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3 years ago

A tree casts a shadow 21m long. The angle of elevation of the sun is 55 degrees. What is the height of the tree?

Mathematics

1 answer:

Orlov [11]3 years ago

4 0

Answer:

The height of the tree is about 30 feet.

Step-by-step explanation:

tan(55) = h/21

*21 *21

21*tan(55)=h

29.99=h

h=29.99=30 feet

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You find an interest rate of 10% compounded quarterly. Calculate how much more money you would have in your pocket if you had us

Elena-2011 [213]

Answer:

see the explanation

Step-by-step explanation:

we know that

step 1

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$r=10\%=10/100=0.10\\n=4$

substitute in the formula above

$A=P(1+\frac{0.10}{4})^{4t}$

$A=P(1.025)^{4t}$

Applying property of exponents

$A=P[(1.025)^{4}]^{t}$

$A=P(1.1038)^{t}$

step 2

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$r=10\%=10/100=0.10$

substitute in the formula above

$A=P(e)^{0.10t}$

Applying property of exponents

$A=P[(e)^{0.10}]^{t}$

$A=P(1.1052)^{t}$

step 3

Compare the final amount

$P(1.1052)^{t} > P(1.1038)^{t}$

therefore

Find the difference

$P(1.1052)^{t} - P(1.1038)^{t}$ ----> Additional amount of money you would have in your pocket if you had used a continuously compounded account with the same interest rate and the same principal.

3 0

3 years ago

How to write six billion sixty- seven million four hundred four thousand thirteen and nineteen thousandths in standard form?

Neko [114]

Standard for would be 6,670,404,013.19

8 0

3 years ago

How do I find number 2?

prisoha [69]

Answer:

y = 3/4x +4

Step-by-step explanation:

From point A to point B, you show a rise of 3 units and a run of 4 units. (The rise is the difference in height of the first two squares; the run is the side length of the first square.) The ratio rise/run = 3/4 is the slope of the line you want.

The upper-left corner of the first square is the y-intercept of the line (4). So, in slope-intercept form, the equation of the dotted line is ...

y = mx + b . . . . . m = slope; b = y-intercept

y = 3/4x + 4

8 0

3 years ago

How do i work this problem y= -3x - 5

Drupady [299]

This is a linear function. you can list out a group of domains or x, then you will get outcomes, which will be your range

7 0

3 years ago

In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The

slamgirl [31]

Answer:

independent: day number; dependent: hours of daylight

d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

1.79 fewer hours on Feb 10

Step-by-step explanation:

a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).

b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,

March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...

d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))

d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

c) d(41) = 10.34, so February 10 will have ...

12.13 -10.34 = 1.79

hours less daylight.

5 0

3 years ago