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2 years ago

Helpppp pleaseee i need a quick answer

Mathematics

2 answers:

Nuetrik [128]2 years ago

7 0

Answer: 100.52

Step-by-step explanation: Circumference of circle = pi • diameter

pi • 16 cm • 2 rotations = 100.52

aleksandr82 [10.1K]2 years ago

4 0

Answer:

32 i think

Step-by-step explanation:

its 16 cm, so 2 full rotations would be 16 times 2

which is 32

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Intersection point of Y=logx and y=1/2log(x+1)

GalinKa [24]

Answer:

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

The Problem:

What is the intersection point of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ ?

Step-by-step explanation:

To find the intersection of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ , we will need to find when they have a common point; when their $x$ and $y$ are the same.

Let's start with setting the $y$ 's equal to find those $x$ 's for which the $y$ 's are the same.

$\log(x)=\frac{1}{2}\log(x+1)$

By power rule:

$\log(x)=\log((x+1)^\frac{1}{2})$

Since $\log(u)=\log(v)$ implies $u=v$ :

$x=(x+1)^\frac{1}{2}$

Squaring both sides to get rid of the fraction exponent:

$x^2=x+1$

This is a quadratic equation.

Subtract $(x+1)$ on both sides:

$x^2-(x+1)=0$

$x^2-x-1=0$

Comparing this to $ax^2+bx+c=0$ we see the following:

$a=1$

$b=-1$

$c=-1$

Let's plug them into the quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{1 \pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$x=\frac{1 \pm \sqrt{1+4}}{2}$

$x=\frac{1 \pm \sqrt{5}}{2}$

So we have the solutions to the quadratic equation are:

$x=\frac{1+\sqrt{5}}{2}$ or $x=\frac{1-\sqrt{5}}{2}$ .

The second solution definitely gives at least one of the logarithm equation problems.

Example: $\log(x)$ has problems when $x \le 0$ and so the second solution is a problem.

So the $x$ where the equations intersect is at $x=\frac{1+\sqrt{5}}{2}$ .

Let's find the $y$ -coordinate.

You may use either equation.

I choose $y=\log(x)$ .

$y=\log(\frac{1+\sqrt{5}}{2})$

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

6 0

2 years ago

Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Denver was $225. Now the cost is $30

liq [111]

Answer:

33.33% increase. 55.56% increase.

Step-by-step explanation:

3 0

2 years ago

A bank manager wants to encourage new customers to open accounts with principals of at least $3,000. He decides to make a poster

ankoles [38]

Assuming that the 4.8% interest rate is an annual interest rate, then, after one year, with a principal of $3,000 we would be able to win 4.8% of $3000:

$3000\times\frac{4.8}{100}=144$

Divide 144 over 12 to find the monthly earnings:

$\frac{144}{12}=12$

Therefore, with a principal of $3,000 we would be earning $12 interest in 1 month.

For the earnings on the first month to be equal to $10, then you would have to win $120 annually, and $120 must be 4.8% of the principal. To find which quantity satisfies that 4.8% of it is equal to $120, divide 120 over 4.8%:

$\frac{120}{4.8\text{ \%}}=\frac{120}{(4.8/100)}=\frac{100}{4.8}\times120=2500$

Therefore, the principal must be equal to $2500 for you to win $10 on the first month, and it would indeed be correct to say that if you open an account with $3000 you will earn at least $10 interest in 1 month.

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10 months ago

What expression is equivalent to 24b-34ab

Svet_ta [14]

It should be 2b(12-17a)

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3 years ago

Lyra and Donna are testing the two-way radios they built for their high school science project. Lyra goes to the top of a buildi

Strike441 [17]

The range of communication is about 55 meters.

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2 years ago