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3 years ago

Determine if the sequence is arithmetic. If it is, find the common difference. Is the sequence a function ?

1 answer:

8 0

$6)\\r=a_{n+1}-a_n\to r=a_2-a_1=a_3-a_2=a_4-a_3=...\\\\a_1=-7;\ a_2=-10;\ a_3=-11;\ a_4=-13\\\\a_2-a_1=-10-(-7)=-10+7=-3\\a_3-a_2=-11-(-10)=-11+10=-1\\\\a_3-a_2\neq a_2-a_1\\\\\text{It's not an arithmetic sequence}$

$\r=\dfrac{a_{n+1}}{a_n}\\\\r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...\\\\8.)\\a_1=4;\ a_2=20;\ a_3=100;\ a_4=500\\\\r=\dfrac{20}{4}=\dfrac{100}{20}=\dfrac{500}{100}=5\\\\10.)\\a_1-30;\ a_2=-45;\ a_3=-50;\ a_4=-65\\\\\dfrac{a_2}{a_1}=\dfrac{-45}{-30}=\dfrac{3}{2}\\\\\dfrac{a_3}{a_2}=\dfrac{-50}{-45}=\dfrac{10}{9}\\\\\dfrac{a_2}{a_1}\neq\dfrac{a_3}{a_2}\\\\\text{It's not a geometric sequence}$
$12.)\\a_1=-7;\ a_2=-14;\ a_3=-21;\ a_4=-28\\\\\dfrac{a_2}{a_1}=\dfrac{-14}{-7}=2\\\\\dfrac{a_3}{a_2}=\dfrac{-21}{-14}=\dfrac{3}{2}\\\\\dfrac{a_2}{a_1}\neq\dfrac{a_3}{a_2}\\\\\text{It's not a geometric sequence}\\\\\text{It's a function}$

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Find the volume of the composite figure. Explain your thought, explain how your arrived at your answer. SHOW YOUR WORK FOR FULL

Bond [772]

At the bottom of the composite figure we have half a sphere, of radius 10 in.

The volume of this hemisphere would be half the volume of the full sphere, or:

(1/2)(4/3)π(10 in)^3, or (2/3)π(1000 in^3), or (2000/3)π in^3.

On top is the cone of radius 10 and slant height 15 in. To find the volume of this cone-shaped solid, we'll need the height of the cone. This can be found using the Pyth. Thm. as follows:

15^2 = 10^2 + h^2, where h is the height of the cone.

225 = 100 + h^2, so that h= √125, or 5√5. The height of the cone is 5√5 in.

Then the volume of the cone is V = (1/3)(base)(height)

= (1/3)(π)(100 in^2)(5√5 in)

= 500√5/3(π) in^3

The total volume of the composite solid is then

(2000/3)(π in^3) + ( 500√5/3(π) ) in^3), or

(π/3)(4+√5) in^3. This comes out to 6.53 in^3, to the nearest hundredth.

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3 years ago

How much is 89 km in miles?

laila [671]

89 km would be about 55.3 miles! that's the best answer, but if they want you to round then I'd say choose 55 miles

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3 years ago

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A shipping company charged $15 to ship a package and 5% to insure the package. What was the total cost to ship this particular i

Crank

The shipping would be 15.75 because 5% of 15 is 0.75, so add 15 to 0.75 and the answer is 15.75 :)

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3 years ago

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Math problem help me

Ratling [72]

Answer:

$y=3x+2$

Step-by-step explanation:

To find the equation, use the slope-intercept formula:

$y=mx+b$

m is the slope and b is the y-intercept. Now, it'll really help to draw a line through the points, connecting them. If you look at point (0,2), we can see that this is the y-intercept (where a point sits on the y-axis when x=0). You can insert this into the equation by taking the y value:

$(0,2)\\y=mx+2$

Now, take any two points to find the slope. To make it easier, I'll use (1,5) and (0,2). Use the slope formula for when you know two points:

$\frac{y(2)-y(1)}{x(2)-(x1)} =\frac{rise}{run}$

Rise over run is the change in the y-axis over the change in the x-axis. Insert values:

$(1(x1),5(y1))\\(0(x2),2(y2))\\\\\frac{2-5}{0-1}$

Solve:

$\frac{2-5}{0-1}=\frac{-3}{-1}$

Since both are negative, the result is a positive:

$\frac{-3}{-1}=\frac{3}{1} =3$

Insert this into the equation as m, the slope:

$y=3x+2$

Done.

6 0

3 years ago

Find the? inverse, if it? exists, for the given matrix.<br><br> [4 3]<br><br> [3 6]

True [87]

Answer:

Therefore, the inverse of given matrix is

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

Step-by-step explanation:

The inverse of a square matrix $A$ is $A^{-1}$ such that

$A A^{-1}=I$ where I is the identity matrix.

Consider, $A = \left[\begin{array}{ccc}4&3\\3&6\end{array}\right]$

$\mathrm{Matrix\:can\:only\:be\:inverted\:if\:it\:is\:non-singular,\:that\:is:}$

$\det \begin{pmatrix}4&3 \\3&6\end{pmatrix}\ne 0$

$\mathrm{Find\:2x2\:matrix\:inverse\:according\:to\:the\:formula}:\quad \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}$

$=\frac{1}{\det \begin{pmatrix}4&3\\ 3&6\end{pmatrix}}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}$

$\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc$

$4\cdot \:6-3\cdot \:3=15$

$=\frac{1}{15}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}$

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

Therefore, the inverse of given matrix is

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

4 0

3 years ago