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3 years ago

The point D(2, -5) is rotated 90° counterclockwise around the origin. What are the coordinates of the resulting point, D′?

Mathematics

1 answer:

jeyben [28]3 years ago

8 0

Answer:

D' = (5, 2)

Step-by-step explanation:

Try to join D and the origin using a line. Counterclockwise means in an opposite direction of rotation of the clock hands. So draw another line towards the right which is perpendicular to the previous line to fine the answer. Remember the length of the lines should be equal.

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Delvig [45]

Answer:

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3 years ago

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One afternoon 10 inches of falls in 1 1/4 hours.At this rate how many inches of snow will fall in 1 hour

saul85 [17]

Step-by-step explanation:

The rate of snowfall can be computed as inches of snow per hour.

rate = 10 inches / (1.25 hours).

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3 years ago

Rewrite the statement in mathematical notation. (Let y be the distance from the top of the ladder to the floor, x be the distanc

In-s [12.5K]

Answer:

$\frac{dy}{dt}=\frac{6y}{x}\text{ ft per sec}$

Step-by-step explanation:

Let L be the length of the ladder,

Given,

x = the distance from the base of the ladder to the wall, and t be time.

y = distance from the base of the ladder to the wall,

So, by the Pythagoras theorem,

$L^2 = y^2 + x^2$

$\implies L = \sqrt{y^2 + x^2}$ ,

Differentiating with respect to time (t),

$\frac{dL}{dt}=\frac{d}{dt}(\sqrt{x^2 + y^2})$

$=\frac{1}{2\sqrt{x^2 + y^2}}\frac{d}{dt}(x^2 + y^2)$

$=\frac{1}{2\sqrt{x^2 + y^2}}(2x\frac{dx}{dt}+2y\frac{dy}{dt})$

$=\frac{1}{\sqrt{x^2 +y^2}}(x\frac{dx}{dt}+y\frac{dy}{dt})$

Here,

$\frac{dy}{dt}=-6\text{ ft per sec}$

Also, $\frac{dL}{dt} = 0$ ( Ladder length = constant ),

$\implies \frac{1}{\sqrt{x^2 +y^2}}(x(-6)+y\frac{dy}{dt})=0$

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$y\frac{dy}{dt}=6x$

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3 years ago

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Vlad1618 [11]

Answer:

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3 years ago

On March 1, 2022, Carla Vista Co. acquired real estate, on which it planned to construct a small office building, by paying $79,

const2013 [10]

Answer:

Cost of the land = $90,900

Step-by-step explanation:

Cash Paid for the construction = $79,000

Cost of demolition of the old warehouse = $8,000

Salvage (i.e Proceeds from the salvaged materials) = $1,660

Additional Expenditure before construction began

Attorney's fee = $1,160

Real estate broker's fee = $4,400

Architect's fee = $8,660 ( Note that this will be capitalized to building cost)

Driveways and parking lot = $13,800 ( Note that this is capitalized to land improvements)

Sum of additional expenditure = Attorney's fee + Real estate broker's fee

Sum of the additional expenditure = 1160 + 4400

Sum of the additional expenditure = $5,560

Cost of the land = Cash paid + cost of demolition + Additional expenditure - salvage

Cost of the land = 79000 + 8000 + 5560 - 1660

Cost of the land = $90,900

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