A triangle has two constant sides of length 6 ft and 2 ft. The angle between these two sides is increasing at a rate of 0.1 rad/sec. Find the rate at which the area of the triangle is changing when the angle between the two sides is

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: Length of ladder is l= 10ft X=8 ft, dx/dt= 18ft/sec From the fig l =[ x2 + y2 ]0.5= 10 a) from…

Q: a ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given, A ladder 10 ft long rests against a vertical wall. Let x be the distance between the bottom…

Q: A rocket is fired vertically upward from the ground with an initial velocity of 580 ft / sec. How…

A: Given : Initial velocity = 580 ft/sec

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given: Length of a ladder which rests against a vertical wall is 10 ft. Let the distance between…

Q: A 10​-ftladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: A 13-foot ladder is leaning against a house when its base starts to slide away. By the time the…

A:

Q: A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A kite 100 feet above the ground moves horizontally at a speed of 10ft/s. At what rate is the angle…

A: Let the horizontal distance be x. From the given data of question: And the diagram is:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: To find: The rate at which the angle between the ladder and the ground  is changing

Q: 3. A ladder 14 ft long is leaning against a fence 8 ft high, with the upper end projecting over the…

A: Find the changing rate of anlge

Q: A 40-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 7…

A: Find the rate of the top of ladder sliding down.

Q: A conical tank with an upper radius of 4 m and a height of 5 m drains into a cylindrical tank with a…

A:

Q: If the rate of change of the side length of an equilateral triangle is 2br / sec, what is the rate…

A: Please rate and feel free to ask any query about any part of the question.  I have used applications…

Q: A ladder 25 ft long is leaning against a wall. If the bottom of the ladder is pulled 10.…

A: We need to find change in angle.

Q: a) Water runs into a conical tank at the rate of 9 ft^3/min. The tank stands point down & has a…

A: Since multiple questions are asked, we will solve the first question for you. To get the solutions…

Q: If a ladder of length 20 ft which is leaning against a vertical wall has its upper end sliding down…

A: Given:         Length of ladder =20 ft    dhdt=-2 ft/sec

Q: Given a cylinder surmounted on both ends by a hemisphere, find the rate of change of its volume with…

A: Given:     Cylinder is surmounted by hemisphere at both ends.And height of cylinder is 5 meter.

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: It is given that,

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: →cosθ = BaseHypotenuse→sinθ = 1-cos2θ→dcosθdθ = -sinθ

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A ladder 13 feet long is leaning against the wall. If the base of the ladder is pushed toward the…

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A light is on the top of a 12 ft tall pole and a 5 ft 6 inches tall person is walking away from the…

A:

Q: A fish is reeled in at a rate of 1 foot per second from a bridge 15 ft. above the water. At what…

A:

Q: 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is…

A:

Q: Two sides of a triangle are 10 m and 11 m (base) in length and the angle between them is increasing…

A: Given,   Two sides of a triangle are 10m and 11m basein length i    and the angle between them is…

Q: Two sides of a triangle are 9 m and 10 m in length and the angle between them is increasing at a…

A: Let a & b are the side than form the angle θ.∴Area A =12ab sinθ  ⇒A=12×9×10 sinθ   a=9mb=10m…

Q: A light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is waking away from the pole…

A: Given that:Height of the poll is 12 ft and height of the person is 5 ft 6 in or 5.5 ft.Let x and y…

Q: Water is running out of a conical funnel at the rate of 1 in3/sec. If the radius of the base of the…

A:

Q: and passes directly over a tracking telescope on the ground. When the angle of elevation is ?/4,…

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given a ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away…

Q: A kite, 120 ft above the ground, is moving horizontally at the rate of 10 ft/sec. At what rate is…

A:

Q: A 13 ft. ladder is leaning against a house while the base is pulled away at a constant rate of 1…

A: We need to find the rate at which top of ladder sliding down

Q: A 35-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 8…

A: Let BC = x = distance from the base of wall to bottom of the ladderAB = y = distance from the base…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: To determine the rate of change of angle between the ladder and the ground.

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A 10​-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: Given: A 10​-ft ladder is leaning against a house when its base starts to slide away. By the…

Q: A kite 100ft  above the ground moves horizontally at a speed of 8ft/s  At what rate is the angle…

A: Let x= horizontal distance L= length of string,  Then a rough sketch of the problem is as follows:

Q: A kite 100ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle…

A: Using triangle find angle then find the rate of change of angle

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At which rate is the angle…

A: Given,  Consider the height of the lite from the ground is 100 ft. The speed is dxdt=8 ft/s. To find…

Q: If the radius of a sphere increases at a rate of 0.5 m/sec, then the rate at which the volume of the…

A: Let the radius of the sphere be r. Then the volume of the sphere is: V=43πr3…

Q: Two sides of a triangle are 17.8 m and 27 m in length and the angle between them is increasing at a…

A: In this question we have to use some properties of triangle and differentiation. According to the…

Q: . A vertical cylinder is leaking water at a rate of 1 ft /sec. If the cylinder has a height of 10 ft…

A:

Q: A 15-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 3…

A:

Q: A kite is 30 ft. high and is moving horizontally at a rate of 10 ft./min. At what rate is the string…

A: Calculate the rate in the following way:-

Q: find the rate at which the area is increasing

A: Given an isoscles triangle has a constant length of 4 ft. Angle Ø between these sides increases at…

Q: . A kite 100 ft above the ground moves horizontally at aspeed of 8 fts. At what rate is the angle…

A: At what rate is the angle between the stringand the horizontal decreasing when 200 ft of string has…

Q: A balloon ascending at the rate of 12 ft/sec is at a height 80 ft above the ground when a package is…

A: Sol:-v0=12 ft/secHeight = h = 80 ftThen, y-y0=v0t-12gt2

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.