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Pre calculus week 1 20 wewo summary of answer key and guidelines
Science,Technology&Society (GE6116)
PREC-2111-2012S Pre-Calculus
Week 3
1 st^ Attempt 9/
A circle can be centered anywhere in the coordinate plane.
A: True
Find the standard equation of the hyperbola which satisfies the given
conditions:
Vertices (-2, 8) and (8, 8), a focus (12, 8)
A: (x−3) 25 2 −(y−8) 56 2 =1(x−3)225−(y−8)256=
What are the coordinates of the center of the circle given by the equation x^2 +y -16x-^2 8y+31=0?
A: (8,4)
Give the standard equation of the circle satisfying the given condition: center at the origin, radius 4Give the standard equation of the circle satisfying the given condition: center at the origin, radius 4.
A: x + y = 16^2
What is the standard form of the equation of the circle x + y + 10x – 4y – 7 = 0?^2
A: (x + 5) + (y – 2)^2 2 = 6^2
Where is the center of the circle? (x-h)^2 +(y-k) =r^2
A: (h,k)
What kind of symmetry does a circle have?
A: All of the answer choices are correct.
Determine the asymptotes of the equation:
A:
What does r refer to in the following equation? (x-h)^2 +(y-k) =r^2
A: The square of the radius of a circle.
Give the coordinates (enclose the coordinates in parentheses) of the foci, vertices, and covertices of the ellipse with
2 nd^ Attempt 8/
A semielliptical tunnel has height 9 ft and a width of 30 ft. A truck that is about to pass through is 12 ft wide and 8.3 ft high. Will this truck be able to pass through the tunnel?
A: No
A parabola has focus F(-2, -5) and directrix x = 6. Find the standard equation of the parabola.
A: (y + 5) 2 = -16(x - 2)
Find the standard equation of the ellipse which satisfies the given conditions.
b. center (5,3), horizontal major axis of length 20, minor axis of length 16.
Answer:
Determine the focus of the parabola with the equation x - 6x + 5y = -34.^2
Enclose answers in parentheses.
For example: (7, 8)
A: (3, -6.25)
Give the standard equation of the circle satisfying the given condition in Figure 1.
A: (x+3) 2 + (y+1) 2 = 25
Using the equation for the circle find its radius: x 2 + y 2 + 6x + 2y + 6 = 0.
A: r = 2
Find the standard equation of the ellipse which satisfies the given conditions.
e. focus (-6, -2), covertex (-1,5), horizontal major axis
A:
Give the asymptotes of the hyperbola with equation 9x 2 - 4y 2 - 90x - 32y = -305.
A:
What is the standard form of the equation of the circle x + 14x + y - 6y - 23 = 0?^2
A: (x + 7) + (y - 3)^2 2 = 9^2
3 rd^ Attempt
What does r refer to in the following equation? (x-h)^2 +(y-k) =r^2
A: The square of the radius of a circle.
Determine the directrix of the parabola with the equation x 2 - 6x + 5y = -34. Answer in complete equation.
A: y = -(15/4)
Find the standard equation of the parabola which satisfies the given
condition:
Vertex (-8, 3), directrix x = -10.
Answer: (y - 3) 2 = 10(x + 8)
An orbit of a satellite around a planet is an ellipse, with the planet at one focus of this ellipse. The distance of the satellite from this star varies from 300,000 km to 500,000 km, attained when the satellite is at each of the two vertices. Find the equation of this ellipse, if its center is at the origin, and the vertices are on the x- axis. Assume all units are in 100,000 km
A:
Determine the axis of symmetry of the parabola with the equation x 2 - 6x + 5y = -34. Answer in complete equation.
A: x = 3
What is the standard form of the equation of the circle x + 14x + y - 6y - 23 = 0?^2
A: (x + 7) + (y - 3)^2 2 = 9^2
Using the equation for the circle find its radius: x 2 + y 2 + 6x + 2y + 6 = 0.
A: r = 2
A satellite dish in the shape of a paraboloid is 10 ft across, and 4 ft deep at its vertex. How far is the receiver from the vertex, if it is placed at the focus? Round off your answer to 2 decimal places.
A: 6.
Find the standard equation of the ellipse which satisfies the given conditions.
d. covertices (-4,8) and (10,8), a focus at (3,12)
A:
Find the standard equation of the hyperbola which satisfies the given
condition:
Foci (-4, -3) and (-4, 13), the absolute value of the difference of the distances
of any point from the foci is 14.
A:
Find the standard equation of the parabola which satisfies the given
condition:
Vertex (-4, 2), focus (-4, -1)
A: (x + 4) 2 = -12(y - 2)
Find the standard equation of the hyperbola which satisfies the given
condition:
Foci (-4, -3) and (-4, 13), the absolute value of the difference of the distances
of any point from the foci is 14.
A:
A type of Conic where the plane is horizontal
A: ellipse parabola (wrong) hyperbola(wrong)
Find the standard equation of the hyperbola which satisfies the given
condition:
asymptotes
A:
Give the standard equation of the circle satisfying the given condition: center at (- 4,3), radius sqrt(7).
A: (x+4) + (y-3) = 7^2
Find the standard equation of the parabola with focus F(0, -3.5) and directrix y = 3.5.
A: X 2 = -14y
Find the equation in standard form of the ellipse whose foci are F 1 (-8,0) and F 2 (8,0), such that for any point on it, the sum of its distances from the foci is 20.
A:
Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the given equations: Remember to enclose vertices and focus in parentheses, i.e. (8, 5); (5, 10). For directrix and axis of symmetry, put your answer in a complete equation, i.e. y = 4.7; x = 0
Week 5
Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form.
c. 9x + 24xy + 16y + 90x – 130y = 0^2
Answer:
The orbit of a planet around a star is described by the equation where the star is at one focus, and all units are in millions of kilometers. The planet is closest and farthest from the star, when it is at the vertices. How far is the planet when it is closest to the sun? How far is the planet when it is farthest from the sun?
A: 700 million km, 900 million km
Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes. a. x 2 – 2xy + y 2 – 1 = 0
The x’y’-coordinate system has been rotated θ degrees from the xy-coordinate system. The coordinates of a point in the xy-coordinate system are given. Find the coordinates of the point in the rotated coordinate system.
b. Θ = 30 , (1, 3)o
A:
A whispering gallery has a semielliptical ceiling that is 9 m high and 30 m long. How high is the ceiling above the two foci?
A: 5.4 m
A type of Conic where the plane is tilted and intersects only on one cone to form a bounded curve.
A: ellipse
The term _________ is both used to refer to a segment from center C to a point P on the circle, and the length of this segment.
A: radius
Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes.
A:
The orbit of a planet around a star is described by the equation where the star is at one focus, and all units are in millions of kilometers. The planet is closest and farthest from the star, when it is at the vertices. How far is the planet when it is closest to the sun? How far is the planet when it is farthest from the sun?
A: 700 million km, 900 million km
Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form.
a. xy + 1 = 0
A:
Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form.
5x^2 – 6xy + 5y – 12 = 0^2
Answer:
Rotate the axes to eliminate the xy-term in the equation. Then write the
equation in standard form.
a. xy + 1 = 0
Answer:
A big room is constructed so that the ceiling is a dome that is semielliptical in shape. If a person stands at one focus and speaks, the sound that is made bounces off the ceiling and gets reflected to the other focus. Thus, if two people stand at the foci (ignoring their heights), they will be able to hear each other. If the room is 34 m long and 8 m high, how far from the center should each of two people stand if they would like to whisper back and forth and hear each other?
A: 15 m
Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes.
b. xy – 2y – 4x = 0
Answer:
The x’y’-coordinate system has been rotated θ degrees from the xy-coordinate system. The coordinates of a point in the xy-coordinate system are given. Find the coordinates of the point in the rotated coordinate system.
b. Θ = 30 , (1, 3)o
Answer:
A type of Conic where the plane intersects only on one cone to form an anbounded curve.
A: parabola
The x’y’-coordinate system has been rotated θ degrees from the xy-coordinate system. The coordinates of a point in the xy-coordinate system are given. Find the coordinates of the point in the rotated coordinate system. a.Θ = 45 , (2, 1)o
2x + y = 6
-x + y = 0
A: (2, 2)
Solve the system by the method of elimination and check any solutions
algebraically.
3x + 2y = 10
2x + 5y = 3
A: (4, -1)
Solve the system by the method of elimination and check any solutions
algebraically.
X + 2y = 4
X – 2y = 1
A: (3, 4)
Solve the system by the method of substitution.
1.5x + 0.8y = 2.
0.3x – 0.2y = 0.
A: (1, 1)
A ___________ has a shape of paraboloid, where each cross section is a parabola.
A: satellite dish
Solve the system by the method of substitution:
-x + 2y = 2
3x + y = 15
A: (4, 3)
An airplane flying into a headwind travels the 1800-mile flying distance between Pittsburgh, Pennsylvania and Phoenix, Arizona in 3 hours and 36 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.
A: 550 miles per hour, 50 miles per hour
Use any method to solve the system.
3x – 5y = 7
2x + y = 9
A: (4, 1)
Solve the system by the method of elimination and check any solutions
algebraically.
0.05x – 0.03y = 0.
0.07x + 0.02y = 0.
A:
Solve the system by the method of substitution. Check your solution
graphically.
2x + y = 6
-x + y = 0
A: (2, 2)
Solve the system by the method of elimination and check any solutions
algebraically.
X + 2y = 4
X – 2y = 1
A: (3, 4)
Solve the system by the method of substitution:
-x + 2y = 2
3x + y = 15
A: (4, 3)
Solve the system by the method of substitution. Check your solution
graphically.
-2x + y = -
X^2 + y = 25^2
A: (0, -5), (4, 3)
An airplane flying into a headwind travels the 1800-mile flying distance between Pittsburgh, Pennsylvania and Phoenix, Arizona in 3 hours and 36 minutes. On the
Answer:
Calculate the binomial coefficient.
s C 3
A: 10
Expand the expression in the difference quotient and simplify.
F(x) = x^3
A: 3x^2 + 3xh + h , h ≠ 0^2
Find P k+1 for the given P .k
Answer:
Find a formula for the sum of the first n terms of the sequence.
Answer:
Use the Binomial Theorem to expand and simplify the expression.
(y - 4)^3
A: Y^3 - 12y^2 + 48y – 64
Use the Binomial Theorem to expand and simplify the expression.
( x 2/3^ - y1/3)^3
Answer: X^2 – 3x 4/3y1/3^ + 3x 2/3y2/3 – y
The ______ is the point midway between the focus and the directrix.
A: vertex
Find the specified nth term in the expansion of the binomial.
(10x – 3y) , n = 9^12
A: 32,476,950,000x^4 y^8
Find the sum using the formulas for the sums of powers of integers.
A: 120
Find a quadratic model for the sequence with the indicated terms.
Answer:
The shape of this conic section is a bounded curve which looks like a flattened circle.
A: ellipse
Expand the binomial by using Pascal’s Triangle to determine the coefficients.
(x + 2y)^5
A: X^5 + 10x y + 40x^4 3 y^2 + 80x 2 y^3 + 80xy + 32y^4
Calculate the binomial coefficient.
12 C 0
Calculate the binomial coefficient.
12 C 0
A: 1
Use the Binomial Theorem to expand and simplify the expression.
2(x - 3) + 5(x - 3)^5
A: 2x 4 – 24x 3 + 113x 2 – 246x + 207
Use the Binomial Theorem to expand and simplify the expression.
(x + 1)^4
A: X^4 + 4x 3 + 6x 2 + 4x + 1
Use the Binomial Theorem to expand and simplify the expression.
( x 2/3^ – y1/3)^3
A: X^2 – 3x 4/3y1/3^ + 3x2/3y2/3^ – y
Find the sum using the formulas for the sums of powers of integers.
A: 73 71 wrong 72 wrong
Expand the expression in the difference quotient and simplify.
F(x) = x^3
A: 3x^2 + 3xh + h , h ≠ 0^2
Find a quadratic model for the sequence with the indicated terms.
A:
Use the Binomial Theorem to approximate the quantity accurate to three
decimal places.
(2.99)^12
A: 510568.
Use the Binomial Theorem to expand and simplify the expression.
2(x – 3) + 5(x – 3)^5
A: 2x^4 – 24x 3 + 113x 2 – 246x + 207
Use the Binomial Theorem to expand and simplify the expression.
(√ x + 3)^4
A: X + 12x^2 3/2^ + 54x + 108x 1/2+ 81
Find the specified nth term in the expansion of the binomial.
(4x + 3y) , n = 8^9
A: 1,259,712x^2 y^7
Find a quadratic model for the sequence with the indicated terms.
A:
A type of Conic where the plane intersects both cones to form two
unbounded curves
A: hyperbola
Find a formula for the sum of the first n terms of the sequence.
A:
A type of Conic where the plane is horizontal.
A: Circle ellipse (wrong) parabola(wrong) hyperbola (wrong)
3 rd^ Attempt 14/
A structure of ellipse that have the origin as their centers.
