Answer:
Step-by-step explanation:
The diagram illustrating the scenario is shown in the attached photo.
We would determine angle ACB by applying the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/adjacent side
Taking angle ACB as the reference angle,
Tan C = 40/30 = 1.33
Angle ACB = tan^-1(1.33) = 53.1°
The bearing is calculated with respect to the northern direction. Therefore, the bearing of B from C is
180 - 53.1 = 126.9°
Answer:
B. :))
Step-by-step explanation:
Triangles = 180°
78 + 82 + x = 180
160 + x = 180
x = 20
B.
Answer:
The sum of the series is 9.99
Step-by-step explanation:
We are given the series .
So, , where n=3 to 12
Then, we have,
Thus, the common ratio is
Since, the sum of first n terms of a series is .
As n = 3 to 12, then the number of terms = 10, first term=a₃= 5 and r= 0.5
So, the sum of 10 terms is
i.e.
i.e.
i.e.
i.e. S = 9.99
Hence, the sum of the series is 9.99
Answer: 9.99
Step-by-step explanation:
I just took the quiz!
Answer:
1) Reflection
2) Translation
3) Dialation
4) Translation (Hard to see, If it has gotten biggeror smaller, it is dialation)
5) Reflection
Answer:
45
Step-by-step explanation:
do it
To find the minimum value of the sum of the squares of distances, we can use calculus. The minimum value can be expressed as $233/9$.
To find the minimum value of $PA^2 + PB^2 + PC^2$, we need to find the point $P$ that minimizes the sum of the squares of the distances from $P$ to $A$, $B$, and $C$. Let's denote the coordinates of $P$ as $(x, y)$. Using the distance formula, we can find the expressions for the squares of the distances:
The sum of these expressions is $PA^2 + PB^2 + PC^2$:
$PA^2 + PB^2 + PC^2 = (x - 5)^2 + (y - 12)^2 + x^2 + y^2 + (x - 14)^2 + y^2$
Simplifying the expression:
$PA^2 + PB^2 + PC^2 = 3x^2 + 3y^2 - 38x - 24y + 365$
To find the minimum value, we can use calculus. Taking the partial derivatives of this expression with respect to $x$ and $y$ and setting them to zero, we can find the critical points. The coordinates of the point $P$ that minimizes the sum of the squares of the distances are $(x, y) = (13/3, 8/3)$. Plugging these values into the expression, we get:
$PA^2 + PB^2 + PC^2 = (13/3)^2 + (8/3)^2 = 233/9$
Therefore, the minimum value can be expressed as $233/9$, and $m + n = 233 + 9 = 242$.
Learn more about Sum of squares of distances here:
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Answer:
11
Step-by-step explanation:
Let's start with the total number of points (100) and take what we already know, away.
We know the name is worth one point.
99 points left over
Let's divide by the 9 questions there are to see if they all equal the same.
They do because 99/9 is 11 points each!
Very glad I could help!!