Find the magnitude and direction of CD for the given coordinates. Round answers to the nearest tenth.

El triángulo ABC es equilátero y L, M y N son los puntos medios de BC, AB y CA respectivamente. Si MN = 3, ¿cuál es el valor de

Flauer [41]

The value of ML = 3, using the mid-point theorem of triangles.

According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."

In the question, we are given that triangle ABC is an equilateral triangle, and L, M, and N are the midpoints of BC, AB, and CA respectively.

Thus, by the midpoint theorem, we can say that:

MN || BC, and MN = (1/2)BC,
ML || AC, and ML = (1/2)AC, and
NL || AB, and NL = (1/2)AB.

Assuming AB = BC = AC = x units, we get:

MN = (1/2)BC = x/2,
ML = (1/2)AC = x/2, and
NL = (1/2)AB = x/2.

Thus, the triangle LMN is an equilateral triangle.

Thus, MN = ML = NL.

Given MN = 3, we can write the value of ML = 3.

Thus, the value of ML = 3, using the mid-point theorem of triangles.

Learn more about the mid-point theorem of triangle at

brainly.com/question/9635025

#SPJ1

The given question is in Spanish. The question in English is:

"Triangle ABC is equilateral and L, M, and N are the midpoints of BC, AB, and CA respectively. If MN = 3, what is the value of ML?"

4 0

2 years ago

What is the range, min, and max of the function f(x)=13-20x-x²-3x⁴

Naya [18.7K]

Answer:

range: (-∞, 29.4336]
min: -∞
max: 29.4336

Step-by-step explanation:

I found these using a graphing calculator. (See attached)

The function is a polynomial of 4th degree with a negative leading coefficient. (The coefficient of the 4th-degree term is -3.) Therefore, it opens downward and has a range that extends to -∞. This function only has one global maximum and no local minimum.

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The maximum can be found by solving the cubic equation that results from taking the derivative of this function and finding the root of that:

df/dx = -12x^3 -2x -20 = 0

There are formulas for the solutions of a cubic, but the one negative real root of this cubic can be found easily with a graphing calculator using iteration:

x ≈ -1.13879908894.

Dividing by -2, the above derivative function can be written as ...

g(x) = 6x^3 +x +10

The one real zero of it can be found using Newton's Method iteration.

The Newton's Method iterator function is

h(x) = x - g(x)/g'(x)

where g'(x) is the derivative of g(x), often available as a function on the graphing calculator.

The starting value for the iteration can be the x-value obtained from the graph: -1.139. It only takes about 2 or 3 iterations to find x to the precision of the calculator: x = h(h(x)). This x is the x-coordinate of the maximum, so f(x) is the maximum value: 29.4335546516.

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The attachments show the function definitions and their use for finding the maximum of f(x) using a TI-84 calculator. Y₁ is the function f(x); Y₂ is its derivative, shown above as g(x). Y₃ is the iterating function, shown above as h(x). The nDeriv( ) function is a calculator function that finds the numerical derivative of its argument.

6 0

3 years ago

PLEASE HELP LAW OF COSINES

chubhunter [2.5K]

The Law of Cosine states
cos $C=(a^2+b^2-c^2)/2ab$

so plugging in the numbers gives us

cos $J=(13^2+19^2-11^2)/2(13*19) = 409/494$

We now have cosJ so plug that into your calculator and find arccos (arccos(cos(J)) = J)
arccos $(409/494)=34.11$
rounding your answer will give you 34°

7 0

3 years ago

Read 2 more answers

A phone store employee earns a salary of $450 per week plus 10% comission on her weekly sales. A) What function rule models the

Gelneren [198K]

Answer:

A) $E(w)=450+0.10w$