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LiRa [457]
3 years ago
13

Given f of x equals 5 times x minus 6 for x less than 3, equals x squared for x between 3 and 5 inclusive, and equals 2 times x

plus 15 for x greater than 5 find f '(x) and give its domain.
Mathematics
1 answer:
konstantin123 [22]3 years ago
7 0

Answer:

<em>D. 5 for x less than or equal to 4, equals 2x for x between 4 and 6 including 6, and equals 4 for x greater than 6 Domain: All real number</em>s.

Step-by-step explanation:

Find the complete diagram attached

First we need to get the derivative of the functions

For the function f(x) = 5x - 6

Using the formula

If f(x) = axⁿ

f'(x) = naxⁿ⁻¹

For the function f(x) = 5x - 6

f'(x) = 1(5)x¹⁻¹

f'(x) = 5x⁰

f'(x) = 5

For the function f(x) =x²-2

f'(x) = 2x²⁻¹

f'(x) = 2x

For the function f(x) = 4x+10

f'(x) = 1(4)x¹⁻¹

f'(x) = 4x⁰

f'(x) = 4

Get the domain

The domain is the value of the input variable x for which the functions exists. For the functions given, the domain will be on all real numbers i.e the functions will exists for any value of x on the number line.

Hence Option D is correct

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Simplify by using order of operations: 4 + (9∙2) ÷ (4 - 1) - 4
Stella [2.4K]

Answer:

20

Step-by-step explanation:

Use <u>PEMDAS</u>

P = parenthesis

E = Exponents

M = Multiplication*

D = Division*

A = Addition**

S = Subtraction**

*either can come first, it just depends which comes first in the equation.

**either can come first, it just depends which comes first in the equation.

<em>Step 1 : Write equation</em>   4( 9 × 2 ) ÷ ( 4 -1 ) - 4

<em>Step 2: Solve in parenthesis   </em>4(18) ÷ (3) - 4

<em>Step 3: Solve multiplication   </em> 72 ÷ 3 - 4

<em>Step 4: Solve division               </em>24 - 4

<em>Step 5 : Solve subtraction</em>         20

3 0
3 years ago
Read 2 more answers
A#27 - Surface Area
ollegr [7]

Answer:

Step-by-step explanation:

Surface area is finding the area of each face and adding them up.  So a cube will have 6 faces, each of them a square.  So find the area of one face and you can just add it 6 times.  If the faces are not all the same you have to find them seperately.  I won't do all of your questions, but let me know if you need help with a specific one

1) there are two trianglular faces and three rectangular ones.  The triangles are the same so let's do those.  They have the base and height of 4 and 3, so area of both will be .5*4*3 = 6, so together that makes 12.  now the three rectangular sides.  Right away you can see there is a 3 by 10 one and a 4 by 10 one.  These ahve areas of 30 and 40 respectfully.  The final face has one length of 10 but the last one is actually the last side of the right triangle faces.  Use the Pythagorean theorem to find it, it word out to be 5.  So now we know the last face is 10 by 5 which means an area of 50.  So let's add them all together.  5 faces total with areas of 30, 40, 50, 6 and 6.  Adding them together makes 136.

If you don't get how I did any of that let me know.  In general it's a good idea to mark every face and then find what their sides are.  I'd be happy to help with specific problems.

Now the second part, again I will do the second one because cones are  little less intuitive.  a cone has two faces, the circular base and the actual cone shape.  the surface area of the cone shape is pi*r*L where r is the radius of the base and L is the length of one of the slanted sides.  Now, let's find the area of the two faces.  Area of a circle is pi*r^2 so that's pi*4^2 = 16*pi in number 2.  Then the area of the cone part is pi*r*L = pi*4*14 = 56*pi.  now we sum all the areas of the faces up and get 16*pi + 56*pi = 72*pi.  

Again, I'm happy to answer specific questions, so let me know if you have any.  just keep in mind what I told you so far, find each face, then find each face's area then sum them up.  For cylinders the tubes turn into rectangles where one side is the length of the tube and the other is the circumference, while cones fave two faces, the circular base and the cone shape itself with an area of pi*r*L.  if you want me to check your answers I will totally do that too.  

4 0
3 years ago
P<br> __ =6<br><br> 5<br> What does P mean?
Yuri [45]
To find (P) you turn the fraction into an imoroper fraction 

5x6 =30  

30/5 =6 
p=30 
  
Ps this is easy if your memerized your muliplacation 

5 0
3 years ago
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Answer:

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Step-by-step explanation:

a : b = 3 : 4 ....(given)\\  \\ let \: a = 3x \\ b = 4x \\  \\ (6a - 3b) : (5a + 2b) \\  \\  =  \frac{(6a - 3b)}{(5a + 2b)}  \\  \\  = \frac{6(3x) - 3(4x)}{5(3x) + 2(4x)} \\  \\  =  \frac{18x- 12x}{15x+ 8x} \\  \\  = \frac{6x}{23x} \\  \\  =  \frac{6}{23}  \\  \\ (6a - 3b) : (5a + 2b) = 6  : 23

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