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likoan [24]
3 years ago
10

Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4

Mathematics
1 answer:
Ierofanga [76]3 years ago
7 0
We are given with the focus coordinates of (0,-4) and a directrix equation of y=4,. we are asked for the equation of the parabola. The vertex of the parabola should lie in between the directrix and the focus. Hence, vertex should be at (0,0). the curve goes downwards. and the length of the latus rectum is 4. Hence the equation is x2=-16y
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Find the difference. Enter your answer in lowest terms in the box below as a
lara [203]

Answer:

  76/165

Step-by-step explanation:

The difference of fractions can be found using the formula ...

  a/b -c/d = (ad -bc)/(bd)

<h3>Difference</h3>

Using the given values in the formula, we have ...

  \dfrac{8}{11}-\dfrac{4}{15}=\dfrac{8(15)-11(4)}{11\cdot15}=\dfrac{120-44}{165}=\boxed{\dfrac{76}{165}}

Here, the difference fraction does not need to be reduced. Many calculators and spreadsheets can do this arithmetic for you.

The above formula can also be used for sums of fractions. In that case, the sign changes from minus to plus.

7 0
2 years ago
What is the x-intercept of the following line with this equation -2x+1/2y=18 plz for math
tensa zangetsu [6.8K]

The answer is -9 im sure!

5 0
3 years ago
Which of the following is the equation of a line that passes through (-2,1) and (-4,-3)?
stich3 [128]

Answer:

The equation is y= 2x+5

Step-by-step explanation:

Lets find the slope of the line through the points (-2,1) and (-4,-3).

where x1 = -2,  y1= 1,  x2= -4,  y2 = -3.

Now apply slope formula:

m= y2-y1/ x2-x1

m= -3-1/-4-(-2)

m = -4/-4+2

m= -4/-2

Divide the term by 2:

m = 2

Now we will apply point slope formula:

y-y1 = m (x-x1)

Now substitute the values in the formula:

y-1=2(x-(-2))

y-1 =2(x+2)

y-1=2x+4

Now combine the constants:

y= 2x+4+1

y=2x+5

So the equation is y= 2x+5 ....

3 0
4 years ago
What is the unit ratio for a button of 16 grams and 2 milliliters?
Reika [66]

Answer:

The unit ratio would be 8 grams per milliliters

Step-by-step explanation:

Since, the unit ratio is a fraction with denominator 1,

In other words, the amount of one quantity in unit amount of other quantity is called unit rate or unit ratio.

Here, the amount first quantity = 16 grams,

The amount of second quantity = 2 milliliters,

Thus, unit ratio = \frac{\text{First quantity}}{\text{Second quantity }}

=\frac{16}{2} = 8 grams per milliliters

6 0
3 years ago
The USDA pays schools for each lunch served. As of the 2014–15 school year, it paid $2.98 for each free lunch,
Anestetic [448]

Answer:

$32.80

Step-by-step explanation:

For this case we have that the total daily protein consumption is given by:

Now, we find the percentage corresponding to breakfast:

53g ---------> 100%

17g -----------> x

Where "x" represents the percentage of protein equivalent to breakfast:

Thus, at breakfast approximately 32.08% of the total protein should be consumed.

6 0
3 years ago
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