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inn [45]
2 years ago
6

Plzz help

Mathematics
1 answer:
Lina20 [59]2 years ago
5 0

Answer:

$14

Step-by-step explanation:

40% of 10 is 4

4+10=14

hope this helps

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**Spam answers will not be tolerated**
Morgarella [4.7K]

Answer:

f'(x)=-\frac{2}{x^\frac{3}{2}}

Step-by-step explanation:

So we have the function:

f(x)=\frac{4}{\sqrt x}

And we want to find the derivative using the limit process.

The definition of a derivative as a limit is:

\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

Therefore, our derivative would be:

\lim_{h \to 0}\frac{\frac{4}{\sqrt{x+h}}-\frac{4}{\sqrt x}}{h}

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

=\lim_{h \to 0}\frac{4(\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x})}{h}

Place the 4 in front:

=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}(\frac{\sqrt{x+h}\sqrt x}{\sqrt{x+h}\sqrt x})

Distribute:

=4\lim_{h \to 0}\frac{({\sqrt{x+h}\sqrt x})\frac{1}{\sqrt{x+h}}-(\sqrt{x+h}\sqrt x)\frac{1}{\sqrt x}}{h({\sqrt{x+h}\sqrt x})}

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

=4 \lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

= 4\lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }(\frac{\sqrt x +\sqrt{x+h})}{\sqrt x +\sqrt{x+h})}

The numerator will use the difference of two squares. Thus:

=4 \lim_{h \to 0} \frac{x-(x+h)}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}

Simplify the numerator:

=4 \lim_{h \to 0} \frac{x-x-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}\\=4 \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}

Both the numerator and denominator have a h. Cancel them:

=4 \lim_{h \to 0} \frac{-1}{(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}

Now, substitute 0 for h. So:

=4 ( \frac{-1}{(\sqrt{x+0}\sqrt x)(\sqrt x+\sqrt{x+0})})

Simplify:

=4( \frac{-1}{(\sqrt{x}\sqrt x)(\sqrt x+\sqrt{x})})

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

=4( \frac{-1}{(x)(2\sqrt{x})})

Multiply across:

= \frac{-4}{(2x\sqrt{x})}

Reduce. Change √x to x^(1/2). So:

=-\frac{2}{x(x^{\frac{1}{2}})}

Add the exponents:

=-\frac{2}{x^\frac{3}{2}}

And we're done!

f(x)=\frac{4}{\sqrt x}\\f'(x)=-\frac{2}{x^\frac{3}{2}}

5 0
3 years ago
Your $440 gets 5.8% interest compounded annually for 8 years. What will your
ladessa [460]

Answer:

492.52

Step-by-step explanation:

The formula is P(t) = P(0) x (1+r/n)^nt so...

P(t) = 440 (1+0.058/1)^8

P(t) = 492.52

3 0
3 years ago
The ten's digit of a two digit number is 1 more than 4 times the units' digit. if 63 is subtracted from the number, the order of
ser-zykov [4K]
Let x be the digit in the tens place and y be the digit in the ones place.
so, the digit is xy
<span>
The ten's digit of a two digit number is 1 more than 4 times the units' digit.
</span>x = 4y + 1

<span>63 is subtracted from the number, the order of the digits is reversed
</span>10x + y - 63 = 10y + x
9x - 9y = 63

x = 4y + 1 ------------ (1)
9x - 9y = 63  ---------- (2)

Sub (1) into (2)
9(4y + 1) - 9y = 63
36y + 9 - 9y = 63
27y = 63 - 9
27y = 54
y = 2 ------- sub into (1)

x = 4(2) + 1 = 9

x = 9, y = 2
The number is 92

3 0
3 years ago
What is the square root of 1232348 x 2453
katovenus [111]

54981.35 is the square root

7 0
2 years ago
The points L(10,9)L(10,9), M(10,-5)M(10,-5), N(-1,-5)N(-1,-5), and O(-1,9)O(-1,9) form rectangle LMNOLMNO. Which point is halfwa
Inessa [10]
You are trying to find the halfway point between OO and NN.
OO: (-1,9)    NN: (-1,5)
The x-coordinate does not change, because in both instances it is -1. The y-coordinate is (9-5)/2 AWAY from each point. AKA the number that is equidistant from 5 and 9 (7).

4 0
3 years ago
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