The width of the card to the nearest tenth of an inch is 6.15 inches
<h3>Area of rectangle</h3>
- Width = x
- Length = 2x + 1
- Area = 88 square inches
Area of a rectangle = Length × Width
88 = (2x + 2) × x
88 = 2x² + 2x
2x² + 2x - 88 = 0
x = -b ± √b² - 4ac / 2a
= -2 ± √2² - 4(2)(-88) / 2(2)
= -2 ± √4 - (-704) / 4
= -2 ± √708 / 4
= -1/2 ± √177/2
x = 6.15 or -7.15 inches
The width of the rectangle can not be negative, so, 6.15 inches is the width.
Learn more about rectangle:
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What we have to find in this question
d/dx cos^2(5x^3)
= d/dx [cos(5x^3)]^2
= 2[cos(5x^3)]
= - 2[cos(5x^3)] * sin(5x^3)
= - 2[cos(5x^3)] * sin(5x^3) * 15x^2
= - 30[cos(5x^3)] * sin(5x^3) * x^2
Explanation:
d/dx x^n = nx^(n - 1)
d/dx cos x = - sin x
Chain rule:
d/dx f(g(...w(x))) = f’(g(...w(x))) * g’(...w(x)) * ... * w’(x)
Answer:
Answer in terms of π=144π m^3
Answer by replacing π with 3.14 is 452.16 approximately 452.2m^3
Answer to the nearest whole no. is 452m^3
Step-by-step explanation:
![volume \: of \: a \: cone = \frac{1}{3} \pi {r}^{2} h](https://tex.z-dn.net/?f=volume%20%5C%3A%20of%20%5C%3A%20a%20%5C%3A%20cone%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%7Br%7D%5E%7B2%7D%20h)
![radius = \frac{diametre}{2}](https://tex.z-dn.net/?f=radius%20%3D%20%20%5Cfrac%7Bdiametre%7D%7B2%7D%20)
![radius = 24](https://tex.z-dn.net/?f=radius%20%3D%2024)
![height = 18](https://tex.z-dn.net/?f=height%20%3D%2018)
![slant \: height \: = 30](https://tex.z-dn.net/?f=slant%20%5C%3A%20height%20%5C%3A%20%20%3D%2030)
![first \: step](https://tex.z-dn.net/?f=first%20%5C%3A%20step)
![the \: exact \: volume \: of \: the \: cone \: in \: terms \: of \: \pi](https://tex.z-dn.net/?f=the%20%5C%3A%20exact%20%5C%3A%20volume%20%5C%3A%20of%20%5C%3A%20the%20%5C%3A%20cone%20%5C%3A%20in%20%5C%3A%20terms%20%5C%3A%20of%20%5C%3A%20%5Cpi)
![v = \frac{1}{3} \pi {r}^{2} h](https://tex.z-dn.net/?f=v%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%7Br%7D%5E%7B2%7D%20h)
![\: \: = \frac{1}{3} \times \pi \times 24 \times 18](https://tex.z-dn.net/?f=%20%5C%3A%20%20%5C%3A%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%5Ctimes%20%5Cpi%20%5Ctimes%2024%20%5Ctimes%2018)
![\: \: \: = \frac{432\pi}{3}](https://tex.z-dn.net/?f=%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%3D%20%20%5Cfrac%7B432%5Cpi%7D%7B3%7D%20)
![\: \: \: = 144\pi](https://tex.z-dn.net/?f=%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%3D%20144%5Cpi)
![second \: step](https://tex.z-dn.net/?f=second%20%5C%3A%20step)
![approximate \: answer \: using \: 3.14 \: in \: place \: of \: \pi](https://tex.z-dn.net/?f=approximate%20%5C%3A%20answer%20%5C%3A%20using%20%5C%3A%203.14%20%5C%3A%20in%20%5C%3A%20place%20%5C%3A%20of%20%5C%3A%20%5Cpi)
![144 \times 3.14](https://tex.z-dn.net/?f=144%20%5Ctimes%203.14)
![= 452.16](https://tex.z-dn.net/?f=%20%3D%20452.16)
![approximately \: 452.2](https://tex.z-dn.net/?f=approximately%20%5C%3A%20452.2)
![last \: step](https://tex.z-dn.net/?f=last%20%5C%3A%20step)
![answer \: to \: the \: nearest \: whole \: number](https://tex.z-dn.net/?f=answer%20%5C%3A%20to%20%5C%3A%20the%20%5C%3A%20nearest%20%5C%3A%20whole%20%5C%3A%20number)
![452 {m}^{3}](https://tex.z-dn.net/?f=452%20%7Bm%7D%5E%7B3%7D%20)