Mathematics, 30.11.2019 00:31 lilpeepxliltracy

The altitude (i. e., height) of a triangle is increasing at a rate of 2.5 cm/minute while the area of the triangle is increasing at a rate of 2.5 square cm/minute. at what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 84 square centimeters?

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Answer from: damilysgonzalez2

The base is decreasing at a rate of 7.8571 centimeters per minute.

Step-by-step explanation:

We are given the following information in the question:

The height of a triangle is increasing at a rate of 2.5 cm/minute

$\displaystyle\frac{dh}{dt} = 2.5 \text{ cm per minute}$

The area of the triangle is increasing at a rate of 2.5 square cm/minute.

$\displaystyle\frac{dA}{dt} = 2.5 \text{ square cm per minute}$

Area of triangle is given by:

$A = \displaystyle\frac{1}{2}\times b\times h$

where A is the area of triangle, b is the base of triangle and h is the height of the triangle.

Differentiating, we get,

$A = \displaystyle\frac{1}{2}\times b\times h\\\\\frac{dA}{dt} = \frac{1}{2}\Bigg(b\frac{dh}{dt} + h\frac{db}{dt}\Bigg)$

We have to find rate of change of base of the triangle when the altitude is 7 centimeters and the area is 84 square centimeters

h = 7 cm

A = 84 square centimeters

$84 = \displaystyle\frac{1}{2}\times 7\times b\\\\b = 24\text{ cm}$

Putting the values, we get:

$\displaystyle\frac{dA}{dt} = \frac{1}{2}\Bigg(b\frac{dh}{dt} + h\frac{db}{dt}\Bigg)\\\\2.5 = \frac{1}{2}\Bigg((24)(2.5) + (7)\frac{db}{dt}\Bigg)\\\\5 - 60 = 7\frac{db}{dt}\\\\\frac{dh}{dt} =-7.8571\text{ cm per minute}$

Thus, the base is decreasing at a rate of 7.8571 centimeters per minute.

Answer from: Quest

answer: 35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %, p(e) = 27 % and $p(l\cap e)$ = 4 %

and, we have to find out, $p(l\cup e)$

but, we know that,

$p(l\cup e)= p(l) + p(e) - p(l\cap e)$

which is the required equation that will use to find the probability of a late departure or an early departure.

$p(l\cup e)= 12 + 27 - 4$

$p(l\cup e)= 35 %$

therefore, the probability of a late departure or an early arrival = 35 %

Answer from: Quest

answer: ay

fonsi

oh no, oh no

oh yeah

diridiri, dirididi daddy

sí, sabes que ya llevo un rato mirándote

tengo que bailar contigo hoy (dy)

vi que tu mirada ya estaba llamándome

muéstrame el camino que yo voy (oh)

tú, tú eres el imán y yo soy el metal

me voy acercando y voy armando el plan

solo con pensarlo se acelera el pulso (oh yeah)

ya, ya me está gustando más de lo normal

todos mis sentidos van pidiendo más

esto hay que tomarlo sin ningún apuro

despacito

quiero respirar tu cuello despacito

deja que te diga cosas al oído

para que te acuerdes si no estás conmigo

despacito

quiero desnudarte a besos despacito

firmo en las paredes de tu laberinto

y hacer de tu cuerpo todo un manuscrito (sube, sube, sube)

(sube, sube)

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The altitude (i. e., height) of a triangle is increasing at a rate of 2.5 cm/minute while the area o...

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