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geniusboy [140]
3 years ago
10

What is the interval notation for y<5?

Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
7 0

Hey there!☺

Answer: (-∞, 5)

Explanation:

You need to convert the inequality as an interval notation.

y as interval notation would be written like this:

(-∞, 5)

Hope this helps!

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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)

<em>And from these we can get the direction angles as follows;</em>

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 <em>is just the x component of the vector</em>]

a . j = 1            [<em>the y component of the vector</em>]

a . k = 4          [<em>the z component of the vector</em>]

<em>Also</em>

|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°

<u>Conclusion:</u>

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
3 years ago
A circle has a radius of 5 centimeters. What is the area?
schepotkina [342]

Answer:

25\pi

Step-by-step explanation:

The formula for the area of a circle is A=\pi r^{2}, r is your radius, A is your area, and π is pi (3.1415...). You plug in your radius, or 5 into r, square it, 25, and multiply it by pi. You may be asked to use a certain number of digits of pi, and in that case you multiply for example 3.14 by 25, however 25\pi is the exact answer.

6 0
2 years ago
In a line of students, Jenna is number 8.The teacher says that a rule for a number pattern is add 4. The first student inline sa
Virty [35]

Answer:

Formula for nth term in Arithmetic sequences is:

a_n =a+(n-1)d

where a is the first term, d is the common difference and n is the number of terms.

As per the statement:

The rule for the pattern is add 4.

As the first term in line says the first term i,e 7

a= 7

common difference(d)= 7

As the Jenna number is 8th in line.

Series we get;

7, 11, .........a_8

We have to find the 8th term.

n = 8, a = 7 and d = 4

Using above formula:

a_8 = 7+(8-1)4 = 7+7 \cdot 4 = 7 +28 = 35

Therefore, 35 number should Jenna say.

3 0
3 years ago
Read 2 more answers
What is the y intercept of f(x)=(1/2)*
9966 [12]

Answer:

B. (0,0)

Step-by-step explanation:

The y-intercept of the equation f(x) = 1/2x lies on the y-axis.

This means we need to set x = 0 and solve for y

1/2(0) = 0

Therefore, (0,0) is the y-intercept of this equation.

5 0
3 years ago
Please help:)<br><br> See pic attached
Lostsunrise [7]

Answer:

Adults: 75, girls: 100, Boys: 75

Step-by-step explanation:

2/5 x 250 = 100( girls)

3/10 x 250 = 75 (boys)

250 - (100 + 75) = 250 - 175 = 75 (Adults)

5 0
2 years ago
Read 2 more answers
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