Write each repeating decimal as a fraction. 0.888

How many microseconds are in one second?

dem82 [27]

1 sec = 1000000 microsecond

4 0

3 years ago

Where is the circumcenter of this triangle located?

eduard

We know that the diagonals of a rectangle bisect each other.

So, If we draw the second diagonal of the rectangle, it will bisect the first diagonal, which is the hypotenuse of the triangle.

Also, in a rectangle, the bisectors of the sides and the diagonals are concurrent.

Hence, if we draw bisectors of the two sides of the given triangle, these bisectors and the second diagonal, which is the bisector of the hypotenuse, meet at a point.

Circumcenter of a triangle is nothing but the point of intersection of the bisectors of the sides of the triangle.

Since the above bisectors and the hypotenuse (the first diagonal of the rectangle) are concurrent, the circumcentre lies on the hypotenuse.

Hence, the circumcenter lies on the hypotenuse of the triangle.

7 0

3 years ago

The number of fish in a small bay is modeled by the function F defined by F(t)=10 (t3 â 12t2 + 45t +100), where t is measured in

RSB [31]

The graph of the given function is attached showing characteristics of the function.

The correct responses are;

(a) F'(4) = -30 means that on day 4, the number of fish in the bay is decreasing at a rate of 30 fish per day.

(b) Over the interval 0 ≤ t ≤ 8 the absolute minimum number of fish in the bay is; 1,000.

(c) The values of t at which the rate of change is decreasing is; 3 ≤ t ≤ 8

(d) The rate of change of the number of pelicans flying near is; P' = 10·(3·c² - 24·c + 45)

Reasons:

The given function is; f(t) = 10·(t³ - 12·t² + 45·t + 100)

Where;

t = Number of days

0 ≤ t ≤ 8

(a) The derivative of the given function is presented as follows;

F'(t) = 10 × (3·t² - 2×12·t + 45) = 10·(3·t² - 24·t + 45)

Therefore;

F'(4) = 10 × (3 × 4² - 24 × 4 + 45) = -30

Therefore F'(4) = -30 means that on day 4, the number of fish in the bay is decreasing at 30 fish per day.

(b) The absolute minimum is given as follows;

At a minimum or maximum value, F'(t) = 10·(3·t² - 24·t + 45) = 0

Which gives;

3·(t - 5)·(t - 3) = 0

t = 5, or t = 3

At t = 5, we have;

f(5) = 10 × (5³ - 12 × 5² + 45 × 5 + 100) = 1,500

At t = 3, we have;

f(3) = 10 × (3³ - 12 × 3² + 45 × 3 + 100) = 1,540

Therefore, f(5) = 1,500 is a local maximum

However, at x = 0, we have;

f(0) = 10 × (0³ - 12 × 0² + 45 × 0 + 100) = 1000

At x = 8, we have;

f(8) = 10 × (8³ - 12 × 8² + 45 × 8 + 100) = 2,040

Therefore, the absolute minimum is given at t = 8, where f(t) = 1,000

(c) The values of t at which the rate of change in the number of fish in the

bay is decreasing is between the local maximum at t = 3, and the local

minimum at t = 5, which gives;

The rate of change of the number of fish is decreasing for values of t in the range;

3 ≤ t ≤ 5

(d) P = 10·(t³ - 12·t² + 45·t + 100)

P' = 10·(3·t² - 24·t + 45)

At time t = c, we have;

P' = 10·(3·c² - 24·c + 45)

Based on a similar question online, we have;

(c) The interval over which the rate of change is decreasing

(d) The rate of change of the number of pelicans flying near the bay at t = c

Learn more about differentiation of functions here:

brainly.com/question/1422315

5 0

2 years ago

In triangle abc the measure of angle a = measure of angle b + 30, the measure of angle c = measure of angle b + 60. find the mea

Morgarella [4.7K]

B 60.5
a 90.5
c 120.5
follow the steps in the picture

4 0

4 years ago

Find the values of m and n that make equation true. 8+15i=2m+3ni

Brilliant_brown [7]

gthy67jntgrt67u89i7yu holfcedikjnhfnhtfrolwsfr n/lkjhfwr3n oljfu vikr8hneikoeOPDTE85417

+TE4TE

8 0

3 years ago