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mr Goodwill [35]
1 year ago
14

Find the area of the shape below.

Mathematics
1 answer:
lawyer [7]1 year ago
4 0

9514 1404 393

Answer:

  164π cm²

Step-by-step explanation:

The area of a circle is given by the formula ...

  A = πr²

The radius (r) is half the diameter (d), so the area of a semicircle in terms of its diameter is ...

  1/2A = (1/2)(π)(d/2)² = (π/8)d²

The given shape is the combination of three (3) semicircles. The smallest has a diameter of 6 cm; the middle-sized one has a diameter of (32 cm -6 cm -8 cm) = 18 cm. The largest has a diameter of 32 cm.

The total area will be ...

  area of largest + area of middle-size - area of smallest

  = (π/8)(32² +18² -6²) = (π/8)(1312) . . . . cm²

The area of the shape is 164π cm².

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If a hospital patient is given 100 milligrams of medicine, which leaves the bloodstream at 14% per hour, how many milligrams of
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Answer:

<em>24.66 mg</em><em> of medicine will be left.</em>

Step-by-step explanation:

The given exponential equation is,

A(t)=ie^{rt}

Where,

A(t) = amount after time t

i = initial amount = 100 mg

r = rate of change = -14% = -0.14 (-ve is taken because the amount is decreasing)

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Putting the values,

A(t)=100e^{-0.14\times 10}

=100e^{-1.4}

=24.66\ mg

3 0
2 years ago
Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two dist
Lera25 [3.4K]

Answer:

Sum = -81

Step-by-step explanation:

See the comment for complete question.

Given

c = 36 ----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

x^2 + ax + 36 = 0

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

x = -\alpha and x = -\beta

Using the above roots, the equation can be represented as:

(x + \alpha)(x + \beta) = 0

Open brackets

x^2 + (\alpha + \beta)x + \alpha \beta = 0

To compare the above equation to x^2 + ax + 36 = 0, we have:

a = \alpha + \beta

\alpha \beta = 36

Where: \alpha, \beta and \alpha \ne \beta

The values of \alpha and \beta that satisfy \alpha \beta = 36 are:

\alpha = -1 and \beta = -36

\alpha = -2 and \beta = -18

\alpha = -3 and \beta = -12

\alpha = -4 and \beta = -9

So, the possible values of a are:

a = \alpha + \beta

When \alpha = -1 and \beta = -36

a = -1 - 36 = -37

When \alpha = -2 and \beta = -18

a = -2 - 18 = -20

When \alpha = -3 and \beta = -12

a = -3 - 12 = -15

When \alpha = -4 and \beta = -9

a = -4 - 9 = -13

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

Sum = -37 -20 -15 - 9

Sum = -81

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2 years ago
Given the equation, y=3x – 7 what is the slope of the line?
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<span>y=3x – 7
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Answer:

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Tom has $10 that he wants to use to buy pens and pencils. However, he does not want to buy more pens than pencils. A pen costs $
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If he buys x pens and y pencils

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</span>
<span>You Draw the line y=x [it passes by (0,0), (1,1), (2,2)]

 </span>
<span>Solution: is the points with integer x and y, that belong to the segment of the line 3x +y = 10 between the x-axis and the line y=x. Those points are (1,7) , (2,4), (3, 1).
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