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MariettaO [177]

3 years ago

8

which of these numbers can be classifies as irrational 1/3 ,square root of 16, 0.73737373... or 0.87546201023....? will give bra

nliest!!!!

1 answer:

Verdich [7]3 years ago

3 0

The .87546201023 because it is infinite and a fraction cant be written.
where as .73 can just be put over 99

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What will be the value of

madreJ [45]

The expression as given doesn't make much sense. I think you're trying to describe an infinitely nested radical. We can express this recursively by

$\begin{cases}a_1=\sqrt{42}\\a_n=\sqrt{42+a_{n-1}}\end{cases}$

Then you want to know the value of

$\displaystyle\lim_{n\to\infty}a_n$

if it exists.

To show the limit exists and that $a_n$ converges to some limit, we can try showing that the sequence is bounded and monotonic.

Boundedness: It's true that $a_1=\sqrt{42}\le\sqrt{49}=7$ . Suppose $a_k\le 7$ . Then $a_{k+1}=\sqrt{42+a_k}\le\sqrt{42+7}=7$ . So by induction, $a_n$ is bounded above by 7 for all $n$ .

Monontonicity: We have $a_1=\sqrt{42}$ and $a_2=\sqrt{42+\sqrt{42}}$ . It should be quite clear that $a_2>a_1$ . Suppose $a_k>a_{k-1}$ . Then $a_{k+1}=\sqrt{42+a_k}>\sqrt{42+a_{k-1}}=a_k$ . So by induction, $a_n$ is monotonically increasing.

Then because $a_n$ is bounded above and strictly increasing, the limit exists. Call it $L$ . Now,

$\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}a_{n-1}=L$

$\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}\sqrt{42+a_{n-1}}=\sqrt{42+\lim_{n\to\infty}a_{n-1}}$

$\implies L=\sqrt{42+L}$

Solve for $L$ :

$L^2=42+L\implies L^2-L-42=(L-7)(L+6)=0\implies L=7$

We omit $L=-6$ because our analysis above showed that $L$ must be positive.

So the value of the infinitely nested radical is 7.

4 0

3 years ago

Sally brought a 1 quart container of buttermilk to make pancakes. Her recipe says to use 1/2cups Of butter milk for 3 pancakes.

GrogVix [38]

Answer:

24

Step-by-step explanation:

Quart is a volume unit, equal to a quarter of a gallon. The symbol is "qt"

A quart container is equivalent to 4 cups.

a pancake need only 1/2 cup of butter milk.

We use a rule of three.

if 1/2 cup can make 3 pancakes.

How many pancakes 4 cups can make?

$\frac{4*3}{\frac{1}{2} }$ =24

We only have to multiply the 4 cups of butter milk by the 3 pancakes and the divide it by the 1/2 cup you need to make only 3 pancakes.

3 0

3 years ago

How did he get this 1/2i ? I dont remember studying this definition in calc 1 neither calc 2!

Hitman42 [59]

The $i$ in the denominator is missing in the second expression. It should be

$\sin at=\dfrac{e^{iat}-e^{-iat}}{2i}$

This follows from

$e^{iat}=\cos at+i\sin at$
$e^{-iat}=\cos at-i\sin at$
$\implies e^{iat}-e^{-iat}=2i\sin at$
$\implies \sin at=\dfrac{e^{iat}-e^{-iat}}{2i}$

8 0

4 years ago

An engineer is designing a roller coaster. The tallest peak is 310 feet high.

rusak2 [61]

<h2>Hello!</h2>

The answer is:

The slope of the hill is equal to 2.

<h2>Why?</h2>

To solve the problem, we need to remember that the slope of a line, is the rate of increase or decrease of the line.

From the statement we know that the tallest peak of the roller coaster is 310 feet (y), while the roller coaster travels 155 horizontal feet (x), so, calculating we have:

$Slope=\frac{height}{base}=\frac{y}{x}$

Then, substituting the given information and calculating, we have:

$Slope=\frac{310ft}{155ft}=2$

We have that the slope of the hill is equal to 2.

Have a nice day!

4 0

3 years ago

Mhanifa can you please help me on this? I will mark brainliest!

denpristay [2]

Answer:

y = -4x + 7

Step-by-step explanation:

<u>Given points:</u>

A(-2, -2) and B(6, 0)

The perpendicular bisector passes through the midpoint.

<u>Finding the coordinates of the midpoint first:</u>

x = (-2 + 6)/2 = 2, y = (-2 + 0)/2 = -1

<u>Next finding the slope of AB:</u>

m = (0 - (-2))/(6 - (-2)) = 2/8 = 1/4

The perpendicular lines have negative-reciprocal slopes.

<u>The line will have a slope of -4 and pass through the point (2, -1)</u>

y - (-1) = -4(x - 2)
y + 1 = -4(x - 2) - point-slope form
y = -4x + 7 - slope-intercept form

4 0

3 years ago