Answer:
-8,2
Step-by-step explanation:
Factoring:
(x+8)(x-2)
x is -8 or 2
Answer:
-4a +22b
Step-by-step explanation:
add the ones with same variable
De Moivre's Theorem states that if a complex number is written in the polar coordinate form [ r (cosθ +
sinθ)] and you raise it to the power n, then this can be evaluated by raising the modulus (r) to the power and multiply the argument (θ) by the power. This therefore would give r ⁿ [cos (nθ) +
sin (nθ)].
let A = ∛ <span>(8 cos (4π / 5) + 8 i sin (4π / 5))
</span>⇒ A = ∛ <span>(8 [cos (4π / 5) + i sin (4π / 5)])
</span>
Now by applying De Moivre's Theorem,
⇒ A =
[cos (
×
) +
sin (
×
)
⇒ A = 2 [ cos (
) +
sin (
)
⇒ A = 2 [0.0117 +
0.01297 ] rads
Answer:
Step-by-step explanation:
From the given information:
a)
Assuming the shape of the base is square,
suppose the base of each side = x
Then the perimeter of the base of the square = 4x
Suppose the length of the package from the base = y; &
the height is also = x
Now, the restriction formula can be computed as:
y + 4x ≤ 99
The objective function:
i.e maximize volume V = l × b × h
V = (y)*(x)*(x)
V = x²y
b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):
y + 4x ≤ 99 --- (1)
V = x²y --- (2)
From equation (1),
y ≤ 99 - 4x
replace the value of y into (2)
V ≤ x² (99-4x)
V ≤ 99x² - 4x³
Maximum value V = 99x² - 4x³
At maxima or minima, the differential of
⇒ 198x - 12x² = 0
By solving for x:
x = 0 or x =
Again:
V = 99x² - 4x³
At x =
= -198
Thus, at maximum value;
Recall y = 99 - 4x
when at maximum x =
y = 33
Finally; the volume V = x² y is;
V = 8984.25 inches³
33 units squared
because you split up the shape into 3. you get a 4x6 rectangle and two triangle that come together and make 3x3.
4x6=24
3x3=9
24+9=33
33 units squared