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2 years ago

Shari walks 5 blocks to school each morning.The walk takes 10 minutes

1 answer:

4 0

Answer:
If she walks 5 blocks and it takes 10 minutes each block takes 2 minutes to walk.

10
— = 2 So 2 minutes per block
5

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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)

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

6 0

2 years ago

Find the area of the kite

Thepotemich [5.8K]

Step-by-step answer:

Area of a kite is half of the product of the diagonals.

The length of diagonal in the x-direction is 4+5 = 9

The length of diagonal in the y-direction is 4+4 = 8

Therefore

Area of kite = 8*9/2 = 36 units.

3 0

2 years ago

Read 2 more answers

70.18 divided by 0.9 round the answer to the nearest hundredth

storchak [24]

Answer:

77.98

Step-by-step explanation:

4 0

1 year ago

Read 2 more answers

Which function has no horizontal asymptote? F (x) = StartFraction 2 x minus 1 Over 3 x squared EndFraction f (x) = StartFraction

yanalaym [24]

Answer:

$f(x)=\frac{2x^2}{3x-1}$

Step-by-step explanation:

The function $f(x)=\frac{2x-1}{3x}$ has a horizontal asymptote which is $y=\frac{2}{3}$

The function $f(x)=\frac{x-1}{3x}$ has a horizontal asymptote which is $y=\frac{1}{3}$

The function $f(x)=\frac{2x^2}{3x-1}$ has no horizontal asymptote because the numerator has a degree which is higher than the degree of the denominator,

The function $f(x)=\frac{3x^2}{x^2-1}$ has a horizontal asymptote which is $y=3$

3 0

1 year ago

Read 2 more answers

Every $4,000 spent on cable TV will reach 160 fans while every $2,750 spent on radio ad will reach 125 fans. A stadium has estab

laila [671]

Answer:

Neither of the two advertising options meet the goal.

Step-by-step explanation:

Every $4,000 spent on cable TV will reach 160 fans.

Therefore, the goal of reaching 200000 fans will be fulfilled by $\frac{4000 \times 200000}{160} = 5000000$ dollars i.e. $5 million which is greater than the budget of $3 million.

Now, every $2,750 spent on radio ads will reach 125 fans.

Therefore, the goal of reaching 200000 fans will be fulfilled by $\frac{2750 \times 200000}{125} = 4500000$ dollars i.e. $4.5 million which is again greater than the budget of $3 million.

Therefore, neither of the two advertising options meet the goal. (Answer)

8 0

1 year ago