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3 years ago

For the word problem below, write the steps to solve the problem

Mathematics

1 answer:

Kisachek [45]3 years ago

5 0

Answer:

Volume= base*height*length; Volume= 24*9*24; Volume= 5,184 square feet

Step-by-step explanation:

The lenghth of the square is 24 feet which makes the base 24 since it is a square. So, you just have to multiply 24*24*9 to get the total volume.

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Find the domain of the function y = 3 tan(23x)

solmaris [256]

Answer:

$\mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

In other words, the $x$ in $f(x) = 3\, \tan(23\, x)$ could be any real number as long as $x \ne \displaystyle \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right)$ for all integer $k$ (including negative integers.)

Step-by-step explanation:

The tangent function $y = \tan(x)$ has a real value for real inputs $x$ as long as the input $x \ne \displaystyle k\, \pi + \frac{\pi}{2}$ for all integer $k$ .

Hence, the domain of the original tangent function is $\mathbb{R} \backslash \displaystyle \left\lbrace \left. \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

On the other hand, in the function $f(x) = 3\, \tan(23\, x)$ , the input to the tangent function is replaced with $(23\, x)$ .

The transformed tangent function $\tan(23\, x)$ would have a real value as long as its input $(23\, x)$ ensures that $23\, x\ne \displaystyle k\, \pi + \frac{\pi}{2}$ for all integer $k$ .

In other words, $\tan(23\, x)$ would have a real value as long as $x\ne \displaystyle \frac{1}{23} \, \left(k\, \pi + \frac{\pi}{2}\right)$ .

Accordingly, the domain of $f(x) = 3\, \tan(23\, x)$ would be $\mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

4 0

2 years ago

What is the absolute value of 2 1/2<br><br> Write your answer as a mixed number.

Greeley [361]

Answer:

it is 2 1/2

Step-by-step explanation:

I hope this helps

6 0

2 years ago

Which expression is the right expression?

Juli2301 [7.4K]

D, you have to factor 3 out of 6x squared

5 0

3 years ago

d.) The expression that describes the network of logic gates: Is [A AND (NOT B)] OR (NOT B). Complete the input-output table for

marusya05 [52]

3 0

2 years ago

A certain kind of bacteria multiplies at a rate of 150 percent per hour. When a person’s blood has 45,000,000 of these bacteria,

DIA [1.3K]

Initial number of Bacteria = Ao = 100
Number of Bacteria which make the person ill = A = 45,000,000

Growth rate = r = 150% = 1.50

The equation model for this situation is:

$A= A_{o}(1+r)^{t}$

Using the values in above equation, we can write:

$45000000=100(1+1.5)^{t} \\ \\ 
450000=(2.5)^{t} \\ \\ 
log(450000)=log((2.5)^{t}) \\ \\ 
log(450000)=t*log(2.5) \\ \\ 
t= \frac{log(450000)}{log(2.5)} \\ \\ 
t=14.21$

This means, the person will fall sick after about 14 hours.

8 0

3 years ago

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