The scale of a map is 0.5 inch: 50 miles. on the map, the distance between two cities is 5 inches. what is that actual distance
1 answer:
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Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: <span>(−<span>5/8</span>,−<span>41/16</span>)</span>
Focus: <span>(−<span>5/8</span>,−<span>5/2</span>)</span>
Axis of Symmetry: <span>x=−<span>5/8</span></span>
Directrix: <span>y=−<span>21/8</span></span><span><span> x. y
</span><span><span>−3. </span>20
</span><span><span>−2. </span>5
</span><span><span>−<span>5/8. </span></span><span>−<span>41/16
</span></span></span><span> 0. <span>−1
</span></span><span>1. <span>8
</span></span></span>
Direction: Opens Up
Vertex: <span>(−<span>5/8</span>,−<span>41/16</span>)</span>
Focus: <span>(−<span>5/8</span>,−<span>5/2</span>)</span>
Axis of Symmetry: <span>x=−<span>5/8</span></span>
Directrix: <span>y=−<span>21/8</span></span><span><span> x. y
</span><span><span>−3. </span>20
</span><span><span>−2. </span>5
</span><span><span>−<span>5/8. </span></span><span>−<span>41/16
</span></span></span><span> 0. <span>−1
</span></span><span>1. <span>8
</span></span></span>
Step-by-step explanation:
Let vertical height of ladder from ground be y and
horizontal distance of the base of the ladder from the wall be x respectively.
Length of the ladder = l (constant) = 10 ft
<u>Using Pythagoras theorem</u>:
Differentiate both sides w.r.t time
<u>We know that</u> (After 1 sec, y = 6 ft and x = 8 ft ; dy/dt = 2 ft/sec)
<u>( Ignore - ive sign)</u>
Therefore, bottom of the ladder is sliding away from the wall at a speed of 1.5 ft/sec one second after the ladder starts sliding.