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3 years ago

What is the next number in the pattern below 16,24,32,40,48

Mathematics

2 answers:

avanturin [10]3 years ago

4 0

56 as the pattern is add 8

Charra [1.4K]3 years ago

4 0

56 is the answer add 8

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Differentiate the following by using "limit"

Nat2105 [25]

Answer:

$\rm \displaystyle \frac{d }{dx} \sqrt{x} = \frac{ 1 }{ 2\sqrt{x } }$

Step-by-step explanation:

we want to differentiate the following by using limit:

$\displaystyle \frac{d}{dx} \sqrt{x}$

derivative definition by limit given by

$\rm \displaystyle \frac{d}{dx} = \lim _{\Delta x \to 0} \left( \frac{f(x + \Delta x) - f(x)}{ \Delta x} \right)$

given that,

f(x)=√x

so,

f(x+∆x)=√(x+∆x)

thus substitute:

$\rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ \sqrt{x + \Delta x}- \sqrt{x} }{ \Delta x} \right)$

multiply both the numerator and denominator by the conjugate of the numerator:

$\rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ \sqrt{x + \Delta x}- \sqrt{x} }{ \Delta x} \times \frac{ \sqrt{x + \Delta x} + \sqrt{x} }{\sqrt{x + \Delta x} + \sqrt{x}} \right)$

simplify which yields:

$\rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ (\sqrt{x + \Delta x}) ^{2} - x }{ \Delta x(\sqrt{x + \Delta x} + \sqrt{x})} \right)$

simplify square:

$\rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{ \Delta x \to 0} \left( \frac{ x + \Delta x - x }{ \Delta x(\sqrt{x + \Delta x} + \sqrt{x})} \right)$

collect like terms:

$\rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ \Delta x }{ \Delta x(\sqrt{x + \Delta x} + \sqrt{x})} \right)$

reduce fraction:

$\rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ 1 }{ (\sqrt{x + \Delta x} + \sqrt{x})} \right)$

get rid of ∆x as we are approaching its to 0

$\rm \displaystyle \frac{d }{dx} \sqrt{x} = \frac{ 1 }{ \sqrt{x } + \sqrt{x}}$

simplify addition:

$\rm \displaystyle \frac{d }{dx} \sqrt{x} = \frac{ 1 }{ 2\sqrt{x } }$

and we are done!

7 0

3 years ago

Showton Middle School has 840 students. Teresa surveys a random sample of 60 students and finds that 8 of them have more than 3

Digiron [165]

Answer:

112

Step-by-step explanation:

Total students = 840

Number of students surveyed = 60

Number of students of the 60 with siblings > 3 = 8

Number of students of the 840 with siblings > 3 = 840/60*8 = 112

5 0

3 years ago

Please answer quick, I will choose brainliest answer, thank you!

sammy [17]

The second graph is the correct graph

6 0

4 years ago

Izzy was running up the street. She ran 2.35 and her friend Ozzie ran 2.45. Can you add these decimals?

mojhsa [17]

Yes you can add the decimals

7 0

3 years ago

2x+5-3x=8(x+1); solve for x.

aev [14]

We are given:

2x + 5 - 3x = 8(x + 1)

We can start with several things. First, we can combine the x terms on the left side of the equation, and apply the distributive property on the right side of the equation.

5 - x = 8x + 8

Now, we can add x to both sides, and subtract 8 from both sides to isolate the variable.

5 - x = 8x + 8

-8 + x + x -8

We end up with:

9x = -3

By dividing both sides by 9, we get x = $-\frac{1}{3}$ .