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Is an advanced level math course that prepares students for college-level calculus and covers topics such as functions, trigonometry, and complex numbers.
Use the Binomial Theorem to expand and simplify the expression. (x2/3 - y1/3)3
Solve each equation for exact solutions over the interval [00, 3600]. 2sinθ−1=cscθ
Solve the equation for exact solutions over the interval [0, 2π]. 2–√cos2x=−1
What are the coordinates of the figure below:a
Find the standard form of the equation of the ellipse with the given characteristics: Vertices: (0, 2), (4, 2); endpoints of the minor axis: (2, 3), (2, 1)
Convert the rectangular equation to polar form. Assume a > 0. y2 - 8x - 16 = 0
Convert 2π into degrees.
A structure of ellipse that have the origin as their centers.
Convert the rectangular equation to polar form. Assume a > 0. y = 4
Solve the system by the method of substitution. Check your solution graphically. -2x + y = -5 X2 + y2 = 25
Convert the angle in radians to degrees. 5π/ 4
Find the standard form of the equation of the ellipse with the given characteristics: Vertices: (0, 4), (4, 4); minor axis of length 2
Solve the system by the method of elimination and check any solutions algebraically. 0.05x – 0.03y = 0.21 0.07x + 0.02y = 0.16
Convert π/18 to Degrees.
What does r refer to in the following equation? (x-h)2+(y-k)2=r
What is the quadrant or axis on which the point is located? (-15, 0)
Find the equation in standard form of the ellipse whose foci are F1 (-8,0) and F2 (8,0), such that for any point on it, the sum of its distances from the foci is 20.
Second differences:
What are the coordinates of the center of the circle given by the equation x2+y2-16x-8y+31=0?
Solve the system by the method of substitution.
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.
Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate. 3sin2x−sinx−1=0
Use the Binomial Theorem to expand and simplify the expression. 2(x - 3)4 + 5(x - 3)2
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. x2−4x−8y+2=0
What Quadrant does 294° belongs to?
Find the standard equation of the hyperbola which satisfies the given conditions:
Convert the polar equation to rectangular form. (theta = frac{2pi}{3} )
Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate. ( 3 sin^2 x - sin x - 1 = 0 )
Solve each equation for exact solutions over the interval [00, 3600]. ( (tan theta - 1)( costheta - 1) = 0 )
Find the exact value of the trigonometric function given that sinu=513
Solve the system by the method of elimination and check any solutions algebraically. 3x + 2y = 10 2x + 5y = 3
Find a quadratic model for the sequence with the indicated terms.
Find the standard equation of the hyperbola which satisfies the given condition:
Convert the polar equation to rectangular form.
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 = 90o, (0, 3)
Write the expression as the sine, cosine, or tangent of an angle. sin 3 cos 1.2 - cos 3 sin 1.2
Use the Binomial Theorem to expand and simplify the expression. (3a - 4b)5
Use the Binomial Theorem to expand and simplify the expression. (y - 4)3
Find the standard form of the equation of the ellipse with the given characteristics: Foci: (0, 0), (0, 8); major axis of length 16
Expand the expression in the difference quotient and simplify.
Find the standard form of the equation of the parabola with the given characteristics: Vertex: (0, 4); directrix: y = 2
Solve the system by the method of elimination and check any solutions algebraically.X + 2y = 4 X – 2y = 1
Using the equation for the circle find its radius: x2 + y2 + 6x + 2y + 6 = 0.
What Quadrant does 144° belongs to?
A ___________ has a shape of paraboloid, where each cross section is a parabola.
What is the standard form of the equation of the circle x2 + 14x + y2 - 6y - 23 = 0?
Write the first five terms of the sequence. Assume that n begins with 1.
Solve the system by the method of substitution: -x + 2y = 2 3x + y = 15
What is the quadrant or axis on which the point is located? (-10, -16)
Find the standard form of the equation of the parabola with the given characteristics:
Find the sum using the formulas for the sums of powers of integers.
Write the expression as the sine, cosine, or tangent of an angle. cos 25° cos 15° - sin 25° sin 15°
A type of Conic where the plane intersects only on one cone to form an anbounded curve.
Expand the binomial by using Pascal's Triangle to determine the coefficients. (x - 2y)5
The ______ is the point midway between the focus and the directrix.
Find the exact value of the trigonometric function given that sin u=−725
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
Convert the polar equation to rectangular form. ( r = 2 sin 3 theta )
Expand the binomial by using Pascal's Triangle to determine the coefficients. (2t - s)5
Find a polar equation of the conic with its focus at the pole.
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.
Solve the equation for exact solutions over the interval [0, 2π]. sin 3x = 0
Use the Binomial Theorem to approximate the quantity accurate to three decimal places.
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. x2+y2−6x+4y+9=0
Find the standard equation of the parabola which satisfies the given condition:
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. x2 – 2xy + y2 – 1 = 0
Convert the polar equation to rectangular form. r=4cscθ
Find the center point of the following circle x2 + y2 + 8x + 4y - 3 = 40.
The shape of this conic section is a bounded curve which looks like a flattened circle.
Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate. 2cos2+cosx=1
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. (Large y^2 -4x^2 +4x -2y -4 =0)
r=21−cosθ
Find the standard form of the equation of the parabola with the given characteristics: Vertex: (5, 2); focus: (3, 2)
A circle can be centered anywhere in the coordinate plane.
Convert the polar equation to rectangular form. r = 4
Expand the binomial by using Pascal’s Triangle to determine the coefficients.
Solve the equation for exact solutions over the interval [0, 2π]. 23–√sin2x=3–√
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?
Solve the system by the method of substitution:
Find the exact value of each expression.
Find the standard form of the equation of the ellipse with the given characteristics:
Choose an expression for the apparent nth term of the sequence. Assume that n begins with 1.
Two control towers are located at points Q(-500, 0) and R(500, 0), on a straight shore where the x-axis runs through (all distances are in meters). At the same moment, both towers sent a radio signal to a ship out at sea, each traveling at 300 m/µs. The ship received the signal from Q 3 µs (microseconds) before the message from R.
Use any method to solve the system.
Convert the rectangular equation to polar form. Assume a > 0. x2 + y2 - 2ax = 0
Use the Binomial Theorem to expand and simplify the expression. 2(x - 3)5 + 5(x - 3)2
What are the coordinates of the given figure below:a
Solve the equation for exact solutions over the interval [0, 2π]. 3tan3x=3–√
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 4x2+16y2−4x−32y+1=0
Which answer choice shows the center of the circle with the equation x2 + y2 -8x +14y +57.
Use the Binomial Theorem to expand and simplify the expression. (x2 + y2)4
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?
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. (Large 4x^2+3y^2+8x-24y+51 =0 )
Convert the polar equation to rectangular form. r = 62−3sinθ
Solve the equation for exact solutions over the interval [0, 2π]. (sinfrac{x}{2} = sqrt{2} - sinfrac{x}{2})
Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate. ( 4 cos^2x - 1 = 0)
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.
In order to graph a circle one must graph all the points that are equidistant from:
Solve each equation for exact solutions over the interval [00, 3600]. (tanθ−1)(cosθ−1)=0
Classify the angle as acute, right, obtuse, or straight: 2π/3
What is the standard form of the equation of the circle x2 + y2 + 10x - 4y - 7 = 0?
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. (large 25x^2-10x-200y-119=0)
Give all exact solutions over the interval [0°, 360°].
Write the expression as the sine, cosine, or tangent of an angle. tan2x+tanx1−tan2xtanx
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.
Solve the equation for exact solutions over the interval [0, 2π]. (cos2x = -frac{1}{2} )
Where is the center of the circle? (x-h)2+(y-k)2=r
Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form. 5x2 – 6xy + 5y2 – 12 = 0
Find a formula for the sum of the first n terms of the sequence.
Solve the system by the method of elimination and check any solutions algebraically:
Solve the system by the method of substitution. Check your solution graphically.
Plot the point given in polar coordinates and find two additional polar representations of the point, using -2π < θ < 2π.
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?
Determine all solutions of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate. (2 cos^2 + cos x =1)
Find the exact value of the tangent of the angle by using a sum or difference formula. -165°
Convert the rectangular equation to polar form. Assume a > 0. 3x - y + 2 = 0
Solve the equation for exact solutions over the interval [0, 2π]. cot3x=3–√
Use the Binomial Theorem to expand and simplify the expression. (x + 1)4
Find the standard equation of the ellipse which satisfies the given conditions.
Find the specified nth term in the expansion of the binomial.
Find the standard form of the equation of the parabola with the given characteristics: Focus: (2, 2); directrix: x = -2
What is the quadrant or axis on which the point is located? (7,7)
Solve each equation for exact solutions over the interval [00, 3600]. ((cottheta - sqrt{3})(2sintheta + sqrt{3}) = 0)
Use the Binomial Theorem to expand and simplify the expression.
What kind of symmetry does a circle have?
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.
Solve the equation for exact solutions over the interval [0, 2π]. cos 2x = 3√2
First six terms:
A parabola has focus F(-2, -5) and directrix x = 6. Find the standard equation of the parabola.
Determine the quadrant in which the angle lies. 349°
A type of Conic where the plane is horizontal.
Give the coordinates of the center, foci, and covertices of the ellipse with equation 41x2 + 16y2 + 246x - 192y + 289 = 0. Only vertices are given. Enclose the coordinates in parentheses. For example, (6, 4)
Give all exact solutions over the interval [00, 3600].
Find the exact value of the cosine of the angle by using a sum or difference formula.
Find the standard form of the equation of the ellipse with the given characteristics: Center: (0, 4), a = 2c; vertices:
Expand the binomial by using Pascal’s Triangle to determine the coefficients. (x + 2y)5
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 4x2−y2−4x−3=0
A point in polar coordinates is given. Convert the point to rectangular coordinates.
A type of Conic where the plane is tilted and intersects only on one cone to form a bounded curve.
Solve the equation for exact solutions over the interval [0, 2π]. (sin 3x = -1)
First differences:
A truck that is about to pass through the tunnel from the previous item is 10 ft wide and 8.3 ft high. Will this truck be able to pass through the tunnel?
Find the sum.
Give the coordinates (enclose the coordinates in parentheses) of the foci, vertices, and covertices of the ellipse with equation .
Solve the equation for exact solutions over the interval [0, 2π]. cos2x=−12
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
Solve the equation for exact solutions over the interval [0, 2π]. tan 4x = 0
Determine the vertex of the parabola with the equation x2 - 6x + 5y = -34. Enclose your answers in parentheses.
What is the quadrant or axis on which the point is located? (13, -14)
Solve the system by the method of elimination and check any solutions algebraically.
Give the coordinates (enclose the coordinates in parentheses) of the foci, vertices, and covertices of the ellipse with equation
Convert the angle in radians to degrees. Round to two decimal places. -3.97 radians
What are the coordinates of the figure below: A
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. (Large 100x^2 + 100y^2 - 100x + 400y + 409 =0 )
Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form.
Find Pk+1 for the given Pk.
Convert the angle in degrees to radians. Express answer as a multiple of π. 144°
Solve the equation for exact solutions over the interval [0, 2π]. sinx2=2–√−sinx2
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