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Lesechka [4]
3 years ago
15

(04.04 MC)

Mathematics
1 answer:
sp2606 [1]3 years ago
5 0

Answer:

y = x^2/ 60 + 15

=>( x - h)^2 = 4a[ (x^2/6 + 15) - k ].

Step-by-step explanation:

Okay, in order to solve this question very well, one thing we must keep at the back of our mind is that the representation for the equation of a parabola is given as ; y = ax^2 + bx + c.

That is to say; y = ax^2 + bx + c is the equation for a parabola. So, we should be expecting our answer to be in this form.

So, from the question above we are given that "the satellite dish will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground"

We will make an assumption that the point on the ground is (0,0) and the focus is (0,30). Thus, the vertex (h,k) = (0,15).

The equation that best describes the equation of the satellite is given as;

(x - h)^2 = 4a( y - k). ------------------------(1).

[Note that if (h,k) = (0,15), then, a = 15].

Hence, (x - 0)^2 = (4 × 15) (y - 15).

x^2 = 60(y - 15).

x^2 = 60y - 900.

60y = x^2 + 900.

y = x^2/ 60 + 15.

Hence, we will have;

(x - h)^2 = 4a[ (x^2/6 + 15) - k ].

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Firdavs [7]

Answer:

Emma spend 8 hours in homework in a week and Jared  spends 16 hours in homework in 2 weeks.

Step-by-step explanation:

Two quantities P and Q are said to be in PROPORTION if and only if for all values of P and q, we get:

\frac{P}{Q}  = k

Here, k : PROPORTIONALITY CONSTANT

Case: 1

5 hour piano practice in 1 week.

So, the piano practice in 2 weeks( 1 x 2) =   2 x  5 = 10 hours

But here, it is given to be 12 hours in 2 weeks.

Hence, NOT PROPORTIONAL.

Case 2:

70 words in 60 seconds.

So, the words typed in 210 seconds ( 60 x 3.5) =   70  x  3.5 = 240 words

But here, it is given to be 280 words in 210 seconds.

Hence, NOT PROPORTIONAL.

Case: 3

8 hour homework in 1 week.

So, the homework done in 2 weeks( 1 x 2) =   2 x 8 = 16 hours

It is given to be 16 hours in 2 weeks.

Hence,  PROPORTIONAL.

Case: 4

15 miles  in 78 minutes.

So, the distance covered in 102 minutes (78 x 1.3) =  15 x 1.3 = 19.6 miles

But here, it is given to be 17 miles in 102 minutes.

Hence, NOT PROPORTIONAL.

Case: 5

18 miles  in 45 minutes.

So, the distance covered in 55 minutes (45 x 1.2) =  18 x 1.2  = 21.6 miles

But here, it is given to be 22 miles in 55 minutes.

Hence, NOT PROPORTIONAL.

Hence, the only proportional case is Emma spend 8 hours in homework in a  week and Jared  spends 16 hours in homework in 2 weeks.

6 0
3 years ago
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Answer:

Yes

Step-by-step explanation:

A function is a relation where each input has only one output

The table shown follows this, each input has only one output, therefore it is a function.

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Answer:

What kind of problem?

Step-by-step explanation:

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Enter the correct 9 letter sequence (no space) use all capital letters
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Answer:

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3 years ago
7. The probability that a randomly chosen student will be left-handed is .09: a) In a class of 108, find the probability that th
vampirchik [111]

Solution :

Let x be student will be left handed

P = 0.09

Using the normal approximation to binomial distribution,

a). n = 108,

    μ = np = 9.72

    $\sigma = \sqrt{np(1-p)}$

       $=\sqrt{8.8452}$

       = 2.9741

Required probability,

P(x=8) = P(7.5 < x < 8.5)

$=P\left(\frac{7.5-9.72}{2.9741}< \frac{x-\mu}{\sigma}< \frac{8.5-9.72}{2.9741}\right)$

$=P(-0.75 < z < -0.41)$

Using z table,

= P(z<-0.41)-P(z<-0.75)

= 0.3409-0.2266

= 0.1143

b). P(x=12) = P(11.5 < x < 12.5)

$=P\left(\frac{11.5-9.72}{2.9741}< \frac{x-\mu}{\sigma}< \frac{12.5-9.72}{2.9741}\right)$

$=P(0.60 < z < 0.94)$

Using z table,

= P(z< 0.94)-P(z< 0.60)

= 0.8294 - 0.7257

= 0.1006

7 0
3 years ago
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