Answer:
![y=7x -7](https://tex.z-dn.net/?f=y%3D7x%20-7)
Step-by-step explanation:
We are given two points, the y - intercept and the x - intercept.
The y - intercept being: ( 0, -7 )
The x - intercept being: ( 1, 0 )
The equation of a line in slope - intercept form is:
y = mx + b, where m is the slope and b is the y - intercept.
We already have the y - intercept. So far we have:
y = mx - 7
What we're missing is the slope.
To find the slope, we can use this formula:
, where
and
are the x - coordinates of both points and
and
are the y - coordinates of both points.
![m=\frac{0-(-7)}{1-0} \\\\m=\frac{7}{1}\\m=7](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B0-%28-7%29%7D%7B1-0%7D%20%5C%5C%5C%5Cm%3D%5Cfrac%7B7%7D%7B1%7D%5C%5Cm%3D7)
We now have the missing piece, the slope, so the equation now is:
![y=7x -7](https://tex.z-dn.net/?f=y%3D7x%20-7)
Given expression:
.
![\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5Cleft%28a%5Ccdot%20%5C%3Ab%5Cright%29%5En%3Da%5Enb%5En)
![=256^{\frac{1}{4}}\left(x^{16}\right)^{\frac{1}{4}}](https://tex.z-dn.net/?f=%3D256%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5Cleft%28x%5E%7B16%7D%5Cright%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D)
![256=4^4](https://tex.z-dn.net/?f=256%3D4%5E4)
![256^{\frac{1}{4}}=\left(4^4\right)^{\frac{1}{4}}=4](https://tex.z-dn.net/?f=256%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%3D%5Cleft%284%5E4%5Cright%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%3D4)
![\left(x^{16}\right)^{\frac{1}{4}}=x^{16\cdot \frac{1}{4}}=x^4](https://tex.z-dn.net/?f=%5Cleft%28x%5E%7B16%7D%5Cright%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%3Dx%5E%7B16%5Ccdot%20%5Cfrac%7B1%7D%7B4%7D%7D%3Dx%5E4)
![(256x^{16})^{1/4} =4x^4](https://tex.z-dn.net/?f=%28256x%5E%7B16%7D%29%5E%7B1%2F4%7D%20%3D4x%5E4)
<h3>Therefore, correct option is B option : B.4x^4</h3>
Answer:
Volume
Step-by-step explanation:
the formula for volume is length x width x height so that means 5 x 4 x 15
unless slashs mean division
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:
c
Step-by-step explanation:
the answer is c becuase on the height