Answer:
142.1π in³
Step-by-step explanation:
Given that:
The radius (r) = 7 in
The slant height (y) = 25 in
Then the height (x) can be determined by using the Pythagoras rule:
y² = x² + r²
25² = x² + 7²
125 = x² + 49
125 - 49 = x²
x² = 76
x = √76
x = 8.7
The formula for the volume of a cone is;
= 1/3 πr²h
where;
height(h) is calculated as "x" from above = 8.7
Then;
= 1/3 × π × (7 in)² × 8.7 in
= 142.1π in³
For each <em>x</em> in the interval 0 ≤ <em>x</em> ≤ 5, the shell at that point has
• radius = 5 - <em>x</em>, which is the distance from <em>x</em> to <em>x</em> = 5
• height = <em>x</em> ² + 2
• thickness = d<em>x</em>
and hence contributes a volume of 2<em>π</em> (5 - <em>x</em>) (<em>x</em> ² + 2) d<em>x</em>.
Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:
When the bases are diffenrent and the exponents of a and b are the same, we can multiply a and b first:
a n ⋅ b n = (a ⋅ b) n
Example:
32 ⋅ 42 = (3⋅4)2 = 122 = 12⋅12 = 144
When the bases and the exponents are different we have to calculate each exponent and then multiply:
a n ⋅ b m
Example:
32 ⋅ 43 = 9 ⋅ 64 = 576
The product of x and 5 can be displayed as 5x
Less than -27 can be displayed as < -27
When we combine those two statements, the following inequality is made.
5x < -27
The distance is 54 km if the speed and time are 72 km/h and 45 minutes respectively.
<h3>What is distance?</h3>
Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
Speed = 72 km/h
time = 45 mins = 45/60 = 0.75 hours
We know,
Distance = Speed×time
Distance = 72(km/h)×0.75(h)
Distance = 54 km
Thus, the distance is 54 km if the speed and time are 72 km/h and 45 minutes respectively.
Learn more about the distance here:
brainly.com/question/26711747
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