The number of hours, t, that bacteria spread 10-fold can be modeled by the equation B(t) = B0(10)4t. There are 50 bacteria present initially and a biologist wishes to find out how many hours will elapse until there are 10,000 bacteria present. What is the exact value for the number of hours elapsed, t, in the equation 10,000 = 50(10)4t?

t = (log200)/4 hours

Step-by-step explanation:

10,000 = 50(10)^(4t)

Divide both sides by 50

200 = 10^(4t)

Take the log of both sides

log200 = 4t

Divide both sides by 4

(log200)/4 = t

t = (log200)/4    (exact answer)

t ≈ 0.575257498915995 (numeric approximation)

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.