Question

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1) Dada as matrizes abaixo calcule:

a) A + B

b) B X A

c) A T

d) B T

e) O determinante da matriz B

f) O determinante da matriz A

2) Calcule a área lateral, área da base, área total e o volume de um cone reto cujo
raio da base mede 6 cm, sua geratriz mede 10 cm e sua altura mede?

8a8e2fdce37aa15a7f192dbdd14cf6e0.pdf

Answer 1

Resposta:

Explicação passo a passo:

$1)$

$a)$

$A+B=\left[\begin{array}{cc}1+2&2+3\\-4+6&5+7\\\end{array}\right]$

$A+B=\left[\begin{array}{cc}3&5\\2&12\\\end{array}\right]$

$b)$

$BXA=\left[\begin{array}{ccc}2.1+3.(-4)&2.2+3.5\\6.1+7.(-4)&6.2+7.5\\\end{array}\right]$

$BXA=\left[\begin{array}{ccc}2-12&4+15\\6-28&12+35\\\end{array}\right]$

$BXA=\left[\begin{array}{ccc}-10&19\\-22&47\\\end{array}\right]$

$c)$

$A^{T} =\left[\begin{array}{ccc}1&-4\\2&5\\\end{array}\right]$

$d)$

$B^{T} =\left[\begin{array}{ccc}2&6\\3&7\\\end{array}\right]$

$e)$

$det(B)=2.7-3.6=14-18=-4$

$f)$

$det(A)=1.5-2.(-4)=5+8=13$

$2)$

$r=6\:cm$

$g=10\:cm$

$h=?$

$g^{2} =h^{2}+r^{2}$

$10^{2}=h^{2} +6^{2}$

$100=h^{2}+36$

$h^{2} =100-36$

$h^{2}=64$

$h=\sqrt{64}$

$h=8\:cm$

$A_{base} =\pi r^{2}$

$A_{base} =\pi .6^{2}$

$A_{base} =36\pi \:cm^{2}$

$A_{lateral} =\pi rg$

$A_{lateral} =\pi .6.10$

$A_{lateral} =60\pi \:cm^{2}$

$A_{total}=\pi r.(g+r)$

$A_{total}=\pi.6.(10+6)$

$A_{total}=6\pi .(16)$

$A_{total}=96\pi \:cm^{2}$

$V=\frac{1}{3}\pi r^{2}h$

$V=\frac{1}{3}\pi .6^{2}.8$

$V=\frac{1}{3}\pi .36.8$

$V=\frac{288\pi }{3}$

$V=96\pi \:cm^{3}$