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1 year ago

Write the equation in vertex form for the parabola with focus (7, –27/4) and directrix y= – 13/4

Mathematics

1 answer:

Nataliya [291]1 year ago

7 0

Answer:

x2 +8x +4y +4 = 0

4y= -x2 -8x -4y = -.25*x^2 -2x -1

a = -.25b = -2c = -1

x position of vertex:

h = -b / 2a

h = 2 / 2*-.25h = 2 / -.5h = -4

y position of vertex:

k = ah^2 + bh + ck = -.25*-4^2 + -2*-4 + -1k = -4 +8 -1k = 3

VERTEX = (-4, 3)*

x value of focus =x value of vertex = -4

y value of focus =(1 (-b^2 -4ac)) / 4a

a = -.25 b = -2 c =-1

y value = (1 (-4 -4*-.25*-1)) / 4*-.25

y value = (1 (-4 -4*-.25*-1)) / -1

y value = (1 -4 +1) / -1y value = (-2 / -1)y value = 2

focus value = (-4, 2)

Answer is the last one.

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2 years ago

Given that 1 x2 dx 0 = 1 3 , use this fact and the properties of integrals to evaluate 1 (4 − 6x2) dx. 0

Debora [2.8K]

So, the definite integral $\int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74$

Given that

$\int\limits^1_0 {x^{2} } \, dx = 13$

We find

$\int\limits^1_0 {(4 - 6x^{2} )} \, dx$

<h3>Definite integrals </h3>

Definite integrals are integral values that are obtained by integrating a function between two values.

So, $Integral \int\limits^1_0 {(4 - 6x^{2} )} \, dx$

So, $\int\limits^1_0 {(4 - 6x^{2} )} \, dx = \int\limits^1_0 {4} \, dx - \int\limits^1_0 {6x^{2} } \, dx \\= 4[x]^{1}_{0} - \int\limits^1_0 {6x^{2} } \, dx \\= 4[x]^{1}_{0} - 6\int\limits^1_0 {x^{2} } \, dx \\= 4[1 - 0] - 6\int\limits^1_0 {x^{2} } \, dx\\= 4[1] - 6\int\limits^1_0 {x^{2} } \, dx\\= 4 - 6\int\limits^1_0 {x^{2} } \, dx$

Since

$\int\limits^1_0 {x^{2} } \, dx = 13$ ,

Substituting this into the equation the equation, we have

$\int\limits^1_0 {(4 - 6x^{2} )} \, dx = 4 - 6\int\limits^1_0 {x^{2} } \, dx\\= 4 - 6 X 13 \\= 4 - 78\\= -74$

So, $\int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74$

Learn more about definite integrals here:

brainly.com/question/17074932

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2 years ago

It takes a computer 1.2 seconds to perform an operation. If a task contains eight operations how many seconds will it take for c

serg [7]

Answer:

19.2 seconds

Step-by-step explanation:

1.2 times 8 which equals 9.6

9.6 times 2

7 0

2 years ago

Read 2 more answers

2+4z-18 slove step by step

Marianna [84]

2+4z-18
change it so it's an equation
2+4z-18=0
then get 4z alone on one side by subtracting 4z from both sides
2-18=-4z
-16= -4z
divide both sides by -4

a negative divided by a negative becomes positive
4 =z
plug it in
2+4(4)-18
4x4 is 16
2+16-18=0
0=0

the same can be done for the second one 2+k-8

make it 2+k-8=0

move the k to get it alone so subtract k from both sides

2-8=-1k

-6 = -1K

you can divide by K to make K=6

plug in 2+6-8=0

0=0

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2 years ago

48% of the children in a summer camp are boys. If there are 1536 boys, how many children are there in the summer camp?

Ket [755]

Answer:

3200

Step-by-step explanation:

1536/48 = 32

32x100 = 3200

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2 years ago