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