Answer:
a = -3/2 = -1.5
Step-by-step explanation:
(1+ax) (2+3x)³
Formula
(a+b)^3=a^3+3a^2b+3ab^2+b^3
(1 + ax) [ 2^3 + 3*2^2*3x + 3*2*(3x)^2 + (3x)^3]
(1 + ax) [ 8 + 12*3x + 6*9x^2 + 27x^3]
8 + 12*3x + <u>6*9x^2</u> + 27x^3 + 8ax + <u>36ax^2</u> + 54ax^3 + 27ax^4
coefficient of x^2 is zero
54x^2 + 36ax^2
54 + 36a = 0
36a = -54
a = -3/2
Let w(s,t)=f(u(s,t),v(s,t)) where u(1,0)=−6,∂u∂s(1,0)=5,∂u∂1(1,0)=7 v(1,0)=−8,∂v∂s(1,0)=−8,∂v∂t(1,0)=6 ∂f∂u(−6,−8)=−1,∂f∂v(−6,−8
Blababa [14]

From the given set of conditions, it's likely that you are asked to find the values of

and

at the point

.
By the chain rule, the partial derivative with respect to

is

and so at the point

, we have


Similarly, the partial derivative with respect to

would be found via

Your Answer Is...
20 minutes.
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Answer:
![67.5\text{ [square units]}](https://tex.z-dn.net/?f=67.5%5Ctext%7B%20%5Bsquare%20units%5D%7D)
Step-by-step explanation:
The composite figure consists of one rectangle and two triangles. We can add up the area of these individual shapes to find the total area of the irregular figure.
<u>Formulas</u>:
- Area of rectangle with base
and height
:
- Area of triangle with base
and height
:
By definition, the base and height must intersect at a 90 degree angle.
The rectangle has a base of 10 and a height of 5. Therefore, its area is
.
The smaller triangle to the left of the rectangle has a base of 2 and a height of 5. Therefore, its area is
.
Finally, the larger triangle on top of the rectangle has a base of 5 and a height of 5. Therefore, its area is
.
Thus, the area of the total irregular figure is:
![50+5+12.5=\boxed{67.5\text{ [square units]}}](https://tex.z-dn.net/?f=50%2B5%2B12.5%3D%5Cboxed%7B67.5%5Ctext%7B%20%5Bsquare%20units%5D%7D%7D)
Each concession stand will receive 197 popcorn bags i used a calculator so it is right.