For t > 0, a particle moves along the curve x = a + b sin kt, y = a + b cos kt, where a, b, and k are positive constants.(a)(b) what is the effect on the curve of the following changes? .a, a+b(i) increasing bmoves the center away from the origin along y = xincreases the radius makes the particle move slower and increases the periodmakes the particle move faster and reduces the periodmakes the curve touch both the x- and y-axes at the points (a, 0) and (0, a), respectively(ii) increasing amoves the center away from the origin along y = xincreases the radius makes the particle move slower and increases the periodmakes the particle move faster and reduces the periodmakes the curve touch both the x- and y-axes at the points (a, 0) and (0, a), respectively(iii) increasing kmoves the center away from the origin along y = xincreases the radius makes the particle move slower and increases the periodmakes the particle move faster and reduces the periodmakes the curve touch both the x- and y-axes at the points (a, 0) and (0, a), respectively(iv) setting a and b equalmoves the center away from the origin along y = xincreases the radius makes the particle move slower and increases the periodmakes the particle move faster and reduces the periodmakes the curve touch both the x- and y-axes at the points (a, 0) and (0, a), respectively

Adriveway is 60-feet long by 6-feet wide. the length and width of the driveway will each be increased by the same number of feet. the following expression represents the perimeter of the larger driveway: (x + 60) + (x + 6) + (x + 60) + (x + 6) which expression is equivalent to the expression for the perimeter of the larger driveway? a) 2(x + 66) b) 4x + 33 c) 4(x + 33) d) 4(x + 132)

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. increase the area of the base of the square pyramid by a factor of ten. increase the height of the cylinder by a factor of ten. increase the radius of the cone by a factor of ten. increase the radius of a sphere by a factor of ten. juan wants to build a greenhouse in his back yard. he needs to maximize the ratio of floor area to structure volume in order to provide the most room for plants while minimizing the area to be heated. find the description of the structure that best meets juan’s criteria. a cube with a side length of 12 feet a cone with a diameter of 12 feet and a height of 10 feet a square pyramid with a base side length of 12 feet and a height of 9 feet a hemisphere with a diameter of 12 feet marion has a bicycle that she is planning to take for a ride. the rim of the rear wheel lies 41 cm from the center of the wheel. the tire itself has a thickness of 3 cm.in order to marion to ride her bicycle 96,712 cm, approximately how many rotations will the rear wheel make? 350 15.9 376 5133 an isosceles trapezoid has perimeter of 42 inches. each of the congruent nonparallel sides is 5 inches long, and the trapezoid is 3 inches tall. how long are the two parallel sides? 10 inches and 16 inches 12 inches and 20 inches 16 inches and 16 inches 10 inches and 22 inches

Which mathematical statements are true? 1) if 3 is an odd number, then 3 times 3 is an even number. 2) if 6 is less than 7, then 4 is greater than 7. 3) six is divisible by 3, and 10 is a multiple of 2. 4) the average of the data is greater than the largest value in the data, or it’s less than the largest value in the data. 5) the slope of a linear graph is its rate of change, and the graph’s y-intercept is the initial value. 6) if an equilateral triangle has equal angles, then all its angles will measure 45°.