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2 years ago

Find the range, domain, and intercepts of the function. f(x)=3

1 answer:

6 0

The domain is the set of all real numbers where the function is defined. In this case, the function would be defined everywhere, so all real numbers will satisfy this condition. The range is the domain of the inverse function, which will also have all real numbers as its range. Since this function can be stated as "y = 3" by replacing "f(x)", the intercept would be (0,3).

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From the top of the Eiffel Tower, a jogger is spotted heading toward the tower. When at position A, the angle of depression of t

8090 [49]

325 meters if using full height of 324 meters for tower
277 meters if using observation platform height of 276 meters.
When the depression is 37 degrees, you can create a right triangle with the angles 90, 37, and 53 degrees. The distance from a point directly underneath the observer will be:
h/tan(37)
where
h = height of the observer.

And when the depression is 72 degrees, the distance will be:
h/tan(72)
So the distance between the two points will be the absolute value of:
h/tan(72) - h/tan(37)
=(tan(37)h)/tan(37)tan(72) - tan(72)h/(tan(37)tan(72))
=(tan(37)h - tan(72)h) /(tan(37)tan(72))
=h(0.75355405 - 3.077683537)/(0.75355405 * 3.077683537)
=h(0.75355405 - 3.077683537)/(0.75355405 * 3.077683537)
=h(-2.324129487/2.319200894)
=h*-1.002125125

And since we're looking for absolute value
=h*1.002125125

As for the value of "h" to use, that's unspecified in the problem. If you take h
to be the height of the Eiffel Tower, then it's 324 meters. If you take h to be
the highest observation platform on the Eiffel Tower, then it's 276 meters. In
any case, simply multiply h by the value calculated above:
=h*1.002125125
=324*1.002125125
= 324.6885406 m

=h*1.002125125
=276*1.002125125
=276.5865346

6 0

3 years ago

X + 3 =8 X- 5 =7 Please someone help?

Sav [38]

Step-by-step explanation:

x+3=8

8-5=3 so x=5

7+5=12 / 12-7=5

12-5=7

8 0

2 years ago

Read 2 more answers

A certain company's main source of income is a mobile app. The company's annual profit (in millions of dollars) as a function of

liberstina [14]

Answer:

x = $3, or x = $11

Step-by-step explanation:

The equation given is $P(x)=-2(x-3)(x-11)$

where

P(x) is the profit, and
x is the app price

We want app prices (x's) when profit (P(x)) is 0, so plugging in into the equation:

$P(x)=-2(x-3)(x-11)\\0=-2(x-3)(x-11)\\0=(x-3)(x-11)$

It means (x-3) = 0 OR (x-11) = 0

So, x = 3, or 11

7 0

2 years ago

Read 2 more answers

The second term in a geometric series is 10, and the seventh term is 10,240. Find the sum of the first six terms.

just olya [345]

Answer:

The sum of the first 6 terms is 3,412.5.

Step-by-step explanation:

The second term of the geometric series is given by:

$a_{2}=a_{1}*r$

Where a1 is the first term and r is the common ratio. The seventh term can be written as a function of the second term as follows:

$a_{7}=a_{1}*r^{6} \\a_{7}=a_{2}*r^{5} \\10,240 = 10*r^{5}\\r=\sqrt[5]{1024} \\r = 4$

The sum of "n" terms of a geometric series is given by:

$a_{1} = \frac{10}{4} = 2.5\\S_{n}=a_{1}(\frac{r^{n}-1 }{r-1})\\S_{6}=2.5(\frac{4^{6}-1 }{4-1})\\S_{6}=3,412.5$

The sum of the first 6 terms is 3,412.5.

5 0

2 years ago

Volume of cylinder diameter 10 inches height of 20 inches

stiks02 [169]

$\sf{Volume~of~a~cylinder=\pi r^2h}\\\\V = \pi (\frac{10}{2})^2(20)\\\\V = 5^2 \pi (20)\\\\V = 25 \times 20 \pi\\\\\boxed{\bf{V = 500 \pi\approx1570.8}}$

4 0

2 years ago