Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\sf (\overline{\rm BC})^2 = (\overline{\rm AB})^2 + (\overline{\rm AC})^2[/tex]
[tex]\sf (10)^2 = (8)^2 + (\overline{\rm AC})^2[/tex]
[tex]\sf (\overline{\rm AC})^2 = 100 - 64[/tex]
[tex]\sf (\overline{\rm AC})^2 = 36[/tex]
[tex]\sf \overline{\rm AC} = 6\:m[/tex]
[tex]\boxed{\sf \overline{\rm PC} = \overline{\rm PB}}[/tex]
[tex]\sf (\overline{\rm PC})^2 = (\overline{\rm PA})^2 + (\overline{\rm AC})^2[/tex]
[tex]\sf (8 - \overline{\rm PA})^2 = (\overline{\rm PA})^2 + (6)^2[/tex]
[tex]\sf 64 - 16\overline{\rm PA} + (\overline{\rm PA})^2 = (\overline{\rm PA})^2 + 36[/tex]
[tex]\sf 16\overline{\rm PA} = 28[/tex]
[tex]\sf \overline{\rm PA} = \dfrac{7}{4}\:m[/tex]
[tex]\sf (\overline{\rm PM})^2 = (\overline{\rm PA})^2 - (\overline{\rm MB})^2[/tex]
[tex]\sf (\overline{\rm PM})^2 = \left(8 - \dfrac{7}{4}\right)^2 - (5)^2[/tex]
[tex]\sf (\overline{\rm PM})^2 = \dfrac{625}{16} - 25[/tex]
[tex]\sf \overline{\rm PM} = \dfrac{15}{4}\:m[/tex]
[tex]\sf r = \dfrac{\Delta_{BPM}}{\Delta_{PMC} + \Delta_{PAC}}[/tex]
[tex]\sf r = \dfrac{\dfrac{\overline{\rm PM} \:.\:\overline{\rm MB}}{2}}{\dfrac{\overline{\rm PM} \:.\:\overline{\rm MC}}{2} + \dfrac{\overline{\rm PA} \:.\:\overline{\rm AC}}{2}}[/tex]
[tex]\sf r = \dfrac{\dfrac{75}{8}}{\dfrac{75}{8} + \dfrac{42}{8}}[/tex]
[tex]\boxed{\boxed{\sf r = \dfrac{25}{39}}}[/tex]
Copyright © 2024 ELIBRARY.TIPS - All rights reserved.
Lista de comentários
Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\sf (\overline{\rm BC})^2 = (\overline{\rm AB})^2 + (\overline{\rm AC})^2[/tex]
[tex]\sf (10)^2 = (8)^2 + (\overline{\rm AC})^2[/tex]
[tex]\sf (\overline{\rm AC})^2 = 100 - 64[/tex]
[tex]\sf (\overline{\rm AC})^2 = 36[/tex]
[tex]\sf \overline{\rm AC} = 6\:m[/tex]
[tex]\boxed{\sf \overline{\rm PC} = \overline{\rm PB}}[/tex]
[tex]\sf (\overline{\rm PC})^2 = (\overline{\rm PA})^2 + (\overline{\rm AC})^2[/tex]
[tex]\sf (8 - \overline{\rm PA})^2 = (\overline{\rm PA})^2 + (6)^2[/tex]
[tex]\sf 64 - 16\overline{\rm PA} + (\overline{\rm PA})^2 = (\overline{\rm PA})^2 + 36[/tex]
[tex]\sf 16\overline{\rm PA} = 28[/tex]
[tex]\sf \overline{\rm PA} = \dfrac{7}{4}\:m[/tex]
[tex]\sf (\overline{\rm PM})^2 = (\overline{\rm PA})^2 - (\overline{\rm MB})^2[/tex]
[tex]\sf (\overline{\rm PM})^2 = \left(8 - \dfrac{7}{4}\right)^2 - (5)^2[/tex]
[tex]\sf (\overline{\rm PM})^2 = \dfrac{625}{16} - 25[/tex]
[tex]\sf \overline{\rm PM} = \dfrac{15}{4}\:m[/tex]
[tex]\sf r = \dfrac{\Delta_{BPM}}{\Delta_{PMC} + \Delta_{PAC}}[/tex]
[tex]\sf r = \dfrac{\dfrac{\overline{\rm PM} \:.\:\overline{\rm MB}}{2}}{\dfrac{\overline{\rm PM} \:.\:\overline{\rm MC}}{2} + \dfrac{\overline{\rm PA} \:.\:\overline{\rm AC}}{2}}[/tex]
[tex]\sf r = \dfrac{\dfrac{75}{8}}{\dfrac{75}{8} + \dfrac{42}{8}}[/tex]
[tex]\boxed{\boxed{\sf r = \dfrac{25}{39}}}[/tex]