A plane flying horizontally at an altitude of 1 mile and a speed of 600 miles per hour passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 miles away from the station. Hint: draw a picture and find a right triangle in it!

Q: A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15…

A: 6)

Q: A kite is flying at a height of 40 ft. A boy is flying it so that it is moving horizontally at a…

A: Given: Kite is moving horizontally at a rate of 3 ft per sec. To determine: The rate at which the…

Q: A helicopter takes o from a point 80 m away from an observerlocated on the ground, and rises…

A: Thus when the helicopter is 60 m above the ground the elevation angle of theobserver’s line of sight…

Q: A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A: Consider the following:

Q: A man starts walking north at 2 feet per second from a point P. A minute later a woman starts…

A:

Q: A 13-foot ladder leans against a wall. The foot of the ladder begins to slide away from the wall at…

A:

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: Find the rate at which the water level is rising when the water level is 2 cm.

A:

Q: A kite 160 feet above the ground moves in a direction parallel to the ground at the rate of 5 feet…

A: Let, x= the horizontal distance of the kite y=the length of the string Given that dx/dt=5 ft/sec  We…

Q: sw A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base…

A: Solve the given

Q: A street light is fastened to the top of a 15-ft-high pole. If a 5-ft-tall women walks away from the…

A: In the figure,  AB=15 ft DE=5 ft BD=yDC=xdydt=3 ft/sec

Q: A softball diamond has the shape of a square wide sides 60 ft long. If a player is running from…

A: A softball diamond has the shape of a square with sides 60 ft long. A player is running from second…

Q: A light is hung 15 ft above a straight horizontal path. if a man 6 ft tall is walking away from the…

A: Solution :x=distance from lights=length of shadowlet,height of light,D=15 ftheight of…

Q: A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away fromher at a…

A:

Q: 21. In basebalI, a batter stands 2 feet from home plate as a pitch is thrown with a velocity of 130…

A: Answer is mentioned below

Q: Assuming there is no sag in the string, find the rate at which the kite is moving when 125

A: Considering a right triangle with the data given, the hypotenuse 'c' is 125 feet, base 'b' and the…

Q: A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15…

A:

Q: A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A:

Q: A man cruises his new model Ferrari north 8 mi and then turns east at 12 mi/hr. At what rate was his…

A: Explained below

Q: Consider a pool shaped like the bottom half of a sphere, that is being filled. The radius of the…

A: The volume of hemisphere filled with liquid to height h = πrh2-π3h3

Q: If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

A:

Q: The radius of a circle is increasing at the rate of 0.7 cm/s. what is the rate of

A:

Q: The cone is 12 cm tall and has a radius of 4 cm. If the ice cream fills the cone evenly at a rate of…

A:

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

A:

Q: A jet ascends at a 10° angle from the horizontalwith an airspeed of 550 mi>hr (its speed along…

A: Given: A jet ascends at a 10° angle from the horizontal with an airspeed of 550 mi>hr. Let x be…

Q: The legs of an isosceles right triangle increase in length at a rate of 5 m/s. a. At what rate is…

A:

Q: find the rate of change of the circumference of a circle when the area is increasing at the rate of…

A:

Q: A boat is pulled toward a dock by means of a rope wound on a drum that is located 3 ft above the bow…

A: a rough sketch of the problem will be as follows:

Q: A cylindrical box has a fixed height of 12 inches. Find the rate of change of volume with respect to…

A:

Q: A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A:

Q: ce of a circle is increasing at a rate of 2 cm/s. rea increasing when r= 6 cm?

A: We have to choose the correct answer from the given options according to the given information

Q: A kite is flying at a fixed height of 30 ft. If 50 feet of stringis out alreadyfrom the spool, what…

A: Given: A kite is flying at a fixed height of 30 ft. If 50 feet of string is out already from the…

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

A:

Q: The fixed sides of an isosceles triangle are of length 6 cm. (See the figure.) If the sides slide…

A: Given: The fixed sides of an isosceles triangle are of length 6 cm and the sides slide outward at a…

Q: A rope is attached to the bow of a sailboat coming in for the evening. Assume that the rope is drawn…

A: Given: The rope is drawn in over a pulley 5 feet higher than the bow at the rate of 2 feet per…

Q: Two cars start moving from the same point. One travelssouth at 60 mih and the other travels west at…

A:

Q: A baseball diamond is a square with with side 90 feet (between the bases). A batter hits the ball…

A: Roughly draw the situation first Where x= Distance covered by batter at time t D= Distance of the…

Q: a kite at a height of 60 ft is moving horizontally at a rate of 5 ft/sec away from the boy who flies…

A: Let boy is at the point A, and when 100 ft cord is released the kite is at the point C, which is…

Q: a. How fast is the top of the ladder sliding down the wall when the base of the ladder is 12 feet…

A: It is given that the length of ladder is 13 foot which acts as the hypotenuse of the right angled…

Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: Consider a function y= f(x)  then the derivative f '( x) is the  rate of change of y with respect to…

Q: A boat is pulled toward a pier by means of a taut cable. If the boat is 20 ft below the level of the…

A:

Q: A man walks along a straight path of 4m/s. A searchlight is located on the ground 25m from the path…

A:

Q: A kite is flying at a fixed height of 30 ft. If 50 feet of string is out already from the spool,…

A: With the given details, we can draw a triangle . Here,  h is the vertical height at which kite is…

Q: An angler has a fish at the end of a line. The line is reeled in at 2 ft/sec from a bridge 30 feet…

A:

Q: A hot air balloon is tethered at an angle of elevation of a/6. The rope holding the balloon is being…

A: Given Data: The angle of elevation is: α=π6 The rate at which the rope is being brought is: dxdt=-4…

Q: The base x of the right triangle in the figure increases at a rate of 6 cm/s, while the height remai

A: In this question we will use basic of calculus i.e application of differentiation. We will first…

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: Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the…

A: Given : 1) Oil spills from a ruptured tanker and spreads in a circular pattern.             2)…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.