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Ahat [919]
3 years ago
6

Evaluate x3 - 3y when x = -3 and y = 4.

Mathematics
2 answers:
miskamm [114]3 years ago
8 0
I think the answer is
-9-12=-21
Svetllana [295]3 years ago
4 0

Answer:

Step-by-step explanation:

-3^3-3*4

-27-3*4

-27-12

-37

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Mary is the last person to get on a ferris wheel ride at a fair (the ride begins once she is on). The ferris wheel has a radius
Aleks [24]

Answer:

a) For sketch see attached picture.

 y=-8cos(\pi t)+10

b) Mary will be able to enjoy the scenery for a total of 1.68 min or about 101 seconds.

Step-by-step explanation:

a) In order to find the algebraic representation of the problem, we must start by drawing a sketch of what the problem looks like (see attached picture). Next, we can analyze it to see what function better fits the situation. In this case, since the ride starts at the lowest point, then we are talking about a negative cos function. A cos function has the followng general form:

y= Acos(\omega t - \phi) + C

where:

A= amplitude

\omega=angular speed

t=time

\phi= phase shift

C= vertical shift.

In this case the amplitude will be the radius of the ferris wheel, so:

A=-8

it's negative because it starts at the lowest point.

the angular speed is the angle the ride will move in a given amount of time. In this case:

\omega=\frac{\pi rad}{1 min}

\omega=\pi rad/min

There will be no phase shift for this problem.

the vertical shift is the height of the platform, so:

C= 2

so the algebraic expression is:

y=-8cos(\pi t)+10

b) In order to find the total time for which she will enjoy the ride we must start by building an inequality:

-8cos(\pi t)+10>12

and solve it for t. We can start by turning it into an equation, solve it for t and find the answers that can be found into its domain, in this case D=[0,4]

so we get:

-8cos(\pi t)+10=12

we subtract a 10 from both sides so we get:

-8cos(\pi t)=2

and divide 8 to both sides so we get:

cos(\pi t)=-\frac{1}{4}

Next, we take the inverse cosine to both sides and get different answers:

\pi t = 1.823+2\pi n

and

\pi t=4.46 + 2\pi n

we take both equations and divide them into pi so we get:

t = 0.58+2 n

and

t=1.42 + 2n

so now we find the possible answers that are between 0 and 4 minutes, this is for n=0 and 1, so we get the following times:

t={0.58, 1.42, 2.58, 3.42} min

we can now build our possible intervals for which the ferris wheel is higher than 12 m so we get the following intervals:

(0, 0.58) (0.58, 1.42) (1.42, 2.58) (2.58, 3.42) and (2.58, 4)

so we pick a test value for each of the intervals and test it on our equation. If the equation gives us a number that is greater than 12, then we have a valid interval. If we get a value that is less than 12, then we just discard that interval.

for (0, 0.58) we use 0.5 and get an answer of 10. We discard this interval.

for (0.58, 1.42) we use 1 and get an answer of 18. This is a valid interval.

for (1.42, 2.58) we use a 2 and get an answer of 2. We discard this interval.

for (2.58, 3.42) we use a 3 and get an answer of 18. This is a valid interval.

and finally, for (2.58, 4) we use a 3.5 and get an answer of 10. We discard this interval

So we have two valid intervals now: (0.58, 1.42) and (1.42, 2.58). So now we can use them to find the time for which Mary will enjoy the scenery.

t_{1}=1.42min-0.58min=0.85min

t_{2}=2.58min-1.42min=0.85min

t_{total}=0.85min+0.85min

t_{total}=1.68min

so:

Mary will be able to enjoy the scenery for a total of 1.68 min or about 101 seconds.

8 0
3 years ago
Dan weighs 108 kg. How many pounds does he weigh? Round your answer to the nearest whole pound.
Zarrin [17]
If my math is correct he weighs 238 pounds

6 0
3 years ago
Cases are normally sold full. There were three partially full cases that could be combined to make full cases. The cases were 11
wariber [46]
The answer to this problem is 1 7/16 cases. I hope this helps.
5 0
3 years ago
The multiplication table below can be used to find equivalent ratios.
Natasha_Volkova [10]

Answer:

K

Step-by-step explanation:

Becuse its k hgystdgshxygs

5 0
2 years ago
Read 2 more answers
I dont think i did this right what do u guys think
vaieri [72.5K]

Answer:

see below

Step-by-step explanation:

To find the percent increase, take the new amount and subtract the original amount

25-20 = 5

Divide by the original amount

5/20 = .25

The increase is 25%

100% + 25% = 125%

The new amount is 125% of the old amount

7 0
3 years ago
Read 2 more answers
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