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Anit [1.1K]
2 years ago
13

Write as a polynomial. a(a+9b)^2

Mathematics
1 answer:
Alex Ar [27]2 years ago
4 0
Answer: a^3+81ab^2
First, you square (a+9b) which will become (a^2+81b^2)
Then, you multiply it by a and you will get a^3+81ab^2
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Polygon A B C D E F has 6 sides. Exterior angle A is 62 degrees, exterior angle B is 44 degrees, exterior angle C is 70 degrees,
nevsk [136]

The measure of angle AFE would be 99 degrees.

Step-by-step explanation:

Given that,

Exterior angle A = 62 degrees

Exterior angle B = 44 degrees

Exterior angle C = 70 degrees

Exterior angle D = 60 degrees

Exterior angle E = 43 degrees

Angle AFE = ?

However, for that, we have to find the exterior angle of F.

We know that the sum of exterior angles of polygon is 360 degrees.

Exterior angle( A + B + C + D + E + F) = 360 degrees

Exterior angle F = 360 - Exterior angle( A + B + C + D + E )

Exterior angle F = 360 -  (62 +44 + 70 + 60 + 43 )

Exterior angle F = 360 -  279

Exterior angle F = 81

The, sum of interior and exterior angle is 180 degrees. Therefore, the angle AFE would be 180 - 81 = 99 degrees.

Keywords: polygon, exterior angle

Learn more at:

brainly.com/question/3227215

brainly.com/question/9214411

#LearnwithBrainly

8 0
2 years ago
Read 2 more answers
A dog eats 5 cups of dry dog food in 2 1/2 days.
lisov135 [29]
(5 cups)/(2.5 days) = (2 cups)/(1 day)
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 . . . answer is 2 cups</em></u>

8 0
2 years ago
Divide $200 in the ratio 3:2 what is the result?
Paul [167]
$120 and the ratio is 3:2
$200 6:4 and half
8 0
2 years ago
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X + ky = 1
Marina CMI [18]
X + k y = 1
k x + y = 1  / * ( - k )
----------------
      x + k y = 1
- k² x - k y = - k
--------------------
x - k² x = 1 - k
x ( 1 - k² ) = 1 - k
x = ( 1 - k ) / ( 1 - k² ) = ( 1 - k ) / ( 1 - k ) ( 1 + k )
y = 1 - k( 1 - k )/( 1 - k² )
y = ( 1 - k ) / ( 1 - k² ) = ( 1 - k ) / ( 1 - k ) ( 1 + k )
a ) For  k = - 1 this system has no solution.
b ) For k ≠ - 1 and k ≠ 1, the system has unique solution:
( x , y ) = ( 1/ (1 + k) ,  1/( 1 + k ) ).
c ) For k = 1, there are infinitely many solutions.

3 0
2 years ago
The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi
storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

V = \frac{1}{3}\pi r^{2}h

Differentiate the equation with respect to time t, such that

\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)

\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)

To differentiate the product,

Let r² = u, so that

\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)

Then, using product rule

\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]

Since u = r^{2}

Then, \frac{du}{dr} = 2r

Using the Chain's rule

\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}

∴ \frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]

Then,

\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]

Now,

From the question

\frac{dr}{dt} = 7 m/min

\frac{dV}{dt} = 236 m^{3}/min

At the instant when r = 99 m

and V = 180 m^{3}

We will determine the value of h, using

V = \frac{1}{3}\pi r^{2}h

180 = \frac{1}{3}\pi (99)^{2}h

180 \times 3 = 9801\pi h

h =\frac{540}{9801\pi }

h =\frac{20}{363\pi }

Now, Putting the parameters into the equation

\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]

236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]

236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]

708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}

708 = 30790.75 \frac{dh}{dt} + 76.36

708 - 76.36 = 30790.75\frac{dh}{dt}

631.64 = 30790.75\frac{dh}{dt}

\frac{dh}{dt}= \frac{631.64}{30790.75}

\frac{dh}{dt} = 0.021 m/min

Hence, the rate of change of the height is 0.021 meters per minute.

3 0
2 years ago
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