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kaheart [24]
3 years ago
15

A dish tv satellite dish is the shape of a paraboloid. the dish is 36 inches wide, and 8 inches deep. how many inches should the

receiver be located from the vertex for optimal reception? (round to the nearest thousandth)

Mathematics
1 answer:
MrRa [10]3 years ago
4 0
Refer to the diagram shown below. It shows a vertical cross-section of the paraboloid through its axis of symmetry.

Let the vertex of the parabola be at the origin. Then its equation is of the form
y = bx²

Because the parabola passes through (18,8), therefore
8 = b(18²)
b = 0.02469
The parabola is y = 0.02469x².

The receiver should be placed at the focal point of the paraboloid for optimal reception.
The y-coordinate of the focus is
a = 1/(4b) = 1/0.098765 = 10.125 in

Answer: The receiver is located at 10.125 inches from the vertex.

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Evaluate this expression for the given value of the variable 4 (d+7);d=-2
Paha777 [63]

Exact Form:

d

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d

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Decimal Form:

d

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0.07217269

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6.92782730

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6 0
3 years ago
Read 2 more answers
The volume V of a gas varies inversely as the pressure P and directly as the temperature A certain gas has a volume of 10 liters
Ad libitum [116K]

Answer:

Joint variation states that:

If z is directly proportional to x and inversely proportional to y,

i.e, z \propto x , z \propto \frac{1}{y}

then the equation is in the form: z = k\frac{x}{y} where k is the constant of variation.

From the given information: The volume V of a gas varies inversely as the pressure P and directly as the temperature

i.,e V \propto T , V \propto \frac{1}{P}

by definition of joint variation:

V = k\frac{T}{P}  .....[1] where k is the constant of variation.

It is also given that a certain gas has a volume of 10 liters(L) , a temperature of 300 kelvins(K), and a pressure of 1.5 atmosphere(atm).

Substitute these given values in [1] to solve for k;

10 = k\frac{300}{1.5}

Simplify:

10 = 200k

Divide by 200 both sides we have;

k = \frac{10}{200} =\frac{1}{20}

Now, if a gas has a temperature of 400 kelvins and a pressure of 5 atm.

To find the volume (V);

Now substitute the given data and value of k in [1] we have;

V = \frac{1}{20} \cdot \frac{400}{5} = \frac{20}{5} = 4

Therefore, the Volume of a gas is, 4 liters


5 0
3 years ago
???????????????????????????????????????????????????????????????????????????????????
Mashcka [7]

Answer:

607.75 cm3

Step-by-step explanation:

v = L*w*h

8.5 * 5.5 * 13 = 607.75

607.75 cm3

7 0
2 years ago
Read 2 more answers
Consider the graph that represents the following quadratic equation y=-1/3(x+2)^2+5
makkiz [27]
We have that
<span>y=-1/3(x+2)</span>²<span>+5

using a graph tool
see the attached figure

we know that
1) the graph open downward
2) the vertex of the graphic is the point (-2,5)
3) the axis of symmetry of the graph is x=-2
4) the x intercept values are (-5.873,0)  and (1.873,0)
5) the y intercept value is (0,3.667)
</span><span>
</span>

7 0
3 years ago
The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a. Find the pro
Bogdan [553]

Answer:

Step-by-step explanation:

Let X be the length of pregnancy.

X is N(268, 15)

a) Prob of pregnancy lasting 307 days or longer

= P(X>307) = P(Z>\frac{307-268}{15} )\\=P(Z>2.6)\\

=0.5-0.4953

=0.0047

b) Lowest 2% is 2nd percentile

Z=-2.55

X score = 268-2.55(15)

= 229.75 days

If length of days >230 days then it is not premature.

4 0
3 years ago
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