Mr. Seidel filled up his 14-gallon gas tank for $44.26. What was the price per gallon of gas

Use chain rule to find dw/dt w=ln(x^2 + y^2 + z^2)^(1/2) , x=sint, y=cost, z=tant

son4ous [18]

The chain rule states that

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}$

Since $\ln(x^2+y^2+z^2)^{1/2}=\dfrac12\ln(x^2+y^2+z^2)$ , you have

$\dfrac{\partial w}{\partial x}=\dfrac x{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial x}=\dfrac y{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial z}=\dfrac z{x^2+y^2+z^2}$

and

$\dfrac{\mathrm dx}{\mathrm dt}=\cos t$
$\dfrac{\mathrm dy}{\mathrm dt}=-\sin t$
$\dfrac{\mathrm dz}{\mathrm dt}=\sec^2t$

Also, since $x^2+y^2+z^2=\sin^2t+\cos^2t+\tan^2t=1+\tan^2t=\sec^2t$ , the derivative is

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\sin t\cos t}{\sec^2t}-\dfrac{\sin t\cos t}{\sec^2t}+\dfrac{\tan t\sec^2t}{\sec^2t}$
$\dfrac{\mathrm dw}{\mathrm dt}=\tan t$

4 0

3 years ago

3x−2y=−2 6x−2y=10 solve by elimination

Anvisha [2.4K]

Answer:

x=4 y=7

Step-by-step explanation:

When multiplying 3x by -2, you get -6x. -6x and 6x cross out. You're left with -2y=-2 and -2y=10.

3 0

3 years ago

Y=x+2<br> 3x+3y=6<br> solving systems by substitution

motikmotik

Answer:6

Step-by-step explanation:Reorder

2

and

−

x

-

x

.

y

=

−

x

+

2

y

=

-

x

+

2

3

x

+

3

y

=

6

3

x

+

3

y

=

6

Replace all occurrences of

y

in

3

x

+

3

y

=

6

3

x

+

3

y

=

6

with

−

x

+

2

-

x

+

2

.

y

=

−

x

+

2

y

=

-

x

+

2

3

x

+

3

(

−

x

+

2

)

=

6

3

x

+

3

(

-

x

+

2

)

=

6

Simplify

3

x

+

3

(

−

x

+

2

)

3

x

+

3

(

-

x

+

2

)

.

Tap for more steps...

y

=

−

x

+

2

y

=

-

x

+

2

6

=

6

=

6

Since

6

=

6

=

6

, the equation will always be true.

y

=

−

x

+

2

y

=

-

x

+

2

Always true

Remove any equations from the system that are always true.

y

=

−

x

+

2

6 0

3 years ago

An architect is creating a scale drawing of a school computer lab. The length of the lab is 32 feet and the width of the lab is

just olya [345]

The scale drawing of the computer lab will have a length of 4 centimeter and a widtgh of 6 centimeter.

3 0

3 years ago

Read 2 more answers

Solve for k. k/2 +1/2=3

ikadub [295]

Answer:

$k = 5$

Step-by-step explanation:

Solve for $k$ :

$\frac{k}{2} + \frac{1}{2} = 3$

-Multiply both sides of the equation by the denominator $2$ :

$2 \times \frac{k}{2} + \frac{1}{2} = 3 \times 2$

$k + 1 = 6$

-Subtract both sides by $1$ :

$k + 1 - 1 = 6 - 1$

$k = 5$

So, the value of $k$ is $5$ .

7 0

3 years ago

Mr. Seidel filled up his 14-gallon gas tank for $44.26. What was the price per gallon of gas - to the nearest hundredth?