Use the given graph to determine the limit, if it exists.
Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x.

The distance from the building to the base of the ladder, when the ladder makes an angle of 70 degrees with the ground and the ladder is 25 feet long, can be calculated using the cosine function. The calculated distance is approximately 8.6 feet.

To calculate the distance from the building to the base of the ladder, we have to use the trigonometric function cosine given the information in the problem. The cosine of an angle in a right triangle is defined as the adjacent (which is the distance we wish to find) over the hypotenuse (which is given as 25 feet).

Therefore, we write the equation as follows:

cos(70) = Adjacent/25

To find the 'Adjacent', we rearrange the equation:

Adjacent = 25*cos(70)

When you perform the calculation, you get Approximately 8.6 feet as the distance from the building to the base of the ladder.

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The base of the ladder is approximately 8.5 feet from the building. This is determined using trigonometry and the cosine of the ladder's angle of elevation.

This is a trigonometry problem where we have to find the base of the triangle formed by the ladder, the ground, and the distance from the building. The question gives us the length of the ladder (hypotenuse in the right triangle) and the angle of elevation. We can thus use cosine of the angle (base/hypotenuse) to find the base.

We know that Cosine of 70° is equal to the (base / Hypotenuse). And in the present case, the hypotenuse is given to be 25 ft.

Therefore, calculation will be as follow:

Base = Cosine (70°) * Hypotenuse.

Base = Cosine (70°) * 25 ft.

After calculating, this gives a base length of approximately 8.5 feet. So, the base of the ladder is approximately 8.5 feet from the building.

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3

Applying Distribution Law, we multiply 3 with 6 and 2.

So, 3 * ( 6 -2 ) = ( 3* 6 ) - ( 3 * 2)

so, '?' = 3

Rational Root Theorem:

If the rational number [tex]x=\frac{b}{c}[/tex] is a zero of a higher degree polynomial:

[tex]P(x)=kx^{n}+...+m[/tex]

where all the coefficients are integers. Then [tex]b[/tex] will be a factor of [tex]m[/tex] and [tex]c[/tex] will be a factor of [tex]k[/tex]

1. Use the rational root theorem to enumerate all possible rational zeroes of the polynomial [tex]P(x)[/tex]

2. Evaluate the polynomial from the first step until you can find a zero. Let’s suppose the zero is [tex]x=r[/tex]. It will be a zero if [tex]P(r)=0[/tex]. Then if this is true, write the polynomial as:

[tex]P(x)=(x-r)Q(x)[/tex]

3. Repeat this process using [tex]Q(x)[/tex] this time rather than [tex]P(x)[/tex]. The process finishes until we reach a second degree polynomial, then solve as it is widely known for a quadratic equation.

The equation to determine the number of bacteria in the colony after 6 hours is [tex]f(x) = 100(4)^x[/tex] and after 6 hours, there will be 409,600 bacteria in the colony.

To find the number of bacteria after 6 hours, one would substitute x with 6 in the exponential function [tex]f(x) = 100(4)^x[/tex].

This function models the growth of the bacteria colony, where the initial number of bacteria is 100 and they quadruple every hour.

The variable x represents the number of hours that have passed since the initial measurement at 9:00 a.m.

By substituting x = 6 into the function, we get:

[tex]f(6) = 100(4)^6[/tex]

Now, calculate the value of [tex](4)^6[/tex]:

[tex](4)^6 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 = 4096[/tex]

Then, multiply this by the initial number of bacteria, which is 100:

f(6) = 100 [tex]\times[/tex] 4096

Finally, calculate the total number of bacteria after 6 hours:

f(6) = 409600

Answer:

The answer is word SIMULTANEOUSLY.

Step-by-step explanation:

The alternative that fits best is " d.Simultaneously"

All at once, pandemonium broke loose. Simultaneously, the marching band came around the corner, dogs began barking, the horses pulling the Mayors carriage began to run.

This word maintains the coherence and cohesion of the given text.

Answer:

The alternative that fits best is  " d. Simultaneously"

Step-by-step explanation:

Thus, the complete sentence would read:  "All at once, pandemonium broke loose. Simultaneously the marching band came around the corner, dogs began barking, and the horses pulling the mayor's carriage began to run!"

The explanation for this is that the word "Simultaneously" is the only one that fits the phrase, and maintains the coherence and cohesion of the text.  The words "anyway", "because", and "following", when embedded in the phrase, change the meaning of what the author wanted to go through.

To calculate the height of the cuboid, we convert the width to centimeters and use the volume formula. After conversion, we find the height by dividing the volume (1404cm³) by the product of the length (9cm) and width (13cm), resulting in a height of 12cm.

To find the height of the cuboid, we can use the formula for calculating volume, which is volume = length x width x height. The question gives us the volume of the cuboid as 1404cm³, the length as 9cm, and the width as 130mm. However, we need to ensure all units are the same, so let's convert the width from millimeters to centimeters: 130mm = 13cm (since 1cm = 10mm).

Now, using the formula for volume:

To find the height, we divide the volume by the product of the length and width:

Therefore, the height of the cuboid is 12cm.

Answer: [tex]70a^2b^2c^3[/tex] will be the answer.

Explanation:

Since Given expression is [tex]10abc^2\sqrt{49a^2b^2c^2}[/tex]

We can write, [tex]10abc^2\sqrt{49a^2b^2c^2}= 10abc^2\sqrt{7^2a^2b^2c^2}[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10abc^2\sqrt{(7abc)^2}[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10abc^27abc[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10\times7abc^2abc[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 70abc^2abc[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 70a^2b^2c^3[/tex]

1. The simplified form of the expression [tex]10abc^2[/tex] is simply [tex]10abc^2[/tex] itself.

2. The simplified form of the expression [tex]\sqrt{49a^2b^2c^2}[/tex] is 7abc.

1. Since there are no like terms to combine, and no operations to perform, the expression remains unchanged.

2. The expression [tex]\sqrt{49a^2b^2c^2}[/tex] represents the square root of [tex]49a^2b^2c^2[/tex]. To simplify this, we need to find the square root of each term under the radical.

[tex]\sqrt{49a^2b^2c^2} = \sqrt{49} * \sqrt{a^2} * \sqrt{b^2} * \sqrt{c^2}[/tex]

The square root of 49 is 7, and the square root of any variable raised to the power of 2 is simply the variable itself. So, we have: [tex]\sqrt{49a^2b^2c^2} = 7 * a * b * c[/tex]

To know more about expression:

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the linear function f (x) = 0.05x + 3,

f(x) is the monthly fee and x is the price per minute

Brandon used 20 minutes of his long distance

So x is 20 minutes

We plug in 20 for x

f(x) = 0.05x + 3

f(20) = 0.05(20) + 3 = 4

So total bill is  $4 if Brandon used 20 minutes of his long distance service in a month

Set the situation up as a system of linear equations based on the information provided in the problem. Then, solve the system to get the number of each type of vehicle that the company can buy.

To solve this problem, let's set it up as a system of linear equations. This is a mathematics problem involving problem-solving and linear equations.

Let's denote v as the number of vans, s as the number of small trucks, and l as the number of large trucks.

We know that the total money spent should equal $15 million, and we can express this as:

(35,000v) + (70,000s) + (60,000l) = 15,000,000

We also know that the number of vans is twice the number of small trucks, so we can express this as:

v = 2s

We know also that the total number of vehicles is 310, so we have:

"v + s + l = 310"

Solving these three equations will give us the number of vans, small trucks, and large trucks that the company can buy.

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Two of the three side lengths are given.  To find the area of the triangular piece of land, we'll need to calculate the length of the third side, the side opposite the 100 degree angle.  Use the Law of Cosines for this task.

a^2 = b^2 + c^2 - 2ac*cosA

Here, a^2 = 500^2 + 750^2 - 2(500)(750)cos 100 deg, or

         a^2 = 250000 + 572500 - 750000(-0.1736), or

                = 692264

Then a = +sqrt(692264) = 832 yds

Use Heron's Formula to find the area of the land.

First, calculate s=(a+b+c)/2:  (500+750+832)/2 = 1041=s

According to Heron's Formula, A = sqrt( s(s-a)(s-b)(s-c) )

Here, A = sqrt( 1041*(1041-500)*(1041-750)*(1041-832) )

I will leave this calculation to you to complete.

Suppose the area of the land is A square yards.  Convert this to acres, using the fact that 1 acre = 4840 yd^2.

In acres, the area is 

         1 acre

A* ---------------- = (A/4840) acres

       4840 yd^2

How much will this cost?  Recall that the unit cost of the land is $2300/acre.

Then the total cost will be:

                            $2300

(A/4840) acres * ------------- = 0.475*A dollars.  (Substitute your value for A)

                             1 acre

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