Description : What are the points of intersection of the line 2x plus 5y equals 4 with the curve y squared equals x plus 4?
Last Answer : If: 2x +5y = 4 then 25y^2 = 4x^2 -16x +16If: y^2 = x +4 then 25y^2 = 25x +100So: 4x^2 -16x +16 = 25x +100Transposing terms: 4x^2 -41x -84 = 0Factorizing the above: (4x+7)(x-12) = 0 meaning x = -7/4 or x =12By substitution into original equation points of intersection:(-7/4, 3/2) and (12, -4)
Description : What are the values of x y and k when the line y equals 3x plus 1 is a tangent to the circle x squared plus y squared equals k?
Last Answer : If y = 3x + 1 is a tangent to x² + y² = k (k > 0 since it isa square), then where they meet has a repeated root; they meetat:x² + (3x + 1)² = k→ x² + 9x² + 6x + 1 - k = 0→ 10x² + 6x + (1 - k) = 0This is the ... 3/10→ y = 3 -3/10 + 1 = 9/10 + 1 = 1/10→ point of contact is (-3/10, 1/10) with k = 1/10
Description : What is the perpendicular bisector equation of the line y equals 5x plus 10 spanning the parabola y equals x squared plus 4?
Last Answer : If: y = 5x +10 and y = x^2 +4Then: x^2 +4 = 5x +10Transposing terms: x^2 -5x -6 = 0Factorizing the above: (x-6)(X+1) = 0 meaning x = 6 or x =-1Therefore by substitution endpoints of the line are ... .5 = -1/5(x-2.25) => 5y= -x+114.75Perpendicular bisector equation in its general form: x+5y-114.75= 0
Description : What is the point of contact when the tangent line y equals x plus c touches the circle x squared plus y squared equals 4?
Last Answer : The line meets the circle when:y = x + c→ x² + y² = 4→ x² + (x + c)² - 4 = 0→ x² + x² +2cx + c² - 4 = 0→ 2x² + 2cx + (c² - 4) = 0If the line is a tangent to the circle, this has a repeatedroot. This occurs ... 2 = 0→ (x + √2)² = 0→ x = -√2→ y = x + 2√2= -√2 + 2√2= √2→ point of contact is (-√2, √2)
Description : What are the points of intersection between the line 3x -y equals 5 and the curve 2x squared plus y squared equals 129?
Last Answer : If: 3x-y = 5 then y^2 = (3x_5)^2 => 9x^2 -30x+25If: 2x^2 + y^2 = 129 then y^2 = 129-2x^2So: 9x^2 -30x+25 = 129-2x^2Transposing terms: 11x^2 -30x -104 = 0Factorizing the above: (11x- ... x = 52/11 or x= -2By substituting x into the original equation intersections areat: (52/11, 101/11) and (-2, -11)
Description : What is the value of y when y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?
Last Answer : If the line y = 2x+1.25 is a tangent to the curve y^2 = 10x thenit works out that when x = 5/8 then y = 5/2
Description : If a cos theta plus b sin theta equals 8 and a sin theta - b cos theta equals 5 show that a squared plus b squared equals 89?
Last Answer : There is a hint to how to solve this in what is required to be shown: a and b are both squared.Ifa cos θ + b sin θ = 8a sin θ - b cos θ = 5then square both sides of each to get:a² cos² θ + 2ab cos ... + sin² θ) + b² (sin² θ + cos² θ) = 89using cos² θ + sin² θ = 1â†' a² + b² = 89
Description : What are the points of contact when the line x -y equals 2 crosses the curve x squared -4y squared equals 5 showing work?
Last Answer : If: x -y = 2 then x^2 = (2+y)^2 => 4+4y+y^2If: x^2 -4y^2 = 5 then x^2 = 5+4y^2So: 5+4y^2 = 4+4y+y^2Transposing terms: 3y^2 -4y +1 = 0Factorizing the above: (3y-1)(y-1) = 0 meaning y = 1/3 or y =1By substitution contacts are made at: (7/3, 1/3) and (3, 1)
Description : What is x squared equals 200?
Last Answer : It is a quadratic equation in the one variable.
Description : What are the points of contact between the line x -2y equals 1 and the curve 4y squared -3x squared equals 1?
Last Answer : If: x-2y = 1 Then: x^2 = 4y^2 +4y+1 If: 4y^2 -3x^2 = 1 Then: 4y^2 -3(4y^2 +4y+1) = 1 Removing brackets: 4y^2 -12y^2 -12y -3 = 1 Transposing terms: -8y^2 -12y -4 = 0 Dividing all ... meaning y = -1/2 or -1 By substitution into original linear equation points of contact are at: (0, -1/2) and (-1, -1)
Description : How will you describe the graph of distance vs. time squared?
Last Answer : What is the answer ?
Description : What is 3a squared when a equals to -3?
Last Answer : 6
Description : What number squared equals 12769?
Last Answer : Need answer
Description : What is the ratio of surface area to volume for a sphere with the following measurements surface area equals 588 M squared volume equals 1372 m to the Third?
Last Answer : The ratio appears to be 588 to 1372 or 3 to 7 in its simplest form
Description : How do you factorize x squared plus 7x?
Last Answer : It is: x(x+7) when factorized
Description : What is the solution set of the equation x squared plus 3x - 46?
Last Answer : 49
Description : How do ypu factor X squared minus 13x plus 12?
Last Answer : It is x^2 -13x +12 = (x-1)(x-12) when factored
Description : What is X squared plus x plus x plus one?
Last Answer : It is the same as: x^2 +2x +1 and it is (x+1)(x+1) whenfactored
Description : How do you re-write x squared plus 5x - 3 in vertex form?
Last Answer : 8
Description : What is the point of contact between the line y equals x plus 4 and the circle x2 plus y2 -8x plus 4y equals 30?
Last Answer : Equations: y = x+4 and x^2 +y^2 -8x +4y = 30It appears that the given line is a tangent line to the givencircle and the point of contact works out as (-1, 3)
Description : How do you solve for y and x when x plus y equals 45?
Last Answer : There are infinitely many solutions as x + y = 45 defines astraight line. Pick a value for x and you can calculate the y valueso that x + y = 45.It can be rearranged to get y in terms of x:x + y = 45→ -x + x + y = ... y valuewill be found.eg x = 1 → y = -1 + 45 = 44x = 25 → y = -25 + 25 = 20
Description : What value of b makes y equals x plus b the same as y x What does this value means?
Last Answer : If: y = x+b then y-x = b
Description : The relationship between kinetic energy and the potential energy of a swinging pendulum bob is one of the following. Is it: w) kinetic energy is greater than potential energy x) kinetic ... kinetic energy is equal to potential energy z) kinetic energy plus potential energy equals a constant
Last Answer : ANSWER: Z -- KINETIC ENERGY PLUS POTENTIAL ENERGY EQUALS A CONSTANT
Description : What is the vertex of the graph of the function below y x2 plus 6x plus 5?
Description : What is the vertex of the graph of the function below y x2 - 8x plus 12?
Description : How do you factorise 2x squared minus 13x plus 21?
Last Answer : (x - 3)(2x - 7)
Description : How do you do 3X squared plus 18 plus 9?
Last Answer : The given expression can be simplified to: 3X squared +27
Description : What does The number 14 in the equation y equals 2x plus 14?
Last Answer : In the straight line equation of y = 2x+14 the slope or gadientis 2 and the y intercept is 14
Description : What is the point of contact when the line y equals 2x meets the circle x2 plus y2 -8x -y plus 5 equals 0?
Last Answer : If: y = 2xThen: y^2 = 4x^2If: x^2 +y^2 -8x -y +5 = 0Then: x^2 +4x^2 -8x -2x +5 = 0Transposing terms: 5x^2 -10x +5 = 0Dividing all terms by 5: x^2 -2x +1 = 0Factorizing the above: (x-1)(x-1) = 0 meaning x = 1By substitution into original equations point of contact is madeat: (1, 2)
Description : What are the solutions to the simultaneous equations of y equals -2x and x2 plus y2 equals 80?
Last Answer : If: y = -2x then y ^2 = 4x^2If: x^2 + y^2 = 80 then x^2 +4x^2 = 80So: 5x^2 = 80Divide all terms by 5: x^2 = 16Square root both sides: x = -4 or +4By substitution into the original equation solutions are: (-4,8) and (4, -8)
Description : What is the solution when y equals 2x plus 1 is a tangent to the circle 5y2 plus 5x2 equals 1?
Last Answer : If y = 2x+1 is a tangent line to the circle 5y^2 +5x^2 = 1 thenthe point of contact is at (-2/5, 1/5) because it has equalroots
Description : If z equals yf x2 - y2 show that ydz divided by dx plus xdz divided by dy equals xz divided by y?
Last Answer : 4
Description : The electric field of a point charge varies: w) linearly with distance and inversely with charge x) linearly with distance and inversely with charge squared y) linearly with charge and inversely with distance squared z) linearly with charge and inversely with distance
Last Answer : ANSWER: Z -- LINEARLY WITH CHARGE AND INVERSELY WITH DISTANCE
Description : An object with a mass of 5 kilograms is a distance of 5 meters above the surface of the earth. If the acceleration due to gravity is 10 meters per second squared, the potential energy of the object relative to the ... is: w) 10 joules x) 20 joules y) 100 joules z) 250 joules e) none of the above
Last Answer : ANSWER: Z -- 250 JOULES
Description : A car traveling at a constant velocity of 20 meters per second passes a second car which is initially at rest. The car which was at rest starts accelerating at 10 meters per second squared the instant it is passed ... car. They will meet again in: w) 2 seconds x) 4 seconds y) 6 seconds z) 8 seconds
Last Answer : ANSWER: X -- 4 SECONDS
Description : What is the hydrostatic pressure at the bottom of a pool 6 meters deep? w) 60,000 Newtons per meter squared x) 6,000 Newtons per meter squared y) 600 Newtons per meter squared z) 60 Newtons per meter squared
Last Answer : ANSWER: W -- 60,000 NEWTONS PER METER SQUARED
Description : The acceleration due to gravity on the moon is 1.6 meters per second squared. If a pendulum is whose length is 6.4 meters is placed on the moon, its period will be: w) 1.57 seconds x) 3.14 seconds y) 12.56 seconds z) 25.12 seconds
Last Answer : not real
Description : Carlos is pulling a 40 kilogram cart with a horizontal force of 100 newtons. The force of friction on the cart is 20 newtons. The acceleration of the cart is: w) 2 meters per second squared x) 2.5 meters per second squared y) 20 meters per second squared z) 200 meters per second squared
Last Answer : ANSWER: W -- 2 METERS PER SECOND SQUARED
Description : Ten coulombs of charge are placed on a solid copper sphere. Once the charge has come to rest, the ELECTRIC POTENTIAL inside the sphere is found to be: w) zero x) uniform inside the sphere and ... the sphere y) smaller than the electric potential outside the sphere z) varying as one over r squared
Last Answer : ANSWER: X -- UNIFORM INSIDE THE SPHERE AND EQUAL TO THE ELECTRIC POTENTIAL ON THE SURFACE OF THE SPHERE
Description : Ten coulombs of positive charge are placed on an irregularly-shaped, solid piece of copper. Once the charge has stopped moving, the electric field inside the copper is: w) zero x) changes as one ... squared y) becomes smaller as you approach the center z) becomes larger as you approach the center
Last Answer : ANSWER: W -- ZERO
Description : In physics, a radian per second squared is a unit of: w) angular displacement x) angular velocity y) angular acceleration z) angular momentum.
Last Answer : ANSWER: Y -- ANGULAR ACCELERATION
Description : An object is projected vertically upward near the surface of the earth. At the very top of its path, the object's velocity is zero, and its acceleration is: w) 0 x) 9.8 meters per second squared DOWNWARD y) 9.8 meters per second squared UPWARD z) depends on the mass of the object
Last Answer : ANSWER: X -- 9.8 METERS PER SECOND SQUARED DOWNWARD
Description : If a sled has a constant acceleration of 2 meters per second squared and starts from rest, the distance in meters that it will have covered after 5 seconds is: w) 10 meters x) 20 meters y) 25 meters z) 50 meters
Last Answer : ANSWER: Y -- 25 METERS
Description : The SI unit of pressure is the: w) Torr x) dyne per centimeter squared y) atmosphere z) pascal
Last Answer : ANSWER: Z -- PASCAL
Description : A constant potential difference is applied across the plates of a parallel-plate capacitor. Neglecting any edge effects, the electric field inside the capacitor is: w) constant x) varying as one over r squared y) decreasing as one moves from the positive to the negative plate z) zero
Last Answer : ANSWER: W -- CONSTANT
Description : For a parallel-plate capacitor with plate area "A" and plate separation "d", the capacitance is proportional to which of the following? w) A divided by d squared x) A times d y) A divided by d z) d divided by A
Last Answer : ANSWER: Y -- A DIVIDED BY D
Description : Five coulombs of charge are placed on a thin-walled conducting shell. Once the charge has come to rest, the electric potential inside the hollow conducting shell is found to be: w) zero x) uniform ... sphere y) smaller than the electric potential outside the sphere z) varying as one over r squared.
Last Answer : ANSWER: X -- UNIFORM INSIDE THE SPHERE AND EQUAL TO THE ELECTRIC OTENT
Description : For an infinite sheet of positive charge, the electric field lines: w) run parallel to the sheet of charge x) are perpendicular to the sheet of charge and point in toward the sheet y) are perpendicular to the sheet of charge and point away from the sheet z) fall off as one over r squared
Last Answer : ANSWER: Y -- ARE PERPENDICULAR TO THE SHEET OF CHARGE AND POINT AWAY