84 square inches divided by 14 inches equals 6
84 divided by 14 = s
Answer:
It's the first option.
Step-by-step explanation:
y = cos x transformed to cos (x - π/2) moves the graph π/2 units to the right.
Multiplying by 3 to give 3 cos(x - π/2) stretches the graph 3 units parallel to the y-axis and adding 3 to this moves the graph up 3 units.
So the required equation is y = 3(cos x - π/2) + 3.
3/5 block mile is also 0.6 block mile
4 1/2 miles is also 4.5 miles
How many 0.6mi blocks do you run to run 4.5 miles?
4.5miles/0.6block mi = 7.5 or 7 1/2 blocks will equal 4.5 or 4 1/2 miles.
Check 7.5 blocks x 0.6 block mi = 4.5 miles
Same as you know one quarter equals $0.25 cent. And how many do you need to make one dollar that equals $1.00 ?
1/ .25 = 4 quarters
![\large\underline{\sf{Solution-}}](https://tex.z-dn.net/?f=%5Clarge%5Cunderline%7B%5Csf%7BSolution-%7D%7D)
We have to find out the value of the fraction.
<u>Let us assume that:</u>
![\sf \longmapsto x =2 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2 + ... \infty} } }](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20x%20%3D2%20%2B%20%20%20%5Cdfrac%7B1%7D%7B2%20%2B%20%20%5Cdfrac%7B1%7D%7B2%20%2B%20%20%5Cdfrac%7B1%7D%7B2%20%2B%20...%20%5Cinfty%7D%20%7D%20%7D%20)
<u>We can also write it as:</u>
![\sf \longmapsto x =2 + \dfrac{1}{x}](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20x%20%3D2%20%2B%20%5Cdfrac%7B1%7D%7Bx%7D%20)
![\sf \longmapsto x =\dfrac{2x + 1}{x}](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20x%20%3D%5Cdfrac%7B2x%20%2B%201%7D%7Bx%7D%20)
![\sf \longmapsto {x}^{2} =2x + 1](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20%20%7Bx%7D%5E%7B2%7D%20%20%3D2x%20%2B%201)
![\sf \longmapsto {x}^{2} - 2x - 1 = 0](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20%7Bx%7D%5E%7B2%7D%20%20-%202x%20-%201%20%3D%200)
<u>Comparing </u>the given <u>equation</u> with <u>ax² + bx + c = 0,</u> we get:
![\sf \longmapsto\begin{cases} \sf a =1 \\ \sf b = - 2 \\ \sf c = - 1 \end{cases}](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%5Cbegin%7Bcases%7D%20%5Csf%20a%20%3D1%20%5C%5C%20%5Csf%20b%20%3D%20%20-%202%20%5C%5C%20%5Csf%20c%20%3D%20%20-%201%20%5Cend%7Bcases%7D)
<u>By quadratic formula:</u>
![\sf \longmapsto x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20x%20%3D%20%20%5Cdfrac%7B%20-%20b%20%5Cpm%20%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20-%204ac%20%7D%20%7D%7B2a%7D%20)
![\sf \longmapsto x = \dfrac{2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 1)} }{2 \times 1}](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20x%20%3D%20%20%5Cdfrac%7B2%20%5Cpm%20%5Csqrt%7B%20%7B%28%20-%202%29%7D%5E%7B2%7D%20-%204%281%29%28%20-%201%29%7D%20%7D%7B2%20%5Ctimes%201%7D%20)
![\sf \longmapsto x = \dfrac{2 \pm \sqrt{4 + 4} }{2 \times 1}](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20x%20%3D%20%20%5Cdfrac%7B2%20%5Cpm%20%5Csqrt%7B4%20%2B%204%7D%20%7D%7B2%20%5Ctimes%201%7D%20)
![\sf \longmapsto x = \dfrac{2 \pm \sqrt{8} }{2}](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20x%20%3D%20%20%5Cdfrac%7B2%20%5Cpm%20%5Csqrt%7B8%7D%20%7D%7B2%7D%20)
![\sf \longmapsto x = \dfrac{2 \pm2 \sqrt{2} }{2}](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20x%20%3D%20%20%5Cdfrac%7B2%20%5Cpm2%20%5Csqrt%7B2%7D%20%7D%7B2%7D%20)
![\sf \longmapsto x = 1 \pm\sqrt{2}](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20x%20%3D%201%20%5Cpm%5Csqrt%7B2%7D)
![\sf \longmapsto x = \begin{cases} \sf 1 + \sqrt{2} \\ \sf 1 - \sqrt{2} \end{cases}](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongmapsto%20x%20%3D%20%5Cbegin%7Bcases%7D%20%5Csf%201%20%20%2B%20%5Csqrt%7B2%7D%20%5C%5C%20%5Csf%201%20-%20%20%5Csqrt%7B2%7D%20%20%5Cend%7Bcases%7D)
<u>But </u><u>"</u><u>x"</u><u> cannot be negative. Therefore:</u>
![\sf :\implies x = 1 + \sqrt{2}](https://tex.z-dn.net/?f=%20%5Csf%20%3A%5Cimplies%20x%20%3D%201%20%2B%20%5Csqrt%7B2%7D)
So, the value of the fraction is 1 + √2.