Sry idk wish I could know but good luck
LM is 6.9 to 1dm and LM is 8
For the derivative tests method, assume that the sphere is centered at the origin, and consider the
circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined
1
by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner
by
x2+y2+z2=r2 =⇒z= r2−(x2+y2).
Then the volume of a box with this coordinate for the corner is given by
V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),
and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the
boundary of this domain, so we need only consider critical points contained inside the domain in order
to carry this optimization out.
For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint
x2 + y2 + z2 = r2<span>. </span>
Absolute Value
Absolute Value
means ...
... only how far a number is from zero:
<span>
<span><span>
</span>
<span>
<span>
"6" is 6 away from zero,
and "−6" is also 6 away from zero.
So the absolute value of 6 is 6,
and the absolute value of −6 is also 6 </span>
</span>
</span></span>
More Examples:
<span><span>The absolute value of −9 is 9</span><span>The absolute value of 3 is 3</span><span>The absolute value of 0 is 0</span><span>The absolute value of −156 is 156</span></span>
No Negatives!
So in practice "absolute value" means to remove any negative
sign in front of a number, and to think of all numbers as positive (or
zero).
Absolute Value Symbol
To show that we want the absolute value of something, we put
"|" marks either side (they are called "bars" and are found on the right
side of a keyboard), like these examples:
<span>
<span><span>
|−5| = 5
|7| = 7
</span>
</span></span>
Sometimes absolute value is also written as "abs()", so abs(−1) = 1 is the same as <span>|−1| = 1</span>
Answer:
B. m ∠ 1 = 90° and m ∠ 2 = 90°
Step-by-step explanation:
For most situations, the conjecture would probably be true, but there is one exception that makes this statement false.
When two right angles are supplementary, none of them is acute.
For an angle to be acute it needs to be lesser than 90°, and for a pair of angles to be supplementary they should add up to exactly 180°.
With a pair of right angles (90° each), their sum adds up to 180° but neither of them are acute.
Therefore, the answer is B. m ∠ 1 = 90° and m ∠ 2 = 90°
