HELP NEEDED AND ASAP!!!!! 30 POINTS

Mathematics

1 answer:

liraira [26]3 years ago

4 0

Answer: The answer to question 1 is 180 in. The answer to question 2 is 54 in. sq. And the answer to question 3 is (2,3)

Step-by-step explanation:

To solve question 1, we need to identify the remaining length of the shape. I've done that in an image below. The next step is to add all of those sides together. It would be 20+20+20+20+20+10+10+60 = 180 inches in length.

To solve question 2, all you need to do is follow the formula A = [h(b) x b] /2

Which may look scary but never fear! Written in understandable words it essentially says, multiply the height by the base then divide by 2.

A = (6 x 18) ÷ 2

A = 108 ÷ 2

A = 54 meters squared

For the last question, I'm not sure what the formula is, but I have a way of doing it that isn't too confusing. Simply add the x values and add the y values, then divide them by 2 to get their halve. Now the new x and y values are your midpoint. (Do not add the x + y values, only the x + x and y + y)

See :

-3 + 7 = 4 4 ÷ 2 = 2

8 + (-2) = 6 6 ÷ 2 = 3

So your new coordinates are (2,3)

I hope this helped you understand :)

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

erma4kov [3.2K]

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: