A quarterback can throw a football in a perfect parabolic arc to a receiver 40 yards downfield. • The quarterback lets go of the ball 6 feet above the ground and the receiver catches the ball 6 feet above the ground. • The ball reaches a maximum height of 16 feet above the ground halfway to the receiver. Receiver Defender Quarterback

Q: A fireplace arch must be constructed in the shape of a semi-ellipse. The opening must be 60 cm high…

A:

Q: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by…

A: Given, The  dish is 64 feet across its opening, and 4 feet deep at its center

Q: A sealed-beam headlight is in the shape of a paraboloid of revolution (parabolic shaped). The bulb,…

A:

Q: Janiah is a softball player who plays second base (position 4). She can throw a softball in a…

A: The diagram of the curve and softball is:

Q: A new window for an ultra-modern home is being constructed in the shape of an ellipse. The height of…

A: Given window is in a form of ellipse  Height of window is 10 feet Width of window is 6 feet Major…

Q: A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100 feet.The…

A: Given: A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100…

Q: A soccer ball is kicked from a point 23 m to the left of the half way line and lands at a point 17 m…

A: We use the equation in the form y=a(x-r)(x-s) Given Data: r=-23 and s=17

Q: A mirror is shaped like a paraboloid of revolution and will be used to concentrate the rays of the…

A: 4.17 feet

Q: suppose that the bulb of a flashlight is placed at the focus of its parabolic reflector. if the…

A:

Q: Jim, standing at one focus of a whispering gallery,is 6 feet from the nearest wall.His friend is…

A: Given: Jim is standing at the focus of a whimpering gallery is 6 feet. His friend is standing at the…

Q: The major axis of the elliptical path in which the earth moves around the sun isapproximately…

A: We know that the length of the major axis of an ellipse is 2a. So 2a=186,000,000. Find the value of…

Q: An artist bends a long plank of wood into the shape of a parabola. The horizontal distance between…

A:

Q: The cables of the middle part of a suspension bridge are in the form of a parabola, and the towers…

A: Explained below

Q: A suspension bridge has twin towers that are 1300 feet apart. Each tower extends 180 feet above the…

A: We have to find  the height of the cable at a point 200 feet from the center of the bridge.

Q: The transverse axis of a hyperbola is 8 and the distance between foci is 12. Find the length of the…

A: The length of the transverse axis of a hyperbola is 8. It is known that the length of transverse…

Q: The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of…

A: Parabola is a locus of such points whose distance is equal from a fixed point and fixed line. The…

Q: The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of…

A: The casting has diameter 8  inches. Hence 2x=8, we have, x=4 inches Also depth = 1 inch, hence, y=1

Q: A race track is in the shape of an ellipse. The track is 100 feet long and 50 feet wide. Find the…

A:

Q: 2. The arch of a bridge is in the shape of a semi ellipse having a horizontal span of 40 meters and…

A: To find the height at the required value then you should have the equation of the ellipse.

Q: The line segment perpendicular to the axis of symmetry, passing through the focus and with endpoints…

A: Given:The line segment perpendicular to the axis of symmetry, passing through the focus and with…

Q: Janiah is a softball player who plays second base (position 4). She can throw a softball in a…

A: Horigontal Range = 70 feet Maximum Height = 20 ft - 5 ft = 15 ft   Let , the initial velocity = v…

Q: The distance between the vertices of an ellipse is 10. The distance between the foci is 6. What is…

A: Given query is to find the distance between directrices.

Q: A lithotripter is used to disintegrate kidney stones. The patient is placed within an elliptical…

A: We have to find the distance between the electrode and the kidney stone in order to shatter the…

Q: Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. y + 9x² =…

A:

Q: What is a parabola? Describe its shape.

A: We have to define parabola and describe it shape.

Q: State whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A:

Q: Janiah can throw a softball in a perfect parabolic arc which is 70 feet, if Janiah does not feel…

A: Given that:-  Janiah can throw a soft ball in a    perfect parabolic arc             pitcher…

Q: A building facade is in the shape of a semi ellipse, with the major axis as the span. If the span is…

A:

Q: 5. Explain the distinguishing feature of the distance between the foci and a point on the ellipse.

A: Every ellipse has two axes of symmetry. The foci always lie on the major axis, and the sum of the…

Q: The earth revolves around the sun along an ellipse. The sun lies in the focus of the ellipse. The…

A: Given: The earth revolves around the sun along an ellipse. The sun lies in the focus of the ellipse.…

Q: The cables of a suspended-deck suspension bridge are in the shape of a parabola. The pillars…

A: Here we us ethe standard form of the parabola vertex at (h,k) is  (x- h)2 =4a(y-k)

Q: The major axis of the elliptical path in which the earth moves around the sun is approximately…

A: We have to determine apogee and perigee of the earth where it is given that major axis of the…

Q: If the focal length of a parabola is 6 units and the vertex is (3, 2), is it possible to determine…

A: Focal length of a parabola is 6 units and the vertex is (3, 2).

Q: The center of a clock is 60cm above the ground. The minute hand on the clock is 23cm long and starts…

A: topic- trigonometric equations

Q: The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of…

A: How far from the vertex should the light bulb be placed?

Q: A football is kicked from the ground 70 yards along a parabolic path. The maximum height of the ball…

A: Find the height of ball 5 yards before it hits the ground.Consider, x-axis be the yards and y- axis…

Q: A satellite dish has the shape of a parabola when viewed from the side. The receiver (which is at…

A:

Q: 1. Janiah is a softball player who plays second base (position 4). She can throw a softball in a…

A: (A) .

Q: The major axis of the elliptical path in which the earth moves around the sun is approximately 186,…

A: Given: 2a=186,000,000e=160

Q: The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of…

A: Here we use the concept of conic section

Q: The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of…

A: The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of…

Q: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by…

A: Explanation: According to the given situation,  center of the parabola is (0,0) It means two points…

Q: The pitcher is 20 feet away in front of Janiah and the pitcher is only able to reach up to 8 feet…

A: Given that, Janiah can throw a softball in a perfect parabolic arc Pitcher is 20 feet away in front…

Q: The earth revolves around the sun along an ellipse. The sun lies in the focus of the ellipse . The…

A: To Determine: Find the length of of the semi minor axis of the ellipse and the eccentricity of the…

Q: The cable of a suspension bridge is in the form of a parabola. The towers supporting the cable are…

A: Given that The cable of a suspension bridge is in the form of a parabola. The towers supporting the…

Q: The vertices of an ellipse of eccentricity 0.5 lie at the points (0, +-2). Where do the foci lie?

A: The vertices of an ellipse of eccentricity is 0.5 lies on (0,+-2). Find the foci

Q: A bridge is built in the shape of semielliptical arch. It has a span of 112 feet. The height of the…

A: Let the equation of the ellipse is x2a2+y2b2=1 Here, span of arc is 112 feet ⇒2a=112 ⇒a=56…

Q: The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of…

A: Given data: The diameter of the reflector is 4 inches and a depth of 1 inch. it means x=2 and y=1.…

Q: What is the length of the transverse axis of the hyperbola whose foci are (0, -5) and (0,5) , and…

A: The foci of Hyperbola are:   (0, -5)  and  (0, 5). Length of transverse axis of Hyperbola is:  2a…

Q: A satellite in a 100 mile high circular orbit around the earth has a velocity of approximately…

A: Assuming the general form of(y - k) = (1/4p)(x - h)^2If we say the origin is at the point (0,0). The…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.