Expand everything in the limit:
We have 
approaching 0, and in particular 
, so we can cancel a factor in the numerator and denominator:
Alternatively, if you already know about derivatives, consider the function 
, whose derivative is 
.
Using the limit definition, we have
which is exactly the original limit with 
. The derivative is 
, so the value of the limit is, again, -14.
Answer:
y = -3/2x - 5
Step-by-step explanation:
y = mx + b
The line intercepts the Y-axis at -5, so b = -5
From one point to another is 6/-4, which simplifies to -3/2. So m = -3/2.
So to find the equation of the line we just need to plug in the m and b.
Which gives us y = -3/2x - 5 as the slope-intercept equation of the line.
Answer:
7a^6b
Step-by-step explanation:
Using the pascal triangle to do this binomial expansion, we find out that the coefficient is 7. The a variables start at the power to which you are expanding and reduce by 1 for every consecutive term. The b variables start at the power of 0 and increase by 1 for every consecutive term. Using this information, we find out that the second term in the binomial expansion (a+b)^7 is 7a^6b
Note that the power of b in the second term is b^1 which is the same as b
Answer:
6000 in³
Step-by-step explanation:
To solve this problem, we simply have to find the volume of the shipping container that will be just enough to contain the 20 soda boxes.
To do this, we find the volume of each soda box and multiply it by the total number of soda boxes held by the shipping container.
Volume of the box = L * B * H
L = length = 15 in
B = breadth = 4 in
H = height = 5 in
V = 15 * 4 * 5 = 300 in³
This is the volume of each soda box.
The volume of 20 soda boxes will then be:
V = 20 * 300 = 6000 in³
This is the volume of 20 soda boxes and hence, the minimum size the shipping container can be.
Answer:
x = 1
y = 4
Step-by-step explanation:
5x + 2y = 13
x + 2y = 9
Add both equations.
6x + 4y = 22
Solve for x.
6x = 22 - 4y
x = 22/6 - 4/6y
Put x as 22/6 - 4/6y in the second equation and solve for y.
22/6 - 4/6y + 2y = 9
-4/6y + 2y = 9 - 22/6
4/3y = 16/3
y = 16/3 × 3/4
y = 48/12
y = 4
Put y as 4 in the first equation and solve for x.
5x + 2(4) = 13
5x + 8 = 13
5x = 13 - 8
5x = 5
x = 5/5
x = 1
