the center is at the origin of a coordinate system and the foci are on the y-axis, then the foci are symmetric about the origin.
The hyperbola focus F1 is 46 feet above the vertex of the parabola and the hyperbola focus F2 is 6 ft above the parabola's vertex. Then the distance F1F2 is 46-6=40 ft.
In terms of hyperbola, F1F2=2c, c=20.
The vertex of the hyperba is 2 ft below focus F1, then in terms of hyperbola c-a=2 and a=c-2=18 ft.
Use formula c^2=a^2+b^2c
2
=a
2
+b
2
to find b:
\begin{gathered} (20)^2=(18)^2+b^2,\\ b^2=400-324=76 \end{gathered}
(20)
2
=(18)
2
+b
2
,
b
2
=400−324=76
.
The branches of hyperbola go in y-direction, so the equation of hyperbola is
\dfrac{y^2}{b^2}- \dfrac{x^2}{a^2}=1
b
2
y
2
−
a
2
x
2
=1 .
Substitute a and b:
\dfrac{y^2}{76}- \dfrac{x^2}{324}=1
76
y
2
−
324
x
2
=1 .
Answer:
The student added the discount instead of subtracting the discount.
They also did not calculate the tax correctly.
Step-by-step explanation:
Original price is 499
Discount = original price * percent off
Discount = 499 * .18
=89.82
The sale price = original price minus the discount
sale price = 499-89.82
sale price = 409.18
Sales tax = sale price * tax rate
= 409.18 * 8.875%
=409.18*.08875
=36.314725
Rounding to the nearest cent
36.31
Final cost = sale price + sales tax
=409.18+36.31
445.49
The student added the discount instead of subtracting the discount.
They also did not calculate the tax correctly.
Step-by-step explanation:
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Answer:
1
Step-by-step explanation:
