I assume there are some plus signs that aren't rendering for some reason, so that the plane should be
.
You're minimizing
subject to the constraint
. Note that
and
attain their extrema at the same values of
, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.
The Lagrangian is
Take your partial derivatives and set them equal to 0:
Adding the first three equations together yields
and plugging this into the first three equations, you find a critical point at
.
The squared distance is then
, which means the shortest distance must be
.
The inequalities which matches the graph are: x ≥ ₋1.5 and ₋1.5 ≤ x
Given, a number line is moving from ₋3 to ₊5 .
Next a mark is made at ₋1.5 and everything to its left is shaded which means not visible.
When we mark the point and shade the left part of it then we can start applying the inequality expressions.
And from that we can match the applicable inequalities while observing the graph.
- For the first inequality ₋1.5 ≥ x.Here,x value ranges from ₋1.5 to ₊5, hence we take this as an inequality expression.
- Next, if we consider x ≤ ₋1.5, then here x value will range from ₋1.5 to ₋3. where the region is shaded. Hence this expression doesn't satisfy the graph.
- the next expression is ₋1.5 ≤ x. here the value will again range in the shaded area so it is not applicable.
- ₋1.5 ≥ x, here the values will satisfy the graph.
- remaining inequality expressions does not support the graph.
Therefore the only inequalities the graph represents is x ≥ ₋1.5 and ₋1.5 ≤ x
Learn more about "Linear Inequalities" here-
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Answer:
C
Step-by-step explanation:
Calculate AC using Pythagoras' identity in ΔABC
AC² = 20² - 12² = 400 - 144 = 256, hence
AC = 
= 16
Now find AD² from ΔACD and ΔABD
ΔACD → AD² = 16² - (20 - x)² = 256 - 400 + 40x - x²
ΔABD → AD² = 12² - x² = 144 - x²
Equate both equations for AD², hence
256 - 400 + 40x - x² = 144 - x²
-144 + 40x - x² = 144 - x² ( add x² to both sides )
- 144 + 40x = 144 ( add 144 to both sides )
40x = 288 ( divide both sides by 40 )
x = 7.2 → C
Answer:
Part A:
We are given that E is 3 more than D. This means that to get the value of E, we will simply add 3 to the value of D
Therefore:
E = D + 3
Part B:
We are given that F is 5 less than D. This means that to get the value of F, we will simply subtract 5 from the value of D
Therefore:
F = D - 5
Part C:
To get the value of E-F, we will simply subtract the equation we obtained from part B from the equation we obtained from part A
Therefore:
E - F = (D+3) - (D-5)
E - F = D + 3 - D + 5
E - F = 8
Hope this helps :)
Step-by-step explanation:
Answer:
the area = 25
Step-by-step explanation:
a= side length x side length
a = 5 x 5
a = 25
