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3 years ago

Given two terms in artimetic sequence find the common diffrence , the explicit formula,and recursive formula. a11=110 and a37=37

Mathematics

1 answer:

umka2103 [35]3 years ago

7 0

$a_{37}-a_{11}=(37-11)d=26d\\\\26d=370-110\\\\26d=260\ \ \ |:26\\\\\boxed{d=10}$

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you earn 10 points for every coin you collect in a video game. then you find a star that triples your score. write and simplify

Tomtit [17]

Answer:

The required expression for total number of points you earn is $P=10c+3p$ .

Step-by-step explanation:

Consider the provided information.

Let c represents the coin and p represents the points before getting star.

You earn 10 points for every coin you collect in a video game.

$p=10c$ ......(1)

You find a star that triples your score.

$star=3p$

Now the total number of points you earn is(P):

$P=10c+3p$

Substitute the value of p from equation 1.

$P=10c+3(10c)$

$P=40c$

5 0

4 years ago

Element X decays radioactively with a half life of 12 minutes. If there are 160

Salsk061 [2.6K]

Answer:

It would take 75.8 minutes for the element to decay to 2 grams.

Step-by-step explanation:

The number of grams of element x, after t minutes, is given by the following equation:

$X(t) = X(0)(1-r)^{t}$

In which X(0) is the initial amount and r is the decay rate.

There are 160 grams of Element X

This means that X(0) = 160.

$X(t) = X(0)(1-r)^{t}$

$X(t) = 160(1-r)^{t}$

Half life of 12 minutes.

This means that X(12) = 0.5*X(0) = 0.5*160 = 80. So

$X(t) = 160(1-r)^{t}$

$80 = 160(1-r)^{12}$

$(1 - r)^{12} = 0.5$

$\sqrt[12]{(1 - r)^{12}} = \sqrt[12]{0.5}$

$1 - r = 0.9438$

$X(t) = 160(1-r)^{t}$

$X(t) = 160(0.9438)^{t}$

How long would it take for the element to decay to 2 grams?

This is t for which X(t) = 2. So

$X(t) = 160(0.9438)^{t}$

$2 = 160(0.9438)^{t}$

$(0.9438)^{t} = \frac{2}{160}$

$\log{(0.9438)^{t}} = \log{\frac{2}{160}}$

$t\log{0.9438} = \log{\frac{2}{160}}$

$t = \frac{\log{\frac{2}{160}}}{\log{0.9438}}$

$t = 75.8$

It would take 75.8 minutes for the element to decay to 2 grams.

6 0

3 years ago

Last month, Margo bought a tree that grows 2.5 cm each day. It was 5 cm tall when she bought it and now it is 65 cm tall. Write

IgorLugansk [536]

The equation is: 5+2.5d=65
The number of days Margo has owned the plant is 24 :)
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3 years ago

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spayn [35]

Answer:

Complementary

Step-by-step explanation:

The two angles are complementary because the angles are both a part of a right angle (a 90-degree angle), so they will both add up to 90 degrees, making them complementary.

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Ivenika [448]

Answer:

Step-by-step explanation:

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3 years ago