Answer:
-1.17 volts
Step-by-step explanation:
The difference between "a" and "b" generally means "a-b". Here, the difference between the potentials is ...
-0.41 V - 0.76 V = -1.17 V
_____
Sometimes, when we talk about the difference, we mean the positive difference. If that is what is intended here, it is 1.17 volts.
If C is between A and B, then, we can write the equation
![AB = AC + CB](https://tex.z-dn.net/?f=AB%20%3D%20AC%20%2B%20CB)
Substitute the value of AB and the expressions for AC and CB in terms of x.
![40 = (2x+10)+(3x-5)](https://tex.z-dn.net/?f=40%20%3D%20%282x%2B10%29%2B%283x-5%29)
We can now solve for x.
![40-10+5= 2x+3x](https://tex.z-dn.net/?f=40-10%2B5%3D%202x%2B3x)
![35=5x](https://tex.z-dn.net/?f=35%3D5x)
Dividing by 5.
![7=x](https://tex.z-dn.net/?f=7%3Dx)
![AB=40](https://tex.z-dn.net/?f=AB%3D40)
![AC=2(7)+10](https://tex.z-dn.net/?f=AC%3D2%287%29%2B10)
![AC=14+10](https://tex.z-dn.net/?f=AC%3D14%2B10)
![AC=24](https://tex.z-dn.net/?f=AC%3D24)
![BC=3(7)-5](https://tex.z-dn.net/?f=BC%3D3%287%29-5)
![BC=21-5](https://tex.z-dn.net/?f=BC%3D21-5)
![BC=16](https://tex.z-dn.net/?f=BC%3D16)
Answer:
B = 34.2°
C = 58.2° or 121.8°
c= 10.6
Step-by-step explanation:
Step 1
Finding c
We calculate c using Pythagoras Theorem
c²= a² + b²
c = √a² + b²
a= 8, b = 7
c = √8² + 7²
c = √64 + 49
c = √(113)
c = 10.630145813
Approximately c = 10.6
Step 2
Find B
We solve this using Sine rule
a/sin A = b/sin B
A = 40°
a = 8
b = 7
Hence,
8/sin 40° = 7/sin B
8 × sin B = sin 40° × 7
sin B = sin 40° × 7/8
B = arc sin (sin 40° × 7/8)
B ≈34.22465°
Approximately = 34.2°
Step 3
We find C
Find B
We solve this using Sine rule
b/sin B = c/sin C
B = 34.2°
b = 7
c = 10.6
C = ?
Hence,
7/sin 34.2° = 10.6/sin C
7 × sin C = sin 34.2 × 10.6
sin C = sin 34.2° × 10.6/7
C = arc sin (sin 34.2° × 10.6/7)
C = arcsin(0.85)
C= 58.211669383
Approximately C = 58.2°
Or = 180 - 58.2
C = 121.8°
Answer: $216
Step-by-step explanation:
Hope it helped
Answer:
The constant of proportionality is 54.
k = 54
c as a function of d:
![c(d) = \dfrac{54}{d^2}](https://tex.z-dn.net/?f=c%28d%29%20%3D%20%5Cdfrac%7B54%7D%7Bd%5E2%7D)
![c(7) = \dfrac{54}{49}](https://tex.z-dn.net/?f=c%287%29%20%3D%20%5Cdfrac%7B54%7D%7B49%7D)
Step-by-step explanation:
We are given the following in the question:
c is inversely proportional to the square of d.
![\Rightarrow c\propto \dfrac{1}{d^2}\\\\\Rightarrow c = \dfrac{k}{d^2}\\\\\text{where k is constant of proportionality}](https://tex.z-dn.net/?f=%5CRightarrow%20c%5Cpropto%20%5Cdfrac%7B1%7D%7Bd%5E2%7D%5C%5C%5C%5C%5CRightarrow%20c%20%3D%20%5Cdfrac%7Bk%7D%7Bd%5E2%7D%5C%5C%5C%5C%5Ctext%7Bwhere%20k%20is%20constant%20of%20proportionality%7D)
When c = 6, d = 3.
Plugging the values, we get,
![6 = \dfrac{k}{3^2}\\\\\Rightarrow k = 6\times 3^2 = 54](https://tex.z-dn.net/?f=6%20%3D%20%5Cdfrac%7Bk%7D%7B3%5E2%7D%5C%5C%5C%5C%5CRightarrow%20k%20%3D%206%5Ctimes%203%5E2%20%3D%2054)
Thus, the constant of proportionality is 54.
c as a function of d can be written as:
![c(d) = \dfrac{54}{d^2}](https://tex.z-dn.net/?f=c%28d%29%20%3D%20%5Cdfrac%7B54%7D%7Bd%5E2%7D)
We have to find value of c when d = 7.
Putting values, we get,
![c(7) = \dfrac{54}{(7)^2}=\dfrac{54}{49}](https://tex.z-dn.net/?f=c%287%29%20%3D%20%5Cdfrac%7B54%7D%7B%287%29%5E2%7D%3D%5Cdfrac%7B54%7D%7B49%7D)
is the required value of c.