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Artist 52 [7]
2 years ago
14

Find the dot product of the position vectors whose terminal points are (14, 9) and (3, 6).

Mathematics
1 answer:
erma4kov [3.2K]2 years ago
6 0

Answer:

Step-by-step explanation:

The formula for the dot product of vectors is

u·v = |u||v|cosθ

where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.

|u|=\sqrt{14^2+9^2} which is \sqrt{277}

|v|=\sqrt{3^2+6^2} which is \sqrt{45}

I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.

We also need the angle, which of course has its own formula.

cos\theta=\frac{uv}{|u||v|} where uv has ITS own formula:

uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.

uv = 96.

To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:

cos^{-1}\theta=\frac{96}{111.64676} which returns an angle measure of 30.7. Plugging that all into the dot product formula:

u*v=\sqrt{277}*\sqrt{45}cos(30.7) gives you a dot product of 96

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We have seen that isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use
Naddik [55]

Question has missing figure, the figure is in the attachment.

Answer:

The measure of ∠1 is 65°.

The measure of ∠2 is 65°.

The measure of ∠3 is 50°.

The measure of ∠4 is 115°.

The measure of ∠5 is 65°.

Step-by-step explanation:

Given,

We have an isosceles triangle which we can named it as ΔABC.

In which Length of AB is equal to length of BC.

And also m∠B is equal to m∠C.

ext.m∠C= 115°(Here ext. stands for exterior)

We have to find the measure of angles angles 1 through 5.

Solution,

For ∠1.

∠1 and ext.∠C makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

\angle1+ext.\angle C=180\°

On putting the values, we get;

\angle 1+115\°=180\°\\\\\angle1=180\[tex]\therefore m\angle2=65\°-115\°=65\°[/tex]

Thus the measure of ∠1 is 65°.

For ∠2.

Since the given triangle is an isosceles triangle.

So, m\angle1=m\angle2

Thus the measure of ∠2 is 65°.

For ∠3.

Here ∠1, ∠2 and ∠3 are the three angles of the triangle.

So we use the angle sum property of triangle, which states that;

"The sum of all the angles of a triangle is equal to 180°".

\therefore \angle1+\angle2+\angle3=180\°

Now we put the values and get;

65\°+65\°+\angle3=180\°\\\\130\°+\angle3=180\°\\\\\angle3=180\°-130\°=50\°

Thus the measure of ∠3 is 50°.

For ∠4.

∠4 and ∠2 makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

\angle2 +\angle 4 =180\°

Substituting the values of of angle 2 to find angle 4 we get;

65\°+ \angle 4 = 180\°\\\\ \angle 4 = 180\°-65\°\\\\\angle 4= 115\°

Thus the measure of ∠4 is 115°.

For ∠5.

∠4 and ∠5 makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

\angle4 +\angle 5 =180\°

Substituting the values of of angle 4 to find angle 5 we get;

115\°+ \angle 5 = 180\°\\\\ \angle 5 = 180\°-115\°\\\\\angle 5= 65\°

Thus the measure of ∠5 is 65°.

Hence:

The measure of ∠1 is 65°.

The measure of ∠2 is 65°.

The measure of ∠3 is 50°.

The measure of ∠4 is 115°.

The measure of ∠5 is 65°.

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Answer:

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Step-by-step explanation:

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Because the graph of the function does not move beyond 4 towards +∞.

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Step-by-step explanation:

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dsp73

Given that:

The expressions are 3z−2, 2x^3+x-12, 9b, 9x-2.

Solution:

Monomial : It contains single terms.

Binomial : It contains two terms.

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Degree of polynomial : It is highest power of the variable.

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9b ,  here b is a constant. So, it is not a polynomial and it is a monomial.

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Step-by-step explanation:

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840/2= 420

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