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3 years ago

How does the graph of y = sec(x + 3) – 7 compare with the graph of y = sec(x)?

Mathematics

2 answers:

jarptica [38.1K]3 years ago

5 0

Answer:

Step-by-step explanation:

Alla [95]3 years ago

3 0

Answer:

The function y = sec(x) shifted 3 units left and 7 units down .

Step-by-step explanation:

Given the function: y = sec(x)

If k is any positive real number, then the graph of f(x) - k is the graph of y = f(x) shifted downward k units.

If p is a positive real number, then the graph of f(x+p) is the graph of y=f(x) shifted to the left p units.

The function $y = \sec(x+3)-7$ comes from the base function y= sec(x).

Since 3 is added added on the inside, this is a horizontal shift Left 3 unit, and since 7 is subtracted on the outside, this is a vertical shift down 7 units.

Therefore, the transformation on the given function is shifted 3 units left and 7 units down

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1 (15 Points]. Prove the following statement: is divisible by 3 if only if it is a sum of three consecutive integers. be ddvisbk

Alinara [238K]

Answer:

First. Let us prove that the sum of three consecutive integers is divisible by 3.

Three consecutive integers can be written as k, k+1, k+2. Then, if we denote their sum as n:

n = k+(k+1)+(k+2) = 3k+3 = 3(k+1).

So, n can be written as 3 times another integer, thus n is divisible by 3.

Second. Let us prove that any number divisible by 3 can be written as the sum of three consecutive integers.

Assume that n is divisible by 3. The above proof suggest that we write it as

n=3(k+1)=3k+3=k + k + k +1+2 = k + (k+1) + (k+2).

As k, k+1, k+2 are three consecutive integers, we have completed our goal.

Step-by-step explanation:

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3 years ago

In the figure, ABCD is a parallelogram and its area 15 48 cm". Find DM and DN.

matrenka [14]

More information is needed to solve the problem.

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3 years ago

the height of a cylinder is three times the diameter of the base . The surface area of thre ylinder is 126pi ft^2. What is thr r

Over [174]

The answer is 3 ft

The surface area (SA) of a cylinder with radius r and height h is:
SA = 2πr² + 2πrh = π(2r² + 2rh)

We have:
SA = 126π ft²
h = 3 * d
d = 2r
h = 3 * 2r = 6r

126π = π(2r² + 2rh)
126 = 2r² + 2rh
126 = 2r² + 2r * 6r
126 = 2r² + 12r²
126 = 14r²
r² = 126/14
r² = 9
r = √9
r = 3

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3 years ago

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3 years ago

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8090 [49]

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