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3 years ago

Given the explicit rule, f(n) = 2n - 3, generate the first four terms in the sequence.

Mathematics

1 answer:

Vikki [24]3 years ago

5 0

Answer: -1, 1, 3, 5

Step-by-step explanation:

F(n)= 2n-3

F(1)=2(1)-3= -1

F(2)=2(2)-3= 1

F(3)=2(3)-3= 3

F(4)=2(4)-3=5

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10x4 ones= how many ones

kiruha [24]

The answer is 40 because they're are 4 groups of ten so it would go like 10,20,30,and 40.=)

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3 years ago

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The perimeter of a right triangle is 24 ft, and one of its legs measures 6 ft. Find the length of the other leg and the hypotenu

Mrrafil [7]

Answer:

Step-by-step explanation:

We know the perimeter of a triangle is the sum of all the sides( two legs and one hypotenuse).

By pythagoras we know that

$h^2= a^2+b^2.$

and the perimeter is $P=h+a+b$ .

Since P=24 and a=6 we have these equations:

$h^2=36+b^2\\24=h+6+b$

From the last equation we have $h=18-b$ . Replace h in the first equation we get that

$(18-b)^2=36+b^2$

$18^2-36b+b^2=36+b^2\\288=36b\\b=\frac{288}{36}=8$

and h=18-8=10

5 0

3 years ago

one thrid of fruits stalls are apples the rest of the fruit are oranges and pears there are 340 pears and 80 more oranges than a

Andrej [43]

1/3 of all=apples
2/3=rest=oranges+pears

pears=340
oranges=80+apples

ok

pears+oranges=2/3
apples=1/3
so pears+oranges=2(apples)
340+80+apples=2(apples)
minus apples
340+80=apples
420=apples

420 apples
420=apples=1/3 of total

420 times 3=1260 fruits total

8 0

3 years ago

Iliana was part of a group that was working on changing 0.4 repeated to a fraction. Each member of the group had a different ans

amm1812

$\bf 0.444444444\overline{4}\impliedby \textit{and keeps on going}\\\\
-------------------------------\\\\
\textit{let's say }\boxed{x=0.444444444\overline{4}}\quad \textit{ thus }10\cdot x=4.44444444\overline{4}
\\\\\\
\textit{wait a minute! }4.44444444\overline{4}\textit{ is really just }4+0.444444444\overline{4}$

$\bf \textit{but we know }x=0.444444444\overline{4} \textit{ so then }4+0.444444444\overline{4}=\boxed{4+x}
\\\\\\
\textit{wait a second! }10\cdot x\implies 10x=4.444444444\overline{4}=4+x
\\\\\\
thus\qquad 10x=4+x\implies 10x-x=4\implies 9x=4\implies \boxed{x=\cfrac{4}{9}}$

you can check in your calculator.

anyhow, to get the "recurring decimal to fraction", you start by setting to some variable, "x" in this case, then move the repeating part to the left of the point by multiplying it by some power of 10, and then do the equating.

3 0

3 years ago

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HELP i’m having trouble with my homework assignments

Aleksandr-060686 [28]

Answer:

Collin: about $401 thousand

Cameron: about $689 thousand

Step-by-step explanation:

A situation in which doubling time is constant is a situation that can be modeled by an exponential function. Here, you're given an exponential function, though you're not told what the variables mean. That function is ...

$P(t)=P_0(2^{t/d})$

In this context, P0 is the initial salary, t is years, and d is the doubling time in years. The function gives P(t), the salary after t years. In this problem, the value of t we're concerned with is the difference between age 22 and age 65, that is, 43 years.

In Collin's case, we have ...

P0 = 55,000, t = 43, d = 15

so his salary at retirement is ...

P(43) = $55,000(2^(43/15)) ≈ $401,157.89

In Cameron's case, we have ...

P0 = 35,000, t = 43, d = 10

so his salary at retirement is ...

P(43) = $35,000(2^(43/10)) ≈ $689,440.87

___

Sometimes we like to see these equations in a form with "e" as the base of the exponential. That form is ...

$P(t)=P_{0}e^{kt}$

If we compare this equation to the one above, we find the growth factors to be ...

2^(t/d) = e^(kt)

Factoring out the exponent of t, we find ...

(2^(1/d))^t = (e^k)^t

That is, ...

2^(1/d) = e^k . . . . . match the bases of the exponential terms

(1/d)ln(2) = k . . . . . take the natural log of both sides

So, in Collin's case, the equation for his salary growth is

k = ln(2)/15 ≈ 0.046210

P(t) = 55,000e^(0.046210t)

and in Cameron's case, ...

k = ln(2)/10 ≈ 0.069315

P(t) = 35,000e^(0.069315t)

5 0

3 years ago