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2 years ago

Overlapping triangles

Mathematics

1 answer:

never [62]2 years ago

5 0

Answer:

Overlapping triangles are triangles that occupy some of the same space. They share lines or angles! Sometimes it is beneficial to pull the triangles apart and look at them separately in order to use them in math problems. Just like workers' duties can overlap, so can the area of triangles!

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Irrational number formula

alexgriva [62]

Answer:

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2 years ago

Correct answer gets brainliest!<br>find two expressions whose difference is 3x + 4

il63 [147K]

Answer:

(7x+4) and (4x)

Step-by-step explanation:

The two expressions are (7x+4) and (4x)

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2 years ago

-3x + 3y =3<br> -5x + y =13 Solve as a whole number

anzhelika [568]

Answer:

X = 3 x − 14

y = − x + 5

Step-by-step explanation:

Solve for the first variable, then substitute the result into the other equation.

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2 years ago

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A bicycle company has designed and built a new model of sports bicycle. They have determined that the profit for the sale of the

ycow [4]

The answer would be c)$120

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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

2 years ago

Overlapping triangles ​

Overlapping triangles