Answer:
z = 3
Step-by-step explanation:
Since the points are collinear then the slopes between the points are equal.
Calculate the slope m using the slope formula
m = 
with (x₁, y₁ ) = P (2, - 3) and (x₂, y₂ ) = Q (3, - 2)
m = 
= 1
Repeat with
(x₁, y₁ ) = Q (3, - 2) and (x₂, y₂ ) = R (8, z )
m = 
= 
, then
= 1 ( multiply both sides by 5 )
z + 2 = 5 ( subtract 2 from both sides )
z = 3
Answer:
Yes , function is continuous in [0,2] and is differentiable (0,2) since polynomial function are continuous and differentiable
Step-by-step explanation:
We are given the Function
f(x) =
The two basic hypothesis of the mean valued theorem are
- The function should be continuous in [0,2]
- The function should be differentiable in (1,2)
upon checking the condition stated above on the given function
f(x) is continuous in the interval [0,2] as the functions is quadratic and we can conclude that from its graph
also the f(x) is differentiable in (0,2)
f'(x) = 6x - 2
Now the function satisfies both the conditions
so applying MVT
6x-2 = f(2) - f(0) / 2-0
6x-2 = 9 - 1 /2
6x-2 = 4
6x=6
x=1
so this is the tangent line for this given function.
white : milk : dark
w : m : d
The ratio of white to not white is 3:4
w : (m+d) = 3:4
The ratio of not dark to dark is 17:4.
(w+m) : d = 17:4
---------
We treat the colons as fraction bars and cross multiply.
4w = 3(m+d) = 3m + 3d
4w + 4m = 17 d
Subtracting,
4m = 17d - (3m+3d) = 14d - 3m
7m = 14 d
m/d = 14/7
m:d = 2:1
Since w:(m+d)=3:4 let's make m+d a multiple of 4.
m:d = 8:4
w : (m+d) = 3:4 = 9:12
w:m:d = 9:8:4
Answer: 9:8:4
Check:
white to non white 9 to 8+4=12 = 3:4, good
non dark to dark (9+8):4=17:4, good
Answer:
-3
Step-by-step explanation:
.
Otto von Bismarck
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In the 1860s, Otto von Bismarck, then Minister President of Prussia, provoked three short, decisive wars against Denmark, Austria, and France, aligning the smaller German states behind Prussia in its defeat of France. In 1871 he unified Germany into a nation-state, forming the
German Empire
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