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2 years ago

What is the product? (5r − 4)(r2 − 6r + 4)

Mathematics

2 answers:

Kamila [148]2 years ago

7 0

Answer:

Step-by-step explanation:

thank me later

stiks02 [169]2 years ago

5 0

(5r - 4)(r² - 6r + 4)

distributive property of multiplication.

5r(r² - 6r + 4) - 4(r² - 6r + 4)
5r³ - 30r² + 20r - 4r² + 24r - 16

group like terms and simplify.

5r³ - 30r² - 4r² + 20r + 24r - 16

5r³ - 34r² + 44r - 16 Choice A.

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The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 88/(2 + x2 + y2), where T is measured in °C and x,

-Dominant- [34]

Answer:

$D_uT(3,1)=-\frac{44}{9}*\frac{1}{\sqrt{2} } \approx-3.46$

Step-by-step explanation:

To find the rate of change of temperature with respect to distance at the point (3, 1) in the x-direction and the y-direction we need to find the Directional Derivative of T(x,y). The definition of the directional derivative is given by:

$D_uT(x,y)=T_x(x,y)i+T_y(x,y)j$

Where i and j are the rectangular components of a unit vector. In this case, the problem don't give us additional information, so let's asume:

$i=\frac{1}{\sqrt{2} }$

$j=\frac{1}{\sqrt{2} }$

So, we need to find the partial derivative with respect to x and y:

In order to do the things easier let's make the next substitution:

$u=2+x^2+y^2$

and express T(x,y) as:

$T(x,y)=88*u^{-1}$

The partial derivative with respect to x is:

Using the chain rule:

$\frac{\partial u}{\partial x}=2x$

Hence:

$T_x(x,y)=88*(u^{-2})*\frac{\partial u}{\partial x}$

Symplying the expression and replacing the value of u:

$T_x(x,y)=\frac{-176x}{(2+x^2+y^2)^2}$

The partial derivative with respect to y is:

Using the chain rule:

$\frac{\partial u}{\partial y}=2y$

Hence:

$T_y(x,y)=88*(u^{-2})*\frac{\partial u}{\partial y}$

Symplying the expression and replacing the value of u:

$T_y(x,y)=\frac{-176y}{(2+x^2+y^2)^2}$

Therefore:

$D_uT(x,y)=(\frac{1}{\sqrt{2} } )*(\frac{-176x}{(2+x^2+y^2)^2} -\frac{176y}{(2+x^2+y^2)^2})$

Evaluating the point (3,1)

$D_uT(3,1)=(\frac{1}{\sqrt{2} } )*(\frac{-176(3)-176(1)}{(2+3^2+1^2)^2})=(\frac{1}{\sqrt{2} })* (-\frac{704}{144})=(\frac{1}{\sqrt{2} }) ( - \frac{44}{9})\approx -3.46$

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2 years ago

Paula, a college student, earned $3,600 one summer. During the following semester, she spent $2,500 for tuition, $650 for rent,

Softa [21]

So to get the $ spent on misc items, just add up the other expenses and subtract it from 3600:

$2500+650+430=3580\\ \\ 3600-3580=\$ 20$

Now to put them into fractions.

Tuition: $\frac{2500}{3600}=\frac{25}{36}$

Rent: $\frac{650}{3600}=\frac{65}{360}$

Food: $\frac{430}{3600}=\frac{43}{360}$

Misc: $\frac{20}{3600}=\frac{1}{180}$

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Answer:

The answer for edgednuity is

The length of side AD is 8 units.

The length of side A'D' is 4 units.

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Step-by-step explanation:

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