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melomori [17]
3 years ago
7

A rectangle has perimeter 20m. Express the area of the rectangle as a function of the length of one of its sides.

Mathematics
1 answer:
MArishka [77]3 years ago
7 0
<h2>Area of rectangle is 10L-L²</h2>

Step-by-step explanation:

Let L be the length and W be the width.

Perimeter of rectangle = 2 ( L + W )

That is

           2 ( L + W ) = 20

               L + W = 10

                     W = 10 - L

We need to express the area of the rectangle as a function of the length of one of its sides.

           Area = Length x Width

              A = LW

               A = L(10 - L) = 10L-L²

Area of rectangle is 10L-L²

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The sensitive period for language is from 7 months in utero up to 5.5 to 6 years of age. There are several aspects of language f
OleMash [197]

Answer:

The sensitive period for language is from 7 months in utero up to 5.5 to 6 years of age. There are several aspects of language from spoken language, to written language and reading. ... The sensitive period for learning to speak is from is from 7 months to 2.5-3 years of age.

Step-by-step explanation:

7 0
2 years ago
What is the diameter of a hemisphere with a volume of 257 m^3
Alex73 [517]

Answer:

9.9

Step-by-step explanation:

\text{Volume of Hemisphere}\text{:}

Volume of Hemisphere:

\,\,257

257

\text{Volume of Sphere}\text{:}

Volume of Sphere:

\,\,514

514

Double volume of hemisphere to get volume of the entire sphere

\text{Volume of a Sphere:}

Volume of a Sphere:

V=\frac{4}{3}\pi r^3

V=

3

4

​

πr

3

514=

514=

\,\,\left(\frac{4}{3}\pi\right) r^3

(

3

4

​

π)r

3

514=

514=

\,\,(4.1887902)r^3

(4.1887902)r

3

Evaluate 4/3pi in calc

\frac{514}{4.1887902}=

4.1887902

514

​

=

\,\,\frac{(4.1887902)r^3}{4.1887902}

4.1887902

(4.1887902)r

3

​

Evaluate \frac{4}{3}\pi

3

4

​

π in calc

122.7084611=

122.7084611=

\,\,r^3

r

3

\sqrt[3]{122.7084611}=

3

 

122.7084611

​

=

\,\,\sqrt[3]{r^3}

3

 

r

3

​

Cube root both sides

4.9692575=

4.9692575=

\,\,r

r

\text{Then the diameter equals }9.938515

Then the diameter equals 9.938515

diameter is radius times 2

\text{Final Answer:}

Final Answer:

d\approx 9.9\text{ m}

d≈9.9 m

Round to nearest tenth

4 0
3 years ago
I WILL GIVE YOU 20 POINTS AND THE BRAINLYEST
fiasKO [112]

Answer/Step-by-step explanation:

✍️Slope of the line using two points, (2, 2) and (6, 10),

slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 2}{6 - 2} = \frac{8}{4} = 2

✍️To find the equation of the line in slope-intercept form, we need to find the y-intercept (b).

Substitute x = 2, y = 2, and m = 2 in y = mx + b, and solve for b.

2 = (2)(2) + b

2 = 4 + b

2 - 4 = b

-2 = b

b = -2

Substitute m = 2 and b = -2 in y = mx + b.

✅The equation would be:

y = 2x + (-2)

y = 2x - 2

✍️To find the value of a, plug in (a, 8) as (x, y) into the equation of the line.

8 = 2(a) - 2

8 = 2a - 2

Add 2 to both sides

8 + 2 = 2a

10 = 2a

Divide both sides by 2

\frac{10}{2} = a

5 = a

a = 5

✍️To find the value of b, plug in (4, b) as (x, y) into the equation of the line.

b = 2(4) - 2

b = 8 - 2

b = 6

5 0
3 years ago
Please help me with ptomblem
marysya [2.9K]

Answer:

When p^2 - 4p is subtracted from p^2 + p - 6, the result is 5p - 6. To get p - 9, subtract 4p + 3 from the result.

Step-by-step explanation:

✔️Subtracting p^2 - 4p from p^2 + p - 6:

(p^2 + p - 6) - (p^2 - 4p)

p^2 + p - 6 - p^2 + 4p (Distributive property)

Collect like terms

p^2 - p^2 + p + 4p - 6

5p - 6

✔️Subtracting p - 9 from 5p - 6:

(5p - 6) - (p - 9)

5p - 6 - p + 9 (distributive property)

Add like terms

4p + 3

3 0
2 years ago
The line y = hx - 2 where h &gt; 0 meets the curve 3y² = 9x² - 6x + 1.
I am Lyosha [343]

Answer:

h=6

Step-by-step explanation:

since y =hx -2 is an equation for a line which intersects with the curve 3y^2 = 9x^2 - 6x +1. The point of intersection, let's say (x_1,y_1), should satisfy the two equations. As a result, the value of y in the second equation can be replaced with the value of y in the first equation as the following,

3y^2 = 3(hx-2)^2 = 9x^2 - 6x +1\\3(h^2x^2 -4hx + 4) = 9x^2 - 6x + 1\\3h^2 x^2 -12hx +12 = 9x^2 - 6x +1

therefore, the latter equation can be rewritten in a quadratic equation form as the following,

(9 - 3h^2) x^2 + (12h-6)x + (1-12) = (9 - 3h^2) x^2 + (12h-6)x -11 = 0

if the line is tangent to the curve, it means that the line touches the curve at one point, therefore the discernment of the second order equation will be equal to zero for the famous quadratic equation solution.

b^2 -4ac =0

where a=9-3h^2, b=12h-6 and c=-11, as a result, the following equations can be deduced,

(12h-6)^2 - 4*(9-3h^2)*(-11) = (144h^2 -144h +36) - (36 -12h^2)*(-11)=\\(144-(-12)*(-11)h^2 )  -144h +36 -(36*(-11)) =\\12 h^2 -144h +432 =0

therefore, dividing both sides by 12

h^2 -12 +36 =0\\(h-6)^2 =0\\h=6

8 0
2 years ago
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