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3 years ago

Please help quickly.

Mathematics

1 answer:

Thepotemich [5.8K]3 years ago

3 0

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ h(t_2)}}-{{ h(t_1)}}}{{{ t_2}}-{{ t_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}
\\\\\\
h(t)=300-16t^2\quad 
\begin{cases}
t_1=0\\
t_2=3
\end{cases}\implies \cfrac{h(3)-h(0)}{3-0}\implies \cfrac{h(3)-h(0)}{3}$

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Using the side of a building as one side and fencing for the other three sides, a rectangular garden will be constructed. Given

scZoUnD [109]

Answer:

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

The maximum area is 450 feet²

Step-by-step explanation:

The garden is fencing for three sides only, That means the length of the fencing is equal to the sum of the length of the three sides

Assume that garden is y feet long and x feet wide and the fencing will cover on side of y feet and two sides of x feet

∵ The sum of the length of the 3 sides = y + x + x

∴ The sum of the length of the 3 sides = y + 2x

- The length of the fencing is equal to the sum of the sides

∵ The fencing is 60 feet

- Equate y + 2x by 60

∴ y + 2x = 60

- Find y in terms of x by subtracting 2x from both sides

∴ y = 60 - 2x

<em>To find the dimensions which make the maximum area, find the area of the garden, then substitute y by x, and differentiate it with respect to x, then equate the differentiation by 0 to find the value of x, and substitute this value in the equation of y to find y and in the equation of the area to find the maximum area</em>

∵ The formula of the area of a rectangle is A = l × w

∵ l = y and w = x

∴ A = x y

- Substitute the value of y above in A

∵ A = x(60 - 2x)

- Multiply bracket by x

∴ A = 60x - 2x²

Now differentiate x with respect to x

∵ A' = 60(1) - 2(2)x

∴ A' = 60 - 4x

- Equate A' by 0 to find x

∴ 0 = 60 - 4x

- Add 4x to both sides

∴ 4x = 60

- Divide both sides by 4

∴ x = 15

- Substitute the value of x in the equation of y to find it

∵ y = 60 - 2(15)

∴ y = 30

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

To find the maximum area substitute x by 15 in the equation of the area

∵ A = 60(15) - 2(15)²

∴ A = 900 - 450

∴ A = 450

The maximum area is 450 feet²

5 0

3 years ago

PLEASE ALL YOU NEED TO DO IS MATCH NUMBERS *Drag the tiles to the correct boxes to complete the pairs. Match the algebraic addit

katrin2010 [14]

Answer:

1) A = (3 + 5·i) + (2 - 3·i)

2) A = (-3 + 5·i) + (-2 - 3·i)

3) A = (-3 + 5·i) + (2 + 3·i)

4) A = (3 - 5·i) + (2 + 3·i)

Step-by-step explanation:

1) For the first chart, we have;

To go from the start point to get the new line, we add the coordinates of the red line end point to the coordinates of the starting line end point as follows

A = (3 + 5·i) + (2 - 3·i)

2) For the second chart, we have;

To go from the start point to get the new line, we add the coordinates of the red line end point to the coordinates of the starting line end point as follows

A = (-3 + 5·i) + (-2 - 3·i)

3) For the third chart, we have;

To go from the start point to get the new line, we add the coordinates of the red line end point to the coordinates of the starting line end point as follows

A = (-3 + 5·i) + (2 + 3·i)

4) For the fourth chart, we have;

To go from the start point to get the new line, we add the coordinates of the red line end point to the coordinates of the starting line end point as follows

A = (3 - 5·i) + (2 + 3·i)

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3 years ago

For each of the following expressions rewrite it in a way that would make it easier to simplify. State whether you used the asso

Elis [28]

1. 15(10 - 2)....distribute....150 - 30 = 120
2. (24 + 18) + (12 + 6).....commutative....(24 + 6) + (12 + 18) = 30 + 30 = 60
3. 5 * 13 * 2.....commutative.....5 * 2 * 13 = 10 * 13 = 130
4. 94 + 17 + 53 + 6....commutative...94 + 6 + 17 + 53 = 100 + 70 = 170
5. 25(14) ...distribute..25 * 10 + 25 * 4 = 250 + 100 = 350
6. 25 * (4 * 17)...associative....(25 * 4) * 17 = 100 * 17 = 1700

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