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Hatshy [7]
3 years ago
14

A particle moves along a straight line. The distance of the particle from the origin at time t is modeled by the equation below.

​s(t)equals2 sine t plus 3 cosine t Find a value of t between 0 and StartFraction pi Over 2 EndFraction that satisfies the equation ​s(t)equalsStartFraction 2 plus 3 StartRoot 3 EndRoot Over 2 EndFraction .
Mathematics
1 answer:
laiz [17]3 years ago
4 0

Answer:

The value of t that will satisfy the equation is π/6 (which is 30 degrees)

Step-by-step explanation:

The function that models the movement of the particle is given as;

S(t) = 2 sin(t) + 3 cos (t)

Now we want to the value of t between 0 and pi/2 that satisfies the equation;

s(t) = (2+ 3√3)/2 = 1 + 3√3/2

What we do here is simply find that value of t that would ensure that;

2sin(t) + 3cos(t) = 1 + 3√3/2

Without any need for rigorous calculations, this value of t can be gotten by inspection.

From our regular trigonometry, we know that the sin of angle 30 is 1/2 and its cos value is √3/2

We can make a substitution for it in this equation.

We obtain the following;

2 sin(30) + 3cos (30) and that is exactly equal to 1 + 3√3/2

Do not forget however that we have a range. And the range in question is between 0 and π/2

Kindly that π/2 in degrees is 90 degrees

So our range of values here is between 0 and 90 degrees.

So to follow the notation in the question, the value within the range that will satisfy the equation is π/6

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What is the pattern of the trend line equation in this graph?
kondaur [170]

The pattern of the trend line from what we can see here shows the existence of a positive upward trend.

<h3>What is a positive upward trend?</h3>

We can see that the graph has fluctuations which have an upward trend over the years. This upward trend can be gotten from the straight line that was drawn on the graph.

It slants to the top. This shows us that the trend is positive and rising over the period of time that we have in the graph. In the graph, the upward trend can be seen from the fact that there has been a rise in the temperature of the city over the time period that was illustrated. The increase in temperature rose from 31.5 to 33 degrees period of time.

Hence we can conclude that The pattern of the trend line from what we can see here shows the existence of a positive upward trend.

Read more on trend lines here: brainly.com/question/27194207

#SPJ1

4 0
2 years ago
Find the lateral area of the regular pyramid<br><br> L.A. =
Arisa [49]

Answer:

FOR REGULAR PYRAMID with those dimension.

L.A = 96

FOR HEXAGONAL PYRAMID with those dimension

L.A = 171.71

Step-by-step explanation:

Please the question asked for L.A of a REGULAR PYRAMID, but the figure is a HEXAGON PYRAMID.

Hence I solved for both:

FOR REGULAR PYRAMID

Lateral Area (L.A) = 1/2* p * l

Where p = Perimeter of base

P = 4s

P = 4 * 6

P = 24cm

l = slanted height

l = 8cm

L.A = 1/2 * 24 * 8

L.A = 1/2 ( 192)

L.A = 96cm ^ 2

FOR AN HEXAGONAL PYRAMID

Lateral Area = 3a √ h^2 + (3a^2) / 4

Where:

a = Base Edge = 6

h = Height = 8

L.A = 3*6 √ 8^2 + ( 3*6^2) / 4

L.A = 18 √ 64 + ( 3 * 36) / 4

L.A = 18 √ 64 + 108/4

L.A = 18 √ 64+27

L.A = 18 √ 91

L.A = 18 * 9.539

L.A = 171.71

8 0
3 years ago
Tyler can swim 1/2 miles in 1/3 hours at a constant speed. At this rate , how fast does Tyler swin in miles for hours?
gladu [14]
Miles. Hours

1/2 = 1/3
1 = 2/3
1 1/2 = 3/3 or 1

= 1
8 0
2 years ago
A 9-foot piece of twine costs $9.72. What is the price per inch?
brilliants [131]
9 feet = 108 inches
$9.72 divided by 108= 0.09
8 0
3 years ago
Read 2 more answers
Based on aâ poll, among adults who regret gettingâ tattoos, 18â% say that they were too young when they got their tattoos. Assum
Sergeeva-Olga [200]

Answer:

a) 20.44% probability that none of the selected adults say that they were too young to get tattoos.

b) 35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c) 56.34% probability that the number of selected adults saying they were too young is 0 or 1.

d) No

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they say they were too young when they got their tattoos, or they don't say that. Each adult is independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

18% say that they were too young when they got their tattoos.

This means that p = 0.18

Eight adults who regret getting tattoos are randomly selected

This means that n = 8

a. Find the probability that none of the selected adults say that they were too young to get tattoos.

This is P(X = 0).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{8,0}.(0.18)^{0}.(0.82)^{8} = 0.2044

20.44% probability that none of the selected adults say that they were too young to get tattoos.

b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

This is P(X = 1).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{8,1}.(0.18)^{1}.(0.82)^{7} = 0.3590

35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

Either a. or b.

20.44 + 35.90 = 56.34

56.34% probability that the number of selected adults saying they were too young is 0 or 1.

d. It we randomly select 9 adults. Is 1 a significantly low number who day that they were too young to get tattoos?

Now n = 9

It is significantly low if it is more than 2.5 standard deviations below the mean.

The mean is E(X) = np = 9*0.18 = 1.62

The standard deviation is \sqrt{V(X)} = \sqrt{n*p*(1-p)} = \sqrt{9*0.18*0.82} = 1.15

1 > (1.62 - 2.5*1.15)

So the answer is no.

5 0
3 years ago
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