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)
The amount A when the principal P is compounded continuously is given by the formula :
![A=P E^{rt}](https://tex.z-dn.net/?f=%20A%3DP%20E%5E%7Brt%7D%20%20)
Here r is rate of interest and t is time .
In the question P=1600 ,r=6.5%=0.065 ,t= 6 years
Substituting these values in the formula
![A=(1600) e^{0.065 times 6}](https://tex.z-dn.net/?f=%20A%3D%281600%29%20e%5E%7B0.065%20times%206%7D%20%20)
A= 1600(1.48)
A=2363.17
Balance after 6years is $2363.17
If the unknown side is a leg, the hypotenuse must be 26 (the longest of the other two sides). Then the Pythagorean theorem tells you
... 26² = 24² + y²
... y = √(26² -24²) = √100 = 10
The appropriate choice is
... 10
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You may recognize that this triangle is double the often-used Pythagorean triple (5, 12, 13).
15.01
tan(65) = BC/7
BC = 7*tan(65)