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shusha [124]
3 years ago
9

What is the relationship between limits and derivatives? Explain with examples of your own.

Mathematics
1 answer:
andre [41]3 years ago
5 0

Answer:

Step-by-step explanation:

Assume you have a function of x, call it f(x).

The limit of the function as x approaches some number represents the value of f with respect to x.  

The derivative of f(x) represents the rate of change of the function at x.

So the derivative would give you the rates of change of the function as x approaches some number.  

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Simplify the following expressing. Show your work and explain each step. <br><br> 7-(5-3(2+6(2^2)))
Anon25 [30]

Answer:

80

Step-by-step explanation:

7-(5-3(2+6(2^2)))

When a question has multiple signs, the rule of BODMAS is used. That is, Bracket Of Division Multiplication Addition and Subtraction. The question above will therefore be solved in that order.

The first bracket, we have 2^2

That gives 4

Rewriting the question will give

7-(5-3(2+6(4)))

The question in the next bracket will follow

(2+6(4))

In this bracket too, we have the plus sign and the multiplication sign, so the multiplication will first be solved, them addition will follow.

(2+24)

(26)

Rewriting the question again, we have

7-(5-3(26))

And then, we have the last bracket

(5-3(26))

But we have both the Subtraction sign and the Multiplication sign in this bracket also, so the multiplication will first be solved, before the Subtraction.

(5-3(26))

(5-78)

(-73)

And lastly we have

7-(-73)

7+73

80

5 0
3 years ago
Daniela is a stain glass artist; she created the window below for her living room. What is
OLga [1]
The window has a shape of a semi-circle (half of a circle).

We know the diameter d = 12 ft.

The area of a (complete) circle is given by the formula:
A = π × r²

The radius can be found by halving the diameter:
r = d ÷ 2
  = 12 ÷ 2
  = 6 ft

Therefore the area of the circle will be:
<span>A = π × r²
    = 3.14 × 6</span>²
    = <span>3.14 × 36
    = 113.04 ft²

And the area of the semi-circle:
A = </span><span>113.04 </span>÷ 2
   = 56.52 ft²

Hence, the area of the window will be 56.52 ft².
3 0
3 years ago
Farmer tom has chickens and sheep he counts 48 heads and 134 legs how many sheep does he have
just olya [345]
Because each chicken has 2 legs you divide 134 by 2 which is 67 then 24 which basically means he has 36 sheep in total. Hope this helped
4 0
2 years ago
I need help with #4 a-d
lesya [120]

a repeating decimal is placed over 9's instead of 0's.   for example: 0.23 = \frac{23}{100}, but 0.232323... = \frac{23}{99}

a) x = 0.121212

b) 100(x) = 100(0.121212)

    100x  = 12.1212

c)  100x = 12.1212

-  <u>        x =   0.1212</u>

     99x  =  12

         x  = \frac{12}{99}

d) -2\frac{12}{99}  <em>= -2\frac{4}{33} when simplified</em>

The number is rational becase it has a repeating decimal

6 0
3 years ago
Please help with #5 and #8! I don’t really know all of the info to find the volume! (Composite Figures)
bagirrra123 [75]
It looks like you're doing good with breaking-down the composite into digestible pieces. So, don't stress too much!

Keep in mind that the area for a 3D shape is Bh, where "B" is the area of a face & "h" is the height.

#5
Shape A is 3X4X9.
First, calculate the area of a face:

9X4= 36

Multiply by height:

36X3= 108

The process is the same with shape B.
3X4X8
Calculate area of face:

8X4= 32

Multiply by height:

32X3= 96

Now you add both areas:

108+96= 204 cubic feet

I think you're doing pretty good, just don't over think things too much. Try #8 with the similar process seen here. Just comment if you get stuck.

Hope this helps!
6 0
3 years ago
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