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Sauron [17]
3 years ago
12

Write an equation for the translation of the function. y = cos x; translated 6 units up

Mathematics
2 answers:
Yakvenalex [24]3 years ago
6 0
It's just y= cos(x)+6
nlexa [21]3 years ago
5 0

Answer:

y=cos(x)+6.

Step-by-step explanation:

We are asked to write an equation for the translation of the function y=cos(x) to 6 units upwards.

Let us recall transformation rules.

f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}

f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}

f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}

f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}

Since we need to shift our given function 6 units upwards, so we will add 6 to our given function outside the parenthesis as:

y=cos(x)+6

Therefore, our required equation would be y=cos(x)+6.

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Dennis_Churaev [7]
1/25 i don’t know if this is right but here you go
5 0
2 years ago
A taxi company charges a $2.00 base fare plus an additional fare based on a per-mile rate and a per-minute rate. Ryan's first ta
Fed [463]

A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles

<h3>How can the length of the third ride be calculated?</h3>

The base fare = $2.00

Let <em>x </em>represent the per-mile rate, and let <em>y </em>represent the per-minute rate, we have;

The cost of Ryan's first taxi ride = $8.50

Distance traveled in the first ride = 3.0 miles

Time taken during the first ride = 7 minutes

Therefore;

2 + 3•x + 7•y = 8.5

Which gives;

3•x + 7•y = 8.5 - 2 = 6.5

  • 3•x + 7•y = 6.5...(1)

Distance traveled in the second ride = 7.0 miles

Duration of the second ride = 14 minutes

The second ride cost = $16.00

Therefore;

2 + 7•x + 14•y = 16

Which gives;

7•x + 14•y = 16 - 2 = 14

  • 7•x + 14•y = 14...(2)

Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;

(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1

x = 1

  • The per-mile rate, <em>x </em>= $1

3•x + 7•y = 6.5

7•y = 6.5 - 3•x

7•y = 6.5 - 3×1 = 3.5

y = 3.5/7 = 1/2 = 0.5

  • The per-minute rate, <em>y </em>= $0.5

Duration of the third taxi ride = 10 minutes

Cost of the third ride = $13.50

Therefore;

2 + 1×a + 10×y = $13.50

Where <em>a </em>is the distance traveled during the third ride, we have;

2 + 1×a + 10×0.5 = $13.50

2 + a + 5 = 13.5

a = 13.5 - 2 - 7 = 4.5

  • The third ride was, <em>a </em>= 4.5 miles

Learn more about simultaneous linear equations here:

brainly.com/question/24085666

#SPJ1

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