I think the volume of cylinder B will be the same as that of cylinder A that is 360cm³
This is because the volume of the cylinder is dependent on the base and the perpendicular height, therefore, the slanting of the cylinder wont change its volume
This might be a problem considering he would have no money left considering unless I made a mistake all the numbers add up to 1,400 so considering this he won't have money to spend if he get in a situation that he needs to spend
(I am not 100% sure this is the answer you are looking for)
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work
EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same
For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y
For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4
Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.
Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the
x²y = -4 ... (I)
Condition 2: Real parts are the same
x² + y = -3 ... (II)
We have a system of equations since both conditions must be satisfied
x²y = -4 ... (I)
x² + y = -3 ... (II)
We can rearrange equation (II) so that we have
y = -3 - x² ... (II)
Substituting into equation (I)
x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0
Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.
Solve for y:
y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4
So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:
-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i
x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i
They result in conjugates
A
(-2c-3d) (- 11) (- 2c-3d) (- 11) left parenthesis, minus, 2, c, minus, 3, d, right parenthesis, left parenthesis, minus, 11, right parenthesis
C
(66c + 99d) \ cdot \ dfrac {1} {3} (66c + 99d) ⋅ 3
1 left parenthesis, 66, c, plus, 99, d, right parenthesis, dot, start fraction, 1, divided by, 3, end fraction
<span> E
11\cdot(2c+3d)11⋅(2c+3d)11, dot, left parenthesis, 2, c, plus, 3, d, right parenthesis
</span> answer
(-2c-3d) (- 11) = 22c + 33d
(66c + 99d) * 1/3 = 22c + 33d
11 * ( 2c+3d) = 22c + 33d
Mrs. Smythe = x
Daughter = y
x = 2y
(x - 10) + (y - 10) = 46
x - 10 + y - 10 = 46
x + y - 20 = 46
x + y = 66
Put 2y in for x
2y + y = 66
3y = 66
y = 66/3
y = 22
The daughter is 22
The mother = 44
