Inverse function. sketch the graph of each function.

Please solve with explanation I’ve been asking all day (this is not a multiple choice question)

Anastaziya [24]

Answer:

a) $SA = 522.9~cm^2$

b) $V_{cone} = 670.2~cm^3$

c) $V_{empty} = 1340.4~cm^3$

Step-by-step explanation:

a)

For a cone,

$SA = \pi r (L + r)$

where L = slant height

$L = \sqrt{r^2 + h^2}$

We have r = 8 cm; h = 10 cm

$L = \sqrt{(8~cm)^2 + (10~cm)^2}$

$L = \sqrt{164~cm^2}$

$SA = (\pi)(8~cm)(\sqrt{164~cm^2} + 8~cm)$

$SA = 522.9~cm^2$

b)

$V_{cone} = \dfrac{1}{3}\pi r^2 h$

$V_{cone} = \dfrac{1}{3}(\pi)(8~cm)^2(10~cm)$

$V_{cone} = 670.2~cm^3$

c)

$V_{cylinder} = \pi r^2 h$

empty space = volume of cylinder - volume of cone

$V_{empty} = V_{cylinder} - V_{cone}$

$V_{empty} = \pi r^2 h - \dfrac{1}{3}\pi r^2 h$

$V_{empty} = (\pi)(8~cm)^2(10~cm) - \dfrac{1}{3}(\pi)(8~cm)^2(10~cm)$

$V_{empty} = 1340.4~cm^3$

3 0

3 years ago

Graphing exponential functions and then State the domain, range and asymptote

Luda [366]

9514 1404 393

Answer:

D: all real numbers

R: f(x) > 0

A: f(x) = 0

(-∞, 0), (+∞, +∞)

vertical stretch by a factor of 2; left shift 2 units

Step-by-step explanation:

The transformation ...

g(x) = a·f(b(x -c)) +d

does the following:

vertical stretch by a factor of 'a'
horizontal compression by a factor of 'b'
translation right by 'c' units
translation up by 'd' units

For many functions, horizontal coordinate changes are indistinguishable from vertical coordinate changes. Exponential functions tend to be one of those.

__

Using the above notation, you seem to have f(x) = 3^x, and g(x) = 2f(x+2). The transformation is a vertical stretch by a factor of 2, and a translation left 2 units.

__

As with all exponential functions, ...

the domain is "all real numbers"
the range is all numbers above the asymptote: f(x) > 0
the horizontal asymptote is f(x) = 0

The function is a growth function, so ...

x → -∞, f(x) → 0
x → ∞, f(x) → ∞

_____

<em>Additional comment</em>

The left shift is equivalent to an additional vertical stretch. The function could be rewritten as ...

f(x) = 18(3^x)

with no left shift and a vertical stretch by a factor of 18 instead of 2.

6 0

3 years ago

Find the surface area of the rectangular and triangular prisms

harina [27]

Is there a picture to this????

if your just asking how to find the area of something all you need to do is multiply all the numbers together and the total is the area.
For example if its 8cm,3cm,2cm all you need to do is multiply them together
8x3x2=48 so your area is 48cm

7 0

3 years ago

Please help, i don’t know how to work this out!!

victus00 [196]

Answer:

40 degrees

Step-by-step explanation:

so, a triangle is 180 degrees. you know that one angle is 60 degrees.

180= 60+ 2x + x

this is the equation of the triangle

120=3x

simplify

40=x

x= 40 degrees

hope this helps :)

5 0

2 years ago

If the area of a baseball diamond (shape of a square) is 8100 ft squared, how would you find the distance from 1st base to 3rd b

Readme [11.4K]

Answer:

Exact distance = $90\sqrt{2}$ feet
Approximate distance = 127.2792 feet.

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Explanation:

The area of the square is 8100 square feet, abbreviated ft^2.

Apply the square root to find the distance from any base to its adjacent counterpart (eg: from 1st to 2nd base). So we get sqrt(8100) = 90 ft as that side distance. Notice that 90*90 = 8100.

If you were to draw a line from 1st base to 3rd base, then you would split the square into two congruent right triangles. Each right triangle is isosceles (the two legs being 90 ft each).

Use the pythagorean theorem to find the hypotenuse.

$a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{90^2+90^2}\\\\c = \sqrt{2*90^2}\\\\c = \sqrt{2}*\sqrt{90^2}\\\\c = \sqrt{2}*90\\\\c = 90\sqrt{2} \ \text{ ... exact distance}\\\\c \approx 127.2792 \ \text{ ... approximate distance}\\\\$

The distance from 1st to 3rd base is roughly 127.2792 feet.

5 0

2 years ago

Inverse function. sketch the graph of each function.​

Inverse function. sketch the graph of each function.