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2 years ago

Evaluate the expression. |-1/3 (1^10+ 9 - 2^3|

Mathematics

1 answer:

defon2 years ago

5 0

Answer:

2/3

Step-by-step explanation:

|-1/3 * (1^10+9-2^3)|=

|-1/3 * (1+9-8)|=

|-1/3 * (2)|=

|-2/3 |=

2/3

Since |a|= a if 'a' is a positive number

and |a|= -a if 'a' is a negative number

The answer always is a positive number

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Use the definition of the derivative to differentiate v=4/2 pie r^3

nata0808 [166]

I suspect 4/2 should actually be 4/3, since 4/2 = 2, while 4/3 would make V the volume of a sphere with radius r. But I'll stick with what's given:

$\displaystyle \frac{dV}{dr} = \lim_{h\to0} \frac{2\pi(r+h)^3-2\pi r^3}{h}$

$\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{(r^3+3r^2h+3rh^2+h^3)- r^3}{h}$

$\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{3r^2h+3rh^2+h^3}{h}$

$\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} (3r^2+3rh+h^2)$

$\displaystyle \frac{dV}{dr} = 2\pi \cdot 3r^2 = \boxed{6\pi r^2}$

In Mathematica, you can check this result via

D[4/2*Pi*r^3, r]

3 0

2 years ago

Xavier Martinez took out a $5,000 loan at 7.5% interest for reconstructing his patio. His monthly payment on the 12-month loan w

Norma-Jean [14]

Paying off the entire loan = 12 * 437.26 = 5,247.12 
He paid 6 * 437.26 = 2,623.56 
He then paid 2,556.03

2,623.56 plus = 2,556.03 = 5,179.59 

 5,247.12 minus 5,179.59 =
67.53 the amount of money he saved.

3 0

3 years ago

Read 2 more answers

Definition: An event that is made up of two or more outcomes is called

Illusion [34]

A compound event, I believe

8 0

3 years ago

Identify the property that justifies step 1 when solving the equation

Ierofanga [76]

Answer:

Distributive Property

Step-by-step explanation:

Answer choice a is correct because you are distributing 2 to each term in the parentheses. When you multiply 2 to each factor in the parentheses, it simplifies to 2x-2, thus making the new equation 6x+2x-2=30

3 0

3 years ago

What is the square root of -2i?

Studentka2010 [4]

Answer:

1-i and -1+i

Step-by-step explanation:

We are to find the square roots of $z=0-2i$ . First, convert from Cartesian to polar form:

$r=\sqrt{a^2+b^2}\\r=\sqrt{0^2+(-2)^2}\\r=\sqrt{0+4}\\r=\sqrt{4}\\r=2$

$\theta=tan^{-1}(\frac{b}{a})\\ \theta=tan^{-1}(\frac{-2}{0})\\\theta=\frac{3\pi}{2}$

$z=2(\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2})$

Next, use the formula $\displaystyle \sqrt[n]{r}\biggr[\cis\biggr(\frac{\theta+2\pi k}{n}\biggr)\biggr]$ where $\displaystyle k=0,1,2,...\:,n-1$ to find the square roots: