All categories

3 years ago

What equation describes the same line as y-6 = -4 (x+1)

Mathematics

1 answer:

olga55 [171]3 years ago

3 0

Answer: y=-4x+2

Step-by-step explanation: Move all terms not containing Y to the right side of the equation.

You might be interested in

A closed cylindrical vessel contains a fluid at a 5MPa pressure. The cylinder, which has an outside diameter of 2500mm and a wal

Julli [10]

Answer:

1) Increase in the diameter equals 3.5 mm

2) Increase in the length equals $0.0003724L_{i}$ where $L_{i}$ is the initial length of the vessel.

Step-by-step explanation:

The diametric strain in the vessel is given by

$\epsilon_{D} =\epsilon_{diam}-\nu \epsilon _{axial}$

We have

$\epsilon _{diam}=\frac{\sigma _{hoop}}{E}\\\\\sigma _{hoop}=\frac{\Delta P\times D}{2t}\\\\\therefore \epsilon _{diam}=\frac{\Delta P\times D}{2t\times E}$

Applying values we get

$\therefore \epsilon _{diam}=\frac{5\times 10^{6}\times 2.5}{2\times 20\times 10^{-3}\times 193\times 10^{9}}\\\\\therefore \epsilon _{diam}=\frac{5}{3088}$

Similarly axial strain is given by

$\epsilon _{diam}=\frac{\sigma _{axial}}{E}$

$\sigma _{axial}=\frac{\Delta P\times D}{4t}\\\\\therefore \epsilon _{axial}=\frac{\Delta P\times D}{4t\times E}$

Applying values we get

$\therefore \epsilon _{axial}=\frac{5\times 10^{6}\times 2.5}{4\times 20\times 10^{-3}\times 193\times 10^{9}}\\\\\therefore \epsilon _{diam}=\frac{2.5}{3088}$

Hence The effect of axial strain along the diameter is given by

$-\nu \epsilon _{axial}$

Applying values we get

$-\nu \epsilon _{axial}=-0.27\times \frac{2.5}{3088}=-0.0002185$

hence

$\epsilon _{D} =\frac{5}{3088}-0.0002185\\\\\epsilon =0.00140$

Now by definition of strain we have

$\epsilon _{D} =\frac{D_{f}-D_{i}}{D_{i}}\\\\\therefore D_{f}=D_{i}+\epsilon D_{i}\\\\D_{f}=2.5+0.0014\times 2.5\\\\\therefore D_{f}=2503.5mm$

Increase in the diameter is thus 3.5 mm

Using the same procedure for axial strain we have

$\epsilon_{axial} =\epsilon_{axial}-\nu \epsilon _{diam}$

Applying values we get

$\epsilon_{axial} =\frac{2.5}{3088}-0.27\times \frac{5}{3088}$

$\epsilon_{axial} =0.0003724$

Now by definition of strain we have

$\epsilon _{axial} =\frac{L_{f}-L_{i}}{L_{i}}\\\\\therefore \Delta L=0.0003724L_{i}$

where $L_{i}$ is the initial length of the cylinder.

6 0

4 years ago

Please explain 12 and13and please please please hurry!

pantera1 [17]

Answer:

12. a = 2

13. $x = \dfrac{4}{3}$

Step-by-step explanation:

12.

6a(a + 3) = 2a(3a + 5) + 16

First, distribute 6a on the left side, and distribute 2a on the right side.

6a² + 18a = 6a² + 10a + 16

Subtract 6a² from both sides.

18a = 10a + 16

Subtract 10a from both sides.

8a = 16

Divide both sides by 8.

a = 2

13.

$\dfrac{1}{3}x + \dfrac{1}{2}x = \dfrac{1}{3}(x + 2)$

The LCD of 2 and 3 is 6. We multiply both sides of the equation by 6 to get rid of all denominators.

$6 \times \dfrac{1}{3}x + 6 \times \dfrac{1}{2}x = 6 \times \dfrac{1}{3}(x + 2)$

$\dfrac{6}{3}x + \dfrac{6}{2}x = \dfrac{6}{3}(x + 2)$

$2x + 3x = 2(x + 2)$

Combine like terms on the left side. Distribute the 2 on the right side.

$5x = 2x + 4$

Subtract 2x from both sides.

$3x = 4$

Divide both sides by 3.

$x = \dfrac{4}{3}$

6 0

2 years ago

The equation AB is y=2x + 4. Write an equation of a line parallel to line AB in slop-intercept form that contains point (3,-2)

FrozenT [24]

A line parallel to y=2x+4 that contains the point (3,-2) is y=2x-8. The line is parallel because it has the same slope as AB, and we can find the intercept by plugging in (3,-2) into slope-intercept form and solving for b.

5 0

3 years ago

Suppose that there are 32 people in your statistics class and you are divided into 16 teams of 2 students each. You happen to me

siniylev [52]

Answer:

Step-by-step explanation:

8 0

3 years ago

Jessica skated 4 laps in 82 seconds.how long does it take her to skate 16 laps

valentina_108 [34]

It would take 328 seconds or 5 minutes and 47 seconds

8 0

4 years ago