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nlexa [21]
2 years ago
5

How is the derivative of a function related to the slop of the function?

Mathematics
1 answer:
statuscvo [17]2 years ago
7 0

Hi there!

The derivative of the function is the slope of the function at a specific x-value, or its instantaneous rate of change.

For example, take the equation y = x².

Using the power rule, we get:

y' = 2x

If we plug in any x-value into this equation, we can find the slope of the function at any point.

Ex:

x = 0; 2(0) = slope of 0

x = 2; 2(2) = slope of 4

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Use the Binomial Theorem to expand each binomial (5x-4y)^3
jek_recluse [69]
You should know that:

(a+b)(a+b)(a+b)

=a(a+b)(a+b)+b(a+b)(a+b)

=a(a²+2ab+b²)+b(a²+2ab+b²)

=a³+2a²b+ab²+a²b+2ab²+b³

=a³+3a²b+3ab²+b³

-----------------

If a=5x and b=-4y

(5x+(-4y))³

=(5x-4y)³

=(5x)³+3(5x)²(-4y)+3(5x)(-4y)²+(-4y)³

=125x³+3(25x²)(-4y)+15x(16y²)-64y³

=125x³+75x²(-4y)+240xy²-64y³

=125x³-300x²y+240xy²-64y³
5 0
3 years ago
Solve -2a -5 > 3 Which graph shows the solutions?
gogolik [260]

Answer: a< -4 D

Step-by-step explanation:

5 0
3 years ago
What is the value of the expression 5^2 + 2^2?
leva [86]
It would be 7x7 + 2x2 = 53
8 0
2 years ago
GOAT is a parallelogram. Find the length of AG.
Scilla [17]

Answer:

AG = 16

Step-by-step explanation:

If you have a parallelogram, then the diagonals are bisected, meaning GS and SA are congruent, same with OS and ST. So, because 8 + 8 = 16, the length of AG = 16.

3 0
3 years ago
If 30g of sugar is needed to make 4 cakes how much grams of sugar is needed to make 7 cakes
arsen [322]
There's two ways to do this.

The first way:
Work out the amount of sugar needed to make one cake, and then multiply that by 7.

30 grams ÷ 4 cakes = 7.5 grams for 1 cake.
7.5 grams × 7 cakes = 52.5 grams for 7 cakes.

The second way:
Work out the ratio of sugar:cake by doing 7 ÷ 4, and then multiplying that value by 30.

7 cakes ÷ 4 cakes = 1.75
1.75 × 30 grams = 52.5 grams for 7 cakes. 

Either way, the answer is 52.5 grams.
6 0
3 years ago
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