Find the next numbers 5, 1, 7, 0, 9, -1, 11...

Es

polet [3.4K]

The fence encloses at 22 ft2

8 0

3 years ago

Read 2 more answers

An Equilateral Triangle has sides that all measure 10 inches. What is

densk [106]

Answer:

easy peasy lemon squeasy

Step-by-step explanation:

1. base of triangle: it is an equilateral triangle, so any side of the triangle you take is the base, (usually the largest side of the triangle is the base)

so that would be => 10 inches,

2. a property of an equilateral triangle is that , the median of the triangle coincides with the height of the triangle,

therefore, the height bisects the base and makes a right triangle with another side, therefore by using the Pythagoras theorem, we find it to be 8.66(approx)

now,

area of the triangle would be (putting the values we just found in the formula given)

=> [(10)(8.66)]/ 2

=>43.3 square inches

4 0

3 years ago

Write a quadratic relation in the form y = ax2 + bx + c with roots 4 and - 3 and

pochemuha

Answer:

y = 2*x^2 - 2*x - 24

Step-by-step explanation:

If we have a quadratic function with roots a and b, we can write the equation for that function as:

y = f(x) = A*(x - a)*(x - b)

Where A is the leading coefficient.

In this case, we know that the roots are: 4 and -3

Then the function will be something like:

f(x) = A*(x - 4)*(x - (-3) )

f(x) = A*(x - 4)*(x + 3)

Now we need to determine the value of A.

We also know that the graph of the function passes through the point (3, -12)

This means that:

f(3) = -12

Then:

-12 = A*(3 - 4)*(3 + 3)

-12 = A*(-1)*(6)

-12 = A*(-6)

-12/-6 = A

2 = A

Then the equation is:

y = f(x) = 2*(x - 4)*(x + 3)

Now we need to write this in standard form, so we just need to expand the equation:

y = f(x) = 2*(x^2 + x*3 - x*4 - 4*3)

y = f(x) = 2*(x^2 - x - 12)

y = f(x) = 2*x^2 - 2*x - 24

Then the relation is:

y = 2*x^2 - 2*x - 24

4 0

3 years ago

Find the radius of convergence, r, of the series. ∞ xn 2n − 1 n = 1 r = 1 find the interval, i, of convergence of the series. (e

Bingel [31]

Assuming the series is

$\displaystyle\sum_{n\ge1}\frac{x^n}{2n-1}$

The series will converge if

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|$

We have

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|=|x|\lim_{n\to\infty}\frac{\frac1{2n+1}}{\frac1{2n-1}}=|x|-\lim_{n\to\infty}\frac{2n-1}{2n+1}=|x|$

So the series will certainly converge if $-1$ , but we also need to check the endpoints of the interval.

If $x=1$ , then the series is a scaled harmonic series, which we know diverges.

On the other hand, if $x=-1$ , by the alternating series test we can show that the series converges, since

$\left|\dfrac{(-1)^n}{2n-1}\right|=\dfrac1{2n-1}\to0$

and is strictly decreasing.

So, the interval of convergence for the series is $-1\le x$ .

6 0

3 years ago

A cube made out of lead has a mass of 12 grams. A side of the cube has length 1 cm. What would be the mass of the cube whose sid

Ulleksa [173]

Answer:

<h3><em><u>The mass of a lead cube whose </u></em><em><u>side </u></em><em><u>have length 1.5 cm is 40.5 </u></em><em><u>grams</u></em></h3>

Step-by-step explanation:

<u>1. Let's review the information given to</u>

<u>1. Let's review the information given tous to answer the question correctly:</u>

<u>1. Let's review the information given tous to answer the question correctly:Mass of the cube made out of lead</u> = 12

= 12grams

Side of the cube <em>= 1 cm</em>

2. <em><u>What would be the mass of a lead</u></em>

<em><u>What would be the mass of a leadcube whose sides have length 1.5 cm?</u></em>

<em><u>What would be the mass of a leadcube whose sides have length 1.5 cm?For answering the question, let's</u></em>

<em><u>What would be the mass of a leadcube whose sides have length 1.5 cm?For answering the question, let'scalculate the volume of the cube and</u></em>

<em><u>What would be the mass of a leadcube whose sides have length 1.5 cm?For answering the question, let'scalculate the volume of the cube andthen its density, this way:</u></em>

<h3>Volume = Height* Width * Length</h3><h3>Volume=1*1*1</h3><h3>Volume =1 cm</h3>

Let's recall the formula of the density:

Density Mass/Volume, therefore:

Density of the lead <em><u>= 12/1= 12 gr/</u></em><em><u>cm</u></em>

<em><u>Now, let's calculate the volume of the</u></em>

<em><u>Now, let's calculate the volume of thesecond cube:</u></em>

<h3><em>Volume = Height Width Length</em></h3><h3><em>Volume = Height Width LengthVolume 1.5 * 1.5 1.5</em></h3><h3><em>Volume = Height Width LengthVolume 1.5 * 1.5 1.5Volume =3.375 cm3</em></h3>

<u>Finally, let's calculate the mass, using</u>

<u>Finally, let's calculate the mass, usingthe density of the lead we already</u>

<u>Finally, let's calculate the mass, usingthe density of the lead we alreadyknow:</u>

<h3>Density = Mass/Volume</h3><h3><em>12 Mass/3.375</em></h3><h3><em>12 Mass/3.375Mass 12 *3.375</em></h3><h3><em>12 Mass/3.375Mass 12 *3.375Mass = 40.5 gramss</em></h3>

8 0

2 years ago