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Dmitrij [34]
2 years ago
13

(a) By what least number must 27 be divided to make it perfect square​

Mathematics
2 answers:
Free_Kalibri [48]2 years ago
5 0

Answer:

3

Step-by-step explanation:

When you divide 27 by 3 it will give you 9 and the square root of 9 gives you a perfect answer indicating that 3 is the least number that must be divided into 27

weeeeeb [17]2 years ago
4 0

Answer:

\fbox {3}

Step-by-step explanation:

<u>First, prime factorize 27</u> :

⇒ 27 = 3 × 3 × 3

If 27 was divided by 3, it would give 3 × 3, which would give 9, a perfect square.

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they are corresponding angles

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You deposit $900 in a savings account. The account earns 4% simple interest per year. What is the balance after 8 years? What is
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3 years ago
An open box with a square base is to have a volume of 18 ft^3.
kotegsom [21]

Answer:

2.29 ft of side length and 1.14 height

Step-by-step explanation:

a) Volume V = x2h, where x is side of square base and h is hite.

Then surface area S = x2 + 4xh because box is open.

b) From V = x2h = 6 we have h = 6/x2.

Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.

We get S as function of one variable x. To get minimum we have to find derivative S' = 2x - 24/x2 = 0, from here 2x3 - 24 = 0, x3 = 12, x = (12)1/3 ≅ 2.29 ft.

Then h = 6/(12)2/3 = (12)1/3/2 ≅ 1.14 ft.

To prove that we have minimum let get second derivative: S'' = 2 + 48/x3, S''(121/3) = 2 + 48/12 = 6 > 0.

And because by second derivative test we have minimum: Smin = (12)2/3 + 4(12)1/3(12)1/3/2 = 3(12)2/3 ≅ 15.72 ft2

5 0
2 years ago
Eben, an alien from the planet Tellurango, kicks a football from field level. The equation for the football’s height in meters,
Luden [163]

<span>The maxima of a differential equation can be obtained by getting the 1st derivate dx/dy and equating it to 0.</span>

<span>Given the equation h = - 2 t^2 + 12 t       , taking the 1st derivative result in:</span>

dh = - 4 t dt + 12 dt

<span>dh / dt = 0 = - 4 t + 12   calculating for t:</span>

t = -12 / - 4

t = 3 s

Therefore the maximum height obtained is calculated by plugging in the value of t in the given equation.

h = -2 (3)^2 + 12 (3)

h = 18 m

This problem can also be solved graphically by plotting t (x-axis) against h (y-axis). Then assigning values to t and calculate for h and plot it in the graph to see the point in which the peak is obtained. Therefore the answer to this is:

<span>The ball reaches a maximum height of 18 meters. The maximum of h(t) can be found both graphically or algebraically, and lies at (3,18). The x-coordinate, 3, is the time in seconds it takes the ball to reach maximum height, and the y-coordinate, 18, is the max height in meters.</span>

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3 years ago
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