Answer:
Part) A
Density=Mass/volume
Part) B
volume displaced by crown> volume displaced by gold brick
Step-by-step explanation:
Density=Mass/volume
Mass=Density(volume)
The jeweler replace gold with equal weighed silver but as gold has a higher density than silver, the jeweler must put more volume of silver to balance it. Hence the overall volume of crown increases.
2. In bath, Archimedes discovered that the amount of water displaced in tub is equal to the volume of the body that was placed in it.
He then compares the volume of water displaced by a gold brick and the volume of water displaced by the jeweler made crown and when the volumes do not come equal then there is evidence. The volume of water must rises higher in case of crown than in case of brick of gold due to inclusion of silver in it!
Answer:
1r + 8(400) = 3(r+400)
1r + 320 = 3r + 120
2r = 200
r = 200 / 2 = 1000
1400 * 3 = 420
100 + 320 = 420
Step-by-step explanation:
The given expression is in the form (a+b)(a-b) where
a = 5
b = sqrt(3)
Recall that
(a+b)(a-b) = a^2-b^2
is the difference of squares formula
If a = 5, then a^2 = 25
If b = sqrt(3), then b^2 = (sqrt(3))^2 = 3
The squaring undoes the square root. The two opposites cancel out.
So using a^2 = 25 and b^2 = 3, we can say
(a+b)(a-b) = a^2-b^2 = 25-3 = 22
Therefore,
(5+sqrt(3))(5-sqrt(3)) = 22
Answer: B) 22
Answer:
larger number=29;smaller number=18
Step-by-step explanation:
let assume the two numbers are X and Y
where X is the larger number and Y is the smaller number.
From the question the larger number is 7 less than twice the smaller number. in mathematical terms this can be denoted as;
X=2Y - 7→→→→→→ equation 1
Also it was stated in the question that the sum of the two numbers is 47 which can be denoted as;
X + Y = 47→→→→→→ equation 2
Now from equation 1, X is mathematically expressed as 2Y - 7. Having known this we substitute X as 2Y - 7 into equation 2 then we have 2Y - 7 + Y = 47.
collecting like terms we have
2Y + Y = 47 + 7
solving arithmetically we have;
3Y = 54
divide both sides by 3 we have;
Y = 18.
Now if you recall from equation 1;
X = 2Y - 7;
since we now know Y as 18 we substitute Y as 18 in equation one then we have;
X = 2(18) - 7;
X =36 - 7
X = 29.