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3 years ago

Find the area of shaded part .

Mathematics

1 answer:

Firlakuza [10]3 years ago

5 0

Answer:

Area of big rectangle= 5m× 3m

= 15m²

Area of small rectangle=1m× 1m

=1m²

Area of shaded part= Area of big rectangle- Area of a small rectangle

= 15m²-1m²

= 14m²

Step-by-step explanation: Hope it helps

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A carnival game awards a prize if Kasey can shoot a basket. The charge is $5.00 for the first shot, then $2.00 for each addition

nydimaria [60]

Answer:

its $25 if he completes all 11 shots

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2 years ago

Read 2 more answers

Water is leaking out of a large barrel at a rate proportional to the square rooot of the depth of the water at that time. If the

sdas [7]

Answer:

It will take about 35.49 hours for the water to leak out of the barrel.

Step-by-step explanation:

Let $y(t)$ be the depth of water in the barrel at time $t$ , where $y$ is measured in inches and $t$ in hours.

We know that water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. We then have that

$\frac{dy}{dt}=-k\sqrt{y}$

where $k$ is a constant of proportionality.

Separation of variables is a common method for solving differential equations. To solve the above differential equation you must:

Multiply by $\frac{1}{\sqrt{y}}$

$\frac{1}{\sqrt{y}}\frac{dy}{dt}=-k$

Multiply by $dt$

$\frac{1}{\sqrt{y}}\cdot dy=-k\cdot dt$

Take integral

$\int \frac{1}{\sqrt{y}}\cdot dy=\int-k\cdot dt$

Integrate

$2\sqrt{y}=-kt+C$

Isolate $y$

$y(t)=(\frac{C}{2} -\frac{k}{2}t)^2$

We know that the water level starts at 36, this means $y(0)=36$ . We use this information to find the value of $C$ .

$36=(\frac{C}{2} -\frac{k}{2}(0))^2\\C=12$

$y(t)=(\frac{12}{2} -\frac{k}{2}t)^2\\\\y(t)=(6 -\frac{k}{2}t)^2$

At t = 1, y = 34

$34=(6 -\frac{k}{2}(1))^2\\k=12-2\sqrt{34}$

So our formula for the depth of water in the barrel is

$y(t)=(6 -\frac{12-2\sqrt{34}}{2}t)^2\\\\y(t)=\left(6-\left(6-\sqrt{34}\right)t\right)^2\\$

To find the time, $t$ , at which all the water leaks out of the barrel, we solve the equation

$\left(6-\left(6-\sqrt{34}\right)t\right)^2=0\\\\t=3\left(6+\sqrt{34}\right)\approx 35.49$

Thus, it will take about 35.49 hours for the water to leak out of the barrel.

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3 years ago

At what point is the following function continuous?

liubo4ka [24]

Check the picture below.

something worth noticing $\bf \cfrac{x^2-x-6}{x-3}\implies \cfrac{(\underline{x-3})(x+2)}{\underline{x-3}}\implies x+2$

so, we're really graphing x+2, with a hole at x = 3, however, when x = 3, we know that f(x) = 5, but but but, when x = 3, x+2 = 5, so we end up with a continuous line all the way, x ∈ ℝ, because the "hole" from the first subfunction, gets closed off by the second subfunction in the piece-wise.

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3 years ago

What is the product of −3 1/4 and −1 1/2 ? Enter your answer as a mixed number, in simplified form, in the box.

EastWind [94]

Hi DerpyIntelligence!
The product is addition so we do -3 1/4+-1 1/2. We solve it like this. We separate each part like this (-3)+(-1/4)+(-1)+(-1/2) then we solve the whole parts (-3)+(-1)=(-4). Next we find out the LCD of (-1/4) and (-1/2) which is 4 so we change (-1/2) to (-2/4) than we add (-1/4) which is (-3/4). Finally we add the wholes to the fractions (-4)+(-3/4)=(-4 3/4)
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2 years ago

Read 2 more answers

What multiplies to -900 and adds to 5?

liq [111]

Xy = -900
x + y = 5

x + y = 5
x - x + y = -x + 5
y = -x + 5

xy = -900
x(-x + 5) = -900
  x(-x) + x(5) = -900
-x² + 5x = -900
-x² + 5x + 900 = 0
-1(x²) - 1(-5x) - 1(-900) = 0
  -1(x² - 5x - 900) = 0
-1 -1
x² - 5x - 900 = 0
x = -(-5) ± √((-5)² - 4(1)(-900))
  2(1)
x = 5 ± √(25 + 3600)
2
x = 5 ± √(3625)
2
x = 5 ± 5√(145)
2
x = 2.5 ± 2.5√(145)

  x + y = 5
2.5 ± 2.5 √(145) + y = 5
- (2.5 ± 2.5√(145) - (2.5 ± 2.5√(145)
y = 2.5 ± 2.5√(145)
  (x, y) = (2.5 ± 2.5√(145), 2.5 ± 2.5√(145))

The two numbers that add up to 5 and multiply to -900 are 2.5 ± 2.5√(145).

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3 years ago

Find the area of shaded part .​

Find the area of shaded part .