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Kryger [21]
3 years ago
5

Determine the infinite limit. lim (x + 6) / (x + 7) xââ7â

Mathematics
1 answer:
scoray [572]3 years ago
6 0

Answer:

\lim_{x \to \infty} \frac{x+6}{x+7} = 1

Step-by-step explanation:

You have to calculate the following limit:

\lim_{x \to \infty} \frac{x+6}{x+7}

To solve the previous limit, you can factor x from numerator and denominator of the function, and use the fact that c/∞ = 0 with c a constant.

\lim_{x \to \infty} \frac{x+6}{x+7}=  \lim_{x \to \infty}\frac{x(1+\frac{6}{x})}{x(1+\frac{7}{x})}=\lim_{x \to \infty}\frac{1+6/x}{1+7/x}=\frac{1+0}{1+0}=1

Hence, the limit is 1, L = 1

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10 Points!
Gekata [30.6K]
In this sequence, a₁ equals -1. 

The difference between each term is +3, so the coefficient for n will be 3.

In the sequence, a₂ equals 2. The following equation will fit this sequence, and will be your answer:

a_n = -1 + 3(n - 1)

Proof:
a_1 = -1 + 3(1 - 1) = -1 + 3(0) = -1

a_2 = -1 + 3(2 - 1) = -1 + 3(1) = -1 + 3 = 2
7 0
4 years ago
Write an equation in standard form of the line that passes through (0,5) and has the slope m=−2
Ray Of Light [21]
Y=-2x+5
The standard form is y=mx+b, since m is the slope you would put -2 in substitute for it and since (0,5) has a zero as the x and a number as the y that gives you the b which is the y-intercept.
3 0
3 years ago
Patty is 50 mi. due north of Todd. Emma is due east of Todd. The angle between the direction of the shortest distance from Emma
hammer [34]
For this it would be helpful if you draw a diagram of the situation. You will see that a right triangle can be formed from the problem. We use trigonometric functions to solve. We do as follows:

sin 40 = 50/y
tan 40 = 50/x


Solving we obtain,
x = 60 mi
y = 78 mi

Hope this answers the question. Have a nice day.
4 0
3 years ago
Read 2 more answers
How on earth do u do this?
11111nata11111 [884]

Answer:

  ΔABC ≅ ΔZXN

Step-by-step explanation:

Find the letters of the matching parts of the triangles.

A is the right angle; as is Z.

B is the angle where 10 meets 26; as is X.

C is the remaining angle; as is N.

__

Corresponding vertices are listed in the same order:

  ΔABC ≅ ΔZXN

4 0
4 years ago
The designated market area (DMA) of Boston has approximately 3 million television households. Audience research shows that 45 pe
inna [77]

Answer:

22.2%

Step-by-step explanation:

The Program rating of a program is the percentage of TV households in an area that are tuned to a specific program during a specific time period.

The designated market area (DMA) of Boston has approximately 3 million television households.

Audience research shows that 45 percent of these households had their sets turned on during a particular Saturday evening.

45% of 3 Million = 0.45 X 3000000 = 1,350,000

Out of these 1,350,000, 300,000 households were watching Sports Stories.

Therefore, the program rating for Sports Stories in the Boston DMA is:

\frac{300000}{1350000} X 100 =22.2\%

3 0
3 years ago
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