All categories

2 years ago

Convert the radian measure to degrees. (Round to the nearest hundredth when necessary): −5π8

Mathematics

2 answers:

Anna71 [15]2 years ago

8 0

Answer:

The required answer is -112.5°.

Step-by-step explanation:

Consider the provided radian measure.

$\frac{-5\pi}{8}$

To convert from radians to degrees multiply the provided radian with $\frac{180}{\pi}$ .

Consider the provided radian measure and multiply it by $\frac{180}{\pi}$ .

$\frac{-5\pi}{8}=\frac{-5\pi}{8}\times \frac{180}{\pi}$

$\frac{-5\pi}{8}=\frac{-5}{8}\times 180$

$\frac{-5\pi}{8}=\frac{-5}{2}\times45$

$\frac{-5\pi}{8}=\frac{-225}{2}$

$\frac{-5\pi}{8}=-112.5^0$

Hence, the required answer is -112.5°.

xxMikexx [17]2 years ago

5 0

Answer:

$\frac{-5}{8}\pi =-112.5$

Step-by-step explanation:

We know that 1π rad=180°

Hence we can use a proper relation

$\pi = 180\\-5\frac{\pi }{8}=x$

Solving for x results

$x=\frac{-5}{8}*180=\frac{-5}{2}*45=\frac{-225}{2}=112,5$

You might be interested in

The density of granite is about 2.75 grams per cubic centimeter. Suppose you have a granite countertop for a kitchen that is 1 m

stellarik [79]

Answer:

$330\ kg$

Step-by-step explanation:

Remember that

1 kg=1,000 g

1 m= 100 cm

The volume of the granite countertop in cubic centimeters is equal to

$V=(100)(300)(4)\ cm^{3}$

The density in kg per cubic centimeter is equal to

$D=2.75(\frac{1}{1,000}) \frac{kg}{cm^{3}}$

Multiply the density by the volume

$2.75(\frac{1}{1,000})(100)(300)(4)$

$2.75(120)=330\ kg$

6 0

2 years ago

Evaluate \dfrac14c+3d

Crank

Answer: $\frac{45}{2}$

Step-by-step explanation:

<h3> The exercise is: " Evaluate $\frac{1}{4}c + 3d$ when $c = 6$ and $d = 7$ </h3>

Given the following expression:

$\frac{1}{4}c + 3d$

You can follow these steps in order to evaluate it:

1. Substitute $c = 6$ and $d = 7$ into the expression provided in the exercise:

$\frac{1}{4}(6) + 3(7)$

2. Solve the multiplications. Remember that:

$\frac{a}{b}*\frac{c}{d}=\frac{ac}{bd}$

Then:

$=\frac{6}{4} +21$

3. Reduce the fraction. Notice that the numerator 6 and the denomiantor 4 can be both divided by 2. Then:

$=\frac{3}{2} +21$

4. Solve the addition:

$=\frac{3}{2} +\frac{21}{1}$

Since the number 21 has a denominator 1, the Least Common Denominator is:

$LCD=2$

Then, the sum is:

$=\frac{3+42}{2}=\frac{45}{2}$

5 0

2 years ago

Read 2 more answers

There are 600 pages in a novel. Rui feng reads 150 pages of the novel on friday and 40% of the remaining pages on sunday express

nadya68 [22]

Step-by-step explanation:

percentage

current number/total number * 100

150/400*100 is 37.5%

5 0

2 years ago

Find all x in set of real numbers R Superscript 4 that are mapped into the zero vector by the transformation Bold x maps to Uppe

sukhopar [10]

Answer:

$x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right]$

Step-by-step explanation:

According to the given situation, The computation of all x in a set of a real number is shown below:

First we have to determine the $\bar x$ so that $A \bar x = 0$

$\left[\begin{array}{cccc}1&-3&5&-5\\0&1&-3&5\\2&-4&4&-4\end{array}\right]$

Now the augmented matrix is

$\left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\2&-4&4&-4\ |\ 0\end{array}\right]$

After this, we decrease this to reduce the formation of the row echelon

$R_3 = R_3 -2R_1 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&2&-6&6\ |\ 0\end{array}\right]$

$R_3 = R_3 -2R_2 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right]$

$R_2 = 4R_2 +5R_3 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&4&-12&0\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right]$

$R_2 = \frac{R_2}{4}, R_3 = \frac{R_3}{-4} \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&1\ |\ 0\end{array}\right]$

$R_1 = R_1 +3 R_2 \rightarrow \left[\begin{array}{cccc}1&0&-4&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right]$

$R_1 = R_1 +5 R_3 \rightarrow \left[\begin{array}{cccc}1&0&-4&0\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right]$

$= x_1 - 4x_3 = 0\\\\x_1 = 4x_3\\\\x_2 - 3x_3 = 0\\\\ x_2 = 3x_3\\\\x_4 = 0$

$x = \left[\begin{array}{c}4x_3&3x_3&x_3\\0\end{array}\right] \\\\ x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right]$

By applying the above matrix, we can easily reach an answer

5 0

2 years ago

Upgrading a certain software package requires installation of 68 new files. Files are installed consecutively. The installation

ser-zykov [4K]

Answer:

The probability that the whole package is uppgraded in less then 12 minutes is 0,1271

Step-by-step explanation:

The mean distribution for the length of the installation (in seconds) of the programs will be denoted by X. Using the Central Limit Theorem, we can assume that X is normal (it will be pretty close). The mean of X is 15 and the variance is 15, hence, the standard deviation is √15 = 3.873.

We want to find the probability that the full installation process takes less than 12 minutes = 720 seconds. Then, in average, each program should take less than 720/68 = 10.5882 seconds to install. Hence, we want to find the probability of X being less than 10.5882. For that, we will take W, the standariation of X, given by the following formula

$W = \frac{X-\mu}{\sigma} = \frac{X-15}{3.873}$

We will work with $\phi$ , the cummulative distribution function of the standard Normal variable W. The values of $\phi$ can be found in the attached file.

$P(X < 10.5882) = P(\frac{X-15}{3.873} < \frac{10.5882-15}{3.873}) = P(W < -1,14)$

Since the density function of a standard normal random variable is symmetrical, then $\phi(-1.14) = 1-\phi(1.14) = 1-0.8729 = 0.1271$

Therefore, the probability that the whole package is uppgraded in less then 12 minutes is 0,1271.

Download pdf

7 0

2 years ago