Write the first four terms of sequence Rule:start at 28.6, subtract 3.1

Mathematics

1 answer:

Gekata [30.6K]3 years ago

6 0

28.6, 25.5, 22.4, 19.3... hope this helps!!

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What are the first nine multiples of 5, and 3?

andrezito [222]

First 9 multiples of 5:

$\begin{gathered} 5\cdot1=5 \\ 5\cdot2=10 \\ 5\cdot3=15 \\ 5\cdot4=20 \\ 5\cdot5=25 \\ 5\cdot6=30 \\ 5\cdot7=35 \\ 5\cdot8=40 \\ 5\cdot9=45 \end{gathered}$

First 9 multiples of 3:

$\begin{gathered} 3\cdot1=3 \\ 3\cdot2=6 \\ 3\cdot3=9 \\ 3\cdot4=12 \\ 3\cdot5=15 \\ 3\cdot6=18 \\ 3\cdot7=21 \\ 3\cdot8=24 \\ 3\cdot9=27 \end{gathered}$

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1 year ago

Solve the equation on the interval [0,2π]

WARRIOR [948]

$\bf 16sin^5(x)+2sin(x)=12sin^3(x)
\\\\\\
16sin^5(x)+2sin(x)-12sin^3(x)=0
\\\\\\
\stackrel{common~factor}{2sin(x)}[8sin^4(x)+1-6sin^2(x)]=0\\\\
-------------------------------\\\\
2sin(x)=0\implies sin(x)=0\implies \measuredangle x=sin^{-1}(0)\implies \measuredangle x=
\begin{cases}
0\\
\pi \\
2\pi 
\end{cases}\\\\
-------------------------------$

$\bf 8sin^4(x)+1-6sin^2(x)=0\implies 8sin^4(x)-6sin^2(x)+1=0$

now, this is a quadratic equation, but the roots do not come out as integers, however it does have them, the discriminant, b² - 4ac, is positive, so it has 2 roots, so we'll plug it in the quadratic formula,

$\bf 8sin^4(x)-6sin^2(x)+1=0\implies 8[~[sin(x)]^2~]^2-6[sin(x)]^2+1=0
\\\\\\
~~~~~~~~~~~~\textit{quadratic formula}
\\\\
\begin{array}{lcccl}
& 8 sin^4& -6 sin^2(x)& +1\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array} 
\qquad \qquad 
sin(x)= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}
\\\\\\
sin(x)=\cfrac{-(-6)\pm\sqrt{(-6)^2-4(8)(1)}}{2(8)}\implies sin(x)=\cfrac{6\pm\sqrt{4}}{16}
\\\\\\
sin(x)=\cfrac{6\pm 2}{16}\implies sin(x)=
\begin{cases}
\frac{1}{2}\\\\
\frac{1}{4}
\end{cases}$

$\bf \measuredangle x=
\begin{cases}
sin^{-1}\left( \frac{1}{2} \right)
sin^{-1}\left( \frac{1}{4} \right)
\end{cases}\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}~,~\frac{5\pi }{6}\\
----------\\
\approx~0.252680~radians\\
\qquad or\\
\approx~14.47751~de grees\\
----------\\
\pi -0.252680\\
\approx 2.88891~radians\\
\qquad or\\
180-14.47751\\
\approx 165.52249~de grees
\end{cases}$

3 0

3 years ago

a and b can do a piece of work in 12 days, b and c in 15 days and c and a in 20 days. how much time will a alone take to finish

nydimaria [60]

A and b can do a piece of work in 12 days. If a alone have to finish the job among b and c so

A and b=12
A (24 days alone without b)

So if b and c 15 days and c 20 days. If a have to do all I would add 24 and 15 and 20 which would be 59 days

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3 years ago

Can someone please help me with 10-16 it’s due tomorrow!!! Please

VMariaS [17]

10) V=πr² *h= π*10²*12≈3770
11) V=A(base)*h= (3√3/2)*(9²)*10=2104
A(base)=(P*a)/2=(6*9*3√3)/2=9*9*3√3/2

12)V=πr² *h=π*18² *6≈6107
13)V=4*3*12=144
14) h(triangle)=√(5²-3²)=√16=4
A(base)=(3*4)/2=6
V=A(base)* height (prism)=6*2=12
15) V=A(base)*h= (3√3/2)*(6²)*11= 1029
16)V=A(base)*h=2(1+√2)5²*22≈2656

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3 years ago

A clothing store is having a sale on T-shirts. The first T-shirt you buy costs $7, and every additional shirt costs

asambeis [7]

Answer:

Is an arithmetic sequence

Step-by-step explanation:

This is an arithmetic sequence, because it is a sequence of numbers in which the common difference between consecutive terms is 5

4 0

3 years ago

Read 2 more answers