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Minchanka [31]
3 years ago
12

Evaluate x-2 for x = -3.

Mathematics
1 answer:
Katen [24]3 years ago
5 0
I think the answer is -3-2= -5
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What is the range of the function f(x)=(x-4)^2-5
uranmaximum [27]

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

Vertex (4 , -5)

This function opens upward and has min. value = -5

So range y >=  - 5

So answer is A. -5 <= f(x) < ∞

4 0
3 years ago
Read 2 more answers
Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1
algol [13]

Find the critical points of f(x,y):

\dfrac{\partial f}{\partial x}=-2x=0\implies x=0

\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12

All three points lie within D, and f takes on values of

\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}

Now check for extrema on the boundary of D. Convert to polar coordinates:

f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t

Find the critical points of g(t):

\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0

\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2

\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi

where n is any integer. There are some redundant critical points, so we'll just consider 0\le t< 2\pi, which gives

t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3

which gives values of

\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}

So altogether, f(x,y) has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0
3 years ago
Tell whether the lines of the pair of equations are parallel, perpendicular, or neither.
tino4ka555 [31]
First Equation:

y= -\frac{3}{4} x+2

Second Equation can be written as:

y= \frac{3}{4}x+2

Slope of first equation is -3/4 and slope of second equation is 3/4. 
Slope of parallel lines must be equal, and slope of perpendicular lines are the negative reciprocal of each other. None of these conditions can be seen for given two equations.

So, the two lines are neither parallel nor perpendicular.
So correct option is C
7 0
3 years ago
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Jamal has $ 15.00 to spend at the concession stand. He buys nachos for $7.50, and he wants to purchase some Sour Straws for $1.5
soldier1979 [14.2K]

Answer: 5 sour straws

Step-by-step explanation: If he spends 7.50, then he still has 7.50 left. 7.50 / 5= 1.50

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3 years ago
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Please someone solve for X, I don’t think it needs rounding but I couldn’t come up with an answer.
agasfer [191]

Answer:

x= 10 In (17)

Step-by-step explanation:

5 0
3 years ago
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