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3 years ago

Write an equation that represents the function. (linear equations)

Mathematics

1 answer:

irinina [24]3 years ago

3 0

Answer:

y = 2x + 2

Step-by-step explanation:

First solve for the slope using $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

$\frac{8-2}{3-0}$ = 2

Plug the slope into the slope intercept form equation y = mx + b

y = 2x + b

To solve for b, plug in any (x, y) point on the table.

2 = 2(0) + b

2 = b

Now you can plug the b value into your equation.

y = 2x + 2

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Write each expression as a single natural logarithm. ln 3+ ln 4

Oduvanchick [21]

Expression as a single natural logarithm is 2.48490664979.

<h3>What is natural logarithm?</h3>

ln 3+ ln 4

ln (3×4)

ln(12) =2.48490664979

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

To learn more about natural logarithm from the given link:

brainly.com/question/20785664

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5 0

1 year ago

Three consecutive integers whose sum is 363.

Alex777 [14]

Answer: 120,131,122
Your three integers are x, x+1, and x+2
x+x+1+x+2=363
3x+3=363
3x=360
x=120
x+1=121
x+2=122

7 0

3 years ago

Read 2 more answers

Dan has a favorite number. His number has the digit 8 in the ones place and 5 in tens place. What is Dan's favorite number.

tino4ka555 [31]

Wouldn't it be 58 or 8.5?

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3 years ago

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4x – 9y = 7 –2x 3y = 4 what number would you multiply the second equation by in order to eliminate the x-terms when adding to th

steposvetlana [31]

Multiply equation II by 2 and then add up the equations.

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3 years ago

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Ex 7) Imagine a mile-long bar of metal such as the rail along railroad tracks. Suppose that the rail is anchored on both ends an

Fantom [35]

9514 1404 393

Answer:

about 44.5 feet

Step-by-step explanation:

We can write relations for the height of the rail as a function of initial length and expanded length, but the solution cannot be found algebraically. A graphical solution or iterative solution is possible.

Referring to the figure in the second attachment, we can write a relation between the angle value α and the height of the circular arc as ...

h = c·tan(α) . . . . . . where c = half the initial rail length

Then the length of the expanded rail is ...

s = r(2α) = (c/sin(2α)(2α) . . . . . . where s = half the expanded rail length

Rearranging this last equation, we have ...

sin(2α)/(2α) = c/s

It is this equation that must be solved iteratively. We find the solution to be ...

α ≈ 0.0168538794049 radians

So, the height of the circular arc is ...

h = 2640.5·tan(0.0168538794049) ≈ 44.4984550191 . . . feet

The rail will bow upward by about 44.5 feet.

_____

<em>Additional comments</em>

Note that s and c in the diagram are half the lengths of the arc and the chord, respectively. The ratio of half-lengths is the same as the ratio of full lengths: c/s = 2640/2640.5 = 5280/5281.

We don't know the precise shape the arc will take, but we suspect is is not a circular arc. It seems likely to be a catenary, or something similar.

We used Newton's method iteration to refine the estimate of the angle from that shown on the graph. The iterator used is x' = x -f(x)/f'(x), where x' is the next guess based on the previous guess of x. Only a few iterations are required obtain an angle value to full calculator precision.

3 0

3 years ago