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2 years ago

Help help help plz plz plz

Mathematics

1 answer:

DaniilM [7]2 years ago

5 0

Answer:

Yes

Step-by-step explanation:

What would you do if he said ok so he said yes would go?

I told him god bless him and to keep working in his vocabulary.

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Answer:

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Step-by-step explanation:

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2 years ago

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Antifreeze lowers the freezing point of the engine coolant. According to the data in the table, what percent of antifreeze would

Strike441 [17]

B: 33% and dont click that link its a virus.

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3 years ago

What is natural number

Triss [41]

Answer:

natural no.s are those no.s which don't have any negative integer or any fractional value

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3 years ago

The equation of a circle is given below. x^{2}+(y-2.25)^{2} = \dfrac{196}{169}x 2 +(y−2.25) 2 = 169 196 x, squared, plus, left

Lostsunrise [7]

Center = $(h,k) = (0,2.25)$
Radius = $r = \frac{14}{13}$

Step-by-step explanation:

Here we have following equation : $x^{2}+(y-2.25)^{2} = \dfrac{196}{169}$

We need to find the center & radius of this circle . Let's find out:

We know that , Equation of a circle is given by :

⇒ $(x-h)^2+(y-k)^2=r^2$ ........(1)

Here , (h,k) are the co-ordinates of center & r is the radius of circle.Collectively called as a circle with radius r and center at (h,k) . Let's frame given equation in question :

⇒ $x^{2}+(y-2.25)^{2} = \frac{196}{169}$

⇒ $(x-0)^{2}+(y-2.25)^{2} = (\frac{14}{13})^2$

On comparing this equation with equation (1) we get :

Center = $(h,k) = (0,2.25)$
Radius = $r = \frac{14}{13}$

6 0

3 years ago

Read 2 more answers

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

3 years ago