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4 years ago

Find the point P on the parabola y=x^2 closest to the point (3,0).

1 answer:

8 0

<span>if we take square root (x - 3)^2 + y^2
y = x^2
(x - 3)^2 + x^4
f(x) = x^4 + x^2 - 6x + 9.
first derivation:
f'(x) = 4x^3 + 2x - 6.
4x^3 + 2x - 6 = 0.
one solution is x = 1
second derivation
f"(x) = 12x^2 + 2
it is positive for x = 1
hope it helps
</span>

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3 years ago

Q # 7.Write a congruence statement for the pair of triangles

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4 years ago

Determine the most precise name for ABCD (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer.

Sonja [21]

<h3>Answer: Rhombus</h3>

======================================================

Reason:

Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.

$A = (x_1,y_1) = (3,5) \text{ and } B = (x_2, y_2) = (7,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (5-6)^2}\\\\d = \sqrt{(-4)^2 + (-1)^2}\\\\d = \sqrt{16 + 1}\\\\d = \sqrt{17}\\\\d \approx 4.1231\\\\$

Segment AB is exactly $\sqrt{17}$ units long, which is approximately 4.1231 units.

If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.

-------------------------

Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.

Let's find the slope of AB.

$A = (x_1,y_1) = (3,5) \text{ and } B = (x_2,y_2) = (7,6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{6 - 5}{7 - 3}\\\\m = \frac{1}{4}\\\\$

Segment AB has a slope of 1/4.

Do the same for BC

$B = (x_1,y_1) = (7,6) \text{ and } C = (x_2,y_2) = (6,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 6}{6 - 7}\\\\m = \frac{-4}{-1}\\\\m = 4\\\\$

Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.

We don't have perpendicular lines, so the interior angles are not 90 degrees each.

Therefore, this figure is not a rectangle and by extension it's not a square either.

The best description for this figure is a <u>rhombus</u>.

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2 years ago

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olga2289 [7]

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Step-by-step explanation:

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3 years ago

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It takes a turtle 3 ¼ hours to walk 1 ½ miles. How many hours does it take to walk one mile?

Norma-Jean [14]

Answer:

It will take 6/13 hours to walk one mile

Step-by-step explanation:

Here, we want to calculate the number of hours it take to walk one mile

From the question, 1 1/2 miles take 3 1/4 hours

the number of hours it will take to walk 1 mile will be;

1 1/2 divided by 3 1/4

= 3/2 divided by 13/4

= 3/2 * 4/13 = 6/13 hours

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3 years ago