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3 years ago

What’s the fifth term of a sequence whose first term is 5 and whose common ratio is 3?

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

4 0

Answer:

405.

Step-by-step explanation:

This is a geometric sequence where the nth term = a1 r^(n -1).

Here a1 = 5 and r = 3 so

the fifth term a5 = 5(3)^(5-1)

= 5 * 81

= 405.

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A pole that is 3.2m tall casts a shadow that is 1.66m long. at the same time a nearby tower cast a shadow that is 39.5 m long. h

Nikolay [14]

Answer:

76.14 m

Step-by-step explanation:

create a proportion of height/shadow equals height/shadow

3.2/1.66 = h/39.5

cross-multiply:

1.66h = 39.5(3.2)

1.66h = 126.4

h = 76.14

4 0

3 years ago

Please help me, it's also due today!!

Novay_Z [31]

The answer is 110 and the answer for E is 2hrs

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3 years ago

Read 2 more answers

A carpentry shop currently sells 66000 decoy ducks per year at a cost of 16 dollars each. In the previous year when they raised

Rus_ich [418]

Answer:

19 dollars

Step-by-step explanation:

<h2>Buckle up! This is a good one!</h2>

First we have to find the line that goes trough the two points. And it has the form :

$y=mx+b$

<em>m is often called the slope.</em>

Given the two points (66000, 16) and (51000, 21) we find m with this formula:

$m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\m=\frac{21-16}{51000-66000} \\m=-\frac{5}{15000} \\m=-\frac{1}{3000}$

We pick the point (51000,21) and plug it into the equation of the line and we find b:

$y= mx + b\\21=(-\frac{1}{3000} )(51000)+b\\21=-17+b\\21+17=b=38$

<h3>And we have got our line equation</h3>

$y= -\frac{1}{3000}x + 38\\$

<u>Where x represents the quantity and y represents the price.</u>

<u />

<h2>The revenue</h2>

The revenue is price times quantity, since price is y and quantity is x, we get

$y=-\frac{1}{3000} x+38\\y*x=x*(-\frac{1}{3000} x+38)\\yx=-\frac{1}{3000} x^2+38x\\R(x)=-\frac{1}{3000} x^2+38x$

<h3>to maximize the revenue, we get the first derivative:</h3>

$R(x)=-\frac{1}{3000} x^2+38x\\R'(x)=-(2)\frac{1}{3000} x+38\\R'(x)=-\frac{2}{3000} x+38\\\\R'(x)=-\frac{1}{1500} x+38\\\\$

$R'(x)=-\frac{1}{1500} x+38=0\\38=\frac{1}{1500} x\\38*1500=x=57000$

So the quantity that maximizes revenue is 57000,

<h3>let's find out the price by plugging it into the equation:</h3>

$y= -\frac{1}{3000}x + 38\\y= -\frac{1}{3000}(57000) + 38\\y= -19 + 38\\y=19$

<h2>And there you go! 19 dollars is the price the carpentry shop should charge per decoy duck.</h2>

7 0

3 years ago

What is 5/6 and 3/8 as an equivalent fraction

Veronika [31]

Answer:

5/6 - 10/12, 15/18, 20/24

3/8 - 6/16, 9/24, 12/32

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

How mant time could 29 go into 79

anygoal [31]

Only 2 times. After that, there's only enough room in there for 21 more.

These facts all come about as a result of DIVISION. Divide 79 by 29 and you'll see.

8 0

4 years ago