A surveyor measures the distance across a straight river by the following method (Fig. P1.6). Starting directly across from a tree on the opposite bank, she walks d = 100 m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is 0 = 35.0. How wide is the river? Figure P1.6

In general, when a derived unit becomes complicated (involves too many standard units), what is done?

One student uses a meterstick to measure the thickness of a textbook and obtains 4.3 cm 0.1 cm. Other students measure the thickness with vernier calipers and obtain four different measurements: (a) 4.32 cm 0.01 cm. (b) 4.31 cm 0.01 cm, (c) 4.24 cm 0.01 cm, and (d) 4.43 cm 0.01 cm. Which of these four measurements, if any, agree with that obtained by the first student?

The arc length formula says the length s of arc subtended by angle Ɵ in a circle of radius r is given by the equation s=rƟ. What are the dimensions of (a) s, (b) r, and (c) Ɵ?

A fathom is a unit of length, usually reserved for measuring the depth of water. A fathom is approximately 6 ft in length. Take the distance from Earth to the Moon to be 250 000 miles, and use the given approximation to find the distance in fathoms.

A) A pyramid has a height of 488 ft and its base covers an area of 10.0 acres. The volume of a pyramid is given by the expression: V=1/3Bh, where B is the area of the base and h is the height. Find the volume of the pyramid in cubic meters. (1 acre = 43,560ft^2). B) What If? If the height of the pyramid were increased to 525 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increase?

A rectangular box for a new product is designed in such a way that the three dimensions always have a particular relationship defined by the variable x. The volume of the box can be written as (6x^3)+(31x^2)+(53x)+30, and the height is always x+2. What are the width and length of the box?

a) A pyramid has a height of 484 ft and its base covers an area of 11.0 acres (see figure below). The volume of a pyramid is given by the expression V = where B is the area of the base and h is the height. Find the volume of this pyramid in cubic meters. (1 acre = 43,560 ft2) 2.19*10**6 m3 b) What If? If the height of the pyramid were increased to 519 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of th pyramid increase? X %

A sphere of radius r has surface area A = 4πr2 and volumeV = (4/3)πr3. If the radius of sphere 2 is double the radiusof sphere 1, what is the ratio of (a) the areas, A2/A1 and(b) the volumes, V2 /V1 ?