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kakasveta [241]
3 years ago
15

What’s the slope for (15,8) (10,7)

Mathematics
1 answer:
suter [353]3 years ago
8 0

Answer:

\frac{1}{5} = 0.2  

I hope this helps!

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Use f’( x ) = lim With h ---> 0 [f( x + h ) - f ( x )]/h to find the derivative at x for the given function. 5-x²
beks73 [17]
<h2>Answer:</h2>

The derivative of the function f(x) is:

                 f'(x)=-2x

<h2>Step-by-step explanation:</h2>

We are given a function f(x) as:

f(x)=5-x^2

We have:

f(x+h)=5-(x+h)^2\\\\i.e.\\\\f(x+h)=5-(x^2+h^2+2xh)

( Since,

(a+b)^2=a^2+b^2+2ab )

Hence, we get:

f(x+h)=5-x^2-h^2-2xh

Also, by using the definition of f'(x) i.e.

f'(x)= \lim_{h \to 0} \dfrac{f(x+h)-f(x)}{h}

Hence, on putting the value in the formula:

f'(x)= \lim_{h \to 0} \dfrac{5-x^2-h^2-2xh-(5-x^2)}{h}\\\\\\f'(x)=\lim_{h \to 0} \dfrac{5-x^2-h^2-2xh-5+x^2}{h}\\\\i.e.\\\\f'(x)=\lim_{h \to 0} \dfrac{-h^2-2xh}{h}\\\\f'(x)=\lim_{h \to 0} \dfrac{-h^2}{h}+\dfrac{-2xh}{h}\\\\f'(x)=\lim_{h \to 0} -h-2x\\\\i.e.\ on\ putting\ the\ limit\ we\ obtain:\\\\f'(x)=-2x

      Hence, the derivative of the function f(x) is:

          f'(x)=-2x

3 0
3 years ago
Read 2 more answers
Let f(x)=x^4-3x^3+5x-3, f(-2)
BabaBlast [244]
f(-2)=(-2)^4-3(-2)^3+5(-2)-3&#10;\\f(-2)= 16+24-10-3\\&#10;f(-2)=30-10-3\\&#10;f(-2)=17
8 0
3 years ago
Calculate the sum of the multiples of 4 from 0 to 1000
allochka39001 [22]

Answer:

sum is 125,500

sum in summation notation is \sum\limits_{n=0}^n a+nd= (2a+(n-1)d)n/2

Step-by-step explanation:

This problem can be solved using concept of arithmetic progression.

The sum of n term terms in arithmetic progression is given by

sum = (2a+(n-1)d)n/2

where

a is the first term

d is the common difference of arithmetic progression

_____________________________________________________

in the problem

series is multiple of 4 starting from 4 ending at 1000

so series will look like

series: 0,4,8,12,16..................1000

a is first term so

here a is 0

lets find d the common difference

common difference is given by nth term - (n-1)th term

lets take nth term as 8

so (n-1)th term = 4

Thus,

d = 8-4 = 4

d  can also be seen 4 intuitively as series is multiple of four.

_____________________________________________

let calculate value of n

we have last term as 1000

Nth term can be described

Nth term = 0+(n-1)d

1000 =   (n-1)4

=> 1000 = 4n -4

=> 1000 + 4= 4n

=> n = 1004/4 = 251

_____________________________________

now we have

n = 1000

a = 0

d = 4

so we can calculate sum of the series by using formula given above

sum = (2a+(n-1)d)n/2

       = (2*0 + (251-1)4)251/2

       = (250*4)251/2

     = 1000*251/2 = 500*251 = 125,500

Thus, sum is 125,500

sum in summation notation is \sum\limits_{n=0}^n a+nd= (2a+(n-1)d)n/2

3 0
3 years ago
The cost of a unit is made up of $6.25 material cost, $4.75 labour cost, and $3.25 overhead. What is the ratio that exists betwe
blsea [12.9K]

Answer:

The ratio that exist between this three elements are 25 : 19 : 13.

Step-by-step explanation:

Ratio compares one thing to another. Ratios indicate the comparison of the size of a number to another . One trick about ratio is that you can multiply or divide the ratios by same number. For example the ratio of boy to girls can be represented as 3 : 4. If you multiply the ratios by 2 you will get the ratio 6 : 8 and it still represent the same ratios of boys to girls. Ratios can be written as a fraction for example 3/4 for our example.

The cost of the unit is made up of $6.25 , $4.75 and $3.25.

$6.25  $4.75  $3.25 . Let us multiply by 100 to remove the decimals.

625 : 475 : 325 . Now let simplify the ratios by dividing through by 25.

625/25 : 475/25 : 325/25 . The simplest ratios can be written as follows

The ratios are 25 : 19 : 13.

6 0
3 years ago
Find the sum or difference <br> 1/2 - 1/14<br> A.3/7<br> B.2/7<br> C.4/7
pogonyaev

Answer:

A.3/7

Step-by-step explanation:

1/2 - 1/14

We need to get a common denominator of 14

1/2 * 7/7 = 7/14

7/14 - 1/14 = 6/14

We can simplify by dividing the top and bottom by 2

3/7

7 0
3 years ago
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