Determine the slope and the y intercept . 4x+y=3 please help

Answer:

I'm not sure

Using continuity concepts, it is found that the function is left-continuous at x = 1.

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A function f(x) is said to be continuous at x = a if:

• If only , the function is left-continuous.

• If only , the function is right-continuous.

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The piece-wise definition of the function is:

We have to check the continuity at the points in which the definitions change, that is, x = 0 and x = 1.

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At x = 0:

• The definition at 0 is
• Approaching x = 0 from the left, we have values less than 0, thus:

• Approaching x = 0 from the right, we have values greater than 0, thus:

Since the limits are equal, and also equal to the definition at the point, the function is continuous at x = 0.

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At x = 1:

• The definition at 1 is

• Approaching x = 1 from the left, we have values less than 1, thus:

• Approaching x = 1 from the right, we have values greater than 1, thus:

To the right, the limit is different, thus, the function is only left continuous at x = 1.

A similar problem is given at brainly.com/question/21447009

Answer:

the function is continuous from the left at x=1 and continuous from the right at x=0

Step-by-step explanation:

a function is continuous from the right , when

when x→a⁺ lim f(x)=f(a)

and from the left when

when x→a⁻ lim f(x)=f(a)

then since the functions presented are continuous , we have to look for discontinuities only when the functions change

for x=0

when x→0⁺ lim f(x)=lim  e^x = e^0 = 1

when x→0⁻ lim f(x)=lim  (x+4) = (0+4) = 4

then since f(0) = e^0=1 , the function is continuous from the right at x=0

for x=1

when x→1⁺ lim f(x)=lim  (8-x) = (8-0) = 8

when x→1⁻ lim f(x)=lim e^x = e^1 = e

then since f(1) = e^1=e , the function is continuous from the left at x=1

Answer:

4 1/2

Step-by-step explanation:

5 apples - 1/2 apple =

4 1/2 apple

or

9/2

Answer:

wire for square to maximize total area = 23 m

Wire to minimize total area = 2.019 m

Step-by-step explanation:

For the square, let's say the total length of the square is "y" m.

Thus, length of one side is = y/4

And area of the square = (y/4) = y²/16

Since the wire is 23 m, then total length of equilateral triangle is; 23 - y.

Thus, length of one side of equilateral triangle = (23 - y)/3

Using trigonometric ratio, we can find the height of the triangle and thus area.

Area of triangle = (√3)/4) × ((23 - y)/3)²

Area of triangle = (√3)/36)(23 - y)²

So, total area of square and triangle is;

A_total = (y²/16) + (√3)/36)(23 - y)²

Now, extremizing this function by derivatives, we have;

dA/dy = (y/8) - (√3)/18)(23 - y)

d²A/dy² = ⅛ + (√3)/18)

So, d²A/dy² > 0

Now,let's find the maximum or minimum of the function.

So, we equate dA/dy to zero.

Thus;

(y/8) - (√3)/18)(23 - y) = 0

y/8 = (√3)/18)(23 - y)

(y/8) + (√3)/18)y = 23((√3)/18)

Multiply through by 8 to give;

y + 0.0962y = 2.2132

1.0962y = 2.2132

y = 2.2132/1.0962

y = 2.019 m

2.019 will be a minimum because d²A/dy² > 0

The maximum will occur at a boundary of the allowed values. Thus, the absolute maximum is for y = 23.

Note that a square has more area than a triangle and as such it is normal for the square to get the largest area over the triangle and therefore we will have to use all of the wire to construct the square.

Making a proportion helps solve this problem. Cm on top, km on bottom.

1 9

---- = ----

20 ?

Cross multiply to get 1? = 180

? = 180.

The distance is 180 km.

Final answer:

The conversion of 9 cm on the map to an actual distance, using the given scale of 1 cm for 20 km, results in an actual distance of 180 kilometers.

Explanation:

The question is asking for the actual distance corresponding to 9 cm on the map. According to the given scale on the map, 1 cm corresponds to an actual distance of 20 km. So to find out how many kilometers 9 cm on the map would be in real life, we simply multiply the length measured on the map by the distance each centimeter represents. This gives us:

9 cm * 20 km/cm = 180 km

So, according to the map, 9 cm corresponds to an actual distance of 180 kilometers.

Learn more about Map Scale Conversion here:

brainly.com/question/32219836

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Final answer:

Graphs that represent functions have one input corresponding to one output. Examples include straight lines, parabolas, and sine waves.

Explanation:

Graphs that represent functions are those in which every input has exactly one output. In other words, there can only be one value of y for each value of x.  For example, a straight line, a parabola, or a sine wave are graphs that represent functions.

On the other hand, graphs that do not represent functions may have one input value mapping to multiple output values or no output values at all. Examples of such graphs include circles, ellipses, or a graph with one vertical line intersecting it at multiple points.

It's important to note that in a function, the vertical line test can be used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, then the graph does not represent a function.

Learn more about Graphs here:

brainly.com/question/31779454

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