"What is the solution to the pair of equations represented by p(x) and f(x)?" Lines p and f intersect at the point (6,2).
"Write any two solutions for f(x)." That's an odd question! I'd suggest it means to choose any point on the line f(x). One such point could be (1,-3).
"What is the solution to the equation p(x) = g(x)?" p and g intersect at the point (3,6).
Answer: Either 25.0 or 25 depending on how your teacher wants you to format the answer
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Explanation:
To start off, it probably helps to translate what the question wants.
It states "For the pilot of airplane B, calculate the angle between the lines of sight to the airplane at C and Jenny's airplane [at point A]".
This fairly long, and possibly complex, sentence boils down to "find angle B"
To find angle B, we need to find the length of side 'a' first
Let,
a = x
b = 4.2
c = 5.7
Note how the lowercase letters (a,b,c) are opposite their uppercase counterparts (A,B,C). This is often the conventional way to label triangles. The lowercase letters are usually for the side lengths while the upper case is for the angles.
We have angle A = 120 degrees
Plug these values into the law of cosines formula below. Then solve for x
a^2 = b^2 + c^2 - 2*b*c*cos(A)
x^2 = 4.2^2 + 5.7^2 - 2*4.2*5.7*cos(120)
x^2 = 17.64 + 32.49 - 47.88*cos(120)
x^2 = 17.64 + 32.49 - 47.88*(-0.5)
x^2 = 17.64 + 32.49 + 23.94
x^2 = 74.07
x = sqrt(74.07)
x = 8.60639297266863
x = 8.6064
So side 'a' is roughly 8.6064 kilometers when we round to four decimal places
Now we'll use this to find angle B
Use the law of cosines again, but this time, the formula is slightly altered so that angle B is the focus instead of angle A
Plug in the side lengths (a,b,c). Solve for angle B
b^2 = a^2 + c^2 - 2*a*c*cos(B)
(4.2)^2 = (8.6064)^2 + (5.7)^2 - 2*(8.6064)*(5.7)*cos(B)
17.64 = 74.07012096 + 32.49 - 98.11296*cos(B)
17.64 = 106.56012096 - 98.11296*cos(B)
17.64 - 106.56012096 = 106.56012096 - 98.11296*cos(B)-106.56012096
-88.92012096 = -98.11296*cos(B)
(-88.92012096)/(-98.11296) = (-98.11296*cos(B))/(-98.11296)
0.906303519535034 = cos(B)
cos(B) = 0.906303519535034
arccos(cos(B)) = arccos(0.906303519535034)
B = 25.0005785532867
It's a bit messier this time around, but we get the approximate angle
B = 25.0005785532867
which rounds to
B = 25.0 degrees
when we round to the nearest tenth. We can write "25.0" as simply "25"
Answer:
there is three parts to this answer
Step-by-step explanation:
this first part is
A= 2.5
B= 49 feet
and finally
C= 0.75 seconds
Answer:
long term goal is to take on bigger, more challenging targets so I can assess my abilities. I plan on shaping myself during this initial time so that I'm prepared to deliver on bigger targets later. Although I've been in this field for a while now, I haven't been able to utilize my entire set of skills.
Step-by-step explanation:
hope it helps a little idk how to answer that completely
Answer:
There is no significant evidence to conclude that the mean weight of laundry detergent is being underfilled or overfilled.
Step-by-step explanation:
The null hypothesis ; H0 : μ = 32
The alternative hypothesis : H1 : μ ≠ 32
The null hypothesis is the initial truth statement, therefore, when the Null hypothesis cannot be rejected, the conclusion goes thus :
There is no significant evidence to conclude that there is difference in the mean weight of laundry detergent. Hence, detergent is neither being underfilled or overfilled.
