Answer:
Step-by-step explanation:
28. Area of the circle = π
where r is the radius of the circle.
Given diameter = 14m, therefore radius = 
= 7m
Now area of the circle = 49
or = 49 * 3.14 * 3.14 = 483.12
29. Volume of cylinder = πh = π*
* 3 = 6.75π cu. feet or 21.195 cu. feet
30. A ball resembles a sphere. Volume of the sphere = 
Given diameter = 30inches; Therefore, radius = 15 inches
Now, Volume of the ball = 
= 4500π cu. inches or 14310 cu.inches
The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
Learn more about prime numbers here:
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Rhombus, <span>opposite angles are congruent
One angle is 35 so the opposite angle will be 35 also.
Sum of interior angles in a rhombus equal 360
360 - 35 - 35 = 290
290/2 = 145 (The other two angles will be congruent)
Answer:
The remaining three angles will be 35</span>°<span>, 145</span>°<span>, 145</span>°<span>
</span>
Answer:
-17/10 is 1.7 is a rational number
Step-by-step explanation:
In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. ... Moreover, any repeating or terminating decimal represents a rational number.
