What is the quoteint of<br> 3/4 and 5/6

Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.) 3 217

Soloha48 [4]

Answer:

$f(216) \approx 6.0093$

Step-by-step explanation:

Given

$\sqrt[3]{217}$

Required

Solve

Linear approximated as:

$f(x + \triangle x) \approx f(x) +\triangle x \cdot f'(x)$

Take:

$x = 216; \triangle x= 1$

So:

$f(x) = \sqrt[3]{x}$

Substitute 216 for x

$f(x) = \sqrt[3]{216}$

$f(x) = 6$

So, we have:

$f(x + \triangle x) \approx f(x) +\triangle x \cdot f'(x)$

$f(215 + 1) \approx 6 +1 \cdot f'(x)$

$f(216) \approx 6 +1 \cdot f'(x)$

To calculate f'(x);

We have:

$f(x) = \sqrt[3]{x}$

Rewrite as:

$f(x) = x^\frac{1}{3}$

Differentiate

$f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}$

Split

$f'(x) = \frac{1}{3} \cdot \frac{x^\frac{1}{3}}{x}$

$f'(x) = \frac{x^\frac{1}{3}}{3x}$

Substitute 216 for x

$f'(216) = \frac{216^\frac{1}{3}}{3*216}$

$f'(216) = \frac{6}{648}$

$f'(216) = \frac{3}{324}$

So:

$f(216) \approx 6 +1 \cdot f'(x)$

$f(216) \approx 6 +1 \cdot \frac{3}{324}$

$f(216) \approx 6 + \frac{3}{324}$

$f(216) \approx 6 + 0.0093$

$f(216) \approx 6.0093$

6 0

3 years ago

Solve. 90<img src="https://tex.z-dn.net/?f=x" id="TexFormula1" title="x" alt="x" align="absmiddle" class="latex-formula"> = 27.

Irina-Kira [14]

Answer: $x$ ≈ $0.732$

Step-by-step explanation:

You need to find the value of the variable "x".

To solve for "x" you need to apply the following property of logarithms:

$log(m)^n=nlog(m)$

Apply logarithm on both sides of the equation:

$90^x=27\\\\log(90)^x=log(27)$

Now, applying the property mentioned before, you can rewrite the equation in this form:

$xlog(90)=log(27)$

Finally, you can apply the Division property of equality, which states that:

$If\ a=b,\ then\ \frac{a}{c}=\frac{b}{c}$

Therefore, you need to divide both sides of the equation by $log(90)$ . Finally, you get:

$\frac{xlog(90)}{log(90)}=\frac{log(27)}{log(90)}\\\\x=\frac{log(27)}{log(90)}$

$x$ ≈ $0.732$

7 0

3 years ago

24 POINTS!!!! help please. No work needed....

Mrrafil [7]

I’m more than happy to help you

8 0

3 years ago

onsider the following hypothesis test: H 0: 50 H a: > 50 A sample of 50 is used and the population standard deviation is 6. U

kondaur [170]

Answer:

a) z(e) > z(c) 2.94 > 1.64 we are in the rejection zone for H₀ we can conclude sample mean is great than 50. We don´t know how big is the population .We can not conclude population mean is greater than 50

b) z(e) < z(c) 1.18 < 1.64 we are in the acceptance region for H₀ we can conclude H₀ should be true. we can conclude population mean is 50

c) 2.12 > 1.64 and we can conclude the same as in case a

Step-by-step explanation:

The problem is concerning test hypothesis on one tail (the right one)

The critical point z(c) ; α = 0.05 fom z table w get z(c) = 1.64 we need to compare values (between z(c) and z(e) )

The test hypothesis is:

a) H₀ ⇒ μ₀ = 50 a) Hₐ μ > 50 ; for value 52.5

b) Hₐ μ > 50 ; for value 51

c) Hₐ μ > 50 ; for value 51.8

With value 52.5

The test statistic z(e) ??

a) z(e) = ( μ - μ₀ ) /( σ/√50) z(e) = (2.5*√50 )/6 z(e) = 2.94

2.94 > 1.64 we are in the rejected zone for H₀ we can conclude sample mean is great than 50. We don´t know how big is the population .We can not conclude population mean is greater than 50

b) With value 51

z(e) = ( μ - μ₀ ) /( σ/√50) ⇒ z(e) = √50/6 ⇒ z(e) = 1.18

z(e) < z(c) we are in the acceptance region for H₀ we can conclude H₀ should be true. we can conclude population mean is 50

c) the value 51.8

z(e) = ( μ - μ₀ ) /( σ/√50) ⇒ z(e) = (1.8*√50)/ 6 ⇒ z(e) = 2.12

2.12 > 1.64 and we can conclude the same as in case a

8 0

3 years ago

Klara has decided to file her tax return electronically. How will she benefit from e-filing?

damaskus [11]

Answer:

C. If she's expecting a tax refund, e-filing can expedite the refund from the IRS.

Step-by-step explanation:

Filing the tax return electronically provides some benefits like doing it in an easy way as the website has a step by step process that guides people through it and it allows to be more accurate as the program checks what you do. Also, it helps to save time and it allows to receive the tax refund faster because e-filing give you the possibility to ask for a deposit on your account instead of waiting for a check to arrive. According to this, the answer is that Kiara will benefit from e-filing because if she's expecting a tax refund, e-filing can expedite the refund from the IRS.

7 0

3 years ago

What is the quoteint of 3/4 and 5/6