All categories

3 years ago

Suppose g(x) = 2^x and h(x) = x^2. Which is greater, g(15) or h(15)?

Mathematics

1 answer:

trasher [3.6K]3 years ago

3 0

G(15)

g= 2^15 = 32768
h= 15^2 = 225

You might be interested in

What is -1 = 5/8b + 3/8

andrew-mc [135]

Answer:

exact form - b = -11/5

decimal form - b = -2.2

Mixed number form - b = -2 1/5

4 0

3 years ago

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

A 176 inch pole is leaning up against a wall, but is sliding down the wall so that the vertical distance between the top of the

natta225 [31]

Answer:

... Wall, But Is Sliding Down The Wall So That The Vertical Distance Between The Top Of The Pole And The Floor Is Decreasing At A Rate Of 4 Inches Per Second. How Fast Is The Horizontal Distance Between The Bottom Of The Pole And ... A 176 inch pole is leaning up against a wall, but is sliding down the wall so that the ...

Step-by-step explanation:

3 0

3 years ago

Diego has $500 in his savings account. Each month, he takes out $20 to pay for karate class.

Firlakuza [10]

Answer:

500- (m*20)=?

Step-by-step explanation:

3 0

2 years ago

Need help please. Thanks in advance

S_A_V [24]

3x+4=10
Subtract 4 from both sides
3x=6
Divide both sides by 3
X=2

Sides = 10,10,5

Problem 5. 4x+1=29
Subtract 1 from both sides
4x=28
X=7

7 0

3 years ago