Step-by-step explanation:
Well they made 19 clay, where 12 were vases. That means 7 were not vases. She randomly chooses 16 clay objects, which then also means 3 were left behind. so if the vases are 12/19, which is approximately 63%, then 63% of the objects are vases. Makes sense, right? Well now we need to multiply that by the initial 11 in the question. After all of this work..
Answer: 6.9474 or 6.94736.
Please mark as Brainliest.
If she went 10 miles upstream in the same time as she went 20 miles downstream, that means the downstream speed is twice the upstream speed.
The speed is still water is 9 mph.
The speed of the current is c.
Going downstream, the current adds speed, so the sped downstream is 9 + c.
The speed upstream is 9 - c.
9 + c is twice 9 - c.
9 + c = 2(9 - c)
9 + c = 18 - 2c
3c = 9
c = 3
Answer: The speed of the current is 3 mph.
Check:
9 + c = 12
9 - c = 6
By taking into the account the speed of the current, the downstream speed, 12 mph, is indeed twice the upstream sped, 6 mph.
Y + 4 = -3/4x --------------------> y = -3/4x - 4
We draw region ABC. Lines that connect y = 0 and y = x³ are vertical so:
(i) prependicular to the axis x - disc method;
(ii) parallel to the axis y - shell method;
(iii) parallel to the line x = 18 - shell method.
Limits of integration for x are easy x₁ = 0 and x₂ = 9.
Now, we have all information, so we could calculate volume.
(i)
![V=\pi\cdot\int\limits_0^9(x^3)^2\, dx=\pi\cdot\int\limits_0^9x^6\, dx=\pi\cdot\left[\dfrac{x^7}{7}\right]_0^9=\pi\cdot\left(\dfrac{9^7}{7}-\dfrac{0^7}{7}\right)=\dfrac{9^7}{7}\pi=\\\\\\=\boxed{\dfrac{4782969}{7}\pi}](https://tex.z-dn.net/?f=V%3D%5Cpi%5Ccdot%5Cint%5Climits_0%5E9%28x%5E3%29%5E2%5C%2C%20dx%3D%5Cpi%5Ccdot%5Cint%5Climits_0%5E9x%5E6%5C%2C%20dx%3D%5Cpi%5Ccdot%5Cleft%5B%5Cdfrac%7Bx%5E7%7D%7B7%7D%5Cright%5D_0%5E9%3D%5Cpi%5Ccdot%5Cleft%28%5Cdfrac%7B9%5E7%7D%7B7%7D-%5Cdfrac%7B0%5E7%7D%7B7%7D%5Cright%29%3D%5Cdfrac%7B9%5E7%7D%7B7%7D%5Cpi%3D%5C%5C%5C%5C%5C%5C%3D%5Cboxed%7B%5Cdfrac%7B4782969%7D%7B7%7D%5Cpi%7D)
Answer B. or D.
(ii)
![V=2\pi\cdot\int\limits_0^{9}(x\cdot x^3)\, dx=2\pi\cdot\int\limits_0^{9}x^4\, dx= 2\pi\cdot\left[\dfrac{x^5}{5}\right]_0^9=2\pi\cdot\left(\dfrac{9^5}{5}-\dfrac{0^5}{5}\right)=\\\\\\=2\pi\cdot\dfrac{9^5}{5}=\boxed{\dfrac{118098}{5}\pi}](https://tex.z-dn.net/?f=V%3D2%5Cpi%5Ccdot%5Cint%5Climits_0%5E%7B9%7D%28x%5Ccdot%20x%5E3%29%5C%2C%20dx%3D2%5Cpi%5Ccdot%5Cint%5Climits_0%5E%7B9%7Dx%5E4%5C%2C%20dx%3D%0A2%5Cpi%5Ccdot%5Cleft%5B%5Cdfrac%7Bx%5E5%7D%7B5%7D%5Cright%5D_0%5E9%3D2%5Cpi%5Ccdot%5Cleft%28%5Cdfrac%7B9%5E5%7D%7B5%7D-%5Cdfrac%7B0%5E5%7D%7B5%7D%5Cright%29%3D%5C%5C%5C%5C%5C%5C%3D2%5Cpi%5Ccdot%5Cdfrac%7B9%5E5%7D%7B5%7D%3D%5Cboxed%7B%5Cdfrac%7B118098%7D%7B5%7D%5Cpi%7D)
So we know that the correct answer is D.
(iii)
Line x = h
![V=2\pi\cdot\int\limits_0^9\big((18-x)\cdot x^3\big)\, dx=2\pi\cdot\int\limits_0^9(18x^3-x^4)\, dx=\\\\\\=2\pi\cdot\left(\int\limits_0^918x^3\, dx-\int\limits_0^9x^4\, dx\right)=2\pi\cdot\left(18\int\limits_0^9x^3\, dx-\int\limits_0^9x^4\, dx\right)=\\\\\\=2\pi\cdot\left(18\left[\dfrac{x^4}{4}\right]_0^9-\left[\dfrac{x^5}{5}\right]_0^9\right)=2\pi\cdot\Biggl(18\biggl(\dfrac{9^4}{4}-\dfrac{0^4}{4}\biggr)-\biggl(\dfrac{9^5}{5}-\dfrac{0^5}{5}\biggr)\Biggr)=\\\\\\](https://tex.z-dn.net/?f=V%3D2%5Cpi%5Ccdot%5Cint%5Climits_0%5E9%5Cbig%28%2818-x%29%5Ccdot%20x%5E3%5Cbig%29%5C%2C%20dx%3D2%5Cpi%5Ccdot%5Cint%5Climits_0%5E9%2818x%5E3-x%5E4%29%5C%2C%20dx%3D%5C%5C%5C%5C%5C%5C%3D2%5Cpi%5Ccdot%5Cleft%28%5Cint%5Climits_0%5E918x%5E3%5C%2C%20dx-%5Cint%5Climits_0%5E9x%5E4%5C%2C%20dx%5Cright%29%3D2%5Cpi%5Ccdot%5Cleft%2818%5Cint%5Climits_0%5E9x%5E3%5C%2C%20dx-%5Cint%5Climits_0%5E9x%5E4%5C%2C%20dx%5Cright%29%3D%5C%5C%5C%5C%5C%5C%3D2%5Cpi%5Ccdot%5Cleft%2818%5Cleft%5B%5Cdfrac%7Bx%5E4%7D%7B4%7D%5Cright%5D_0%5E9-%5Cleft%5B%5Cdfrac%7Bx%5E5%7D%7B5%7D%5Cright%5D_0%5E9%5Cright%29%3D2%5Cpi%5Ccdot%5CBiggl%2818%5Cbiggl%28%5Cdfrac%7B9%5E4%7D%7B4%7D-%5Cdfrac%7B0%5E4%7D%7B4%7D%5Cbiggr%29-%5Cbiggl%28%5Cdfrac%7B9%5E5%7D%7B5%7D-%5Cdfrac%7B0%5E5%7D%7B5%7D%5Cbiggr%29%5CBiggr%29%3D%5C%5C%5C%5C%5C%5C)
Answer D. just as before.
Answer:
If X repeats and y does not it is not an example of a function. But if the y repeats and has two different x values that can be known as a function.
For an example ( 1 , 3) and (1, 4) thats not an example of a function because the x value is repeating but if its ( 1, 4) and (2,4) a thats
a function because no x value is repeating the x value is known as an independent value. Does that make sense?
"This relation is definitely a function because every x-value is unique and is associated with only one value of y. So for a quick summary, if you see any duplicates or repetitions in the x-values, the relation is not a function."
