1) If an object on Earth is propelled upward with an initial velocity of 32 feet per second, then its height after t seconds is given by h = 32t - 16t2 Find the maximum height attained by the object and the number of seconds it takes to hit the ground. 2) Suppose ABC is a right triangle with sides of lengths a, b, and
1. Find the exact value of the sine, cosine, and tangent of the angle. 11pie/12 2. Find all solutions of the equation in the interval [0, 2pie). Sin(x-5pie/6)-sin(x+ 5pie/6) =1 3. Find the exact value of sin2x using the double angle formula. Please help explain the use of the double angle formula. Sin x=1/7,
You interviewed an employee of an association representing the tire industry. The federal government mandates safety testing of all tires manufactured in the United States. Recently there has been concern that the rubber used in the tires could deteriorate while in store inventories. In September 2003, a safety group asked the U
Solve for x 4cos²x - 2=0 sec2x + 5tanx=-2
You are interviewing for a position with an association representing the tire industry. The federal government mandates safety testing of all tires manufactured in the United States. Recently there has been concern that the rubber used in the tires could deteriorate while in store inventories. In September 2003, a safety group a
Elena likes to climb a vertical rock wall at an amusement park. From a point that is 10M from the base of the wall, the angle of the elevation of the top of the wall is 72 degree. What is the height of the wall, to the nearrest metre?
Find the volume of the solid generated by revolving the region described about the Y axis: x=sqrt(cos((pi)y/4)), -2 </= y </= 0, x=0 Using the formula V=integral(pi)[R(y)]^2dy
Prove this identity: 7. sin(x+y)/sin(x-y) = coty +cotx / coty - cot x 8. simplify: 2 sinxcos³x - 2 sin³xcosx 9. If cosx=-1/4 and pie/2<x<pie, the cos (pie/6 - x) = ? 10. Prove this identity: cos 8x = cos²4x - sin²4x.
Caitlyn is a landscaper who is creating a triangular planting garden. The homeowner, Lisa, wants the garden to have two equal sides and contain an angle of 120°. Also, Lisa wants the longest side of the garden to be exactly 6 m. a)How long is the plastic edging that Caitlyn will need to surround the garden? b) What will
Solve: (0°<0<360°) 2sin 2x + 2 = 1
Prove : tanx + 1 / tanx = 1 / sinx cos x I'm not quite sure how I would prove this, I know it is a certain formula, but I don't not know how it applies.
A radio station is going to construct a 12 foot tower for a new antenna on top of a tall building. The tower will be supported by three cables, each attached to the top of the tower and to points on the roof of the building which are 5 feet from the base of the tower. What is the total length of these three cables? 39 feet Ca
Use factoring, the quadratic formula, or identities to solve the equations. Find all solutions in the interval (0,2pi) 65. 3 sin²x - 8 sin x - 3 = 0 answer x=3.4814, 5.9433 67. 2 tan²x + 5 tan x + 3 = 0 answer x= 3pi/4, 7pi/4, 2.1588, 5.3004 69. cotxcosx=cosx ans. x=pi/4, pi/2, 5pi/4, 3pi/2 71. cos x csc
1. Alternating currents are given by: and By making use of the Compound Angle Formulae determine: a. The maximum value of the resultant current b. Its frequency c. Its Phase angle 2. The voltage and current in a circuit are given by: and By making use of Products to Sums Formulae determin
1. The hypotenuse of a 30-60-90 triangle is 9. Find the perimeter. 2. I am so lost with this one its not funny (-.6t/40) _______________ The displacement, d=-7e cos(√(pi/3)^2-0.36/1600) t) Should read: d= negative seven (e) to the negative .6t divided by 40, COS (pi divided
Please explain how to work these problems in steps 1. Prove this identity: sin(x+y)/sin(x-y) = coty+cotx/coty-cotx 8. Simplify: 2sinxcos³x-2sin³xcosx 9. If cosx=-¼and Pi/2 < x < pi, then cos (pi/6 - x) = ? 10. Prove this identity: cos8x=cos²4x-sin²4x.
Prove the following identities..."not an identity" is an option. Please explain in detail and in steps how to perform the following: 1. cot²x-cos²x=cos²xcot²x 3. tanx= square rt of sec²x-1 4. sinx/1-cotx + cosx/1-tanx=cosx+sinx 5. cotx-1/1-tanx = cscx/secx 6. cosxsiny=1/2(sin(x+y)-sin(x-y).
Find the exact value of the expression(Consider interval is [0,pi] I) 1) sin^-1 SQRT3 / 2 = pi/3 2) arctan(-1) = 3pi / 4 3) csc^-1 2 = pi/6 4) sec^-1 SQRT(2) = pi/4 II) We were given the example to derive sin^-1x as follows. y=sin^-1 (x) siny = x (cosy)(dy/dx) = 1 (dy/dx) = 1/cosy = 1 / (SQRT(1-sin^2 (y)) = 1
A. As a group, work together to submit the answers to the following problems. Use the Small Group Discussion Board to divide tasks, discuss strategies for solving problems, and check each other's work. The finished product should be one combined document for the entire group, showing all calculations and graphical representat
Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. The Pythagorean Theorem states that the square of
43. Express cos 3 in terms of cos x. ans. cos3x=4cos^3x-3cosx 47. 2 cos 2y sin 2 y ans. sin 4y 51. sin 16x = 2 sin 8 x cos 8x ans. sin 16x=sin (2(8x))= 2 sin 8x cos 8x 55.cos 4x=2cos2x-1 ans. not an identity
Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point? Can you show me how you got the answer?
If a right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90° angle). How do I find the hypotenuse when the other 2 sides' measurements are 3 feet and 4 feet?
How is this problem solved? Please show all steps domain: 1 ≤ t ≤ e^π∕4 ∫ 4dt ∕ t(1 + ln²t)
What is the solution? Evaluate the integral: ∫ds∕ 9-4s² domain: 0 ≤s≤3√2∕4
How do you do the following type of problem? Please show each step. sec (tan^-1 2x)
Could someone help me with the problem and provide all the steps please. y'' + 4y' + 5y = 35e^(-4x) y(0)=-3, y'(0)=1
A ranger in fire tower A spots a fire at a direction of 295 degrees. A ranger in fire tower B, located 45 miles at a direction of 45 degrees from tower A, spots the same fire at direction of 255 degrees. How far from tower A is the fire? From tower B? In mountain communities, helicopters drop chemical retardants over areas w
Cos(5x)cos(7x)cos(11x)=3 / (sqrt3) How is this problem done? I don't need an exact answer as much as I need the steps leading up to the answer. Calculators aren't permitted so maybe that'll help?
A recent land survey was conducted on a vacant lot where a commercial building is to be erected. The plans for the future building construction call for a building having a roof supported by two sets of beams. The beams in the front are 8 feet high and the back beams are 6.5 feet high. The distance between the front and back bea