A ladder 10 feet long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall, and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ=π/3?

Step-by-step explanation:

Given:

Length of ladder, y = 10 ft

θ = π/3 rad

Using cosine rule,

Sin θ = opposite/hypotenuse

Sin θ = x/y

Sin θ = x/10

Differentiating both sides with respect to dθ,

10 × cos θ × dθ = dx

10 cos θ = dx/dθ

dx/dθ = 10 × cos π/3

= 5 ft/radians.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.