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sweet [91]
3 years ago
10

A sequence of numbers a1, a2, a3, . . . is defined as follows: a1 = 3, a2 = 5, and every term in the sequence after a2 is the pr

oduct of all terms in the sequence preceding it,
e.g., a3 = (a1)(a2) and a4 = (a1)(a2)(a3). if an = t and n > 2, what is the value of an+2 in terms of t ?
Mathematics
1 answer:
Hoochie [10]3 years ago
3 0
Since n>2 n 
n can be 3 for example

so a3=t 

and from the sequence we know a3 = 15 
because it is the product of a1(3) and a2( 5)

so t = 15 

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What is the solution of the system of equations? y = –3x + 8 y = –5x – 2
jekas [21]
y=-3x+8 \\ y=-5x-2 \\  \\ -3x+8=-5x-2 \\ -3x+5x=-2-8 \\ 2x=-10 \\ x=- \frac{10}{2}  \\ x=-5 \\ y=-3(-5)+8=15+8=23  \\ \\ \boxed{-5,23}
6 0
2 years ago
Read 2 more answers
number of bacteria in a certain population Increases according to a continuous exponential growth model with How many hours does
vladimir1956 [14]

Answer:

It takes 1.77 hours for the population to double.

Step-by-step explanation:

Equation for population growth:

The equation for population growth, after t hours, with a growth rate parameter of r, as a decimal, is given by:

P(t) = P(0)(1+r)^t

Growth rato parameter of 48% per hour

This means that r = 0.48. So

P(t) = P(0)(1+r)^t

P(t) = P(0)(1+0.48)^t

P(t) = P(0)(1.48)^t

How many hours does it take the size of the sample to double?

This is t for which P(t) = 2P(0). So

P(t) = P(0)(1.48)^t

2P(0) = P(0)(1.48)^t

(1.48)^t = 2

\log{(1.48)^t} = \log{2}

t\log{1.48} = \log{2}

t = \frac{\log{2}}{\log{1.48}}

t = 1.77

It takes 1.77 hours for the population to double.

3 0
3 years ago
You have worked as a guide at the aquarium for two summers. This summer you have been offered the job again, but with a 4 percen
olga nikolaevna [1]

Answer:

More earn this summer per month = $30 more

Entire summer earning (for 2.5 months) = $1950

Step-by-step explanation:

For 2.5 months, you got 1875 dollars, so per month salary is:

1875/2.5 = $750 per month

This summer, you got a 4% raise, that means:

4% = 4/100 = 0.04

The raise is:

0.04 * 750 = $30 raise

So, new monthly salary is:

750 + 30 = $780

So, assuming you will work 2.5 months again this summer, you total earnings would be:

2.5 * 780 = $1950

8 0
3 years ago
Line segment AB has a length of 15 and angle a=35degrees . A segment with a length of 12 will form the third side of the triangl
PtichkaEL [24]

Answer:

C = 45.8 or C = 117.69

Step-by-step explanation:

Remark

Only SSA gives the possibility of 2 answers. This one does not give that opportunity. There is one unique answer. We'll discuss 2 and zero after finding 1 answer. On looking at it again, the question might be ambiguous. We'll check that out as well.

Given

AB = 15

<A = 35

point C opposite line AB such that CB = 12 These givens give a unique answer.

Solution

Sin(35) / 12 = Sin(C) / 15                     Multiply both sides by 15

15*Sin(35) / 12 = Sin(C)                       Find 15/12

1.25*sin(35) = Sin(C)                           Write Sin(35)

1.25*0.5736 = Sin(C)                          Multiply the left

0.71697 = Sin(C)                                 Take the inverse Sin

C = 45.805 degrees                          This is the angle opposite AB

Angle B = 180 - 35 - 45.805 = 99.2

Ambiguous Case                    

If AC = 12 we have another answer entirely. This is SAS which will give just 1 set of answers for the triangle. The reason the case is ambiguous is because we don't exactly know where that 12 unit line is. It could be AC or BC.

I will set up the Sin law for you, and let you solve it

Sin(B) / 12 = Sin(35)/15

When you solve for Sin(B) as done above you, get 0.45886 from which B = 27.31 degrees

C = 180 - 35 - 27.31 = 117.69

So that's two values that C could have. I think that's all given these conditions.

Two Cases or None

<A = 35 degrees

AC = 15

CB = 12

This should give you two possible cases or none. You can check which by finding the height of the triangle from C down to AB (which has no distinct length. The h is 15 * Sin35 = 8.6. If CB < 8.6, there are no solutions. If CB < AC then if CB > that 8.6, there are 2 solutions.

7 0
2 years ago
A store is having a Winter Blowout sale, where all their winter clothes are on sale for 75% off. Michael spent a total of $89.92
gogolik [260]

Answer:

89.92 \div 25 = 3.5968  \times 100 = 359.68

therefore the answer is 359.68$

8 0
3 years ago
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