Use the concept of Lagrange multipliers.
Answer:
-1/4
Step-by-step explanation:
4x - 15 = -16
4x = -1
x = -1/4
The main factor when x values are high is the nature of the function. For example, polynomial functions intrinsically grow slower than exponential functions when x is high. Also, the greater the degree of the polynomial, the more the function grows in absolute value as x goes to very large values.
In specific, this means that our 2 exponential functions grow faster than all the other functions (which are polynomial) and thus they take up the last seats. Also, 7^x grows slower than 8^x because the base is lower. Hence, the last is 8^x+3, the second to last is 7^x.
Now, we have that a polynomial of 2nd degree curves upwards faster than a linear polynomial when x is large. Hence, we have that the two 2nd degree polynomials will be growing faster than the 2 linear ones and hence we get that they fill in the middle boxes. Because x^2+4>x^2, we have that x^2+4 is the 4th from the top and x^2 is the 3rd from the top.
Finally, we need to check which of the remaining functions is larger. Now, 5x+3 is larger than 5x, so it goes to the 2nd box. Now we are done.
Let x represent the length of the shortest side. Then the longest side is
... 2x -7 . . . . . . 7 ft shorter than twice the shortest side
and the 3rd side is
... x +2 . . . . . . 2 ft longer than the shortest side.
The perimeter is the sum of the side lengths,
... x + (2x -7) + (x +2) = 59 . . . . . the given perimeter length
... 4x -5 = 59 . . . . collect terms
... 4x = 64 . . . . . . add 5
... x = 16 . . . . . . . . divide by 4
Then the other sides are
... 2×16 - 7 = 25 . . . . . longest side
... 16 +2 = 18 . . . . . . . . third side
The side lengths are 16 ft, 18 ft, and 25 ft.
Answer:
The answer to your question is:
x = -8; y = 1 ; z = -4
Step-by-step explanation:
Δ = ![\left[\begin{array}{ccc}-5&1&-4\\2&4&3\\6&-3&-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%261%26-4%5C%5C2%264%263%5C%5C6%26-3%26-2%5Cend%7Barray%7D%5Cright%5D)
= 40 + 24 + 18 - (-4 + 45 - 96)
= 82 + 55
= 137
Δx = ![\left[\begin{array}{ccc}60&1&-4\\-12&4&3\\-52&-3&-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D60%261%26-4%5C%5C-12%264%263%5C%5C-52%26-3%26-2%5Cend%7Barray%7D%5Cright%5D)
= - 480 - 144 - 156 - ( 24 - 540 + 832)
= -780 -316
= - 1096
Δy =
= 40 + 24 + 18 - ( - 4 + 45 - 96)
= 82 + 55
= 137
Δz = ![\left[\begin{array}{ccc}-5&1&60\\2&4&-12\\6&-3&-52\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%261%2660%5C%5C2%264%26-12%5C%5C6%26-3%26-52%5Cend%7Barray%7D%5Cright%5D)
= 1040 - 360 - 72 - ( - 104 - 180 + 1440)
= 608 - 1156
= -548
x = -1096/ 137 = -8
y = 137 / 137 = 1
z = -548 / 137 = -4
