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3 years ago

A den has a circular rug. According to the tag, the rug has an area of 3.14 square meters.

Mathematics

1 answer:

arsen [322]3 years ago

3 0

Answer:

Diameter = 2 m

Radius = 1 m

Area = 3.14 m²

Circumference = 6.28 m

Step-by-step explanation:

✔️Area of the circular rug is already given as 3.14 m²

✔️find radius (r):

Area = πr²

Thus,

Take π as 3.14

3.14*r² = 3.14

Divide both sides by 3.14

r² = 3.14/3.14

r² = 1

find the square root of both sides

r = √1

radius (r) = 1 m

✔️Diameter = 2*r = 2*1 = 2 m

✔️ Circumference = 2πr

r = 1 m

π = 3.14

Thus,

Circumference = 2*3.14*1 = 6.28 m

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Answer:

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3 years ago

What is the answer to the question

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The equation of the parallel line is y = –2x – 11.

Solution:

Given equation of the line is y = –2x – 5.

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Point-slope formula:

$y-y_1=m(x-x_1)$

Substitute the given values in the formula, we get

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4 years ago

If a person takes a prescribed dose of 10 milligrams of Valium, the amount of Valium in that person's bloodstream at any time ca

aleksandr82 [10.1K]

Answer:

(a)8.0mg

(b)36.87 hours

(c)-0.168

Step-by-step explanation:

The amount of Valium in that person's bloodstream at any time can be modeled with the exponential decay function $A ( t ) = 10 e^{ -0.0188 t$ (t in hours)

(a)After 12 Hours

$A ( 12) = 10 e^{ -0.0188*12}\\=7.98\\\approx 8.0 mg $(to the nearest tenth of a milligram)$

(b)If A(t)=5mg

Then:

$5= 10 e^{ -0.0188 t}\\$Divide both sides by 10\\0.5=e^{ -0.0188 t}\\$Take the natural logarithm of both sides\\ln (0.5)=-0.0188 t\\t=ln (0.5) \div (-0.0188)\\$t=36.87 hours (to two decimal places.)$

(c)

$A ( t ) = 10 e^{ -0.0188 t}\\A'(t)=10(-0.0188)e^{ -0.0188 t}\\A'(t)=-0.188e^{ -0.0188 t}\\$At 6 hours, the rate at which the amount of Valium is decaying therefore is:\\A'(6)=-0.188e^{ -0.0188*6}\\$=-0.168 ( to three decimal places)$

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3 years ago

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Tema [17]

1. You have the following quadratic equation and to solve it, you must follow the steps below:

x²+3=9x

2. The form of the equation that you need to apply the quadratic formula, is:

ax²+bx+c=0

3. Then:

x²+3=9x
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4. The quadratic formula is shown below:

x=(-b±√(b^2-4ac))/2a

5. Then, you have:

a=1
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6. When you substitute the values into the quadratic formula, you obtain:

x1=0.34
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