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valentinak56 [21]
3 years ago
6

A function f is​ _____ on an open interval I​ if, for any choice of x1 and x2 in​ I, with 1 less than

Mathematics
1 answer:
Zepler [3.9K]3 years ago
3 0

Answer:

If f(x_1)\leq f(x_2) whenever x_1\leq x_2 f is <em>increasing</em> on I.

If f(x_1)\geq f(x_2) whenever x_1\leq x_2 f is <em>decreasing</em> on I.

Step-by-step explanation:

These are definitions for real-valued functions f:I→R. To help you remember the definitions, you can interpret them in the following way:

When you choose any two numbers x_1\leq x_2 on I and compare their image under f, the following can happen.

  • f(x_1)\leq f(x_2). Because x2 is bigger than x1, you can think of f also becoming bigger, that is, f is increasing. The bigger the number x2, the bigger f becomes.
  • f(x_1)\geq f(x_2). The bigger the number x2, the smaller f becomes so f is "going down", that is, f is decreasing.

Note that this must hold for ALL choices of x1, x2. There exist many functions that are neither increasing nor decreasing, but usually some definition applies for continuous functions on a small enough interval I.

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lions [1.4K]
The answer is x= 2/75
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3 years ago
A company is making building blocks. Each building block is a cube and has volume 125/729 ft cubed . How long is each side of th
MariettaO [177]

Answer: The length of each side of the building block is 0.56 feet

Step-by-step explanation:

A company is making building blocks. Each building block is a cube and has volume 125/729 ft cubed . Each of the building blocks has 6 faces which are squares, 8 vertices and 12 edges.

Since a square has all sides to be equal sides,

The volume of the cube = the volume of the building block =

Product of length,L, width, W and height, H.

Volume of the building block = L × W × H

Since length = width = height,

Volume of cube = L^3

From the information given,

Volume of a building block = 125/729ft cubed

L^3 = 125 / 729

Taking cube root of both sides of the equation,

L = cube root of 125/729

L = 5/9

= 0.56 feet

4 0
3 years ago
Ethan bought 4 packages of pencils. After he gave 8 pencils to his friends, he had 40 pencils
LiRa [457]

He had 40 pencils left after he gave away 8, so originally he had 40 + 8 pencils, which is 48.

Now, he bought 4 packages, which had a total of 48 pencils, so divide 48 by 4, which is 12. He had 12 pencils in each package.

To determine the solution arithmetically, first add 8 to 40, then divide 48 by 4.

To determine the solution algebraically, set up and solve the equation 40 = 4x - 8.

Each package contained 12 pencils.

Hope this helps

8 0
3 years ago
a sewing club is making a quilt consisting of 25 squares with each side of a square measuring 30cm.lf the quilt has 5 rows and 5
Lera25 [3.4K]
The total area is 625 because 25 x 5 = 125. 125 x 5 = 625. that is how you get your answer
5 0
3 years ago
A beekeeper has 65,000 female bees and 700 male bees in one colony. A disease kills % of the female bees and % of the male bees.
Paha777 [63]

Complete Question

A beekeeper has 65,000 female bees and 700 male bees in one colony. A disease kills 25% of the female bees and 14% of the male bees. After the disease hits the colony, the beekeeper decides to sell LaTeX: \frac{1}{2} 1 /2 of the remaining female bees to a friend.

How many total bees are left in the beekeeper’s colony after the disease and sale?

Answer:

24977 bees

Step-by-step explanation:

From the above question:

Number of female bees = 65,000

Number of male bees = 700

A disease kills 25% of the female bees and 14% of the male bees.

Number of female bees killed = 25% × 65,000

= 16,250 bees

Amount of female bees left = 65,000 - 16,250

= 48750 bees

Number of male bees killed = 14% × 700

= 98

Amount of male bees left = 700 - 98

= 602 bees

After the disease hits the colony, the beekeeper decides to sell LaTeX: \frac{1}{2} 1 /2 of the remaining female bees to a friend.

Hence:

1/2 × 48750 bees

= 24375 bees

Total bees are left in the beekeeper’s colony after the disease and sale is calculated as:

24375 female bees + 602 male bees

= 24977 bees

4 0
2 years ago
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