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3 years ago

Help please its geometry

Mathematics

1 answer:

Anna11 [10]3 years ago

4 0

Answer:

Step-by-step explanation:

Opposite angles are equal in a parallelogram. Therefore 2 angles are 112°. Angles in a parallelogram or any quadrilateral are equal to 360°. To find the remaining sides: 360-(112×2) and divide your answer by 2.

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<img src="https://tex.z-dn.net/?f=%5Csf%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Ccfrac%7B%5Csqrt%7Bx-1%7D-2x%20%7D%7Bx-7%7D" id=

BARSIC [14]

<h3>Answer: -2</h3>

======================================================

Work Shown:

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{x-1}-2x }{ x-7 }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \frac{1}{x}\left(\sqrt{x-1}-2x\right) }{ \frac{1}{x}\left(x-7\right) }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \frac{1}{x}*\sqrt{x-1}-\frac{1}{x}*2x }{ \frac{1}{x}*x-\frac{1}{x}*7 }\\\\\\$

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x^2}}*\sqrt{x-1}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x^2}*(x-1)}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x}-\frac{1}{x^2}}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \frac{ \sqrt{0-0}-2 }{ 1-0 }\\\\\\\displaystyle L = \frac{-2}{1}\\\\\\\displaystyle L = -2\\\\\\$

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Explanation:

In the second step, I multiplied top and bottom by 1/x. This divides every term by x. Doing this leaves us with various inner fractions that have the variable in the denominator. Those inner fractions approach 0 as x approaches infinity.

I'm using the rule that

$\displaystyle \lim_{x\to\infty} \frac{1}{x^k} = 0\\\\\\$

where k is some positive real number constant.

Using that rule will simplify the expression greatly to leave us with -2/1 or simply -2 as the answer.

In a sense, the leading terms of the numerator and denominator are -2x and x respectively. They are the largest terms for each, so to speak. As x gets larger, the influence that -2x and x have will greatly diminish the influence of the other terms.

This effectively means,

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{x-1}-2x }{ x-7 } = \lim_{x\to\infty} \frac{ -2x }{ x} = -2\\\\\\$

I recommend making a table of values to see what's going on. Or you can graph the given function to see that it slowly approaches y = -2. Keep in mind that it won't actually reach y = -2 itself.

5 0

3 years ago

Luis is getting balloons for his father's birthday party. He wants each balloon string to be 12 feet long. At the party store, s

zubka84 [21]

Answer:

he will need 224 yards of string

Step-by-step explanation:

56 ballons *12 feet=672 feet

each yard is 3 feet so he will need

1yard--->3feet

X<-------672feet=224 yards

5 0

4 years ago

Read 2 more answers

Please helpppppp yallllll

Snowcat [4.5K]

Answer:6

Step-by-step explanation:

8 0

3 years ago

Evaluate 2•4-8 divided by 4

Vaselesa [24]

Answer:

Step-by-step explanation:

Answer and work are in picture below.

4 0

3 years ago

Ocean sunfish are well known for rapidly gaining a lot of weight on a diet based on jellyfish. The relationship between the elap

Maksim231197 [3]

Answer:

Every day, the mass of the sunfish is multiplied by a factor of <u>[ln(1.34)/6]. </u>

<u></u>

Step-by-step explanation:

You have the following function:

$M(t)=(1.34)^{\frac{t}{6}+4}$

To know what is the factor that multiplies the mass of the sunfish each day, you derivative the function M(t):

$\frac{dM(t)}{dt}=(1.34)^{\frac{t}{6}+4}(\frac{1}{6})ln(1.34)\\\\\frac{dM(t)}{dt}=\frac{ln(1.34)}{6}[(1.43)^{\frac{t}{6}+4}]\\\\\frac{dM(t)}{dt}=\frac{ln(1.34)}{6}M(t)$ (1)

where you have used the following general derivative:

$g(t)=a^{f(t)}\\g'(t)=a^{f(t)}f'(t)ln(a)$

The derivative give you the increase in the mass per day (because t is days). By the expression (1) you can conclude that each day the mass increase a factor of [ln(1.34)/6].

Every day, the mass of the sunfish is multiplied by a factor of <u>[ln(1.34)/6]. </u>

8 0

3 years ago