This question is simple as all we must find is the area of the room. To find the area of a quadrilateral, we should multiply the length by the width. In this case, that is 10 and 5.
10
<u>x5
</u>50
<u>
</u>Using the math above, we can see that Mary needs 50 square yards of carpet to cover the entire dining room floor.<u>
</u>
Answer:
Step-by-step explanation:
cosine x²= cos x²
Rule
Given that,
![=\int ^1_0[\int^3_0(\int^9_{3y} \frac{6cos x^2}{5\sqrt z}dz)dy]dz](https://tex.z-dn.net/?f=%3D%5Cint%20%5E1_0%5B%5Cint%5E3_0%28%5Cint%5E9_%7B3y%7D%20%5Cfrac%7B6cos%20x%5E2%7D%7B5%5Csqrt%20z%7Ddz%29dy%5Ddz)
![=\int^1_0[\int^3_0([\frac{6cos x^2 \times \sqrt z}{5\times \frac{1}{2}}]^9_{3y})dy]dx](https://tex.z-dn.net/?f=%3D%5Cint%5E1_0%5B%5Cint%5E3_0%28%5B%5Cfrac%7B6cos%20x%5E2%20%5Ctimes%20%5Csqrt%20z%7D%7B5%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%7D%5D%5E9_%7B3y%7D%29dy%5Ddx)
![=\int^1_0[\int^3_0([\frac{12cos x^2 \times( \sqrt 9-\sqrt{3y})}{5}])dy]dx](https://tex.z-dn.net/?f=%3D%5Cint%5E1_0%5B%5Cint%5E3_0%28%5B%5Cfrac%7B12cos%20x%5E2%20%5Ctimes%28%20%5Csqrt%209-%5Csqrt%7B3y%7D%29%7D%7B5%7D%5D%29dy%5Ddx)
![=\int^1_0[\int^3_0([\frac{12cos x^2 \times( 3-\sqrt{3y})}{5}])dy]dx](https://tex.z-dn.net/?f=%3D%5Cint%5E1_0%5B%5Cint%5E3_0%28%5B%5Cfrac%7B12cos%20x%5E2%20%5Ctimes%28%203-%5Csqrt%7B3y%7D%29%7D%7B5%7D%5D%29dy%5Ddx)
![=\int^1_0[\frac{12cos x^2 \times( 3y-\frac{\sqrt{3}y^\frac{3}{2}}{\frac{3}{2}})}{5}]^3_0dx](https://tex.z-dn.net/?f=%3D%5Cint%5E1_0%5B%5Cfrac%7B12cos%20x%5E2%20%5Ctimes%28%203y-%5Cfrac%7B%5Csqrt%7B3%7Dy%5E%5Cfrac%7B3%7D%7B2%7D%7D%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%7D%7B5%7D%5D%5E3_0dx)
![=\int^1_0[\frac{12cos x^2 \times( 3.3-\frac{2\sqrt{3}.3^\frac{3}{2}}{3})}{5}]^3_0dx](https://tex.z-dn.net/?f=%3D%5Cint%5E1_0%5B%5Cfrac%7B12cos%20x%5E2%20%5Ctimes%28%203.3-%5Cfrac%7B2%5Csqrt%7B3%7D.3%5E%5Cfrac%7B3%7D%7B2%7D%7D%7B3%7D%29%7D%7B5%7D%5D%5E3_0dx)
![=\int^1_0[\frac{12cos x^2 \times( 9-6)}{5}]dx](https://tex.z-dn.net/?f=%3D%5Cint%5E1_0%5B%5Cfrac%7B12cos%20x%5E2%20%5Ctimes%28%209-6%29%7D%7B5%7D%5Ddx)
![=\frac{18}{5}[(x+\frac{sin2x}{2})]^1_0](https://tex.z-dn.net/?f=%3D%5Cfrac%7B18%7D%7B5%7D%5B%28x%2B%5Cfrac%7Bsin2x%7D%7B2%7D%29%5D%5E1_0)
2a 3x4a +3x-5
2a+12a-15
14a-15
i think thats the answer
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:
brainly.com/question/145452
#SPJ1
Answer:
x plus 4 divided by 5 minus 9
x + 4 / 5 - 9
