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Mekhanik [1.2K]
3 years ago
11

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example tha

t disaproves the statement.
The dot product of parallel vectors is zero,
Mathematics
1 answer:
frosja888 [35]3 years ago
5 0

Answer:

False

Step-by-step explanation:

the <u>dot product</u> between two vectors A and B is:

A·B=ABcos\theta

where \theta is the angle between the vectors, if they are parallel, this angle is zero. so  \theta=0

and so the dot product is:

A·B =ABcos(0)

and since  cos (0)=1

the dot product is equal to

A·B=AB

The dot product of parallel vectors is NOT zero

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​Find all roots: x^3 + 7x^2 + 12x = 0 <br> Show all work and check your answer.
Aliun [14]

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

<u>Solution:</u>

We have been given a cubic polynomial.

x^{3}+7 x^{2}+12 x=0

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

x^{3}+7 x^{2}+12 x=0

x\left(x^{2}+7 x+12\right)=0   ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

x^{2}+7 x+12=0

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}

<em><u>Therefore, the two roots are:</u></em>

\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}

And,

\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

4 0
3 years ago
The teacher said we could estimate but give a good reason for that estimate​
lyudmila [28]

Answer:

$11, even if you do work a job thats not that hard you should still be making a good amount of money

Step-by-step explanation:

I just used my opinion

5 0
3 years ago
A triangle that has no sides of equal length and one angle greater than 90° is which type of triangle?
Ganezh [65]

Answer:

It’s a obtuse triangle/scalene triangle

Step-by-step explanation:

Giving the information that is provided if the sides are not equal then it seems to be that the correct answer would be Obtuse Scalene

6 0
2 years ago
Read 2 more answers
Many televisions are classified by the length of the diagonal of their screens. A 60 in. television has a screen height of 32 in
Colt1911 [192]
The 60 inch is diagonal of or the hypotenuse of the TV so we are going to use a^2+b^2=c^2 and let width to be a, then we solve the problem.
a^2=c^2-b^2
oh, take the square root of both sides.
a=((c^2-b^2))^(1/2)
plug 60 for c, 32 for b, and the Width is equal to 50.75 for significant figures.

7 0
3 years ago
A cone is cut by a plane parallel to its base. The small cone on top is similar to the large cone, with a similarity ratio of 1
Pavel [41]

Answer:

<h2>1:1</h2>

Step-by-step explanation:

The ratio between the volume of the small cone to that of the frustum is 1:1.

Notice that the bigger cone is double than the smaller cone, which means the smaller cone is half of the volume of the bigger cone, if you wipe the small one, you would have the frustum with the same volume as the wiped part, because if you delete the smaller cone, you would be deleting half volume of the bigger cone, giving at the end a relation 1 : 1 between the frustum and the smaller cone.

5 0
3 years ago
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