Answer:
51
Step-by-step explanation:
The order goes as follows:
Lower Extreme, Lower Quartile, Median, Higher Quartile, Higher Extreme
The Higher Extreme is the highest quantity.
I am joyous to assist you anytime.
Answer:
![Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}](https://tex.z-dn.net/?f=Area%3D7%5C%2C%5Cpi%5C%2C%5Csqrt%7B%5Cfrac%7B53%7D%7B4%7D%7D%5C%2C%5C%2C%5Cfrac%7B25%7D%7B2%7D)
Step-by-step explanation:
Let's use the integral formula for the surface area of revolution of the function y(x) around the x-axis, which is:
![Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx](https://tex.z-dn.net/?f=Area%3D%5Cint%5Climits%5Eb_a%20%7B2%5C%2C%5Cpi%5C%2Cy%5C%2C%5Csqrt%7B1%2B%28%5Cfrac%7Bdy%7D%7Bdx%7D%20%29%5E2%7D%20%7D%20%5C%2C%20dx)
and which in our case, we can obtain the following:
![y=\frac{7}{2} \,x\\\frac{dy}{dx} =\frac{7}{2} \\(\frac{dy}{dx})^2=\frac{49}{4} \\\sqrt{1+(\frac{dy}{dx})^2} =\sqrt{1+\frac{49}{4} } =\sqrt{\frac{53}{4} }](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B7%7D%7B2%7D%20%5C%2Cx%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%5Cfrac%7B7%7D%7B2%7D%20%5C%5C%28%5Cfrac%7Bdy%7D%7Bdx%7D%29%5E2%3D%5Cfrac%7B49%7D%7B4%7D%20%5C%5C%5Csqrt%7B1%2B%28%5Cfrac%7Bdy%7D%7Bdx%7D%29%5E2%7D%20%3D%5Csqrt%7B1%2B%5Cfrac%7B49%7D%7B4%7D%20%7D%20%3D%5Csqrt%7B%5Cfrac%7B53%7D%7B4%7D%20%7D)
Recall as well that
, which gives us the limits of integration:
![Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx\\Area=\int\limits^5_0 {2\,\pi\,(\frac{7}{2}\,x) \,\sqrt{\frac{53}{4} } } \, dx\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\, \int\limits^5_0 {x} \, dx \\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{x^2}{2} |\limits^5_0\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}](https://tex.z-dn.net/?f=Area%3D%5Cint%5Climits%5Eb_a%20%7B2%5C%2C%5Cpi%5C%2Cy%5C%2C%5Csqrt%7B1%2B%28%5Cfrac%7Bdy%7D%7Bdx%7D%20%29%5E2%7D%20%7D%20%5C%2C%20dx%5C%5CArea%3D%5Cint%5Climits%5E5_0%20%7B2%5C%2C%5Cpi%5C%2C%28%5Cfrac%7B7%7D%7B2%7D%5C%2Cx%29%20%5C%2C%5Csqrt%7B%5Cfrac%7B53%7D%7B4%7D%20%7D%20%7D%20%5C%2C%20dx%5C%5CArea%3D7%5C%2C%5Cpi%5C%2C%5Csqrt%7B%5Cfrac%7B53%7D%7B4%7D%7D%5C%2C%5C%2C%20%5Cint%5Climits%5E5_0%20%7Bx%7D%20%5C%2C%20dx%20%5C%5CArea%3D7%5C%2C%5Cpi%5C%2C%5Csqrt%7B%5Cfrac%7B53%7D%7B4%7D%7D%5C%2C%5C%2C%5Cfrac%7Bx%5E2%7D%7B2%7D%20%7C%5Climits%5E5_0%5C%5CArea%3D7%5C%2C%5Cpi%5C%2C%5Csqrt%7B%5Cfrac%7B53%7D%7B4%7D%7D%5C%2C%5C%2C%5Cfrac%7B25%7D%7B2%7D)
If we compare it with the geometry formula:
Lateral surface of cone = ![\frac{1}{2} \,\,(Base_{circ})\,\,(slant\,height)= \frac{1}{2} (2\,\pi\,\frac{7}{2} 5)\.(\sqrt{5^2+(\frac{35}{2})^2 } =\frac{7}{2} \,\pi\,25\.\,\sqrt{\frac{53}{4} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5C%2C%5C%2C%28Base_%7Bcirc%7D%29%5C%2C%5C%2C%28slant%5C%2Cheight%29%3D%20%5Cfrac%7B1%7D%7B2%7D%20%282%5C%2C%5Cpi%5C%2C%5Cfrac%7B7%7D%7B2%7D%205%29%5C.%28%5Csqrt%7B5%5E2%2B%28%5Cfrac%7B35%7D%7B2%7D%29%5E2%20%7D%20%3D%5Cfrac%7B7%7D%7B2%7D%20%5C%2C%5Cpi%5C%2C25%5C.%5C%2C%5Csqrt%7B%5Cfrac%7B53%7D%7B4%7D%20%7D)
which is exactly the expression we calculated with the integral.
Answer:
A.
Step-by-step explanation:
5 is added each time
3 + 5 = 8
8 + 5 = 13
13 + 5 = 18
Answer:
3.2 (and the equation is 3.4 + x = 6.6)
Step-by-step explanation:
the word problem is written as:
3.4 + x = 6.6
we want to solve for x.
to isolate x by itself, subtract 3.4 from both sides. (3.4 - 3.4=0 & 6.6 - 3.4 = 3.2)
now we have x = 3.2
so x equals 3.2
hope this helps!! :)