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3 years ago

What are the coordinates of the point (-1,9) after a clockwise rotation of 90 degree about the origin

Mathematics

1 answer:

Elina [12.6K]3 years ago

7 0

The rule for clockwise rotation of 90 degrees about the origin is (-y, x).

So (-1,9) would now be (-9,1).

Hope this Helps!!

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Find angle A in the following triangle. <br><br> A. 35.54 <br> B. 35.67<br> C. 36.24<br> D. 36.77

BartSMP [9]

Tan(Angle) = Opposite leg / Adjacent leg

Tan(A) = 5/7

A = Arctan(5/7)

A = 35.54 degrees.

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3 years ago

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In a large apartment building, 35 of the apartments have a balcony and 55 do not. An apartment us randomly selected as part of a

Vadim26 [7]

11/18 probability

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Ava and Kelly ran a road race, starting from the same place at the same time. Ava ran at an average speed of 6 miles per hour. K

zalisa [80]

<h2>Hello!</h2>

The answer is:

It will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.

To calculate how long after they start they will be 3/4 miles apart, we need to write two equations.

So, writing the equations, we have:

Calculations for Ava:

We have the following information,

$v_{Ava}=6mph$

Then, writing the equation,

$x_{Ava}=x_{o}+v_{Ava}*t$

$x_{Ava}=x_{o}+v_{6mph}*t$

Calculations for Kelly:

We have the following information,

$v_{Kelly}=8mph$

We need to calculate when Kelly will be 3/4 miles apart of Ava, so, it's position will be the Ava's position plus 3/4 miles.

Then, writing the equation,

$x_{Ava}+0.75miles=x_{o}+v_{Kelly}*t$

$x_{Ava}+0.75miles=x_{o}+v_{8mph}*t$

Now, substituting Ava's speed into the second equation, we have:

$x_{o}+6mph*t+0.75miles=x_{o}+8mph*t$

$6mph*t+0.75miles=+8mph*t$

$8mph*t-6mph*t=0.75miles$

$2mph*t=0.75miles$

$t=\frac{0.75miles}{2mph}=0.375hours$

Hence, we have that it will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.

Have a nice day!

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3 years ago

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Verify that P = Ce^t /1 + Ce^t is a one-parameter family of solutions to the differential equation dP dt = P(1 − P).

NemiM [27]

Answer:

See verification below

Step-by-step explanation:

We can differentiate P(t) respect to t with usual rules (quotient, exponential, and sum) and rearrange the result. First, note that

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Now, differentiate to obtain

$\frac{dP}{dt}=(\frac{ce^t}{1+ce^t})'=\frac{(ce^t)'(1+ce^t)-(ce^t)(1+ce^t)'}{(1+ce^t)^2}$

$=\frac{(ce^t)(1+ce^t)-(ce^t)(ce^t)}{(1+ce^t)^2}=\frac{ce^t+ce^{2t}-ce^{2t}}{(1+ce^t)^2}=\frac{ce^t}{(1+ce^t)^2}$

To obtain the required form, extract a factor in both the numerator and denominator:

$\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)$

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mr_godi [17]

Answer:

since its made from cast iron or aluminium or stainless steel it's a conductor

Step-by-step explanation:

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3 years ago