A patio is made of two sections. One is shaped like a trapezoid, and the other like a semicircle. The bases of the trapezoid are 12 feet and 8 feet. The height of the trapezoid is 4 feet. The diameter of the semicircle is the same as the trapezoid's shorter base. Find the patio's area. Use 3.14 for pi.

65.12 ft^2

Step-by-step explanation:

Patio's area = area of trapezoid + area of semicircle

Area of a trapezoid = 1/2  x (sum of the lengths of the parallel sides) x height

1/2 x ( 12 + 8) x 4 = 40 ft^2

Area of semicircle =  (1/2)πr²

r = 8/2 = 4ft

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

(1/2) x 3.14 x 4^2 = 25.12 ft^2

Area of patio = 40 ft^2 +  25.12 ft^2  = 65.12 ft^2

t = 40

25.12

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47