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Phantasy [73]
2 years ago
10

The length of a rectangle is the sum of the width and 3. The area of the rectangle is 54 units. What is the width, in units, of

the rectangle?
Mathematics
1 answer:
zimovet [89]2 years ago
8 0

Answer:

Let a be the width and b the length

a+3=b

a*b=54

a(a+3)=54

a^2+3a-54=0

a=6

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An oil tank is leaking into a lake at a rate of 0.1 m3/day. The oil slick forms a semicircular disk whose center is at the leak
gregori [183]

Answer:

17.9  m/s

Step-by-step explanation:

Volume of the slick =  0.5 x π r² h--------------------------------- (1)

Where r = radius of slick

           h = thickness of slick, 10⁻⁶m

If 0.5m³ of oil leaked, then the radius of the semicircular slick can be calculated from equation (1)

V  =  0.5 x π r² h

0.5=  0.5 x  π x  r² x 10⁻⁶

r²   =  10⁶/ π

r =     10³/√π

dV/dt =   πrh dr/dt  + 0.5π r² dh/dt----------------------------------- (2)

Asumming the film thickness is constant , equation (2) becomes

dV/dt =   πrh dr/dt-------------------------------- (3)

dV/dt = 0.1m³/day

r=  10³/√π

dr/dt= rate of expansion of the slick

Substituting  into (3);

0.1 =  π x 10³/√π x 10⁻⁶ x dr/dt

dr/dt = 0.1  x 10⁶/ ( π x 10³/√π)

       =  17.9479 m/s

       ≅  17.9  m/s

8 0
3 years ago
What is a positive angle less than 360 degrees that is conterminal with 540 degrees
jekas [21]

Answer:

Please check the explanation.

Step-by-step explanation:

As we have to determine a positive angle less than 360 degrees that is conterminal with 540 degrees.

so

  • Subtract 360° from 540°

540° - 360° = 180°

The resulting angle of 180° is positive, less than 360°, and coterminal with 540°.

7 0
2 years ago
Sixty-five campers arrive. Nine go home early. If 8 people sleep in 1 tent, how many tents will the campers need?
allsm [11]

65-9=56

56 divided by 8 is 7

So they will need 7 tents

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3 years ago
A triangle is graphed in the coordinate plane. The vertices of the triangle have coordinates (–3, 1), (1, 1), and (1, –2). What
vladimir2022 [97]

Answer:

The perimeter of the triangle is 12\ units

Step-by-step explanation:

Let

A(-3,1),B(1,1),C(1,-2)

we know that

The perimeter of triangle is equal to

P=AB+BC+AC

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

step 1

Find the distance AB

A(-3,1),B(1,1)

substitute in the formula

AB=\sqrt{(1-1)^{2}+(1+3)^{2}}

AB=\sqrt{(0)^{2}+(4)^{2}}

AB=4\ units

step 2

Find the distance BC

B(1,1),C(1,-2)

substitute in the formula

BC=\sqrt{(-2-1)^{2}+(1-1)^{2}}

BC=\sqrt{(-3)^{2}+(0)^{2}}

BC=3\ units

step 3

Find the distance AC

A(-3,1),C(1,-2)

substitute in the formula

AC=\sqrt{(-2-1)^{2}+(1+3)^{2}}

AC=\sqrt{(-3)^{2}+(4)^{2}}

AC=5\ units

step 4

Find the perimeter

P=AB+BC+AC

substitute the values

P=4+3+5=12\ units

6 0
3 years ago
Rewrite -15 - -8 as a sum of 2 addends
barxatty [35]

Answer:

-3+-4

Step-by-step explanation:

3 0
2 years ago
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