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3 years ago

Tell whether each function is linear or nonlinear. The new tell whether the function is increasing or decreasing.

Mathematics

1 answer:

DerKrebs [107]3 years ago

4 0

Answer:

increasing and linear

Step-by-step explanation:

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What is the intersection of plane ABC and plane CDH

katovenus [111]

The intersection of plane ABC and plane CDH is <u>line DC</u>.

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3 years ago

Jerry drew JKL and MNP so that K= N,L= P, JK=6, and MN=18. Are JKL and MNP similar? IF so, identify the similarity postulate or

Nesterboy [21]

The right answer is similar-aa

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3 years ago

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Vertices A and B of triangle ABC are on one bank of a river, and vertex C is on the opposite bank. The distance between A and B

Anna71 [15]

Answer:

The length of side b is 179 ft

Step-by-step explanation:

Given triangle ABC in which

∠A = 33°, ∠B = 63°, c=200

we have to find the length of b

In ΔABC, by angle sum property of triangle

∠A+∠B+∠C=180°

33°+63°+∠C=180°

∠C=180°-33°-63°=84°

By sine law,

$\frac{\sin \angle A}{a}=\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}$

$\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}$

$\frac{\sin 63^{\circ}}{b}=\frac{\sin 84^{\circ}}{200}$

$b=200\times \frac{\sin 63^{\circ}}{\sin 84^{\circ}}=179.182887\sim 179 ft$

The length of side b is 179 ft

Option C is correct.

7 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).

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3 years ago

Evaluate 3a+15+bc−6, when a=7, b=3, and c=15.<br><br> Enter your answer in the box.

melamori03 [73]

I think it's 75.
____________

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3 years ago

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