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2 years ago

Write a function to describe the following scenario.

Mathematics

1 answer:

Tanya [424]2 years ago

4 0

Answer: Taxi driver has at most $10 to spend on the cab ride, he can travel at most 12.7 miles.

Step-by-step explanation:

A Taxi driver charges a flat rate = 7.25 dollars

taxi fare for 1 mile = 0.65 dollars

Suppose we consider Total money taxi driver can spend = 10 dollars

Let taxi driver travel x miles

Total charges = flat rate charge + taxi fare for each mile(distance) travelled

Find the value y = [?] + [?]x

suppose these two question marks indicate z1,z2

replace with y=10 and z1=1.75 and z2=0.65 values

Then y = [z1] + [z2]x

10 = 1.75 + 0.65(x)

0.65(x) = 10 - 1.75

0.65(x)= 8.25

x = 8.25/0.65

x = 12.7 miles

If Taxi driver has at most $10 to spend on the cab ride, he can travel at most 12.7 miles.

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4 calories per minute/ y=4x+0

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Through (7,2); parallel to 3x-y=8.

Dovator [93]

Answer:

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Step-by-step explanation:

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3 years ago

Answer questions 13. And 14. Please! Show minimal work...

ale4655 [162]

13. The equation of the given function is $y=4sin[\frac{(t-\frac{4}{3})}{2}]-2$

14. The equation of the cotangent function is $y=cot[2(t-\frac{1}{3})]+2$

Step-by-step explanation:

Let us revise the transformation of the trigonometric function:

y = a f[b(x + c)] + d, where

Amplitude is a
f represents the trigonometry function
Period is 2π/b
Phase shift is c (positive is to the left)
Vertical shift is d

13.

∵ y = a sin( $\frac{2\pi t}{T}$ ), where a is the amplitude

and T is the wave in seconds

∵ The amplitude is 4

∴ a = 4

∵ The period is 4π

∴ T = 4π

From the rules above

∵ The period is 2π/b

∴ T = $\frac{2\pi }{B}$

∴ 4π = $\frac{2\pi }{b}$

- By using cross multiplication

∴ 4π(b) = 2π

- Divide both sides by 4π

∴ b = $\frac{1}{2}$

∵ The phase shift is $-\frac{4}{3}\pi$

∵ c is the phase shift

∴ c = $-\frac{4}{3}\pi$

∵ The vertical shift is -2

∵ d is the vertical shift

∴ d = -2

Now substitutes the values of a, b, c and d in the form of the equation below

∵ y = a sin[b(t + c)] + d

∴ $y=4sin[\frac{1}{2}(t-\frac{4}{3})]-2$

You can write it as $y=4sin[\frac{(t-\frac{4}{3})}{2}]-2$

The equation of the given function is $y=4sin[\frac{(t-\frac{4}{3})}{2}]-2$

14.

y = cot[b(t + c)] + d

∵ The period = π

∵ The period is 2π/b

- Equate π by 2π/b to find b

∴ π = $\frac{2\pi }{b}$

- By using cross multiplication

∴ π(b) = 2π

- Divide both sides by π

∴ b = 2

∵ The phase shift is $-\frac{1}{3}\pi$

∵ c is the phase shift

∴ c = $-\frac{1}{3}\pi$

∵ The vertical shift is 2

∵ d is the vertical shift

∴ d = 2

Now substitutes the values of b, c and d in the form of the equation below

∵ y = cot[b(t + c)] + d

∴ $y=cot[2(t-\frac{1}{3})]+2$

The equation of the cotangent function is $y=cot[2(t-\frac{1}{3})]+2$

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