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3 years ago

Find the area of a circle with radius, r = 5.81m. Give your answer rounded to 2 DP.

Mathematics

2 answers:

Zanzabum3 years ago

7 0

Answer:

A=πr×r

π=3.142, r=5.81

A=3.142×5.81×5.81

A=106.0906~106.09

brilliants [131]3 years ago

6 0

A≈106.05m²

hope that help

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Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=xy; 6x y=10

Pepsi [2]

There is a maximum value of 7/6 located at (x, y) = (5/6, 7).

The function given to us is f(x, y) = xy.

The constraint given to us is 6x + y = 10.

Rearranging the constraint, we get:

6x + y = 10,

or, y = 10 - 6x.

Substituting this in the function, we get:

f(x, y) = xy,

or, f(x) = x(10 - 6x) = 10x - 6x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = 10 - 12x ... (i)

Equating to 0, we get:

10 - 12x = 0,

or, 12x = 10,

or, x = 5/6.

Differentiating (i), with respect to x again, we get:

f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 5/6.

The value of y, when x = 5/6 is,

y = 12 - 6x,

or, y = 12 - 6*(5/6) = 7.

The value of f(x, y) when (x, y) = (5/6, 7) is,

f(x, y) = xy,

or, f(x, y) = (5/6)*7 = 7/6.

Thus, there is a maximum value of 7/6 located at (x, y) = (5/6, 7).

Learn more about maximum and minimum at

brainly.com/question/2437551

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7 0

2 years ago

Use simple interest to find the ending balance. $215 at 8% for 8 years

ira [324]

Answer:

$ 352.6

Step-by-step explanation:

SI = P (1 + rt)

= 215 [ 1 + (0.08) x 8]

= 215 (1 + 0.64)

= 215 (1.64)

= $ 352.6

3 0

3 years ago

Read 2 more answers

Find the area and the circumference of a circle with a diameter of 17cm

frosja888 [35]

Answer:

Step-by-step explanation:

d = 17 cm

r = 17/2 = 8.5 cm

Circumference of circle = πd

= 3.14 * 17

= 53.38 cm

Area of circle = πr²

= 3.14 * 8.5 * 8.5

= 226.865 cm²

6 0

3 years ago

21(z+50)= 1,071 distrbultive property

Harman [31]

Answer:

The value of z is 1.

Step-by-step explanation:

Given:

$21(z+50) = 1071$

We need to solve the problem using distributive property.

Solution:

For the given equation we will apply distributive property;

By Definition of Distributive property which states that;

"The distributive property lets you multiply a sum by multiplying each addend separately and then add the products."

example = $a(b+c) = a\times b +a\times c =ab +ac$

So we get;

$21\times z + 21\times 50 = 1071\\\\21z + 1050 =1071$

Now by using Subtraction property we will subtract both side by 1050 we get;

$21z+1050-1050=1071-1050\\\\21z=21$

Now Dividing both side by 21 by using Division property we get;

$\frac{21z}{21}=\frac{21}{21}\\\\z=1$

Hence The value of z is 1.

8 0

3 years ago

Write the equation of the line that passes through the two points: (-4, 11) and (2,-4)

snow_tiger [21]

Answer:

y= - $\frac{5}{2}$ x+1

Step-by-step explanation:

Utilize the formula of $\frac{y2-y1}{x2-x1}$ to find the distance between two points, or in this case, the equation of the line that passes through two points.

Applying the given points to identify the slope

1. Plug the coordinates into the y and x values. $\frac{-4-11}{2+4}$ =- $\frac{15}{6}$ .

1.5. Simplify; divide both the numerator and the denominator by 3. - $\frac{5}{2}$ .

Applying slope and a point to find the y-intercept of the equation of a line

1. Utilize the formula of y=mx. Though this sounds strange, morph the sign of equality into subtraction.

1.5. Result: y-mx

2. Do this for both points.

First point: (-4,11)

y-mx

11 + $\frac{5}{2}$ (-4)

11 + -10 (11-10)

Plug the result and the slope into y=mx+b to find the slope of the line.

Result: y=- $\frac{5}{2}$ x+1.

Check your answer to confirm that the value of y is true for both points

1. Do the same thing you did with the first point, but use the second point this time.

y-mx

-4 + $\frac{5}{2}$ (2)

-4 + 5

Plug the result and the slope into y=mx+b to find the slope of the line.

Result: y=- $\frac{5}{2}$ x+1. Identical to point one's result.

In conclusion, both of the results are the same. Therefore, the equation of the line must be y=- $\frac{5}{2}$ x+1.

3 0

4 years ago