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2 years ago

Use the drawing tool(s) to form the correct answer on the provided number line.

Mathematics

1 answer:

Nat2105 [25]2 years ago

7 0

Answer:

j=42.36

Step-by-step explanation:

=15 to original answer

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A side of the triangle below has been extended to form an exterior angle of 132 degrees. Find the value of x.

Lemur [1.5K]

Answer:

48°

Step-by-step explanation:

m∠x plus 132° equals 180°, so x equals 180 minus 132, or 48°.

6 0

2 years ago

3 ounces of cinnamon cost $2.40. There are 16 ounces in 1 pound how much the cinnamon cost per pound

faltersainse [42]

16 ounces in a pound
2.40 for 3 ounces
16 divided by 3 = 5.333
$2.40 * 5.333 =$
12.8
Approx $12.80 for 1 pound of cinnamon

3 0

2 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

2 years ago

Which place is the 7 in 115.87

kirill [66]

Answer:

Hundredth

Step-by-step explanation:

Hundrends, Tens, decimal, tenth, hundredth

4 0

2 years ago

What number is represented by point P?

likoan [24]

Answer:

0.0057

Step-by-step explanation:

Narrow it down.
The point P is between 5 * 10^-3 and and 6*10^-3
When you go to the bottom line, P is on the 7th division from the left.
Going from left to right increases P
P is on a line that goes between 5 and 6. Each division is 1/10. So P is in the tenth place.
One of the answers is 5.7 * 10^-3
The other answer is .0057
I really don't know which one to choose because we are given no direction. As a programmer, 0.0057 would be easier to program. I would choose it.
If it is not correct, then 5.7 * 10^-3 is the answer.

4 0

2 years ago