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Ad libitum [116K]
3 years ago
6

Which equation is represented by the graph below?

Mathematics
1 answer:
gregori [183]3 years ago
6 0

Answer:

y = e^x - 4

Step-by-step explanation:

The missing options are

y = ln x - 3

y = ln x - 4

y = e^x - 3

y = e^x - 4

The function is defined in quadrant 3 and increases exponentially, then it is not a logarithm.

f(x) crosses the y-axis at (0, -3). Replacing x = 0 the last option, we get:

y = e^0 - 4 = 1 - 4 = -3

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Show whether or not y=x+3 is tangential to the curve y^2=x​
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The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.

y² = x

Take the derivative of both sides with respect to x, assuming y = y(x) :

2y dy/dx = 1

dy/dx = 1/(2y)

Solve for y when dy/dx = 1 :

1 = 1/(2y)

2y = 1

y = 1/2

When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.

This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :

x = y²   ⇒   y = y² + 3   ⇒   y² - y + 3 = 0

has no real solution for y.

3 0
2 years ago
Matt's Mechanics charges $45.95 per hour to do a car repairs plus $30.50 for waste disposal. Write an equation to represent this
katrin2010 [14]

Answer:

45.95x + 30.50

Step-by-step explanation:

<u>Step 1:  Convert words into an expression</u>

Matt's Mechanics charges $45.95 per hour to do a car repairs plus $30.50 for waste disposal.

<em>45.95x + 30.50</em>

<em />

Answer:  45.95x + 30.50

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First, you would have to do 11x + 3x Since you're combining like terms.

Now your problem is 14x + 40 = -24

Now you would do 40 - -24 which is now 40+24 and equal to 64.

Now you divide 14 by 64 and you get 4.5
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