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Contact [7]
2 years ago
7

Does this graph represent a function? Why or why not?

Mathematics
1 answer:
Molodets [167]2 years ago
7 0

Answer:

D

Step-by-step explanation:

This function passes the vertical line test.

The vertical line test test is done by drawing a vertical line anywhere on the graph. If the line goes through two points or more then it isn't a function.

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A leading bank is coming up with an investment that pays 8 percent interest compounded semiannually. What is the investment's ef
uranmaximum [27]
The effective rate is calculated in the following way:
r =  {(1 +  \frac{i}{n} )}^{n} - 1
where r is the effective annual rate, i the interest rate, and n the number of compounding periods per year (for example, 12 for monthly compounding).
our compounding period is 2 since the bank pays us semiannually(two times per year) and our interest rate is 8%
so lets plug in numbers:
r = {(1 +  \frac{8\%}{2}) }^{2}  - 1 \\ r =  {(1 +  \frac{1}{25}) }^{2}  - 1 \\ r =  \frac{676}{625}  - 1 \\ r = 0.0816 \: or \: 8.16\%
5 0
3 years ago
A rock thrown vertically upward from the surface of the moon at a velocity of 36​m/sec reaches a height of s = 36t - 0.8 t^2 met
Verdich [7]

Answer:

a. The rock's velocity is v(t)=36-1.6t \:{(m/s)}  and the acceleration is a(t)=-1.6  \:{(m/s^2)}

b. It takes 22.5 seconds to reach the highest point.

c. The rock goes up to 405 m.

d. It reach half its maximum height when time is 6.59 s or 38.41 s.

e. The rock is aloft for 45 seconds.

Step-by-step explanation:

  • Velocity is defined as the rate of change of position or the rate of displacement. v(t)=\frac{ds}{dt}
  • Acceleration is defined as the rate of change of velocity. a(t)=\frac{dv}{dt}

a.

The rock's velocity is the derivative of the height function s(t) = 36t - 0.8 t^2

v(t)=\frac{d}{dt}(36t - 0.8 t^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(36t\right)-\frac{d}{dt}\left(0.8t^2\right)\\\\v(t)=36-1.6t

The rock's acceleration is the derivative of the velocity function v(t)=36-1.6t

a(t)=\frac{d}{dt}(36-1.6t)\\\\a(t)=-1.6

b. The rock will reach its highest point when the velocity becomes zero.

v(t)=36-1.6t=0\\36\cdot \:10-1.6t\cdot \:10=0\cdot \:10\\360-16t=0\\360-16t-360=0-360\\-16t=-360\\t=\frac{45}{2}=22.5

It takes 22.5 seconds to reach the highest point.

c. The rock reach its highest point when t = 22.5 s

Thus

s(22.5) = 36(22.5) - 0.8 (22.5)^2\\s(22.5) =405

So the rock goes up to 405 m.

d. The maximum height is 405 m. So the half of its maximum height = \frac{405}{2} =202.5 \:m

To find the time it reach half its maximum height, we need to solve

36t - 0.8 t^2=202.5\\36t\cdot \:10-0.8t^2\cdot \:10=202.5\cdot \:10\\360t-8t^2=2025\\360t-8t^2-2025=2025-2025\\-8t^2+360t-2025=0

For a quadratic equation of the form ax^2+bx+c=0 the solutions are

x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

\mathrm{For\:}\quad a=-8,\:b=360,\:c=-2025:\\\\t=\frac{-360+\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2-\sqrt{2}\right)}{4}\approx 6.59\\\\t=\frac{-360-\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2+\sqrt{2}\right)}{4}\approx 38.41

It reach half its maximum height when time is 6.59 s or 38.41 s.

e. It is aloft until s(t) = 0 again

36t - 0.8 t^2=0\\\\\mathrm{Factor\:}36t-0.8t^2\rightarrow -t\left(0.8t-36\right)\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\\\t=0,\:t=45

The rock is aloft for 45 seconds.

5 0
3 years ago
Andy wants to rent a limo to go to prom, but wants to split the cost with some friends. The limo costs $400 to rent
Fed [463]

Answer:

its would prob be 100 / 4

Step-by-step explanation:

6 0
2 years ago
Farmer Ben has only ducks and cows. He can’t remember how many of each he has, but he doesn’t need to remember because he knows
Maru [420]

Answer:

12 cows - 48 legs

4 ducks- 8 legs

- there are many different numbers you can do but if you want to change the numbers and have more ducks then: for every one cow you take away two more ducks.

Step-by-step explanation:

22 total animals

56 total legs

ducks have 2 legs

cows have 4 legs

12 times 4 = 48 ( 12 cows with 4 legs each cow =  48 legs)

4 times 2 = 8 ( 4 ducks with 2 legs each duck = 8 legs)

6 0
3 years ago
What is the coeficient of a+3b
stiks02 [169]

Answer:

The coefficient is 3

Step-by-step explanation:

The definition of a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4xy).

6 0
3 years ago
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