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3 years ago

At the beginning of spring, Robert planted a small sunflower in his backyard. When it

Mathematics

1 answer:

krek1111 [17]3 years ago

3 0

10 weeks=15 so that’s the length of the sunflower

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If the second term of a geometric sequence of real numbers is -2 and the fifth term is 16 then what is the fourteenth term?

Agata [3.3K]

<h3>Given</h3>

A geometric sequence such that ...

$a_2=-2\quad\text{and}\quad a_5=16$

$a_{14}$

<h3>Solution</h3>

We can use the ratio of the given terms to find the common ratio of the sequence, then use that to find the desired term from one of the given terms. We don't actually need the common ratio (-2). All we need is its cube (-8).

$a_2=a_1r^{(2-1)}=a_1r^1\\a_5=a_1r^{(5-1)}=a_1r^4\\a_{14}=a_1r^{(14-1)}=a_1r^13=a_5r^9\\\\\dfrac{a_5}{a_2}=\dfrac{a_1r^4}{a_1r^1}=r^3=\dfrac{16}{-2}=-8\\\\r^9=\left(r^3\right)^3=(-8)^3=-512\\a_{14}=a_5(-512)\\\\a_{14}=-8192$

7 0

3 years ago

What is 1.21 repeating as a fraction?

DochEvi [55]

$x=1.\overline{21}\\
100x=121.\overline{21}\\
100x-x=121.\overline{21}-1.\overline{21}\\
99x=120\\
x=\dfrac{120}{99}=\dfrac{40}{33}$

6 0

3 years ago

Read 2 more answers

A triangle has side lengths of

alexandr402 [8]

Answer:

P = ( 4y + 6 inches) + ( 8y - B ) inches + ( 5y + 3 ) inches

Step-by-step explanation:

Formula of Perimeter of triangle is = Sum of all sides.

P = A + B + C

6 0

2 years ago

Simplify (Are all division)<br><br>2+4i<br>3i<br><br>3+2i<br>4+i<br><br>2i^11

Alla [95]

$We\ know:\ i=\sqrt{-1}\to i^2=-1$

$\dfrac{2+4i}{3i}=\dfrac{2+4i}{3i}\cdot\dfrac{3i}{3i}=\dfrac{6i+12i^2}{9i^2}=\dfrac{6i+12(-1)}{9(-1)}\\\\=\dfrac{6i-12}{-9}=\dfrac{2i-4}{-3}=\dfrac{4}{3}-\dfrac{2}{3}i$

$\dfrac{3+2i}{4+i}=\dfrac{3+2i}{4+i}\cdot\dfrac{4-i}{4-i}=\dfrac{(3+2i)(4-i)}{4^2-i^2}\\\\=\dfrac{(3)(4)+(3)(-i)+(2i)(4)+(2i)(-i)}{16-(-1)}=\dfrac{12-3i+8i-2i^2}{16+1}\\\\=\dfrac{12+5i-2(-1)}{17}=\dfrac{12+5i+2}{17}=\dfrac{14+5i}{17}=\dfrac{14}{17}+\dfrac{5}{17}i$

$2i^{11}=2i^{10+1}=2i^{10}i^1=2i^{2\cdot5}i=2i(i^2)^5=2i(-1)^5=2i(-1)=-2i$

$Used:\ (a+b)(a-b)=a^2-b^2$

6 0

3 years ago

Please. I need help answering these questions

Goryan [66]

If you're struggling with graphing problems, I'd highly recommend that you check out Desmos and Mathaway. All you have to do is type the equations and it graphs it for you. Here's the first question:

4 0

3 years ago