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vichka [17]
3 years ago
6

Write the equation of a horizontal ellipse with a major axis of 30, a minor axis of 14, and a center at (-9, -7

Mathematics
1 answer:
erma4kov [3.2K]3 years ago
7 0
Recall that the major axis is "a + a" or 2a, whilst the minor axis is "b + b" or 2b.

so if the major axis is 30, then a = 15, and if the minor one is 14, b = 7.

\bf \textit{ellipse, horizontal major axis}
\\\\
\cfrac{(x-{{ h}})^2}{{{ a}}^2}+\cfrac{(y-{{ k}})^2}{{{ b}}^2}=1
\qquad 
\begin{cases}
center\ ({{ h}},{{ k}})\\
vertices\ ({{ h}}\pm a, {{ k}})
\end{cases}\\\\
-------------------------------\\\\
\textit{we know that }
\begin{cases}
a=\frac{30}{2}\\
b=\frac{14}{2}\\
h=-9\\
k=-7
\end{cases}\implies \cfrac{[x-(-9)]^2}{15^2}+\cfrac{[y-(-7)]^2}{7^2}=1
\\\\\\
\cfrac{(x+9)^2}{225}+\cfrac{(y+7)^2}{49}=1
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Thank you for anyone who knows this
katen-ka-za [31]

Answer:  

  • Part (a) Vertex = (-3, -1)
  • Part (b) Vertex = (4, 5)
  • Part (c) function 2; max value = 5

=====================================================

Explanations:

Part (a)

In this case, the vertex is the highest point, so the vertex of function 1 is (-3, -1)

If the parabola was flipped so that it opened upward, instead of downward, then the vertex would be the lowest point.

----------------------------

Part (b)

We could graph this function to see where the highest or lowest point is, but there's another way we could find the vertex using algebra.

The given equation is in the form y = ax^2 + bx + c where in this case

  • a = -2
  • b = 16
  • c = -27

The a and b values are plugged into the formula below to get

h = -b/(2a)

h = -16/(2*(-2))

h = -16/(-4)

h = 4

This is the x coordinate the vertex since the vertex is (h,k)

To find k, we plug that value of h into the original function to find its corresponding y value.

y = -2x^2 + 16x - 27

y = -2(4)^2 + 16(4) - 27

y = -2(16) + 16(4) - 27

y = -32 + 64 - 27

y = 5

We found that h = 4 leads to k = 5. The vertex is (h,k) = (4, 5)

----------------------------

Part (c)

We'll compare the y values of each vertex

  • Function 1 has a vertex of (-3, 1)
  • Function 2 has a vertex of (4, 5)

The vertex with the larger y value is the winner, so that would be function 2. This parabola reaches a higher peak compared to the other curve.

The max value here is y = 5. In other words, it's the maximum output the function can produce.

If you graphed functions 1 and 2 together on the same xy grid (see below), you'll see that the curve for function 2 reaches a higher peak.

7 0
2 years ago
I/3 is equivalent to
IgorC [24]
2/6, 3/9, 4/12, 5/15, 6/18 ect.
Hope this helped!
5 0
3 years ago
Can someone please help explain 3/24 = 33/?
sweet [91]

Answer:

264

Step-by-step explanation:

because 33 is 11 times 3 so you multiply the 24x11 equal 264

33/264

8 0
2 years ago
Read 2 more answers
24 x 12 1/2 x 12 3/4 what is the volume of the fish tank
hjlf

Answer:

The volume is 3825 cubic units

Step-by-step explanation:

To find the volume of the fish tank multiply out the dimensions.

We were given the dimensions as:

24 \times 12 \frac{1}{2}  \times 12 \frac{3}{4}

Change the numbers to improper fractions

24 \times  \frac{25}{2}  \times \frac{51}{4}

We cancel out to get

3 \times 25 \times 51

3825

5 0
3 years ago
Suppose m = 2 + 6i, and | m + n | = 3√10, where n is a complex number.
Ksju [112]

Answer: a) √50

b) n = 1 + 7i

Step-by-step explanation:

first, the modulus of a complex number z = a + bi is

IzI = √(a^2 + b^2)  

The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:

m = 2 + 6i

n = a  + bi

Im + nI = 3√10

Im + n I = √(a^2 + b^2 + 2^2 + 6^2)= 3√10

            = √(a^2 + b^2 + 40) = 3√10

             a^2 + b^2 + 40 = 3^2*10 = 9*10 = 90

             a^2 + b^2 = 90 - 40 = 50

            √(a^2 + b^2 ) = InI = √50

The modulus of n must be equal to the square root of 50.

now we can find any values a and b such a^2 + b^2 = 50.

for example, a = 1 and b = 7

1^2 + 7^2 = 1 + 49  = 50

Then a possible value for n is:

n = 1 + 7i

6 0
3 years ago
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