Answer:
28
Step-by-step explanation:
1) subtract 12 from both sides
2) divide by negative 1
Answer:
Sigma is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase ∑ is used as an operator for summation. When used at the end of a letter-case word, the final form is used
Step-by-step explanation:
Answer:
The estimate of In(1.4) is the first five non-zero terms.
Step-by-step explanation:
From the given information:
We are to find the estimate of In(1 . 4) within 0.001 by applying the function of the Maclaurin series for f(x) = In (1 + x)
So, by the application of Maclurin Series which can be expressed as:

Let examine f(x) = In(1+x), then find its derivatives;
f(x) = In(1+x)

f'(0) 
f ' ' (x) 
f ' ' (x) 
f ' ' '(x) 
f ' ' '(x) 
f ' ' ' '(x) 
f ' ' ' '(x) 
f ' ' ' ' ' (x) 
f ' ' ' ' ' (x) 
Now, the next process is to substitute the above values back into equation (1)



To estimate the value of In(1.4), let's replace x with 0.4


Therefore, from the above calculations, we will realize that the value of
as well as
which are less than 0.001
Hence, the estimate of In(1.4) to the term is
is said to be enough to justify our claim.
∴
The estimate of In(1.4) is the first five non-zero terms.
Equation for volume of cone: v = π*r²*(h/3)
substitute the variables with the known number values:
593.46 = V
r = 9
Solve for h
(593.46) = π*(9)²*(h/3)
Solve for h! :-)
Answer:
132 feet
Step-by-step explanation:
Given that Alejandro is standing at a distance of 140 feet from the base of the tree and his eyes are 6 feet above the ground.
Let AB is the height of the tree and point E is the location of his eyes which is 6 feet above from C on the ground as shown in the figure.
The distance between points A and C, AC=140 feet.
Drawing a horizontal line from point E which meets AB at point D as shown.
As ACED forms a rectangle, so
AC=DE=140 feet ...(i)
CE=AD= 6 feet ...(ii)
The height of the tree, AB=AD+DB
By using equation (ii), AB=6+DB ...(iii)
Now, given that the on watching the top of the tree, the reading on the clinometer is 42 degrees.
So,
In triangle DEB,

[from (i)]
feet
From equation (iii) the height of the tree is
AB=6+126=132 feet.
Hence, the height of the tree is 132 feet.