see attached diagram 2).

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This can be modeled as a right triangle (see diagram 3), with:

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\implies \sf \sin (\theta)=\dfrac{48-r}{48}

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\implies \theta = 41.2^{\circ}\:\sf(1\:d.p.)

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\implies \sin(20^{\circ})=\dfrac{h}{48}

\implies h=48\sin(20^{\circ})

Then add it to the radius:

\implies \sf max\:height=48\sin(20^{\circ})+45\tan(20^{\circ})=32.8\:in\:(1\:d.p.)

(see diagram 4)

------------------------------------------------------------------------------------------

<u>Circle Theorem vocabulary</u>

<u>Secant</u>: a straight line that intersects a circle at two points.

<u>Arc</u>: the curve between two points on the circumference of a circle

<u>Intercepted arc</u>: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.

<u>Tangent</u>: a straight line that touches a circle at only one point.

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