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