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il63 [147K]
4 years ago
10

Se tiene una pirámide regular cuadrangular cuyas caras laterales forman con la base un angulo que mide 53º y el area de la super

ficie lateral es 60 ¿cuanto mide la altura?
Mathematics
1 answer:
SIZIF [17.4K]4 years ago
8 0

Answer:

La altura de la pirámide es de 8.14 unidades.

Step-by-step explanation:

Hay una pirámide cuadrangular regular cuyas caras laterales forman un ángulo que mide 53º con la base y el área de la superficie lateral es 60. ¿Qué altura tiene?

Dado que el área de superficie lateral = 60

Tenemos

Área del triángulo equilátero = (√3 / 4) × a²

 (√3 / 4) × a² = 60

a² = 60 / (√3 / 4) = 80 · √3

a = √ (80 · √3) = 11.77 unidades

La altura inclinada = Altura de la superficie inclinada = a × sin (60) = 11.77 × sin (60)

La altura inclinada = 11.77 × sin (60) = 10.194 unidades

La altura de la pirámide = Altura inclinada × sin (ángulo de caras laterales con la base)

La altura de la pirámide = 10.194 × sin (53) = 8.14 unidades.

La altura de la pirámide = 8.14 unidades.

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Determine the amount needed such that when it comes time for retirement, an individual can make monthly withdraws in the amount
bazaltina [42]

Answer:

The amount needed such that when it comes time for retirement is $396721.78.

Step-by-step explanation:

Given : An individual can make monthly withdraws in the amount of $2,154 for 30 years from an account paying 5.1% compounded monthly.

To find : The amount needed such that when it comes time for retirement?

Solution :

Using the formula of monthly payment,

Monthly payment, M=\frac{\text{Amount}}{\text{Discount factor}}

Discount factor D=\frac{1-(1+i)^{-n}}{i}  

Where,

Amount = ?

Monthly payment  M=$2154

Rate r= 5.1%=0.051

i=\frac{0.05}{12}=0.00425

Time = 30 years  

n=30\times12=360

Substitute all the values,

D=\frac{1-(1+i)^{-n}}{i}

D=\frac{1-(1+0.00425)^{-360}}{0.00425}

D=\frac{1-(1.00425)^{-360}}{0.00425}

D=\frac{1-0.21723}{0.00425}  

D=\frac{0.78277}{0.00425}

D=\$184.1811

Monthly payment, M=\frac{\text{Amount}}{\text{Discount factor}}

2154=\frac{A}{184.1811}

A=2154\times 184.1811  

A=\$396721.778

Nearest cent, A=\$396721.78

Therefore, the amount needed such that when it comes time for retirement is $396721.78.

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4 years ago
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