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ahrayia [7]
1 year ago
5

Please answer! It is due in 20 min.

Mathematics
1 answer:
White raven [17]1 year ago
4 0

Answer:

33

Step-by-step explanation:

90-57=?

57+?=90

57+33=90

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3 years ago
How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y
son4ous [18]

Solution:

Given:

x^2=6y

Part A:

The vertex of an up-down facing parabola of the form;

\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}

Rewriting the equation given;

\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\  \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\  \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\  \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\  \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}

Therefore, the focus is;

(0,\frac{3}{2})

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}

Therefore, the directrix is;

y=-\frac{3}{2}

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11 months ago
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kirill115 [55]

Answer:

mujhe teri byatha ss.jh nhi aarhu hai toh me nhi kar series

Step-by-step explanation:

om

3 0
2 years ago
Find the length of the base of a square pyramid if the volume is 128 cubic inches and has a height of 6 inches
Len [333]

Answer: a = 8

Step-by-step explanation:

Volume of a square based pyramid is given as

\frac{a^{2}h }{3} .

where a is the length of the side and h is the height.

Substituting into the formula , we have

V = \frac{a^{2}h }{3}

128 = a^{2}h /3

384= a^{2} X 6

Divide through by 6

384/6 = a^{2}

64 = a^{2}

Therefore :

a = \sqrt{\frac{64}{1} }

a = 8

6 0
3 years ago
Elevator is on the 16th floor. It goes up 12 floors, down 7 floors, up 3 floors, and then down 5
seropon [69]

Answer:

The elevator stops on the 19th floor.

Step-by-step explanation:

On the 16th floor, goes up 12 floors:

16 + 12 = 28

On the 28th floor, goes down 7 floors:

28 - 7 = 21

On the 21st floor, does up 3 floors:

21 + 3 = 24

On the 24th floor, goes down 5 floors:

24 - 5 = 19

6 0
3 years ago
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