What value goes in the blank to give the unit rate? (Answers may contain decimals)

Ben drinks tea at an incredible rate.He drinks 3 1/2 liters of tea every 2/3 of an hour.Ben drinks tea a constant rate.How many

vampirchik [111]

Answer:

Step-by-step explanation:

2/3 = 0.66

1 hour = 60

60 x 0.66 = 39.6 or 40

In which, 60 - 40 = 20; so he only drinks 3 1/2 liters every 40 minutes.

He drinks 3 1/2 every hour.

3 0

3 years ago

High SchoolMathematics 5 points What is the opposite of the opposite of -1.4? Ask for details Follow Report by Darlasiller 07/03

Alik [6]

The opposite of the opposite of-1.4 is -1.4

5 0

3 years ago

Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) 5, 1,

Dahasolnce [82]

Answer:

The direction cosines are:

$\frac{5}{\sqrt{42} }$ , $\frac{1}{\sqrt{42} }$ and $\frac{4}{\sqrt{42} }$ with respect to the x, y and z axes respectively.

The direction angles are:

40°, 81° and 52° with respect to the x, y and z axes respectively.

Step-by-step explanation:

For a given vector a = ai + aj + ak, its direction cosines are the cosines of the angles which it makes with the x, y and z axes.

If a makes angles α, β, and γ (which are the direction angles) with the x, y and z axes respectively, then its direction cosines are: cos α, cos β and cos γ in the x, y and z axes respectively.

Where;

cos α = $\frac{a . i}{|a| . |i|}$ ---------------------(i)

cos β = $\frac{a.j}{|a||j|}$ ---------------------(ii)

cos γ = $\frac{a.k}{|a|.|k|}$ ----------------------(iii)

And from these we can get the direction angles as follows;

α = cos⁻¹ ( $\frac{a . i}{|a| . |i|}$ )

β = cos⁻¹ ( $\frac{a.j}{|a||j|}$ )

γ = cos⁻¹ ( $\frac{a.k}{|a|.|k|}$ )

Now to the question:

Let the given vector be

a = 5i + j + 4k

a . i = (5i + j + 4k) . (i)

a . i = 5 [a.i is just the x component of the vector]

a . j = 1 [the y component of the vector]

a . k = 4 [the z component of the vector]

Also

|a|. |i| = |a|. |j| = |a|. |k| = |a| [since |i| = |j| = |k| = 1]

|a| = $\sqrt{5^2 + 1^2 + 4^2}$

|a| = $\sqrt{25 + 1 + 16}$

|a| = $\sqrt{42}$

Now substitute these values into equations (i) - (iii) to get the direction cosines. i.e

cos α = $\frac{5}{\sqrt{42} }$

cos β = $\frac{1}{\sqrt{42} }$

cos γ = $\frac{4}{\sqrt{42} }$

From the value, now find the direction angles as follows;

α = cos⁻¹ ( $\frac{a . i}{|a| . |i|}$ )

α = cos⁻¹ ( $\frac{5}{\sqrt{42} }$ )

α = cos⁻¹ ( $\frac{5}{6.481}$ )

α = cos⁻¹ (0.7715)

α = 39.51

α = 40°

β = cos⁻¹ ( $\frac{a.j}{|a||j|}$ )

β = cos⁻¹ ( $\frac{1}{\sqrt{42} }$ )

β = cos⁻¹ ( $\frac{1}{6.481 }$ )

β = cos⁻¹ ( 0.1543 )

β = 81.12

β = 81°

γ = cos⁻¹ ( $\frac{a.k}{|a|.|k|}$ )

γ = cos⁻¹ ( $\frac{4}{\sqrt{42} }$ )

γ = cos⁻¹ ( $\frac{4}{6.481}$ )

γ = cos⁻¹ (0.6172)

γ = 51.89

γ = 52°

Conclusion:

The direction cosines are:

$\frac{5}{\sqrt{42} }$ , $\frac{1}{\sqrt{42} }$ and $\frac{4}{\sqrt{42} }$ with respect to the x, y and z axes respectively.

The direction angles are:

40°, 81° and 52° with respect to the x, y and z axes respectively.

3 0

2 years ago

A flash disk has the capacity of storing 1 megabyte of data. How many kilobytes of data can be stored in the same flash disk

Luden [163]

For this sort of problem, you need to be familiar with prefixes.

So:

megabyte = $1 *10^6$ bytes

kilobyte = $1*10^3$ bytes

and a regular byte would just be $1$

Now, you will need to do a conversion:

$1megabyte*\frac{1*10^6bytes}{1megabyte}*\frac{1*10^{-3}kilobyte}{1byte}$

I'm going to explain this just in case, but we convert megabytes to regular bytes in the first half by using the information I gave you above. (In one megabyte, there are $1*10^6$ bytes!)

In the second fraction thought, remember one kilobyte is $1*10^3$ bytes. However, you usually only see one of each thing on the bottom of fractions, so you need to add a negative sign to the 3. (technically you could just do $\frac{1kilobyte}{1*10^3bytes}$ , but I think it is more correct to do write it out how I did).