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NARA [144]
3 years ago
12

The digit 9 is in the tens place of a whole number. If 9 were moved from the tens place to the hundreds place, how many times gr

eater would the value of 9 be?
​
Mathematics
1 answer:
HACTEHA [7]3 years ago
4 0

The value would be 10 times greater.

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I need help with my math homework. The questions is: Find all solutions of the equation in the interval [0,2π).
Aleksandr-060686 [28]

Answer:

\frac{7\pi}{24} and \frac{31\pi}{24}

Step-by-step explanation:

\sqrt{3} \tan(x-\frac{\pi}{8})-1=0

Let's first isolate the trig function.

Add 1 one on both sides:

\sqrt{3} \tan(x-\frac{\pi}{8})=1

Divide both sides by \sqrt{3}:

\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}

Now recall \tan(u)=\frac{\sin(u)}{\cos(u)}.

\frac{1}{\sqrt{3}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}

or

\frac{1}{\sqrt{3}}=\frac{-\frac{1}{2}}{-\frac{\sqrt{3}}{2}}

The first ratio I have can be found using \frac{\pi}{6} in the first rotation of the unit circle.

The second ratio I have can be found using \frac{7\pi}{6} you can see this is on the same line as the \frac{\pi}{6} so you could write \frac{7\pi}{6} as \frac{\pi}{6}+\pi.

So this means the following:

\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}

is true when x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi

where n is integer.

Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.

So now we have a linear equation to solve:

x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi

Add \frac{\pi}{8} on both sides:

x=\frac{\pi}{6}+\frac{\pi}{8}+n \pi

Find common denominator between the first two terms on the right.

That is 24.

x=\frac{4\pi}{24}+\frac{3\pi}{24}+n \pi

x=\frac{7\pi}{24}+n \pi (So this is for all the solutions.)

Now I just notice that it said find all the solutions in the interval [0,2\pi).

So if \sqrt{3} \tan(x-\frac{\pi}{8})-1=0 and we let u=x-\frac{\pi}{8}, then solving for x gives us:

u+\frac{\pi}{8}=x ( I just added \frac{\pi}{8} on both sides.)

So recall 0\le x.

Then 0 \le u+\frac{\pi}{8}.

Subtract \frac{\pi}{8} on both sides:

-\frac{\pi}{8}\le u

Simplify:

-\frac{\pi}{8}\le u

-\frac{\pi}{8}\le u

So we want to find solutions to:

\tan(u)=\frac{1}{\sqrt{3}} with the condition:

-\frac{\pi}{8}\le u

That's just at \frac{\pi}{6} and \frac{7\pi}{6}

So now adding \frac{\pi}{8} to both gives us the solutions to:

\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}} in the interval:

0\le x.

The solutions we are looking for are:

\frac{\pi}{6}+\frac{\pi}{8} and \frac{7\pi}{6}+\frac{\pi}{8}

Let's simplifying:

(\frac{1}{6}+\frac{1}{8})\pi and (\frac{7}{6}+\frac{1}{8})\pi

\frac{7}{24}\pi and \frac{31}{24}\pi

\frac{7\pi}{24} and \frac{31\pi}{24}

5 0
3 years ago
I need the answer ASAP please help
Fantom [35]

Answer:

5 and 50

Step-by-step explanation:

Constant of proportionality=(10-5)/(2-1)=5

Distance is 5*10=50

5 0
2 years ago
What is the value of the expression 5x2 + 2x when x = 5?
masha68 [24]

Answer:

135

Step-by-step explanation:

Given:

x = 5

To determine a numerical value for the expression, simply substitute the value of "x" into the expression and simplify the expression, if necessary, to determine a specific number for the expression provided.

  • \implies 5x^{2}  + 2x
  • \implies 5(5)^{2}  + 2(5) \longrightarrow \longrightarrow \longrightarrow (x = 5)
  • \implies 5(5)(5)  + 2(5)
  • \implies 125  + 10
  • \implies 135

Therefore, the value of the expression 5x^{2}  + 2x when x = 5 is 135.

Learn more about this topic: brainly.com/question/27675691

7 0
2 years ago
One wall in Zoe's bedroom is 5 feet wide and 8 feet tall. Zoe puts up a poster of her favorite athlete. The poster is 2 feet wid
Marta_Voda [28]
3 feet of width and 5 feet of height.
3 0
3 years ago
Read 2 more answers
A high school of 350 students offers biology and chemistry courses. 213 students are enrolled in biology while 155 students are
NNADVOKAT [17]
350 - 213 - 155 + 78 = 60 students not in either
4 0
3 years ago
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