Since the vertex is (-2,-7) The vertex form of the quadratic function is: f(x) = a (x+2)2 -7 for some value of a. The y intercept is -3 means f(0) = -3 so -3 = a( 0 +2)2 -7 ...

Since the vertex is (-2,-7) The vertex form of the quadratic function is: f(x) = a (x+2)2 -7 for some value of a. The y intercept is -3 means f(0) = -3 so -3 = a( 0 +2)2 -7 ...

Rewrite the equation as y2 (1+ sin2x)2 = cos22x Then replace cos22x with 1 - sin22x The result is an equation quadratic in sin2x The quadratic formula can then be used to get two values for sin2x One is sin2x =...

First work out the molar mass of glucose MM = 6 x 12 + 12 x 1 + 6 x 16 = 180 g The number of moles of glucose is 2.2 x 10-2 / 160 = 0.0001222 moles of glucose. The number of molecules is this number multiplied by the Avogadro...

At the top if the curve, the occupants of the car are accelerating downward with ac = v2 /R where v is the velocity and R = 91 m ((centripetal acceleration) The free body diagram for an occupant shows two forces: 1) , the downward force of gravity = mg ...

For the case of an equal mass elastic collision, the angle between the exit velocities is 90 degrees. Hence second ball moves at an angle 90 - 37 = 53 degrees with respect to the original line of motion.

Let c = the length of string to be used for the circle, and s = the length to be used for the square Then c + s = 22 This is a constraint equation. s is actually the perimeter of the square, so the side of square is s/4 and the area is ...

To see what is going on, work backwards from the answer. Long division (or synthetic division) of (-2s^3-8s^2+4s+40)/(s^3+4s^2+3s) Works out to be -2 with a remainder of (10 s +40) /(s^3 +4 s^2 + 3s) The -2...

The combined gas law can be used to solve this P1 V1 / T1 = P2 V2 / T2 Plugging in P1 =18 ; T1 = 273 ; V2 = 2 V1 ; T2 = 298 and cancelling out the factors of V1 The...

I would say this number belongs to the set of real numbers.

The sides are in the ratio 3:4:5, which is one of the Pythagorean right triangles, so angle A is 90 degrees. The area, A, is A = (1/2) 3 (4) = 6. The area is also equal to: (1/2) ( the altitude from A to BC) 5 6=...

The Stoichiometric balanced equation is NaHCO3 + HCl ==> CO2 + NaCL + H2O Thus the molar ratios are all 1:1 The initial pressure in the flask was not specified, nor was the Kelvin temperature. However, assuming that the...

This problem can be solved using the (external) work = change of energy relation. The friction with the rough surface does negative work on the system. This work = - distance x force = - 1.5 ( .5) 9,81 (,3) = - 2.205 J. The energy of the system starts at (1/2)...

The number sqrt(2)/2 comes up in several places . To make the typing easier I will replace it with .707 and then restore at the end. I am going to limit my analysis to The standard domain restriction on sin-1 . This restricts x to [-.5 , .5] and generates angles in the first...

An upper bound to this series is the geometric series with the general term an = a1 (2/5)n-1 (a1 = 1) The sum of the geometric series is 5/3 . This proves that the problem series converges to a number less than 5/3. I don't...

The idea here is probably that 3i and 2 -i are zeros of the desired polynomial. Since the coefficients are rational, the complex zeros come in complex conjugate pairs. This means that -3i and 2+ i are also zeros. A start on the polynomial is to write ...

The slope of the line 4x + 5y =1 is m = -4/5. The slope of a line perpendicular to this line is the negative reciprocal of -4/5 . The negative reciprocal of -4/5 is 5/4 Thus a line perpendicular will have the equaiton y...

-2+3i polar form (answer)

The magnitude is sqrt [ (-2)2 + 32 ) = sqrt(13) = 3.6 The phase is arctan[ 3 /(-2) ] = - .983 (radian) Final form is 3.6 exp( - .983 i)

Physics Power and Work (answer)

The conversion from horse power to watt is 1 hp = 745.7 W. So 0.28 hp = 208.8 W The total mass that must be raised 245 m is: m = 49 + 2.1 = 51.1 The work that must be done is: W = m g h = (51.1) (9.81) (245) = 122816...

On way of working this type of problem is to assume that one starts with an alloy mass of 1 kg = 1000 g. Then there would be 0.70 x 1000 = 700 g oif Al and .30 x 1000 = 300 g Mg. Since the Molar Mass of Al is 26.982 g /mole , there are 700/ 26.982 = 25.94 molles of...

f(x) = (x- 2)2/3 This is a cusp at x = 2. Other examples can be constructed using piece-wise defined functions with the join point at x = 2