The graph of
... y = 3/4 - 2
is a horizontal line at y = -1.25.
The graph of
... y = (3/4)x - 2
is an upward-sloping line with a rise of 3 for every 4 units to the right. It intercepts the y-axis at y = -2.
Sine = opposite over hypotenuse, so 0.5 = x/12
multiply both sides by 12 to get x by itself and x = 6 cm
Hello!
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Answer:
-2,2
Step-by-step explanation:
Let
![y_1=4x^2-c^2](https://tex.z-dn.net/?f=y_1%3D4x%5E2-c%5E2)
![y_2=c^2-4x^2](https://tex.z-dn.net/?f=y_2%3Dc%5E2-4x%5E2)
We have to find the value of c such that the are of the region bounded by the parabolas =32/3
![y_1=y_2](https://tex.z-dn.net/?f=y_1%3Dy_2)
![4x^2-c^2=c^2-4x^2](https://tex.z-dn.net/?f=4x%5E2-c%5E2%3Dc%5E2-4x%5E2)
![4x^2+4x^2=c^2+c^2](https://tex.z-dn.net/?f=4x%5E2%2B4x%5E2%3Dc%5E2%2Bc%5E2)
![8x^2=2c^2](https://tex.z-dn.net/?f=8x%5E2%3D2c%5E2)
![x^2=c^2/4](https://tex.z-dn.net/?f=x%5E2%3Dc%5E2%2F4)
![x=\pm \frac{c}{2}](https://tex.z-dn.net/?f=x%3D%5Cpm%20%5Cfrac%7Bc%7D%7B2%7D)
Now, the area bounded by two curves
![A=\int_{a}^{b}(y_2-y_1)dx](https://tex.z-dn.net/?f=A%3D%5Cint_%7Ba%7D%5E%7Bb%7D%28y_2-y_1%29dx)
![A=\int_{-c/2}^{c/2}(c^2-4x^2-4x^2+c^2)dx](https://tex.z-dn.net/?f=A%3D%5Cint_%7B-c%2F2%7D%5E%7Bc%2F2%7D%28c%5E2-4x%5E2-4x%5E2%2Bc%5E2%29dx)
![\frac{32}{3}=\int_{-c/2}^{c/2}(2c^2-8x^2)dx](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B3%7D%3D%5Cint_%7B-c%2F2%7D%5E%7Bc%2F2%7D%282c%5E2-8x%5E2%29dx)
![\frac{32}{3}=2\int_{-c/2}^{c/2}(c^2-4x^2)dx](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B3%7D%3D2%5Cint_%7B-c%2F2%7D%5E%7Bc%2F2%7D%28c%5E2-4x%5E2%29dx)
![\frac{32}{3}=2[c^2x-\frac{4}{3}x^3]^{c/2}_{-c/2}](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B3%7D%3D2%5Bc%5E2x-%5Cfrac%7B4%7D%7B3%7Dx%5E3%5D%5E%7Bc%2F2%7D_%7B-c%2F2%7D)
![\frac{32}{3}=2(c^2(c/2+c/2)-4/3(c^3/8+c^3/28))](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B3%7D%3D2%28c%5E2%28c%2F2%2Bc%2F2%29-4%2F3%28c%5E3%2F8%2Bc%5E3%2F28%29%29)
![\frac{32}{3}=2(c^3-\frac{4}{3}(\frac{c^3}{4}))](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B3%7D%3D2%28c%5E3-%5Cfrac%7B4%7D%7B3%7D%28%5Cfrac%7Bc%5E3%7D%7B4%7D%29%29)
![\frac{32}{3}=2(c^3-\frac{c^3}{3})](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B3%7D%3D2%28c%5E3-%5Cfrac%7Bc%5E3%7D%7B3%7D%29)
![\frac{32}{3}=2(\frac{2}{3}c^3)](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B3%7D%3D2%28%5Cfrac%7B2%7D%7B3%7Dc%5E3%29)
![c^3=\frac{32\times 3}{4\times 3}](https://tex.z-dn.net/?f=c%5E3%3D%5Cfrac%7B32%5Ctimes%203%7D%7B4%5Ctimes%203%7D)
![c^3=8](https://tex.z-dn.net/?f=c%5E3%3D8)
![c=\sqrt[3]{8}=2](https://tex.z-dn.net/?f=c%3D%5Csqrt%5B3%5D%7B8%7D%3D2)
When c=2 and when c=-2 then the given parabolas gives the same answer.
Therefore, value of c=-2, 2
Answer:
2 yards
Step-by-step explanation:
10 divided by 5 is 2