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3 years ago

Please Help! Geometry!

Mathematics

1 answer:

UkoKoshka [18]3 years ago

3 0

Step-by-step explanation:

$arcLM = 2\pi .r (\frac{72}{360} )$

$= 2\pi(1) \times 0.2$

$= 0.4\pi$

You might be interested in

The equations that must be solved for maximum or minimum values of a differentiable function w=f(x,y,z) subject to two constrai

sammy [17]

The Lagrangian is

$L(x,y,z,\lambda,\mu)=x^2+y^2+z^2+\lambda(4x^2+4y^2-z^2)+\mu(2x+4z-2)$

with partial derivatives (set equal to 0)

$L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0$

$L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0$

$L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0$

$L_\lambda=4x^2+4y^2-z^2=0$

$L_\mu=2x+4z-2=0\implies x+2z=1$

Case 1: If $y=0$ , then

$4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|$

Then

$x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23$

$\implies x=\dfrac15\text{ or }x=-\dfrac13$

So we have two critical points, $\left(\dfrac15,0,\dfrac25\right)$ and $\left(-\dfrac13,0,\dfrac23\right)$

Case 2: If $\lambda=-\dfrac14$ , then in the first equation we get

$x(1+4\lambda)+\mu=\mu=0$

and from the third equation,

$z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0$

Then

$x+2z=1\implies x=1$

$4x^2+4y^2-z^2=0\implies1+y^2=0$

but there are no real solutions for $y$ , so this case yields no additional critical points.

So at the two critical points we've found, we get extreme values of

$f\left(\dfrac15,0,\dfrac25\right)=\dfrac15$ (min)

and

$f\left(-\dfrac13,0,\dfrac23\right)=\dfrac59$ (max)

5 0

4 years ago

Help asp

Svetradugi [14.3K]

<h3>The temperature drop from the morning to the night is -16.8 F</h3>

Solution:

Given that,

The temperature in the morning was -4 F

At night the temperature dropped to -12.8 F

To find: temperature drop from the morning to the night be represented

From given,

Morning = -4 F

Night = -12.8 F

Therefore,

Temperature drop from the morning to the night = -4 - 12.8 = -16.8 F

Thus the temperature drop from the morning to the night is -16.8 F

3 0

3 years ago

What is the inverse of the function f(x) = 2x – 10?

strojnjashka [21]

Answer:

see explanation

Step-by-step explanation:

let y = f(x) then rearrange making x the subject

y = 2x - 10 ( add 10 to both sides )

y + 10 = 2x ( divide both sides by 2 )

$\frac{y+10}{2}$ = x

Change y back into terms of x

$f^{-1}$ (x) = $\frac{x+10}{2}$

6 0

3 years ago

£980 is divided between Caroline, Sarah & Gavyn so that Caroline gets twice as much as Sarah, and Sarah gets three times as

Nitella [24]

Sarah has received £ 294

Solution:

Given that £980 is divided between Caroline, Sarah & Gavyn

Let "c" be the amount received by caroline

Let "s" be the amount received by sarah

Let "g" be the amount received by gavyn

Caroline gets twice as much as Sarah

amount received by caroline = twice as much as Sarah

amount received by caroline = 2(amount received by sarah)

c = 2s ---- eqn 1

Sarah gets three times as much as Gavyn

amount received by sarah = three times as much as Gavyn

amount received by sarah = 3(amount received by gavyn)

s = 3g ------- eqn 2

Given that total amount is 980

c + s + g = 980 --- eqn 3

Let us solve eqn 1, 2, 3 to get values of "c" "s" "g"

From eqn 2,

$g = \frac{s}{3}$ --- eqn 4

Substitute eqn 1 and eqn 4 in eqn 3

$2s + s + \frac{s}{3} = 980\\\\\frac{6s + 3s + s}{3} = 980\\\\6s + 3s + s = 980 \times 3\\\\10s = 2940\\\\s = 294$

Thus sarah has received £ 294

7 0

3 years ago

(3k^3+4k^2-2)-(5k^2-9)-(7k^3+6k)

mr Goodwill [35]

Answer:

− 4 k3− k 2− 6 k+7

Step-by-step explanation:

I just simplified the expression.

4 0

3 years ago