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2 years ago

BC Round your answer to the nearest hundredth. А 50° ? 3 B

Mathematics

2 answers:

marysya [2.9K]2 years ago

7 0

Answer: BC = 2.30

Step-by-step explanation:

BC = 3sin50

BC = 2.2981333...

BC = 2.30

emmasim [6.3K]2 years ago

6 0

Use the sine function.

sine = opposite side of triangle divided by the hypotenuse.

Here is the set up:

sin(50°) = BC/3

sin(50°)/3 = BC

Use your calculator to simply left side.

Take it from here.

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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

A local little has a total of 60 players ,of whom 40%are right-handed how many are right handed

maks197457 [2]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Use technology or a z-score table to answer the question.

Drupady [299]

Answer:

Step-by-step explanation:

Finding the z-score:

z = (x - μ) / σ

z = (66 - 57) / 9

z = 1

Using a z-score table or calculator:

P(z < 1) = 0.8413

84.13% of 4000 is:

0.8413 (4000) = 3365.2

Rounding up to the nearest whole number, approximately 3366 students will score less than 66. Answer C.

8 0

3 years ago

Write 9.3 million in scientific notation

svetoff [14.1K]

9.3 × 107 would be the scientific notation

3 0

3 years ago

Read 2 more answers

Please help me with this I’m confused please explain

Maksim231197 [3]

Answer:

25. If you look at angle B from the first figure you see a square that indicates a 90 degrees angle, thus the figure shown is a right triangle. You can also see that angle C is said to have 60 degrees. a right triangle has a total angle of 180 degrees. so, 180 - 90 - 60 = 30 degrees. Therefore, angle A is 30 degrees.

27. Now you want the measure of the hypotenuse, and you know this a right triangle. so, simply use the law of sines to find the measure of AC :

4cm/sin(60) = AC/Sin90

AC = 4.62 cm

29. angle z is in the other figure and same stuff, just substract the angles, you have 90 degrees and 30 degrees... 180 - 90 - 30 = 60 degrees

31. Angle Y = 90 degrees

this value is already given, it's the little square that indicates a 90 degrees angle.

26. 5 cm

28. 90 degrees

30. You already found AC, use the pythagorean theorem. sqrt((4.62)^2 - 4^2) = 2.31 cm

32. use pythagoras again, square root(5^2 - 3^2) = 4

So as you can see all the measurements are the same because if you see at the very top of your figures it says ABC = XYZ which means pretty much that they have the same values (notice that there is a little something added to the = sign, watch out for that because that's what indicates that two figures are equal in terms of angles and measures.

7 0

3 years ago