Answer:
T = T
Explanation:
The period of a simple pendulum is given by the formula
Where
l - length of the pendulum
g - acceleration due to gravity
The dimension of the physical quantities are given by,
t - T
l - L
g - m/s² - LT⁻²
Substituting in the above equation,
T = 2π √(L / LT⁻²)
Considering only the dimensional units in the equation
T = √(L / LT⁻²)
T = T
This shows that the formula for a simple pendulum is dimensionally consistent, T = T
Answer:
I=1,2•10³ kg•m/s
Explanation:
v¹=3.5m/s
vf=5m/s
v=5-3.5=1.5m/s
I=p
I=mv=850•1.5=1275 kg•m/s=1,2•10³ kg•m/s
Answer:
97.5%
Explanation:
By the empirical rule (68-95-99.7),
- 68% of data are within <em>μ </em>- <em>σ</em> and <em>μ </em>+ <em>σ</em>
- 95% of data are within <em>μ </em>- 2<em>σ</em> and <em>μ </em>+ 2<em>σ</em>
- 99.7% of data are within <em>μ </em>- 3<em>σ</em> and <em>μ </em>+ 2<em>σ</em>
<em>σ </em> and <em>μ</em> are the standard deviation and the mean respectively.
From the question,
<em>μ</em> = 7.2 cm
<em>σ</em> = 0.38 cm
7.96 = 7.2 + (<em>n</em> × 0.38)
<em>n</em> = 2
Hence, 7.96 represents <em>μ </em>+ 2<em>σ</em>.
P(X < <em>μ </em>+ 2<em>σ</em>) = P(X < <em>μ</em>) + P(<em>μ</em> < X < <em>μ </em>+ 2<em>σ</em>)
P(X < <em>μ</em>) is the percentage less than the mean = 50%.
P(<em>μ</em> < X < <em>μ </em>+ 2<em>σ</em>) is half of P(<em>μ </em>- 2<em>σ</em> < X < <em>μ </em>+ 2<em>σ</em>) = 95% ÷ 2 = 47.5%.
Considering this, for apples that are no more than 7.96 cm,
P(X < 7.96) = P(X < 7.2) + P(7.2 < X < 7.96) = 50% + 47.5% = 97.5%
<em />
They have a different number neutrons.
