Find the length of each segment of a triangle

th and breadth of the field.

405 square meters, find the length of the rectangle.

measures 16 m, find the length of side c

f carbonic ice at temperature -109.5 °C and placed in a room where the ambient temperature is 28.7 °C. The thickness of each (identical) panel of the container is 2.2 cm. In 1.2 day(s), an amount of 3073661 J of heat is conducted through the panels. Find the thermal conductivity of the material which the panels are made of

f carbonic ice at temperature -109.5 °C and placed in a room where the ambient temperature is 28.7 °C. The thickness of each (identical) panel of the container is 2.2 cm. In 1.2 day(s), an amount of 3073661 J of heat is conducted through the panels. Find the thermal conductivity of the material which the panels are made of.

arbitrary point (2 sin 2t, 2 cos 2t, 3t) on the helix. b) Compute the arc length from (0,2,0) to (0,-2,3π/2) c) Compute the vectors T, N and B at (0,-2,3π/2) d) Compute the curvature at (0,-2,3π/2) e) Find the angle between T and the z-axis at (0,-2,3π/2) to the nearest tenth of a degree.

an arbitrary point (2 sin 2t, 2 cos 2t, 3t) on the helix. b) Compute the arc length from (0,2,0) to (0,-2,3π/2) c) Compute the vectors T, N and B at (0,-2,3π/2) d) Compute the curvature at (0,-2,3π/2) e) Find the angle between T and the z-axis at (0,-2,3π/2) to the nearest tenth of a degree.

length and the width of the rug.

terms of a and b. (ii) Explain why a ≠ -3/4b ' ( b) A cylinder has a length equal to 3 times its diameter. Find the total area of the cylinder as a function of its radius.

the context of this question. What length results in the greatest possible area? What is this area?

dimensions of the rectangle.

4 cm2 and DE = 14 cm. Calculate the length of BC. Also, find the area of triangle BCD.

and DE = 14 cm. Calculate the length of BC. Also, find the area of triangle BCD.

e and of the central height.

width is decreased by 2, the result is a rectangle whose area is 8 sq. units more than the area of the original rectangle. Find the dimensions of the original rectangle.

ose the breaking point is uniformly distributed on the chalk. Let X denote the length of the shorter piece and R the ratio of the lengths of the shorter to the longer piece. Then X has uniform distribution on [0; 1 2 ]. (a) (6pts) Find the probability density function of R. (b) (8pts) Find the mean and variance of R.

respectively. if EF is equal to 7.6 cm find the length of PQ

vertical strut extending from the lower arch to the roadway (as shown in the image). Here the lower arch is 80m above sea level and the upper arch is 49m above the roadway. At the vertices, the lower arch is 118m above sea level and the upper arch is 73m above the roadway. Find the quadratic equations which describe the parabolas of the lower arch in: vertex form, y=a(x-h)^2+k; intercept form, y=a(x-α)(x-β) general form, y=ax^2+bx+c The lower arch intersects the roadway 181.5m from the vertex. Calculate how much higher is the upper arch than the lower at the middle of the bridge? Using technology, determine the total length of all 19 pairs of equally-spaced, vertical struts between the lower arch and the roadway.

decimal. Round your final answer to the nearest hundredth.

't change, but throughout the night the height of the mattress is decreasing. The rate at which it decreases varies over time: at the beginning it is just shrinking a tiny bit, but after a while it starts shrinking faster. If the height of the of the mattress follows the formula h=18-0.2x^2, where h is the height in inches and x is the time in hours, and the length of the mattress is always 74 inches, and the width of the air mattress is always 54 inches, please find the rate at which the VOLUME of the air mattress is changing after 2 hours. V ' = cubic inches per hour after 2 hours. (Round to one decimal place, but take a picture of your work and send it to me if you're worried your answer might be slightly off.)

s $8 per foot, but she wants the fourth side, closest to the road, to be chain link, which is $20 per foot. If she wants the fenced in area to be 1160 square feet, find the dimensions that will minimize her cost. What is that minimum cost? (So there are three parts to your answer: length of the rectangle, width of the rectangle, and total cost.) SHOW WORK.

t one type of ball has a radius of 2.4 cm . The length and width of the box's square base are both twice the radius, and the balls are packaged four to a box, so that the height is eight times the radius. Find the percentage of the box that is filled. Round your percentage to the nearest hundredth. Also round all intermediate calculations to four decimal places. The percentage of the box that is filled, to the nearest hundredth, is %

by a line 1 and one fifth inches long on the blueprint.

izontal. Its upper end is connected to a wall by a rope, and its lower end rests on a rough, horizontal sur- face. The coefficient of static friction between the beam and surface is ms. Assume the angle u is such that the static friction force is at its maximum value. (a) Draw a force diagram for the beam. (b) Using the condition of rotational equilibrium, find an expression for the tension T in the rope in terms of m, g, and u. (c) Using the condition of trans- lational equilibrium, find a second expression for T in terms of ms, m, and g. (d) Using the results from parts (a) through (c), obtain an expression for ms L u Figure P12.16 Q/C S vertical component of this force. Now solve the same problem from the force diagram from part (a) by com- puting torques around the junction between the cable and the beam at the right-hand end of the beam. Find (e) the vertical component of the force exerted by the pole on the beam, (f) the tension in the cable, and (g) the horizontal component of the force exerted by the pole on the beam. (h) Compare the solution to parts (b) through (d) with the solution to parts (e) through (g). Is either solution more accurate? 19. Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed (Fig. P12.19). Usually, the drawbridge is lowered to a horizontal position so that the end of the bridge rests on the stone ledge. Unfor- tunately, Lost-a-Lot’s squire didn’t lower the draw- involv- ing only the angle u. (e) What happens if the ladder is lifted upward and its base is placed back on the ground slightly to the left of its position in Figure P12.16? Explain.

e investigations we determined that the program input size can be varied in a wide range and for N-bit input the program result is also always N – Bit long. Additionally we found that the program working time depends significantly on input length N, especially when N is greather than 10- 15 . Our test also revealed, that the program working time depends only on input length ,not the input itself. During our tests, we fixed the following working times (with an accuracy of one hundredth of a second) N = 2 – 16.38 seconds N = 5 – 16.38 seconds N = 10 – 16.44 seconds N = 15 – 18.39 seconds N = 20 – 1 minute 4.22 seconds We also planned to test the program for N = 25 and N = 30, but for both cases the program didn’t finish within half and hour was forced to terminate it. Finally, we decided for N = 30 to not terminate the program,but to wait a little bit longer.The result was 18 hours 16 minutes 14.62 seconds . We repeated the test for N = 30 and it gave us exactly the same result, more than 18 hours. Tasks: a) Find the program working times for the following three cases N = 25, N = 40 and N = 50. b) Explain your result and solution process.

les. Draw a neat diagram and find the distance between the instants when the lighthouse 040° T and 120° T. HINT: This is NOT a problem to be solved using cosine rule. Since the distance is constant, the ship will travel along the arc. You should therefore use radian measure to workout the distance along the arc. Also remember that all bearings are from seawards . 2, The length of a shadow of a vertical flag mast 2.5 meters high is 5.2 meters (shadow's length). Find the sun's altitude. 3, From a ship, a light on the edge of a breakwater bore 045° T . The ship was steering a course of 060° T. After travelling for 30 minutes, the same light bore 280° T and distance off 2.0 nautical miles. Find the speed of the vessel.