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2 years ago

6

Arthur started school in 1969. He is still living. If he was 7 years old when he started school, how old was he in 1980?

1 answer:

scoray [572]2 years ago

4 0

He would be 18 in 180

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How many centimeters are there in 740.2<br> millimeters?

Anna11 [10]

Answer:

There are 74.2 Centimeters

Step-by-step explanation:

If you take 740.2 millimeters and divide it by 10 you well get 74.2 centimeters

5 0

3 years ago

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

<br><br><br><br> <br><br> , find f^{-1}(x)f <br><br>−1<br><br> (x)

Stolb23 [73]

Answer:

Multiply the numerator by the reciprocal of the denominator. Multiply x x by 1 1 . Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=1x f - 1 ( x ) = 1 x is the inverse of f(x)=1x f ( x ) = 1 x .

Step-by-step explanation:

:)

5 0

1 year ago

If you were to roll the dice one time what is the probability it will land on a 3?

Korolek [52]

3/6 because there are six sides to a dice.

6 0

2 years ago

Read 2 more answers

What is the value of 9 cubed?<br><br> 18<br><br> 27<br><br> 81<br><br> 729

exis [7]

Answer is 729

9x9x9 = 729

7 0

2 years ago

Read 2 more answers