Answer:
y = -2
Step-by-step explanation:
8×7=56
then subtract it from 100-56=44 so you lost 56 gallons in 8 minutes and there is 44 left.
Answer:
The answer would be A. because AB/EF=BC/DE
Step-by-step explanation:
AB = 2
EF = 5
BC = 1
DE = 2.5
2/5 = 0.4
1/2.5 = 0.4
The equation AB/EF=BC/DE is correct. All of the others are not.
Answer:
The one which is frequently used is
<em><u>SAS</u></em> criteria for congruency of triangles
Step-by-step explanation:
If_ any _two _sides_ and _angle_ included_ between_ the _sides _of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.
<u>Answer-</u>
<em>After 76 swings</em><em> the angle through which it swings less than 1°</em>
<u>Solution-</u>
From the question,
Angle of the first of swing = 30° and then each succeeding oscillation is through 95% of the angle of the one before it.
So the angle of the second swing = ![(30\times \frac{95}{100})^{\circ}](https://tex.z-dn.net/?f=%2830%5Ctimes%20%5Cfrac%7B95%7D%7B100%7D%29%5E%7B%5Ccirc%7D)
Then the angle of third swing = ![(30\times (\frac{95}{100})^2)^{\circ}](https://tex.z-dn.net/?f=%2830%5Ctimes%20%28%5Cfrac%7B95%7D%7B100%7D%29%5E2%29%5E%7B%5Ccirc%7D)
So, this follows a Geometric Progression.
![(30,\ 30\cdot \frac{95}{100},\ 30\cdot (\frac{95}{100})^2............,0)](https://tex.z-dn.net/?f=%2830%2C%5C%2030%5Ccdot%20%5Cfrac%7B95%7D%7B100%7D%2C%5C%2030%5Ccdot%20%28%5Cfrac%7B95%7D%7B100%7D%29%5E2............%2C0%29)
a = The initial term = 30
r = Common ratio = ![\frac{95}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B95%7D%7B100%7D)
As we have to find the number swings when the angle swept by the pendulum is less than 1°.
So we have the nth number is the series as 1, applying the formula
![T_n=ar^{n-1}](https://tex.z-dn.net/?f=T_n%3Dar%5E%7Bn-1%7D)
Putting the values,
![\Rightarrow 1=30(\frac{95}{100})^{n-1}](https://tex.z-dn.net/?f=%5CRightarrow%201%3D30%28%5Cfrac%7B95%7D%7B100%7D%29%5E%7Bn-1%7D)
![\Rightarrow \frac{1}{30} =(\frac{95}{100})^{n-1}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B1%7D%7B30%7D%20%3D%28%5Cfrac%7B95%7D%7B100%7D%29%5E%7Bn-1%7D)
Taking logarithm of both sides,
![\Rightarrow \log \frac{1}{30} =\log (\frac{95}{100})^{n-1}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Clog%20%5Cfrac%7B1%7D%7B30%7D%20%3D%5Clog%20%28%5Cfrac%7B95%7D%7B100%7D%29%5E%7Bn-1%7D)
![\Rightarrow \log \frac{1}{30} =(n-1)\log (\frac{95}{100})](https://tex.z-dn.net/?f=%5CRightarrow%20%5Clog%20%5Cfrac%7B1%7D%7B30%7D%20%3D%28n-1%29%5Clog%20%28%5Cfrac%7B95%7D%7B100%7D%29)
![\Rightarrow -1.5=(n-1)(-0.02)](https://tex.z-dn.net/?f=%5CRightarrow%20-1.5%3D%28n-1%29%28-0.02%29)
![\Rightarrow 1.5=(n-1)(0.02)](https://tex.z-dn.net/?f=%5CRightarrow%201.5%3D%28n-1%29%280.02%29)
![\Rightarrow n-1=\dfrac{1.5}{0.02}](https://tex.z-dn.net/?f=%5CRightarrow%20n-1%3D%5Cdfrac%7B1.5%7D%7B0.02%7D)
![\Rightarrow n-1=75](https://tex.z-dn.net/?f=%5CRightarrow%20n-1%3D75)
![\Rightarrow n=76](https://tex.z-dn.net/?f=%5CRightarrow%20n%3D76)
Therefore, after 76 swings the angle through which it swings less than 1°