Which function has a range of {y|y ≤ 5}?

Mathematics

2 answers:

Sliva [168]3 years ago

4 0

Answer:

f(x)=-(x-4)^2+5

Step-by-step explanation:

Desmos graphing calculator is a very good help for these type of graphing calculations.

Radda [10]3 years ago

3 0

Range is ouput
testing limints
basically see the vertices
y=a(x-h)^2+k
(h,k) is vertex

also, when a is negative, graph opens down
when a is positive, graph opens up

y<5
k musbe 5

eliminate last 2

since less than, must open down
negative a
second one

f(x)=-(x-4)^2+5 is ansre

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K = [ 14 -13 0 3 8 -1 -10 -2 5 ] find the determinant of K

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$K = \begin{bmatrix}14 & -13 & 0 \\ 3 & 8 & -1 \\ -10 & -2 & 5\end{bmatrix}$

To compute det(K), you can use a simple cofactor expansion along the first row:

$\det(K) = 14\times\det\begin{bmatrix}8 & -1 \\-2 & 5\end{bmatrix} - (-13)\times\det\begin{bmatrix}3 & -1 \\ -10 & 5\end{bmatrix} + 0\times\det\begin{bmatrix}3 & 8 \\ -10 & -2\end{bmatrix} \\\\ \det(K) = 14\times(8\times5-(-1)\times(-2)) + 13\times(3\times5-(-1)\times(-10)) + 0 \\\\ \det(K) = 14\times38 + 13\times5 = \boxed{597}$