UNIDAD III 

RESOLUCION DE TRIANGULOS RECTANGULOS

APLICACIÓN DE LA TRIGONOMETRIA

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UNIDAD II

AREAS  Y PERIMETROS 

Área del triángulo

dibujo

fórmulas

Hallar el área y el perímetro del siguiente triángulo:

dibujo

P = 2 · 11 + 7.5 = 29.5 cm

fórmulas

 

Cuadrado

dibujo

fórmulas

fórmulas

Ejemplo

Calcular el área y el perímetro de un cuadrado de 5 cm de lado.

cuadrado

A = 52 = 25 cm2

Rectángulo

dibujo

fórmulas

fórmulas

Ejemplo

Calcular el área y el perímetro de un rectángulo de 10 cm de base y 6 cm de altura.

rectángulo

P = 2 · (10 + 6) = 32 cm

A = 10 · 6 = 60 cm2

Rombo

dibujo

fórmulas

fórmulas

Ejemplo

Calcular el área y el perímetro de un rombo cuyas diagonales miden 30 y 16 cm, y su lado mide 17 cm.

dibujo

P = 4 · 17 = 68 cm

fórmulas

Área del romboide

dibujo

P = 2 · (a + b)

A = b · h

Ejemplo

Calcular el área y el perímetro de un romboide de 4 y 4.5 cm de lados y 4 cm de altura.

dibujo

P = 2 · (4.5 + 4) = 17 cm

A = 4 · 4 = 16 cm2

Área del trapecio

dibujo

fórmulas

Ejemplo

Calcular el área y el perímetro del siguiente trapecio:

dibujo

fórmulas

Área de un polígono regular

dibujo

fórmulas

n es el número de lados

fórmulas

Ejemplos

Calcular el área y el perímetro de un pentágono regular de 6 cm de lado.

pentágono regular

solución

solución

P = 5 · 6 = 30 cm

solución

Calcular el área y el perímetro de un hexágono regular inscrito en una circunferencia de 4 cm de radio.

dibujo

solución

solución

P = 6 · 4 = 24 cm

 

Perímetro de un círculo

Una circunferencia es el perímetro de un círculo.

radio y diametro de la circunferencia

La longitud de una circunferencia es igual a por el radio.

fórmula

La longitud de una circunferencia es igual a π por el diámetro.

longitud de una circunferencia


 

Ejercicio

Calcular la longitud de una rueda de 90 cm de diámetro.

dibujo

1º A partir del diámetro

fórmula

2º A partir del radio

fórmula

fórmula

AREAS  Y VOLUMNENES   DE LOS CUERPOS SOLIDOS

 

 

Calcula el área lateral, total y el volumen de una pirámide cuadrangular de 10 cm de arista básica y 12 cm de altura.

pirámide cuadrangularapotema lateral de la pirámide

apotema lateral de la pirámide

perímetro

área lateral de la pirámide

área de la pirámide

volumen de la pirámide

Calcula la cantidad de hojalata que se necesitará para hacer 10 botes de forma cilíndrica de 10 cm de diámetro y 20 cm de altura.

dibujo


 

solución

solución


Calcular el área del círculo resultante de cortar una esfera de 35 cm de radio mediante un plano cuya distancia al centro de la esfera es de 21 cm.

radio de una esfera


radio de una esfera

radio de una esfera

 

Calcular el área del círculo resultante de cortar una esfera de 35 cm de radio mediante un plano cuya distancia al centro de la esfera es de 21 cm.

radio de una esfera


radio de una esfera

radio de una esfera

Calcula el volumen, en centímetros cúbicos, de una habitación que tiene 5 m de largo, 40 dm de ancho y 2500 mm de alto.

dibujo


 

solución

solución

solución

solución

 

 

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COMENTARIOS FINALES

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Ukraine has overtaken Greece with ‘three-person baby’!

“The inseparable right of a woman to become a mother with her own genetic material has become a reality,” the president of the Institute of Life in Athens said. He added: “We are very proud to announce international innovation in the field of assisted reproduction, and now we have the opportunity to make the birth of a child a reality for women with several unsuccessful attempts of artificial insemination”.

Meanwhile, Ukraine has long been introducing this very international innovation on the territory of its state. A third world country, as it is often called, is already successfully conducting a unique mitochondrial donation program in local human reproduction centers.
The mitochondrial donation procedure was the next step after donation of eggs and surrogacy. Now, even 40+ years old women have the opportunity to independently carry and give birth to genetically their child. Earlier, many have criticized surrogacy, claiming that it is the exploitation of the female body and the disparagement of honor and dignity of a woman. With mitochondria donation, a barren woman herself carries a baby. The donor only shares healthy mitochondria necessary for successful conception. But even here not everyone is satisfied with the ethical side of the issue.

Thus, some doctors from Britain claim that “the two spheres of application of this method - assistance in conceiving and avoiding transmission of a genetic disease - are very different from a moral point of view”. And therefore, they propose to apply the program only for patients with serious genetic diseases.

Ukraine decided not to dwell only on the genetic cause of childlessness, and successfully uses the method of mitochondrial donation for treatment 40+ women with infertility. Some European doctors believe that this technology may also increase the chances of artificial insemination. Ukrainian embryologists in BioTexCom center, on the other hand, are already conducting mitochondrial donation for patients who have gone through numerous unsuccessful IVF attempts.

To remind, the first “child from three parents” was born in Mexico. Why did the first such children appear not in New York, for example, but in Mexico City and Kyiv - in countries in which no one expected an innovation headship? The answer is simple: because in Mexico and Ukraine it is not prohibited, as for example, in the USA. That is why a team of American doctors traveled to Mexico to conduct such a program there.

The Greek team of doctors also worked together with the Spanish Embryology Center. The Ukrainian experts did everything themselves. They have all the necessary for this - equipment, legality of conducting programs using modern ART, and, most importantly, highly professional specialists in the field of embryology and gynecology.

Today, the global medical community is more focused on helping women with genetic diseases that can be transmitted to the fetus or affect its development and life. Ukrainian specialists, first of all, use mitochondrial donation in the struggle against infertility and the inability of women to carry a child due to mitochondria damage (low functional activity).

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