A hot air balloon is descending

Mathematics

1 answer:

Harlamova29_29 [7]3 years ago

6 0

Answer:

54 3/4

Step-by-step explanation:

18*3=54

1/4*3=3/4

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How do you solve each absolute value by graphing

saw5 [17]

Your question answers itself. You solve by graphing.

I like to subtract one side of the equation from the other, so the solutions are where the graph crosses the x-axis (the resulting function value is zero).

It can be useful to find the "turning point" of each absolute value expression (where its value is zero) and graph that and some points on either side.

7 0

3 years ago

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: