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2 years ago

The sum of two numbers is 12. The difference of the two numbers is 22. Find the two numbers

Mathematics

1 answer:

valentina_108 [34]2 years ago

7 0

Answer:

-5 and 17

Step-by-step explanation:

The sum of two numbers (let's just say number a and number b) is 12.

a + b = 12

The difference between the same two numbers (still a and b) is 22.

b - a = 22

(Move variable a to the right side to get the following.)

b = 22 + a

(This way, we can substitute b = 22 + a into the first equation, a + b = 12, and solve.)

a + (22 + a) = 12

a + a + 22 = 12

2a = -10

a = -5

a + b = 12

-5 + b = 12

b = 17

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3 years ago

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:

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