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sergeinik [125]
3 years ago
9

Find the equation of the parabola with its focus at (5,0) and it’s directrix y=2

Mathematics
1 answer:
Verizon [17]3 years ago
3 0

Answer:

Option A

Step-by-step explanation:

From the question given in the picture attached,

Directrix of the parabola → y = 2

Focus of the parabola → (-5, 0)

Since, focus is below the directrix, parabola will open open downwards.

Equation of the parabola will be in the form of,

y - k = -4p(x - h)²

Here, (h, k) is the vertex of the parabola

p = Distance between vertex and focus or distance between vertex and directrix

Since, distance between vertex and focus = Distance between vertex and directrix

Therefore, vertex of the parabola → (-5, 1)

Now distance (p) between vertex (-5, 0) and focus (-5, 1) = 1 unit

By substituting these values in the equation,

y - 1 = -4(1)[x - (-5)]²

y - 1 = -4(x + 5)²

y = -4(x + 5)² + 1

Option A will be the answer.

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Kryger [21]

Area = Length x width.

Area of room = 15 x 24 = 360 square feet.

Now multiply the square feet by the cost:

360 x 5 = $1800

It will cost $1,800

8 0
3 years ago
Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist
yuradex [85]

Answer:

0 < t < 5 is the required interval for the differential equation (t - 5)y' + (ln t)y = 6t to have a solution.

Step-by-step explanation:

Given the differential equation

(t - 5)y' + (ln t)y = 6t

and the condition y(1) = 6

We can rewrite the differential equation by dividing it by (t - 5) as

y' + [(ln t)/(t - 5)]y = 6t/(t - 5)

(ln t)/(t - 5) is continuous on the interval (0, 5) and (5, +infinity).

6t/(t - 5) is continuous on (-infinity, 5) and (5, +infinity)

We see that for these expressions, we have continuity at the intervals (0, 5) and (5, +infinity).

But the initial condition is y = 6, when t = 1.

The solution to differential equation is certain to exist at (0, 5)

Which implies that

0 < t < 5

is the required interval.

3 0
3 years ago
The Nut Shoppe sells walnuts for $4.00 a pound and cashews for $7.00 a pound. How many pounds of cashews should be mixed with 10
Anton [14]

Answer: He sold 10 pounds of cashews .

Step-by-step explanation:

Since we have given that

Selling price of walnuts = $4.00 a pound

Selling price of cashews = $7.00 a pound

Number of pounds of walnuts = 10

Let number of pounds of cashew be x

Total price at which he sold a mixture = $5.50

According to question,

10\times 4+x\times 7=(10+x)\times 5.50\\\\40+7x=55+5.5x\\\\7x-5.5x=55-40\\\\1.5x=15\\\\x=\frac{15}{1.5}\\\\x=10

Hence, he sold 10 pounds of cashews .

7 0
3 years ago
In each diagram, abc is a straight line. Find the unknown angles.
aleksandr82 [10.1K]

Answer:

The value of ∠b = 180°

Step-by-step explanation:

Given that;

ABC is a straight line

Another angle is 137°

Find:

The value of ∠a

The value of ∠b

Computation:

We know that, ABC is a straight line

So,

137 + The value of ∠a = 180

The value of ∠a = 180 - 137

The value of ∠a = 43°

The value of ∠b = 360 - 137 - The value of ∠a

The value of ∠b = 360 - 137 - 43

The value of ∠b = 180°

6 0
3 years ago
One of the exterior angles of a triangle is 120° and the
Sidana [21]

Answer:

the angles are 80 degrees and 40 degrees

Step-by-step explanation:

The sum of two opposite interior angles equal to the exterior opposite angle.

so;

4x + 2x = 120

x = 120 / 6

x = 20

4x = 80

2x = 40

8 0
3 years ago
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