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3 years ago

How would knowing the slope of a linear function help determine whether a function is increasing or decreasing?

Mathematics

2 answers:

Naya [18.7K]3 years ago

8 0

Answer:

If the slope is positive, it signifies the function is increasing, and if it's negative, it's decreasing. If the slope is exactly 0, the function is stagnant, a horizontal line

leonid [27]3 years ago

7 0

Answer:

Step-by-step explanation:

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Calculate the volume of the prism below with measurements a = 11, b = 5, and c = 10.

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The volume of the prism is 550

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What is the surface area of the right rectangular prism?

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3 years ago

Ethan planted a tree that was 1.85 meter's tall. Several years later, the tree is 5.30 Meter's tall. Which equation can be used

LUCKY_DIMON [66]

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5.30= x+1.5

x equals the difference

Step-by-step explanation:

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3 years ago

To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equati

Ad libitum [116K]

Answer:

$m = \frac{1}{12}$

Step-by-step explanation:

Given

$(x,y) = (36,6)$

$f(x) = \sqrt x$ ----- the equation of the curve

Required

The slope of f(x)

The slope (m) is calculated using:

$m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}$

$(x,y) = (36,6)$ implies that:

$a = 36; f(a) = 6$

So, we have:

$m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}$

$m = \lim_{h \to 0} \frac{f(36 + h) - 6}{h}$

If $f(x) = \sqrt x$ ; then:

$f(36 + h) = \sqrt{36 + h}$

So, we have:

$m = \lim_{h \to 0} \frac{\sqrt{36 + h} - 6}{h}$

Multiply by: $\sqrt{36 + h} + 6$

$m = \lim_{h \to 0} \frac{(\sqrt{36 + h} - 6)(\sqrt{36 + h} + 6)}{h(\sqrt{36 + h} + 6)}$

Expand the numerator

$m = \lim_{h \to 0} \frac{36 + h - 36}{h(\sqrt{36 + h} + 6)}$

Collect like terms

$m = \lim_{h \to 0} \frac{36 - 36+ h }{h(\sqrt{36 + h} + 6)}$

$m = \lim_{h \to 0} \frac{h }{h(\sqrt{36 + h} + 6)}$

Cancel out h

$m = \lim_{h \to 0} \frac{1}{\sqrt{36 + h} + 6}$

$h \to 0$ implies that we substitute 0 for h;

So, we have:

$m = \frac{1}{\sqrt{36 + 0} + 6}$

$m = \frac{1}{\sqrt{36} + 6}$

$m = \frac{1}{6 + 6}$

$m = \frac{1}{12}$

<em>Hence, the slope is 1/12</em>

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3 years ago

the number is 57,733 contains two sets of digits in which one digit is ten times as great as the other. what are the values of t

Afina-wow [57]

In 57,733 the values are:

5 is for tens
The first 7 is for ones
The second 7 is for tenths
The first 3 is for hundredths
The second 3 is for thousandths

Two set of digit in which one digit is ten times as great as the other are 3 and 3, as well as 7 and 7

It's because 0,03 is ten times as much as 0,003 and 7 is ten times as much as 0,7.

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3 years ago

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