Prove the diagonals of a parallelogram bisect one another. Be sure to create and name the appropriate geometric figures.

A dolphin is 42 feet underwater and ascends at a constant rate for 14 seconds until it reaches the surface. Identify and interpr

Cloud [144]

Ok so, based on the graph lets say that x = seconds and y = depth of dolphin. the interception in both points is when they are at 0 i.e when x is equals 0 and y equals 0. So At 0 seconds, the dolphin is 42 feet below the surface. So we say that x = 0, y = -42 and then the y intercepts = -42 so the point of interception is(0 (seconds),-42(depth of the dolphin)) When the clock says it's 14 seconds, the dolphin is even with the surface (0 below the surface this time). So we say that x = 14, y = 0. In this case The x intercept = 14 (14,0). But we need to calculate The slope with the formula= (y2 - y1)/(x2 - x1) = 42/14 = 3. Therefore, the formula for this line is y = 3x - 42.

3 0

2 years ago

Marginal cost At a certain factory the marginal cost is 3(q-4)^2 dollars per unit when the level of production is q units.

viktelen [127]

Answer:

a.) C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH b.) $170

Step-by-step explanation:

(a) Marginal cost is defined as the decrease or increase in total production cost if output is increased by one more unit. Mathematically:

Marginal cost (MC) = change in total cost/change in quantity

Therefore, to derive the equation for total production cost, we need to integrate the equation of marginal cost with respect to quantity. Thus:

Total cost (C) = Integral [3(q-4)^2] dq = -(1/4)*(q-4)^3 + k

where k is a constant.

The overhead (OH) = C(0) = -(1/4)*(0-4)^3 + k = -16 + k

C(q) = -(1/4)*(q^3 - 12q^2 + 48q - 64) + k = -(1/4)*q^3 + 3q^2 - 12q -16 + k

Thus:

C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH

(b) C(14) = -(1/4)*14^3 + 3*14^2 - 12*14 + 436 = -686 + 588 - 168 + 436 = $170

7 0

1 year ago

The sum of Orion and Sagan’s age is 24, and the difference between their ages is 6. Find their ages given that Orion is older th

Katarina [22]

Let's say that Sagan's age is x and Orion is x + 6 (since Sagan is younger by 6 years).

We know that Orion's age + Sagan's age is 24, so x + x + 6 is 24

2x = 18

x = 9

That means that Sagan is 9, and Orion is 9+6 or 15.

6 0

1 year ago

A 3 kg toy car rests st the top of a 0.45 meter ramp. What is its gravitational potential energy?

salantis [7]

<span>gravitational potential energy : P
Gravity : g
Mass : m
height : h

P = mgh = 3 x 9.8 x 0.45 = 13.23 Joule

Potential energy is work , from the known formula

W = Fd ( work = force x distance )

W = P ( in case of potential energy height change)

F is the force acting on the body in case of ideal ramp , the only force acting is the weight of the body

F = mg ( not just <m> as the force is mg (Newton) gravity effect)

d is the displacement in direction of force, as we have considered the force to be the weight not it's component in direction of the ramp , the change in displacement is the change in height so

d = h

W = Fd = (F = mg) x (d = h) = mgh

W = mgh = P

</span>

7 0

2 years ago

Which is one reason why this expression is equal to 0 -3.08+3.08/3.08•4.66

Eduardwww [97]

Step-by-step explanation:

it is equal to zero because n/m where n is the numerator and m is the denominator.

any number where the numerator is zero, the answer will be zero. Zero divided by any number is zero.

For -3.08+3.08=0, and since it is part of the numerator it becomes 0/3.08•4.66 which equals to 0

4 0

1 year ago

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