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MrRissso [65]
3 years ago
14

Sum of interior angles of a convex 14-gon

Mathematics
1 answer:
just olya [345]3 years ago
3 0

Answer: 2160°

Step-by-step explanation:

The sum of angles in a polygon is represented by the formula:

Sum = (n - 2) x 180° where n is the number of sides in the polygon

In this case, the complex polygon has 14 sides (n = 14)

So, (14 - 2) x 180°

= 12 x 180°

= 2160°

Thus, the sum of interior angles of a convex 14-gon is 2160°

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Find f'(x) for f(x) = cos^2(3x^3).
garik1379 [7]

f(x) = \cos^2(3x^3)\\f'(x) = \frac{d}{dx}[\cos^2(3x^3)]\\= 2\cos(3x^3) \cdot \frac{d}{dx}[cos(3x^3)]\\= 2\cos(3x^3) \cdot (-\sin(3x^3)) \cdot \frac{d}{dx}[3x^3]\\= 2\cos(3x^3) \cdot (-\sin(3x^3)) \cdot 9x^2\\= -18x^2\cos(3x^3)\sin(3x^3)

6 0
2 years ago
help pleasee. Find the perimeter of a quadrilateral with vertices at C (2, 1), D (2, 4), E (5, 1), and F (5, 4). Round your answ
vredina [299]
Distance from point C to point D: same x coordinate, 4-1=3; 3 units
Distance form point D to F: same y coordinate, 5-2=3
Perimeter is the measure of all sides
3+3+3+3=12
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8 0
3 years ago
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lbvjy [14]

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Step-by-step explanation:

5 0
2 years ago
Find the area of the region that lies under the parabola y=5x - x^2, where 1≤x≤4. I would definitely like to see some work :)
Elena L [17]

Answer:

  16.5 square units

Step-by-step explanation:

You are expected to integrate the function between x=1 and x=4:

  \displaystyle\text{area}=\int_1^4{(5x-x^2)}\,dx=\left.\left(\dfrac{5}{2}x^2-\dfrac{1}{3}x^3\right)\right|_{x=1}^{x=4}\\\\=\dfrac{5(4^2-1^2)}{2}-\dfrac{4^3-1^3}{3}=37.5-21=\boxed{16.5}

__

<em>Additional comment</em>

If you're aware that the area inside a (symmetrical) parabola is 2/3 of the area of the enclosing rectangle, you can compute the desired area as follows.

The parabolic curve is 4-1 = 3 units wide between x=1 and x=4. It extends upward 2.25 units from y=4 to y=6.25, so the enclosing rectangle is 3×2.25 = 6.75 square units. 2/3 of that area is (2/3)(6.75) = 4.5 square units.

This region sits on top of a rectangle 3 units wide and 4 units high, so the total area under the parabolic curve is ...

  area = 4.5 +3×4 = 16.5 . . . square units

4 0
2 years ago
How do I solve for x here? Use the properties of logarithms to find a value for x. Assume a,b, and M are constants.
Leona [35]

Yes, you're right! The first step is rewriting the equation as

\ln(a) + \ln(b^x) = M

Subtract \ln(a) from both sides:

\ln(b^x) = M-\ln(a)

Use the property \ln(a^b) = b\ln(a) to rewrite the equation as

x\ln(b) = M-\ln(a)

Divide both sides by \ln(b)

x = \dfrac{M-\ln(a)}{\ln(b)}

Alternative strategy:

Consider both sides as exponents of e:

e^{\ln(ab^x)} = e^M

Use e^{\ln(x)} = x to write

ab^x = e^M

Divide both sides by a:

b^x = \dfrac{e^M}{a}

Consider the logarithm base b of both sides:

x = \log_b\left(\dfrac{e^M}{a}\right)

The two numbers are the same: you can check it using the rule for changing the base of logarithms

7 0
3 years ago
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