In order to be differentiable everywhere, 
must first be continuous everywhere, which means the limits from either side as 
must be the same and equal to 
. By definition, 
, and
so we need to have 
.
For to be differentiable at 
, the derivative needs to be continuous at , i.e.
We then need to have
Then
The length is 8. the width is 32.
32(2) = 64
8(2) = 16
64+16 = 80
So the length would be 8 and the width would be 32 since it's 4 times the length.
Hope this helped!
Move constant to other side
add 1
4c^2-8c=1
divide by 4 to make leading coeficient 1
c^2-2c=1/4
take 1/2 of linear coeficient and square it
-2/2=-1, (-1)^2=1
add that to both sides
c^2-2c+1=1/4+1
factor perfect squaer and add
(c-1)^2=5/4
square root both sides
c-1=+/-(√5)/2
add 1
c=1+/-(√5)/2
c=2.12 or -0.12
The surface area of the solid shape is the amount of space on it
The radius of the two cones is 2.93 cm
<h3>How to determine the radius?</h3>
The given parameters are:
- Cone 1: slant height, l = 2r
- Cone 2: slant height, L = 3r
- Surface area = 135. 21 cm²
The surface area of the shape is calculated using:
T = πr(L + l)
So, we have:
135.21 = πr(2r + 3r)
Evaluate
135.21 = 5πr²
Divide both sides by 5π
r² = 135.21/5π
Evaluate the quotient
r² = 8.61
Take the square root of both sides
r = 2.93
Hence, the radius of the cones is 2.93 cm
Read more about surface area at:
brainly.com/question/6613758
Answer:
$909.50
Step-by-step explanation:
$850 x 7% = $59.50 (tax amount)
850 x (1+ 0.07) = $909.50
