Please help me thank you!!

Mathematics

1 answer:

AURORKA [14]2 years ago

5 0

Emma completed the problem correctly i believe

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The coordinates of point D are (7, 4) and the coordinates of point E are (1, −3) . What is the slope of the line that is perpend

Katarina [22]

The slope of a line is given by the change in y coordinates over the change in x coordinate.
The slope of line DE will be (4 - -3)/ (7-1) = 7/6
If M1 and M2 are slopes of two perpendicular lines at a point then
M1× M2 = -1
Thus, the slope of a perpendicular to line DE will be -6/7.

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2 years ago

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liq [111]

35 is your answer (I did it on a triangle calculator)

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2 years ago

You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o

anyanavicka [17]

Answer:

$x =\dfrac{45 \sqrt{6}}{ 2}$

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

$\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}$

In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

= $\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0$