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WINSTONCH [101]

3 years ago

13

Jonathan bought a calculator for X$. Cindy bought the same calculator for 3 times more than Jonathan paid for his calculator. Wh

ich expression represents the amount of money Cindy paid for her calculator ?

1 answer:

Andrej [43]3 years ago

5 0

Answer:

3x or 3*x

Step-by-step explanation:

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Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xe^y + ye^z +

LUCKY_DIMON [66]

Answer:

$D_{\vec{u}}f(0,0,0)=\frac{6}{\sqrt{54}}$

Step-by-step explanation:

We need to find the directional derivative of the function at the given point in the direction of the vector v.

$f(x, y, z)=xe^{y} + ye^{z} + ze^{x}$ ,point (0, 0, 0) and $v=$

By Theorem: If f is a differentiable function of x , y and z , then f has a directional derivative for any unit vector $\overrightarrow{v} =$ and

$D_{\overrightarrow{u}}f(x,y,z)=f_{x}(x,y,z)u_1+f_{y}(x,y,z)u_2+f_{z}(x,y,z)u_3$

where $\overrightarrow{u}=\frac{\overrightarrow{v}}{||v||}$

since, $v=$

then $\overrightarrow{u}=\frac{\overrightarrow{v}}{||v||}$

$\overrightarrow{u}=< \frac{6}{\sqrt{6^{2}+3^{2}+(-3)^{2}}},\frac{3}{\sqrt{6^{2}+3^{2}+(-3)^{2}}},\frac{-3}{\sqrt{6^{2}+3^{2}+(-3)^{2}}} >$

$\overrightarrow{u}=< \frac{6}{\sqrt{54}},\frac{3}{\sqrt{54}},\frac{-3}{\sqrt{54}} >$

The partial derivatives are

$f_{x}(x,y,z)=e^{y}+ze^{x}$

$f_{y}(x,y,z)=xe^{y}+e^{z}$

$f_{z}(x,y,z)=ye^{z}+e^{x}$

Then the directional derivative is

$D_{\vec{u}}f(x,y,z)=(e^{y}+ze^{x})(\frac{6}{\sqrt{54}})+(xe^{y}+e^{z})(\frac{3}{\sqrt{54}})+(ye^{z}+e^{x})(\frac{-3}{\sqrt{54}})$

so, directional derivative at point (0,0,0)

$D_{\vec{u}}f(0,0,0)=(e^{0}+0e^{0})(\frac{6}{\sqrt{54}})+(0e^{0}+e^{0})(\frac{3}{\sqrt{54}})+(0e^{0}+e^{0})(\frac{-3}{\sqrt{54}})$

$D_{\vec{u}}f(0,0,0)=\frac{6}{\sqrt{54}}+\frac{3}{\sqrt{54}}+\frac{-3}{\sqrt{54}}$

$D_{\vec{u}}f(0,0,0)=\frac{6+3-3}{\sqrt{54}}$

$D_{\vec{u}}f(0,0,0)=\frac{6}{\sqrt{54}}$

3 0

4 years ago

Find the percent one number is of another ?

melamori03 [73]

Answer:

Step-by-step explanation:

4 0

3 years ago

Please help and can you explain

NISA [10]

Answer:

x = 6

Step-by-step explanation:

first you would put them equal because they have the same angle: 9x + 10 = 2x + 52

subtract 10 from both sides: 9x = 2x + 42

subtract 2x from both sides: 7x = 42

divide by 7 on both sides x = 6

hope this helps! :)

7 0

3 years ago

If u had 693 cats and 593 died

Katen [24]

Answer:

you would have 100 cats left

4 0

3 years ago

. A bridge over a river is built in the shape of a parabolic arch. The bridge has a span of 100 feet. The height of the arch is

katen-ka-za [31]

Answer:

The height of the arch at its center is 250/9 or about 27.78 feet.

Step-by-step explanation:

We can write an equation to model the parabolic arch.

Let the left-most point of the arch be the origin (0, 0).

Since the bridge has a span of 100 feet, the right-most point must be (0, 100).

We can use the factored form of a quadratic:

$y=a(x-p)(x-q)$

Where <em>p</em> and <em>q</em> are the <em>x-</em>intercepts.

Our <em>x-</em>intercepts are <em>x </em>= 0 and <em>x </em>= 100. Hence:

$y=ax(x-100)$

At a point 40 feet from the center, the height of the arch is 10 feet.

The center is <em>x</em> = 50. So, a point 40 feet from the center can be either <em>x</em> = 10 or <em>x</em> = 90.

So, for instance, when <em>x</em> = 10, <em>y</em> = 10. Substitute and solve for <em>a: </em>

<em /> $10=10a(10-100)$ <em />

So:

$\displaystyle a=-\frac{1}{90}$

The same value will result if we let <em>x</em> = 90 and <em>y</em> = 10.

Hence, our equation is:

$\displaystyle y=-\frac{1}{90}x(x-100)$

The height of the arch at its center will be when <em>x</em> = 50. Hence:

$y(50)=\displaystyle -\frac{1}{90}(50)((50)-100)=\frac{250}{9}\approx 27.78\text{ feet}$

4 0

3 years ago