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2 years ago

What is the derivative of this function?

Mathematics

1 answer:

Alex17521 [72]2 years ago

6 0

$\bf y=\sqrt{x}-\left( \frac{1}{2} \right)^x\implies y=x^{\frac{1}{2}}-\left( \frac{1}{2} \right)^x\implies \cfrac{dy}{dx}=\frac{1}{2}x^{\frac{1}{2}-1}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right)
\\\\\\
\cfrac{dy}{dx}=\frac{1}{2}x^{-\frac{1}{2}}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right)\implies 
\cfrac{dy}{dx}=\cfrac{1}{2\sqrt{x}}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right)$

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Find the final amount for a $1000 investment at 6% interest compounded continuously for 20 years

yarga [219]

Answer:$3207

Step-by-step explanation

A=p(1+r/100)^n

A=1000×(1+6/100)^20

A=1000×(1.06)^20

A=1000×3.207

A=$3207

3 0

2 years ago

If sin just answer the please lol i don't feel like typing ASAP

yaroslaw [1]

Considering that the sine is negative and that the cosine is positive, the angle is on the fourth quadrant, hence option C is correct.

<h3>What are the signs of the sine and of the cosine in each quadrant?</h3>

Quadrant 1: Both positive.

Quadrant 2: Sine positive, cosine negative.

Quadrant 3: Both negative.

Quadrant 4: Sine negative, cosine positive.

Hence, since the sine is negative and that the cosine is positive, the angle is on the fourth quadrant, hence option C is correct.

More can be learned about quadrants at brainly.com/question/28021191

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5 0

1 year ago

Find the x- and y-intercepts of the function f(x) = log(2x + 1) − 1.

Vilka [71]

Answer:

(9/2,0) and (0,-1)

Step-by-step explanation:

y(0) = log(1)-1 = -1

y=0 when log(2x+1) = 1

2x+1 = 10

x = 9/2

6 0

2 years ago

Is -0.5 an integer? Explain.

Drupady [299]

Yes, -0.5 is an integer because it is a negative number. Any number that is positive or negative is an integer.

4 0

2 years ago

Read 2 more answers

At 10 percent interest, how long does it take to quadruple your money?

horsena [70]

It takes about 14.55 years for quadruple your money

Solution:

Given that,

At 10 percent interest, how long does it take to quadruple your money

Rule of 144:

The Rule of 144 will tell you how long it will take an investment to quadruple

Here,

Rate of interest = 10 %

Therefore, number of years to quadruple your money is obtained by dividing 144 by 10

Rule of 144 Formula:

$N = \frac{144}{R}$

Where:

N = Number of many years times.

144 = Is the constant variable.

R = Rate of interest.

$\rightarrow N = \frac{144}{10} = 14.4$

Thus it takes about 14.4 years for quadruple your money.

Another method:

If initial amount is $ 1 and it if quadruples it should be $ 4

We have to find the number of years if rate of interest is 10 %

Let "n" be the number of years

Then we can say,

$Amount = Principal(1+\frac{R}{100})^n$

$4 = 1(1+\frac{10}{100})^n$

$4 = 1(1+0.1)^n\\\\4= 1(1.1)^n\\\\4 = 1.1^n\\\\We\ know\ that,\\\\(1.1)^{14.55} = 1.1^n\\\\We\ know\ that\\\\If\ a^m = a^n\ then\ m = n\\\\Therefore,\\\\14.55 = n\\\\n = 14.55$

Thus Option D 14.55 years is correct

7 0

2 years ago