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2 years ago

Help will mark brainiest!

Mathematics

1 answer:

Darya [45]2 years ago

6 0

Answer:

Sry Im guessing. You divide the actual length of pole by the shadow then multiply it to shadow of the tower...

Step-by-step explanation:

Hope it helps

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La diferencia comun es?

Afina-wow [57]

Answer:

2. el numero contante por que se suma o resta

5 0

2 years ago

Tacoma's population in 2000 was about 200 thousand, and had been growing by about 9% each year. a. Write a recursive formula for

KIM [24]

Answer:

a) The recurrence formula is $P_n = \frac{109}{100}P_{n-1}$ .

b) The general formula for the population of Tacoma is

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) In 2016 the approximate population of Tacoma will be 794062 people.

d) The population of Tacoma should exceed the 400000 people by the year 2009.

Step-by-step explanation:

a) We have the population in the year 2000, which is 200 000 people. Let us write $P_0 = 200 000$ . For the population in 2001 we will use $P_1$ , for the population in 2002 we will use $P_2$ , and so on.

In the following year, 2001, the population grow 9% with respect to the previous year. This means that $P_0$ is equal to $P_1$ plus 9% of the population of 2000. Notice that this can be written as

$P_1 = P_0 + (9/100)*P_0 = \left(1-\frac{9}{100}\right)P_0 = \frac{109}{100}P_0$ .

In 2002, we will have the population of 2001, $P_1$ , plus the 9% of $P_1$ . This is

$P_2 = P_1 + (9/100)*P_1 = \left(1-\frac{9}{100}\right)P_1 = \frac{109}{100}P_1$ .

So, it is not difficult to notice that the general recurrence is

$P_n = \frac{109}{100}P_{n-1}$ .

b) In the previous formula we only need to substitute the expression for $P_{n-1}$ :

$P_{n-1} = \frac{109}{100}P_{n-2}$ .

Then,

$P_n = \left(\frac{109}{100}\right)^2P_{n-2}$ .

Repeating the procedure for $P_{n-3}$ we get

$P_n = \left(\frac{109}{100}\right)^3P_{n-3}$ .

But we can do the same operation n times, so

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) Recall the notation we have used:

$P_{0}$ for 2000, $P_{1}$ for 2001, $P_{2}$ for 2002, and so on. Then, 2016 is $P_{16}$ . So, in order to obtain the approximate population of Tacoma in 2016 is

$P_{16} = \left(\frac{109}{100}\right)^{16}P_{0} = (1.09)^{16}P_0 = 3.97\cdot 200000 \approx 794062$

d) In this case we want to know when $P_n>400000$ , which is equivalent to

$(1.09)^{n}P_0>400000$ .

Substituting the value of $P_0$ , we get

$(1.09)^{n}200000>400000$ .

Simplifying the expression:

$(1.09)^{n}>2$ .

So, we need to find the value of $n$ such that the above inequality holds.

The easiest way to do this is take logarithm in both hands. Then,

$n\ln(1.09)>\ln 2$ .

So, $n>\frac{\ln 2}{\ln(1.09)} = 8.04323172693$ .

So, the population of Tacoma should exceed the 400 000 by the year 2009.

8 0

3 years ago

Read 2 more answers

Please help me with this problem

igor_vitrenko [27]

Draw a circle 5 CM find the length then divid that

7 0

3 years ago

7x10 to the 3rd power, write a pattern to find the value of the expression

myrzilka [38]

Scientific notation is used to express very large or very small values.
Numbers in scientific notation are written in the form of
m × 10 to the power of n
For example:
500 is written as 5 x 10^2 where:
500 = 5 x 10 x 10

Now, let's consider 7 x 10^3:
Following the same procedure:
7 x 10^3 = 7 x 10 x 10 x 10 = 7000
The pattern can be written as:
7 x 10^3 = 7 x 10 x 10^2
= 70 x 10^2
= 70 x 10 x 10^1
= 700 x 10
= 7000

6 0

3 years ago

Wolverine makes a $1000 down payment for a motorcycle and then pays $300 per month. James Bond makes a $2500 down payment for a

Delicious77 [7]

Answer:

Both Wolverine and James Bond will have paid the same amount after 10 months.

Step-by-step explanation:

Let x denotes the number of months after which both Wolverine and James Bond will have paid the same amount.

As Wolverine makes a $1000 down payment for a motorcycle and then pays $300 per month,

Amount paid by Wolverine in x months is equal to $1000+300x$

As James Bond makes a $2500 down payment for a motorcycle and then pays $150 per month,

Amount paid by James Bond in x months is equal to $2500+150x$

To find number of months after which both Wolverine and James Bond will have paid the same amount,

solve $1000+300x=2500+150x$

$1000+300x=2500+150x\\300x-150x=2500-1000\\150x=1500\\x=\frac{1500}{150}=10$

So, both Wolverine and James Bond will have paid the same amount after 10 months.

5 0

3 years ago