Distance formula : d = sqrt (x2 - x1)^2 + (y2 - y1)^2
(-5,8)(10,-7)
d = sqrt (10 - (-5)^2 + (-7 - 8)^2
d = sqrt (10 + 5)^2 + (- 15^2)
d = sqrt (15^2) + (-15^2)
d = sqrt 225 + 225
d = sqrt 450
d = 21.21
Answer:
F is reduced by 31%
Step-by-step explanation:
F = 1/(d²)
now, we increase the distance by 20% (multiply by 1.2).
F new = 1/(1.2×d)² = 1/(1.44×d²) = (1/1.44) × (1/(d²)) =
= 1/1.44 × old F = 0.69 × old F
100 - 69 = 31%
Answer:
Step-by-step explanation:
Let x be the random variable representing the the length of newborn babies (in inches). Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 20 inches
σ = 2.6 inches
the probability that a given infant is between 14.8 and 25.2 inches long is expressed as
P(14.8 ≤ x ≤ 25.2)
For x = 14.8,
z = (14.8 - 20)/2.6 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.023
For x = 25.2
z = (25.2 - 20)/2.6 = 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.98
Therefore,
P(14.8 ≤ x ≤ 25.2) = 0.98 - 0.23 = 0.75
we know that
acceleration due to gravity is 9.8m/s^2
so, we get

and acceleration will always be constant
we know that
integral of acceleration is velocity
so, we can integrate both sides


we are given
v(0)=35m/s
we can use it and find C



now, we can plug it back

we know that
integral of velocity is height
we can integrate it again



now, we have
s(0)=6
we can use it and find C


now, we can plug back C

and we get
.............Answer
Answer:
The diameter decreases at a rate of 0.053 cm/min.
Step-by-step explanation:
Surface area of an snowball
The surface area of an snowball has the following equation:

In which d is the diameter.
Implicit differentiation:
To solve this question, we differentiate the equation for the surface area implictly, in function of t. So

Surface area decreases at a rate of 3 cm2/min
This means that 
Tind the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm.
This is
when
. So




The diameter decreases at a rate of 0.053 cm/min.