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Nimfa-mama [501]
3 years ago
6

What is the 8.356 rounded to the nearest hundredth

Mathematics
2 answers:
rodikova [14]3 years ago
5 0

Answer:

8.356 rounded to the nearest hundredth=8.360

KATRIN_1 [288]3 years ago
3 0

Answer:

8.36

Step-by-step explanation:

The hundredth decimal place is the second digit right of the decimal.

There should be 2 decimal places when rounded to the nearest hundredth.

If the third digit is less than 5, round down. If the third digit is 5 or more, round up.

In 8.356, the third digit is 6. 6 is 5 or more so we round the second digit up.

8.356 => 8.36

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Solving a trigonometric equation involving an angle multiplied by a constant
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In these questions, we need to follow the steps:

1 - solve for the trigonometric function

2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.

3 - Complete these angles with the complete round repetition, by adding

2k\pi,k\in\Z

4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for <em>x</em> to get the solutions.

1 - To solve, we just use algebraic operations:

\begin{gathered} \sqrt[]{3}\tan (3x)+1=0 \\ \sqrt[]{3}\tan (3x)=-1 \\ \tan (3x)=-\frac{1}{\sqrt[]{3}} \\ \tan (3x)=-\frac{\sqrt[]{3}}{3} \end{gathered}

2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:

The value for the angle that give positive

+\frac{\sqrt[]{3}}{3}

is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of

-\frac{\sqrt[]{3}}{3}

Are:

\begin{gathered} \theta_1=\pi-\frac{\pi}{6}=\frac{5\pi}{6} \\ \theta_2=2\pi-\frac{\pi}{6}=\frac{11\pi}{6} \end{gathered}

3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:

\begin{gathered} \theta=\frac{5\pi}{6}+2k\pi,k\in\Z \\ or \\ \theta=\frac{11\pi}{6}+2k\pi,k\in\Z \end{gathered}

Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:

\theta=\frac{5\pi}{6}+k\pi,k\in\Z

4 - Now, we need to solve for <em>x</em>, because these solutions are for all the interior of the tangent function, so:

\begin{gathered} 3x=\theta \\ 3x=\frac{5\pi}{6}+k\pi,k\in\Z \\ x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z \end{gathered}

So, the solutions are:

x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z

4 0
1 year ago
Josh is a software salesperson. His base salary is 2200$ and he makes 70$ more for everycopy of history is fun he sells. What is
natta225 [31]

Answer: \$3,740

Step-by-step explanation:

You know that Josh's base salary is:

base\ salary=\$2,200

And, according to the information given in the exercise, Josh makes $70 more for every copy he sales.

 Knowing this you can determine that his total pay will be the sum of his base salary and the podruct of $70 and the number of copies.

Therefore, if Josh sells 22 copies, then we get that his total pay is:

Total\ pay=\$2,200+(22)(\$70)\\\\Total\ pay=\$3,740

6 0
3 years ago
Graph the equation below by plotting the y-intercept and a second point on the line.
Solnce55 [7]
I don’t know if this helps but…

Slope: 2/3

Y-intercept: (0,-4)

7 0
2 years ago
The difference of two numbers is 15. Five times the smaller number is the same as 9 less than twice the larger number. Find the
kifflom [539]

Answer:

Step-by-step explanation:

"The difference of two numbers is 15."

x-y = 15

x>y

"Five times the smaller number is the same as 9 less than twice the larger number."

5y = 2x-9

y = x-15

substitution

5(x-15) = 2x-9

5x-75 = 2x-9

3x = 66

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7 0
2 years ago
Evaluate cos(37°15').<br><br> 0.7944<br> 0.7960<br> 0.7971
Anvisha [2.4K]

cos(37°15') = cos(37.25°) ≈ 0.7960

15' means 15/60 of a degree, or 0.25 degrees.

_____

Note: the calculator mode is set to <em>Degrees</em>.

5 0
3 years ago
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