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3 years ago

Ap calc multiple choice question; attached below please explain how, please!

Mathematics

1 answer:

anygoal [31]3 years ago

5 0

Answer:

C. $\frac{f(b)-f(1)}{b-1}=20$

General Formulas and Concepts:

Calculus

Mean Value Theorem (MVT) - If f is continuous on interval [a, b], then there is a c∈[a, b] such that $f'(c)=\frac{f(b)-f(a)}{b-a}$

MVT is also Average Value

Step-by-step explanation:

Step 1: Define

$f(x)=e^{2x}$

f'(c) = 20

Interval [1, b]

Step 2: Check/Identify

Function [1, b] is continuous.

Derivative [1, b] is continuous.

∴ There exists a c∈[1, b] such that $f'(c)=\frac{f(b)-f(a)}{b-a}$

Step 3: Mean Value Theorem

Substitute: $20=\frac{ f(b)-f(1)}{b-1}$
Rewrite: $\frac{ f(b)-f(1)}{b-1}=20$

And we have our final answer!

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How many criteria does a living organism have to meet to be classified as living? Justify your answer.

otez555 [7]

1. Living Things are Composed of Cells:
Single-cell organisms have everything they need to be "self-sufficient". In multicellular organisms, specialization increases until some cells do only certain things.
2. Different Levels of Organization:
Living things must be able to organize simple substances into complex ones.
Living things organize cells at several levels:
Tissue - a group of cells that perform a common function.
Organ - a group of tissues that perform a common function.
Organ system - a group of organs that perform a common function.
Organism - any complete living thing
3. Living Things Use Energy:
Living things take in energy and use it, for maintenance and growth.
4. Living Things Respond To Their Environment:
Living things will make changes in response to a stimulus in their environment. A behavior is a complex set of responses.
5. Living Things Grow:
Cell division - the orderly formation of new cells.
Cell enlargement - the increase in size of a cell. Cells grow to a certain size and then divide.
An organism gets larger as the number of its cells increases.
6. Living Things Reproduce:
Reproduction is not essential for the survival of individual organisms, but must occur for a species to survive.
All living things reproduce in one of the following ways:
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7. Living Things Adapt To Their Environment:
Adaptations are traits giving an organism an advantage in a certain environment.
Variation of individuals is important for a healthy species.

8 0

3 years ago

1) 2 (x+3) +3 (5-x)=

Ugo [173]

Answer:

Below

Step-by-step explanation:

1. 2 (x+3) +3 (5-x)=

Simplifying

2(x + 3) + 3(5 + -1x) = 0

Reorder the terms:

2(3 + x) + 3(5 + -1x) = 0

(3 * 2 + x * 2) + 3(5 + -1x) = 0

(6 + 2x) + 3(5 + -1x) = 0

6 + 2x + (5 * 3 + -1x * 3) = 0

6 + 2x + (15 + -3x) = 0

Reorder the terms:

6 + 15 + 2x + -3x = 0

Combine like terms: 6 + 15 = 21

21 + 2x + -3x = 0

Combine like terms: 2x + -3x = -1x

21 + -1x = 0

Solving

21 + -1x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-21' to each side of the equation.

21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0

0 + -1x = 0 + -21

-1x = 0 + -21

Combine like terms: 0 + -21 = -21

-1x = -21

Divide each side by '-1'.

x = 21

Simplifying

x = 21

2. 3 (y+2) -4y=-24y

Simplifying

3(y + 2) + -4y = -24y

Reorder the terms:

3(2 + y) + -4y = -24y

(2 * 3 + y * 3) + -4y = -24y

(6 + 3y) + -4y = -24y

Combine like terms: 3y + -4y = -1y

6 + -1y = -24y

Solving

6 + -1y = -24y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '24y' to each side of the equation.

6 + -1y + 24y = -24y + 24y

Combine like terms: -1y + 24y = 23y

6 + 23y = -24y + 24y

Combine like terms: -24y + 24y = 0

6 + 23y = 0

Add '-6' to each side of the equation.

6 + -6 + 23y = 0 + -6

Combine like terms: 6 + -6 = 0

0 + 23y = 0 + -6

23y = 0 + -6

Combine like terms: 0 + -6 = -6

23y = -6

Divide each side by '23'.

y = -0.2608695652

Simplifying

y = -0.2608695652

3. -(x+2) -2(1-x)=

Simplifying

-1(x + 2) + -2(1 + -1x) = 0

Reorder the terms:

-1(2 + x) + -2(1 + -1x) = 0

(2 * -1 + x * -1) + -2(1 + -1x) = 0

(-2 + -1x) + -2(1 + -1x) = 0

-2 + -1x + (1 * -2 + -1x * -2) = 0

-2 + -1x + (-2 + 2x) = 0

Reorder the terms:

-2 + -2 + -1x + 2x = 0

Combine like terms: -2 + -2 = -4

-4 + -1x + 2x = 0

Combine like terms: -1x + 2x = 1x

-4 + 1x = 0

Solving

-4 + 1x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.

-4 + 4 + 1x = 0 + 4

Combine like terms: -4 + 4 = 0

0 + 1x = 0 + 4

1x = 0 + 4

Combine like terms: 0 + 4 = 4

1x = 4

Divide each side by '1'.

x = 4

Simplifying

x = 4

4. whats ? is the equation

6 0

4 years ago

What are the steps to converting 86,000cm to km

yarga [219]

100 cm = 1 m => 1 cm = 1/100 m so, 86000 cm = 86000 * (1/100) m = 86000/100 m = 860 m now, 1000 m = 1 km => 1 m = 1/1000 km so, 860 m = 860 * (1/1000) km = 860/1000 km = 0.86 km so, 86000 cm = 0.86 km

8 0

3 years ago

Which expression has the same value as -3+(-5)?

Setler [38]

C because both equations make -8

6 0

4 years ago

Read 2 more answers

If f(x)=log10x, what is the approximate value of y in the equation 10^y=5?

Simora [160]

$\bf log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\
-----------------------------\\\\
10^y=5\implies log(10^y)=log(5)\implies ylog(10)=log(5)\\\\\\ y=\cfrac{log(5)}{log(10)}\\\\
-----------------------------\\\\
\textit{Logarithm Change of Base Rule}\\\\
log_{{ a}}{{ b}}\implies \cfrac{log_{{ c}}{{ b}}}{log_{{ c}}{{ a}}}\\\\
-----------------------------\\\\
y=\cfrac{log(5)}{log(10)}\iff y = log_{10}(5)\iff y=log(5)$

7 0

4 years ago