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2 years ago

A 25 foot rope was cut into 2 pieces with the length being a ratio of 5 to 12.

Mathematics

1 answer:

gizmo_the_mogwai [7]2 years ago

8 0

Answer: The short piece is approximately 7.5 feet

Step-by-step explanation: Since the 25 foot rope was cut into 2 pieces and the ratio is 5 to 12, that means the total amount would be 17. 25/17 rounded to the nearest tenths is 1.5. We then multiply 5 by 1.5 because 1.5 is the unit resulting in 7.5. This shows that the shorter piece is approximately 7.5 feet. Hope this helps

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Which expression can be used find 40% of 130?

olya-2409 [2.1K]

40% = 0.40 = 2/5
So multiplying 130 × 2/5 (bc "% of" means multiply)... divide 130 by 5 = 26
What's left over??
2 × 26
4. (26)(2)

6 0

3 years ago

Read 2 more answers

Consider the following equation. f(x, y) = e−(x − a)2 − (y − b)2 (a) Find the critical points. (x, y) = a,b (b) Find a and b suc

murzikaleks [220]

$f(x,y)=e^{-(x-a)^2-(y-b)^2}\implies\begin{cases}f_x=-2(x-a)e^{-(x-a)^2-(y-b)^2}\\f_y=-2(y-b)e^{-(x-a)^2-(y-b)^2}\end{cases}$

Critical points occur where $f_x=f_y=0$ . The exponential factor is always positive, so we have

$\begin{cases}-2(x-a)=0\\-2(y-b)=0\end{cases}\implies(x,y)=\boxed{(a,b)}$

b. As the previous answer established, the critical point occurs at (-3, 8) if $\boxed{a=-3}$ and $\boxed{b=8}$ .

c. Check the determinant of the Hessian matrix of $f(x,y)$ :

$\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}$

The second-order derivatives are

$f_{xx}=(-2+4(x-a)^2)e^{-(x-a)^2-(y-b)^2}$

$f_{xy}=4(x-a)(y-b)e^{-(x-a)^2-(y-b)^2}$

$f_{yx}=4(x-a)(y-b)e^{-(x-a)^2-(y-b)^2}$

$f_{yy}=(-2+4(y-b)^2)e^{-(x-a)^2-(y-b)^2}$

so that the determinant of the Hessian is

$\det\mathbf H(x,y)=f_{xx}f_{yy}-{f_{xy}}^2=\left((4(x-a)^2-2)(4(y-b)^2-2)-16(x-a)^2(y-b)^2\right)e^{-2(x-a)^2-2(y-b)^2}$

$\det\mathbf H(x,y)=(16(x-a)^2(y-b)^2-8(x-a)^2-8(y-b)^2)+4)e^{-2(x-a)^2-2(y-b)^2}$

The sign of the determinant is unchanged by the exponential term so we can ignore it. For $a=x=-3$ and $b=y=8$ , the remaining factor in the determinant has a value of 4, which is positive. At this point we also have

$f_{xx}(-3,8;a=-3,b=8)=-2$

which is negative, and this indicates that (-3, 8) is a local maximum.

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3 years ago

Let line L1 be the graph of 5x + 8y = -9. Line L2 is perpendicular to line L1 and passes through the point (10,10). If line L2 i

AleksandrR [38]

Slope-Intercept Form: y = mx + b, with m = slope and b = y-intercept

So firstly, remember that perpendicular lines have slopes that are negative reciprocals to each other. To find the slope of L1, the easiest method is to convert it into slope-intercept form.

Firstly, subtract 5x on both sides of the equation: $8y=-5x-9$