140 is decreased to 273

De l'Hospital rule applies to undetermined forms like

[tex]\dfrac{0}{0},\quad\dfrac{\infty}{\infty}[/tex]

If we evaluate your limit directly, we have

[tex]\displaystyle \lim_{x\to 0}(1+2x)^{-\frac{3}{x}} = 1^\infty[/tex]

which is neither of the two forms covered by the theorem.

So, in order to apply it, we need to write the limit as follows: we start with

[tex]f(x)=(1+2x)^{-\frac{3}{x}}[/tex]

Using the identity [tex]e^{\log(x)}=x[/tex], we can rewrite the function as

[tex]f(x)=e^{\log\left((1+2x)^{-\frac{3}{x}}\right)}[/tex]

Using the rule [tex]\log(a^b)=b\log(a)[/tex], we have

[tex]f(x)=e^{-\frac{3}{x}\log(1+2x)}[/tex]

Since the exponential function [tex]e^x[/tex] is continuous, we have

[tex]\displaystyle \lim_{x\to 0} e^{f(x)} = e^{\lim_{x\to 0} f(x)}[/tex]

In other words, we can focus on the exponent alone to solve the limit. So, we're focusing on

[tex]\displaystyle \lim_{x\to 0} -\frac{3}{x}\log(1+2x) [/tex]

Which we can rewrite as

[tex]\displaystyle \lim_{x\to 0} -\frac{3}{x}\log(1+2x) = -3\lim_{x\to 0}\frac{\log(1+2x)}{x}[/tex]

Now the limit comes in the form 0/0, so we can apply the theorem: we derive both numerator and denominator to get

[tex]\displaystyle -3\lim_{x\to 0}\frac{\log(1+2x)}{x} = -3 \lim_{x\to 0}\dfrac{\frac{2}{1+2x}}{1} = -3\cdot 2 = -6[/tex]

So, the limit of the exponent is -6, which implies that the whole expression tends to

[tex]e^{-6}=\dfrac{1}{e^6}[/tex]

By applying L'Hospital's rule to the given expression, the limit is found to be 1 as x approaches 0.

L'Hospital's rule can be applied to find the limit of the expression (1+2x)^(-3/x) as x approaches 0. This rule states that if we have an indeterminate form 0/0 or ∞/∞, we can take the derivative of the numerator and denominator separately and then evaluate the limit again.

After simplifying the expressions and substituting x = 0, we find that the limit is equal to 1.

The answer is 4. Any absolute value of a negative number is positive

Answer: 4

Step-by-step explanation: It's important to understand what absolute value really means and that is the absolute value of a number represents that numbers distance from zero on a number line.

The absolute value of -4 is 4. The reason the absolute value of -4 is 4 is that if we graph -4 down here on the number line, you can see that its distance from zero is 4 units.

I have attached a number line below showing the absolute value of -4

Final answer:

To find the time it took for Austin to catch up with Amber, we calculated the distance Amber had covered before Austin started, and then divided that distance by the difference in their speeds, yielding a catch-up time of 5.5 hours.

Explanation:

The question is asking after how many hours Austin will catch up with Amber if they are driving the same route, but start at different times and drive at different speeds. To solve this problem, we can use the concept of relative speed and the equation Distance = Speed × Time. Since Amber left 2 hours earlier, by the time Austin starts, Amber has already covered a certain distance. We can calculate this distance by multiplying Amber's speed (55 mph) by the time she drove alone (2 hours), which gives us 110 miles. Now, Austin catches up by covering the difference in the distance at a relative speed, which is the difference of their speeds. So, the relative speed is Austin's speed (75 mph) minus Amber's speed (55 mph), resulting in 20 mph.

Now we can find the time it took Austin to catch up by dividing the distance Amber covered alone (110 miles) by the relative speed (20 mph). This comes out to 5.5 hours. Thus, Austin catches up with Amber after driving for 5.5 hours.

-4 x -4d=16d

-4 x-5=20

16d+20

Answer: -36d

Step-by-step explanation:

-4(-4d-5)

You have to multiply -4x-4d= -16d

Then do -4x5=-20

After you have to solve -16-20d

Which equals to -36d

Answer:

A

Step-by-step explanation:

sin is opposite/hypotenuse, which is 24/26, simplifying to 12/13

For this case, we have that by definition:

[tex]Sin (C) = \frac {24} {26}[/tex]

That is, the sine of angle C will be given by the leg opposite the angle C divided by the hypotenuse of the traingule.

[tex]Sin (C) = \frac {24} {26}[/tex]

Simplifying:

[tex]Sin (C) = \frac {12} {13}[/tex]

Answer:

Option A

What number do

You need help with

Answer:

a. The snow is accumulating at about 3/2 inches per hour.

Step-by-step explanation:

Since the description of the dependent variable is "inches of snow accumulated" and the description of the independent variable is "hours", the meaning of the slope of a line on the graph of inches versus hours is "inches of snow accumulated per hour." In my opinion this best matches answer choice "a" because of the use of the words "accumulated" and "accumulating".

In plain English, the wording of answer choice "d" means the same thing: snow accumulation means snow height. I believe it can reasonably be argued that choice "d" is also a correct answer to this question.

_____

Please note that the slope of a line on *any* graph has the meaning (unit of dependent variable) per (unit of independent variable).

Answer:

  5 times as large

Step-by-step explanation:

You can think of "10^5" as "green marbles" if you like. Then your question is ...

  5 green marbles is how many times as large as 1 green marble.

Hopefully, the answer is all too clear: it is 5 times as large.

_____

In math terms, when you want to know how many times as large y is as x, the answer is found by dividing y by x:

  y/x . . . . . tells you how many times as large as x is y.

Here, that looks like ...

  [tex]\dfrac{5\times 10^5}{1\times 10^5}\\\\=\dfrac{5}{1} \qquad\text{the factors of $10^5$ cancel}\\\\=5[/tex]

Answer:

5 times as large

Step-by-step explanation:

I did the question

Answer:

[tex]f(x)=3^x[/tex]

Step-by-step explanation:

From the table;

When x=2, [tex]y=9=3^2[/tex]

When x=3, [tex]y=27=3^3[/tex]

When x=4, [tex]y=81=3^4[/tex]

We can infer from the pattern that;

[tex]f(x)=3^x[/tex]

Answer:

The value of [tex]cos\theta[/tex] would be Base/Hypotenuse = EF/DF

Step-by-step explanation:

In figure, we are given a triangle

There is a 90 degree angle in the triangle. Therefore, the triangle is a right triangle.

In a right triangle,

[tex]Sin\theta = \frac{Perpendicular}{Hypotenuse}[/tex]

[tex]Cos\theta = \frac{Base}{Hypotenuse}[/tex]

[tex]Tan\theta = \frac{Perpendicular}{Base}[/tex]

In triangle, the side with right angle and given angle is called base, Therefore

Base = EF

The side opposite to the right angle is called the hypotenuse, so

Hypotenuse = DF

and

Perpendicular = DE

Therefore, the value of [tex]cos\theta[/tex] would be Base/Hypotenuse = EF/DF

Answer:

Hi ! I hope you're doing good

Here is your graph ...I hope it's helpful for you

Step-by-step explanation:

C is the median.

to find the median we need to put all the numbers given in order from smaller to largest

12, 18, 34, 55, 59, 67, 80, 80

then find the middle number of these

well we have to middle numbers 59 and 55

so we need to find the mid number between these two which 57.

The answer to this question is 57

hope this helped

Answer:

The answer is 18

Answer:

  ∠H = 120°

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary:

  ∠H +∠T = 180

  (2x +60) + (x +30) = 180

  3x = 90 . . . . . . . subtract 90, collect terms

  x = 30 . . . . . . . . divide by the coefficient of x

Then the measure of angle H is ...

  ∠H = 2·30 +60 = 120 . . . . . degrees

Answer:

2nd one: AB = 6

Step-by-step explanation:

Because PQ is 4 (Pythagorean triples), you can prove that triangle PBQ is congruent to PAQ by HL. You can then say AQ is equal to 3 becasue of CPCTC. AQ+QB=AB, or 3+3=6. AB=6

Answer:

  10.  D. 5 1/3

  11.  C. 285 cm

  12.  A. 42 units

Step-by-step explanation:

The first two are simple addition problems. (In problem 11, you can replace the addition of 5 identical numbers with a multiplication by 5.) The last problem is also an addition problem, but figuring out what to add can take a little effort.

___

10. The segment addition theorem tells you that for R between S and T:

  ST = SR + RT

  ST = 3 2/3 + 1 2/3 = (3 +1) + (2/3 +2/3) = 4 + 4/3 = 4 + 1 1/3

  ST = 5 1/3

__

11. The definition of a regular polygon is that all of its sides and angles are congruent. A "pentagon" is 5-sided polygon, so your regular pentagon will have 5 sides, each of measure 57 cm. The perimeter is the total length of the sides, so is ...

  P = 57 cm +57 cm +57 cm +57 cm +57 cm

  P = 5×57 cm

  P = 285 cm

__

12. Again, the perimeter is the sum of the side lengths. Here, the length of the top side is easily figured by the difference of x-coordinates (6 units). The length of the left side is recognizable as double the length of the hypotenuse of a 3-4-5 right triangle (10 units). The lengths of the other two sides can be found using the distance formula with the end point coordinates:

  MN = √((-10-8)^2 +(-6-(-3))^2) = √(324 +9) = √333 ≈ 18.248

 LM = √((8-2)^2 +(-3-2)^2) = √(36 +25) = √61 ≈ 7.810

So, the perimeter is ...

  P = 6 + 10 + 18.248 +7.810 = 42.058 ≈ 42 units

_

Here, it is helpful to be familiar with the 3-4-5 right triangle. It has several interesting properties, one of which is that it shows up in algebra problems a lot. Any triangle with this ratio of side lengths is also a right triangle.

In this problem, the difference in coordinates K - N = (-4-(-10), 2-(-6)) = (6, 8) which we recognize as having the ratio 3:4. We could continue with the distance formula:

  NK = √(6^2 +8^2) = √100 = 10

or, we can simply recognize this will be the result based on our familiarity with this triangle.

_

An alternate approach to this problem will also work. You can estimate the length of the perimeter.

The distance between two points is more than the maximum difference of their coordinates and less than the sum of differences of their coordinates. For example, the distance between points N and K will be more than 8 and less than 8+6=14.

If you need to refine this very crude estimate further, you can add 40% of the smallest difference to the largest difference. In this case, that would be ...

  8 + 0.40·6 = 10.4 . . . . . we already know the length is actually 10, so we see this estimate is within 4% of the real length.

For the coordinates in this problem, we can see that the perimeter will be more than the sum of the longest coordinate differences: 6+6+18+8 = 38. This is an important fact, because it eliminates all of the answer choices except 42. If there were any remaining ambiguity as to the answer, we could refine our estimate by adding 40% of the sum of the shortest coordinate differences: 0.40·(0+5+3+6) = 5.6. That would bring our estimate to 38+5.6 = 43.6, within 4% of the actual value of the perimeter.

Some simplification:

[tex]\dfrac{x^{-1}}{x^{-1}+1^{-x}}=\dfrac{x^{-1}}{x^{-1}+1}=\dfrac1{1+\frac1{x^{-1}}}=\dfrac1{1+x}[/tex]

Then

[tex]f(2)=\dfrac1{1+2}=\dfrac13[/tex]

Answer:

$726.02 I had to guess cause I used a calculator but it didn't get to an exact number this is the closet

Answer:

$726.02

Step-by-step explanation:

Answer:

  58 in^2

Step-by-step explanation:

The area of one face of the 3" cube is (3 in)^2 = 9 in^2. Then the 6 faces of that will have an area of ...

  6·9 in^2 = 54 in^2

The area of the top of the paperweight is unaffected by the area of the added cube: the area the smaller cube covers is exactly the same as its exposed top area. So, the net effect of the added 1" cube is to increase the total area by that cube's lateral area: 4 faces at 1 in^2 for each face, a total of 4 in^2.

Then the total surface area of the paperweight is ...

  54 in^2 + 4 in^2 = 58 in^2

Answer:

  (0, -3), (-1, 1)

Step-by-step explanation:

The equation can be simplified to a form more helpful for graphing.

Subtract 7:

  24x +18 = -6y

We note that all of the coefficients are multiples of 6, so we can divide by -6:

  y = -4x -3

This is slope-intercept form, so it tells you that the y-intercept is -3, which means one point on the graph is (0, -3).

The slope is -4, so an x-value in the negative direction will give a more positive y-value. We can choose x=-1 and find y:

  y = -4(-1) -3 = 4 -3 = 1

Then another point on the graph is (-1, 1).

Two points on the graph are (0, -3) and (-1, 1).

The solution to the equation -3(h + 5) + 2 = 4(h + 6) - g is h = -12 and g = -18.

Distribute the negative signs:

-3(h + 5) + 2 = -3h - 15 + 2

Combine constant terms:

-3h - 15 + 2 = 4(h + 6) - g

-3h - 13 = 4h + 24 - g

Isolate h on one side:

-7h - 13 = 24 - g

-7h = 37 - g

h = (37 - g) / -7

Substitute h back into the original equation to solve for g:

-3(h + 5) + 2 = 4(h + 6) - g

-3((37 - g) / -7 + 5) + 2 = 4((37 - g) / -7 + 6) - g

-3(-12 - g + 35) + 2 = 4(-12 - g + 42) - g

Simplify both sides:

11g + 66 = -36g + 108

47g = 42

g = -18

Therefore, the solution is h = -12 and g = -18.

Answer:

13

180-125-42=13

You can find the measure of the missing angle by identifying the fraction of the total circle that the time period represents. For example, the movement from 12 to 3 on a clock represents a quarter of the clock's cycle, which corresponds to a 90 degrees angle.

To find the measure of the missing angle, we must first identify the type of problem it is. Based on the information shared, it seems like it's a problem involving angles in a circle, specifically, how the hour hand of the clock moves.

When the hour hand moves from 12 to 3, we are looking at a quarter (1/4) of a 360 degrees circle, which is identified by 90 degrees.

So, if you're trying to find the measure of a missing angle over a certain period, you can use the fraction of the total circle that the period represents. For example, the quarter period from 12 to 3 on the clock would represent a 90 degrees angle.

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Answer:

Explanation:

1) Principal quantum number, n = 2

2) Second quantum number, ℓ

The possible values of ℓ are from 0 to n - 1.

Hence, since n = 2, there are two possible values for ℓ: 0, and 1.

This gives you two shapes for the orbitals: 0 corresponds to "s" orbitals, and 1 corresponds to "p" orbitals.

3) Third quantum number, mℓ

The possible values for mℓ are from - ℓ to + ℓ.

Hence, the poosible values for mℓ when n = 2 are:

4) Fourth quantum number, ms.

Therfore the full set of possible states (different quantum number for a given atom) for n = 2 is:

That is a total of 8 different possible states, which is the answer for the question.

Answer:

  a. 3 (see below for explanation)

  b. Ln = 4 + 3(n -1)

  c. 48

  d. dn = 6n +2

Step-by-step explanation:

a. The common difference is found by subtracting any given term from the next one: 7 -4 = 3, or 10 -7 = 3. The common difference is 3.

__

b. The general expression for an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 + d(n -1)

Here, the first term is 4 and the common difference is d. We choose to name the n-th term of Levy's sequence "Ln", so we can fill in the numbers to get ...

  Ln = 4 + 3(n -1)

__

c. We can call the terms of Zack's sequence Zn, so we have ...

  Zn = 3·Ln = 3·(4 + 3(n -1)) = 12 +9(n -1)

Putting 5 where n is in this equation, we find ...

  Z5 = 12 +9(5 -1) = 48

The 5th term of Zack's sequence is 48.

__

d. The difference of n-th terms of the two sequences is ...

  dn = Zn -Ln = (3·Ln) - Ln = 2Ln = 2(4 +3(n -1)) = 8 +6(n -1)

  dn = 6n +2

Multiply the first bracket by -4. Multiply the second bracket by -2

-8x+12y+4x-2x-12

Negative and Negative = Positive

Negative and Positive = Negative

Then do -8x+4x-2x

= -6x+12y-12

Answer is D. -6x+12y-12

D. -6x + 12y - 12

First, distribute the -4 and the -2.

-8x + 12y + 4x - 2x - 12

Now, rearrange the expression so the like terms are easier to combine.

-8x + 4x - 2x + 12y - 12

Now, combine the like terms.

-6x + 12y - 12

This is as simple as the expression can get without knowing what the variables are.

The distance between him and school is 1.59 miles. Of course this distance is linear to make this problem simple. He walks with a speed of 3 miles per hour or 0.00083 mile per second.

To calculate time from distance and speed we use this formula: [tex]t=\frac{d}{s}=\frac{3mil}{0.00083mil/s}\approx3614.46sec[/tex] seconds. To convert minutes we divide number of second by 60. [tex]t\div60=3614.46sec\div60\approx\boxed{60.24min}\approx\boxed{1h}[/tex].

It will take him approximately 60 minutes to get to school.

Answer:

20 minutes

Step-by-step explanation:

The wording of this question is a bit strange.  Are you saying that Zeke can walk to school 3 times per hour?  

If so, then the total distance he'd walk in 1 hour would be 3(1.59 miles), or

4.77 miles.  So he walks 4.77 mph.

How long to talk to school?  Divide 1.59 miles by 4.77 mph.  The result is:

1/3 hour or 20 minutes.

The first one u circled is a single rotation

Answer:

The upper left figure has a single rotation.

Step-by-step explanation:

In math and geometry single rotation is what we call a figure that has been rotated by only 90º from an original point and it is usually measured to the right, so in this case from the option the figure that has been rotated only 90º is the one in the upper left corner of the image.

ANSWER

D. 22-8√5

EXPLANATION

We want to expand

[tex](2 \sqrt{5} - 4)(3 \sqrt{5} + 2)[/tex]

We use the distributive property to obtain,

[tex]2 \sqrt{5} (3 \sqrt{5} + 2) - 4(3 \sqrt{5} + 2)[/tex]

We expand to get,

[tex]6(5) + 4 \sqrt{5} - 12 \sqrt{5} - 8[/tex]

Simplify to get,

[tex]22 - 8 \sqrt{5} [/tex]

The correct answer is D.

Answer:

  y = 11.2 in

Step-by-step explanation:

The square of the tangent length is equal to the product of the lengths of the secant from the intersection with the tangent to the near and far circle intersection points.

  9^2 = 5(5+y)

  16.2 = 5+y . . . . . divide by 5

  11.2 = y . . . . . . inches

Answer:

Center: (-5,10)

Radius: 2

Step-by-step explanation:

The equation of the circle in center-radius form is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where the point (h,k)  is the center of the circle and "r" is the radius.

Subtract 121 from both sides of the equation:

[tex]x^2+y^2+121-20y-121=-10x-121\\x^2+y^2-20y=-10x-121[/tex]

Add 10x to both sides:

[tex]x^2+y^2-20y+10x=-10x-121+10x\\x^2+y^2-20y+10x=-121[/tex]

Make two groups for variable "x" and variable "y":

[tex](x^2+10x)+(y^2-20y)=-121[/tex]

Complete the square:

Add [tex](\frac{10}{2})^2=5^2[/tex] inside the parentheses of "x".

Add  [tex](\frac{20}{2})^2=10^2[/tex]  inside the parentheses of "y".

Add [tex]5^2[/tex] and [tex]10^2[/tex] to the right side of the equation.

Then:

[tex](x^2+10x+5^2)+(y^2-20y+10^2)=-121+5^2+10^2\\(x^2+10x+5^2)+(y^2-20y+10^2)=4[/tex]

Rewriting, you get that the equation of the circle in center-radius form is:

 [tex](x+5)^2+(y-10)^2=2^2[/tex]

You can observe that the radius of the circle is:

[tex]r=2[/tex]

And the center is:

[tex](h,k)=(-5,10)[/tex]

Answer:

Step-by-step explanation:

x²+y²+121-20y=-10x

(x²+10x)+(y²-20y)+121=0

(x²+10x+25)-25+(y²-20y+100)-100+121=0

(x+5)² + (y-10)²= 2²

the center is : A(-5;10)  and radius : r = 2

Answer:

A

Step-by-step explanation:

sin(60) can be simplified into sqrt(3)/2.

The sine of 60° is √3/2.

The ratio between the hypotenuse and the leg opposite the angle, when viewed as a component of a right triangle, is the trigonometric function for an acute angle.

Given

height = √3

hypotenuse = 2

sin θ = height/ hypotenuse

sin θ = √3/2

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