Answer:
ΔDBE≅ΔQAP (by RHS criteria)
Step-by-step explanation:
Given that,
,
,
⊥![PE](https://tex.z-dn.net/?f=PE)
and
⊥![PE](https://tex.z-dn.net/?f=PE)
⇒∠PAQ=90° and ∠EBD=90°(definition of perpendicular lines)
Its given that PB=AE,
subtracting AB on both sides,
we get: PB-AE=AB-AE
⇒PA=EB (equals subtracted from equals, the remainders are equals)
Therefore, ΔDBE≅ΔQAP (by RHS criteria)
conditions for congruence:
- ∠DBE=∠QAP=90°(right angle)
- PQ=ED(hypotenuse)
- PA=EB(side)
So, ∡D=∡Q(as congruent parts of congruent triangles are equal)
<span><span><span><span>x2</span>+x</span>−6</span>=<span>−4
</span></span>At first ubtract -4 from both sides.
<span><span><span><span><span>x2</span>+x</span>−6</span>−<span>(<span>−4</span>)</span></span>=<span><span>−4</span>−<span>(<span>−4</span>)
</span></span></span><span><span><span><span>x2</span>+x</span>−2</span>=0
</span>the factor left side of equation.
<span><span><span>(<span>x−1</span>)</span><span>(<span>x+2</span>)</span></span>=0
</span> factors equal to 0.
<span><span><span>x−1</span>=<span><span><span>0 or </span>x</span>+2</span></span>=0
</span><span><span>x=<span><span>1 or
</span>x</span></span>=<span>−2</span></span>
1) We calculate the volume of a metal bar (without the hole).
volume=area of hexagon x length
area of hexagon=(3√3 Side²)/2=(3√3(60 cm)²) / 2=9353.07 cm²
9353.07 cm²=9353.07 cm²(1 m² / 10000 cm²)=0.935 m²
Volume=(0.935 m²)(2 m)=1.871 m³
2) we calculate the volume of the parallelepiped
Volume of a parallelepiped= area of the section x length
area of the section=side²=(40 cm)²=1600 cm²
1600 cm²=(1600 cm²)(1 m² / 10000 cm²=0.16 m²
Volume of a parallelepiped=(0.16 m²)(2 m)=0.32 m³
3) we calculate the volume of a metal hollow bar:
volume of a metal hollow bar=volume of a metal bar - volume of a parallelepiped
Volume of a metal hollow bar=1.871 m³ - 0.32 m³=1.551 m³
4) we calculate the mass of the metal bar
density=mass/ volume ⇒ mass=density *volume
Data:
density=8.10³ kg/m³
volume=1.551 m³
mass=(8x10³ Kg/m³ )12. * (1.551 m³)=12.408x10³ Kg
answer: The mas of the metal bar is 12.408x10³ kg or 12408 kg
I think that 5/3 is not equivalent to this numbers because 2/3 cannot be written in another as 5/3. It can only be written as 6/9 or 4/6. Im not entirely sure but i hope this helped.