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2 years ago

Paul was thinking of a number.Paul doubles it and gets a answer of 13.1.What was the orginal number?

Mathematics

1 answer:

LuckyWell [14K]2 years ago

8 0

Answer:

See below:

Step-by-step explanation:

So first, Paul has a number that he got before he multiplied it, we can call that $p$ , and for his answer after doubling it. we'll call it $n$ .

So with this information, we know that $n=13.1$ so we can use that to make an equation.

$p*2=n\\p*2=13.1$

We can solve it by first dividing on both sides and getting our answer.

$p=\frac{13.1}{2} \\p=6.55$

Cheers! We get our final answer of 6.55.

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I need help with numbers 2,3,4,5,6 I need to graduate so help

Neporo4naja [7]

Answer:

sinα=√3/(2√7)

cosα=5/(2√7)

tanα=5/√3

cscα=(2√7)/√3

secα=(2√7)/5

*note* you can simplify the above further (by rationalizing them), but I think it's probably fine to leave them as is *

3.) g15.9

4.)25.4

5.) 70.8

6.) 36.4

Step-by-step explanation:

Cot is the inverse of toa so cot= adj/opp

This means the traingle's adjacent side is √3 and its opposite is 5

with this information let's figure out the hypotonouse

√3²+5²=c²

3+25=c²

28=c²

√28=c

√28=2√7

which means the triangle's

opposite= √3

hypotonous= 2√7

Adjacent= 5

With all of this we can just plug in the numbers to find the missing information (where α=angle or theta)

sinα=√3/(2√7)

cosα=5/(2√7)

tanα=5/√3

cscα=(2√7)/√3

secα=(2√7)/5

For this one we have the adjacent and need the opposite

we will use TOA

Tan(25)=x/34

34tan(25)=x

x=15.9

4.) For this one we have the adjacent but need the hypotonouse

we will use CAH

cos(48)=17/x

17/cos(48)=x

x=25.4

5.) for number 5 we have the oppsite and hypotonouse and so we'll use SOH

sin(α)=17/18

α=70.8

6.) For this one we have the opposite and adjacent and so we'll use TOA

Tan(α)=(31/42)

α=36.4

8 0

3 years ago

What is 1/2 divided by 3 i got my Awncer but it says I got it wrong:(

sladkih [1.3K]

Answer: A.

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

What is the next step he needs to complete in order to solve the equation?

Lena [83]

Answer:

Divide both sides by -2

4 0

3 years ago

HELPPPP 100 points if you help!!!!

nignag [31]

Answer:

Part A)

Chorus:

$c(t)=15(1.12)^t$

Band:

$b(t)=2t+30$

Part B)

After 9 years:

The chorus will have about 41 people.

And the band will have 48 people.

Part C)

About approximately 11 years.

Step-by-step explanation:

We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.

There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.

Part A)

Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.

So, using the standard form for exponential growth:

$c(t)=a(r)^t$

Where a is the initial population and r is the rate of change.

We will substitute 15 for a and 1.12 for r. Hence:

$c(t)=15(1.12)^t$

This represents the number of people in the chorus after t years.

We are given that 2 new people join the band each year. So, it increases linearly.

Since there are already 30 people in the band, our initial point or y-intercept is 30.

And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:

$b(t)=mt+b$

And by substitution:

$b(t)=2t+30$

This represents the number of people in the band after t years.

Part B)

We want to find the number of people in the chorus and the band after 9 years.

Using the chorus function, we see that:

$c(9)=15(1.12)^9\approx41.59\approx41$

There will be approximately 41 people in the chorus after 9 years.

And using the band function, we see that:

$b(9)=2(9)+30=48$

There will be 48 people in the band after 9 years.

Part C)

We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for t. So:

$15(1.12)^t=2t+30$

Unfortunately, it is impossible to solve for t using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.

Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).

Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.

5 0

2 years ago

URGENT HELP ME PLEASE

Trava [24]

Answer:

(a) $\log_3(\dfrac{81}{3})=3$

(b) $\log_5(\dfrac{625}{25})=2$

(d) $\log_4(\dfrac{64}{16})=1$

(e) $\log_6(36^4)=8$

(f) $\log(100^3)=6$

Step-by-step explanation:

Let as consider the given equations are $\log_3(\dfrac{81}{3})=?,\log_5(\dfrac{625}{25})=?,\log_2(\dfrac{64}{8})=?,\log_4(\dfrac{64}{16})=?,\log_6(36^4)=?,\log(100^3)=?$ .