Thirty nine divided by one thousand
Answer:
![\frac{x^2}{16}-\frac{b^2}{4}=1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B16%7D-%5Cfrac%7Bb%5E2%7D%7B4%7D%3D1)
Step-by-step explanation:
A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.
The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:
![\frac{x^2}{a^2}-\frac{y^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7Ba%5E2%7D-%5Cfrac%7By%5E2%7D%7Bb%5E2%7D%3D1)
The coordinates of the foci is at (±c, 0), where c² = a² + b²
Given that a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:
![\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{4^2}{a^2}-\frac{0}{b^2} =1\\\frac{4^2}{a^2}=1\\ a^2=16\\a=\sqrt{16}=4\\ a=4](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7Ba%5E2%7D-%5Cfrac%7By%5E2%7D%7Bb%5E2%7D%3D1%5C%5C%5Cfrac%7B4%5E2%7D%7Ba%5E2%7D-%5Cfrac%7B0%7D%7Bb%5E2%7D%20%3D1%5C%5C%5Cfrac%7B4%5E2%7D%7Ba%5E2%7D%3D1%5C%5C%20a%5E2%3D16%5C%5Ca%3D%5Csqrt%7B16%7D%3D4%5C%5C%20a%3D4)
The foci c is at +/-2√5, using c² = a² + b²:
![c^2=a^2+b^2\\(2\sqrt{5} )^2=4^2+b^2\\20 = 16 + b^2\\b^2=20-16\\b^2=4\\b=\sqrt{4}=2\\ b=2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2%5C%5C%282%5Csqrt%7B5%7D%20%29%5E2%3D4%5E2%2Bb%5E2%5C%5C20%20%3D%2016%20%2B%20b%5E2%5C%5Cb%5E2%3D20-16%5C%5Cb%5E2%3D4%5C%5Cb%3D%5Csqrt%7B4%7D%3D2%5C%5C%20b%3D2)
Substituting the value of a and b to get the equation of the hyperbola:
![\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\\\frac{x^2}{16}-\frac{b^2}{4}=1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7Ba%5E2%7D-%5Cfrac%7By%5E2%7D%7Bb%5E2%7D%3D1%5C%5C%5C%5C%5Cfrac%7Bx%5E2%7D%7B16%7D-%5Cfrac%7Bb%5E2%7D%7B4%7D%3D1)
Answer:
h(4) = 1/2 (4) - 8 = 2 - 8 = -6
Step-by-step explanation:
Answer:
<h3>Add 47.6 and 39.75, then round the answer</h3>
Step-by-step explanation:
If Ramina found the length of two pieces of ribbon to be 47.6 inches and 39.75 inches, the effective strategy of finding the sum of the two lengths is to:
1) First is to add the two values together
47.6 + 39.75
= (47+0.6)+(39+0.75)
= (47+39)+(0.6+0.75)
= 86 + 1.35
= 87.35
2) Round up the answer to nearest whole number.
87.35 ≈ 87 (note that we couldn't round up to 88 because the values after the decimal point wasn't up to 5)
Option C is correct