Three hundred feet of fencing is available for a rectangular pasture alongside a river, the river serving as one side of the rectangle (so only three sides require fencing). Find the dimensions yielding the greatest area. (Enter your answers as a comma-separated list.)

(150 feet,75 feet)

Step-by-step explanation:

Let

Length of rectangle pasture,l=y

Breadth of rectangle pasture,b=x

Fencing used=300ft

Fencing used=2x+y

300=2x+y

y=300-2x

Area of rectangle pasture=xy

Differentiate w.r.t x

Again, differentiate w.r.t x

Hence, the area is maximum at x=75

Width of rectangle pasture,x=75 feet

Length of rectangle pasture,l=300-2(75)=150 feet

Dimension of rectangle pasture=(l,b)=(150 feet,75 feet)

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.