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3 years ago

I don't understand how to solve this pls help

Mathematics

1 answer:

Charra [1.4K]3 years ago

7 0

the sine function is a many-to-one function and therefore has no inverse function.

However if the domain is restricted to -90° ≤ x ≤ 90°

Then the function is one-to-one for this domain

Thus, $sin^{-1}$ x is defined as the angle such that - π/2 ≤ x ≤ π/2

5π/6 is therefore outwith the domain

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"A 12-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from t

Svet_ta [14]

Answer:

Step-by-step explanation:

The question has typographical errors. The correct question is:

"A 12-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the wall?

Solution:

The ladder forms a right angle triangle with the ground. The length of the ladder represents the hypotenuse.

Let x represent the distance from the top of the ladder to the ground(opposite side)

Let y represent the distance from the foot of the ladder to the base of the wall(adjacent side)

The bottom of the ladder is sliding along the pavement directly away from the building at 3ft/sec. This means that y is increasing at the rate of 3ft/sec. Therefore,

dy/dt = 3 ft/s

The rate at which x is reducing would be

dx/dt

Applying Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side², it becomes

x² + y² = 12²- - - - - - - -1

Differentiating with respect to time, it becomes

2xdx/dt + 2ydy/dt = 0

2xdx/dt = - 2ydy/dt

Dividing through by 2x, it becomes

dx/dt = - y/x ×dy/dt- - - - - - - - - - 2

Substituting y = 5 into equation 1, it becomes

x² + 5 = 144

x² = 144 - 25 = 119

x = √119 = 10.91

Substituting x = 10.91, dy/dt = 3 and y = 5 into equation 2, it becomes

dx/dt = - 5/10.91 × 3

dx/dt = - 1.37 ft/s

7 0

3 years ago

A recipe for 1 lb of trail mix calls for 2.5 oz of chocolate pieces. How many ounces of chocolate pieces are needed to make 5 lb

Murljashka [212]

5 lb of trail mix* (2.5 oz of chocolate pieces/ 1 lb of trail mix)= 12.5 oz of chocolate pieces.
(Note that the unit cancels out so you get the answer)

The final answer is 12.5 oz of chocolate pieces~

5 0

3 years ago

HELP PLEASE!!!! Jerome has 15 albums with 7 baseball cards in each. His friend gives him 8 packages of baseball cards with 13 in

hichkok12 [17]

albums: 15*7 = 105 cards

packages : 8*13 = 104 cards

extra cards 10

total cards =albums+ packages + extra cards

= 105+ 104 + 10

219 cards

4 0

3 years ago