Question

A golden rectangle is a rectangle whose length is approximately 1.6 times its width. The early Greeks thought that a rectangle w

MakcuM [25]

Answer: 234

Step-by-step explanation:

A golden rectangle is a rectangle whose length is approximately 1.6 times its width.

Mike Hallahan would like to plant a rectangular garden in the shape of a golden rectangle.

If he has "234"* feet of fencing is available, find the dimensions of the garden. *Makes more sense.

:

let w = the width of the garden

then

1.6w = the length

:

2(1.6w) + 2w = 234

3.2w + 2w = 234

5.2w = 234

w = 234/5.2

w = 45 ft is the width

and

1.6(45) = 72 ft is the length

:

Check

2(72) + 2(45) =

144 + 90 = 234

6 0

3 years ago

How do I solve to get the answer for: 2t + 8 ≥ −4(t + 1)

Rzqust [24]

2t + 8 ≥ -4t - 4
2t+4t ≥ -8-4
6t ≥-12
t ≥ -12/6
t ≥ -2

4 0

3 years ago

If f is a differentiable function, find an expression for the derivative of each of the following functions

almond37 [142]

12a. Answer: d) x⁶ f'(x) + 6x⁵ f(x)

Step-by-step explanation:

Use the multiplication formula for derivatives:

y = a · b → y' = a'b + ab'

y = x⁶ · f(x)

a = x⁶ b = f(x)

a' = 6x⁵ b' = f'(x)

y' = a'b + ab'

y' = 6x⁵ f(x) + x⁶ f'(x)

***************************************************************

12b. Answer: $\bold{b)\ y=\dfrac{xf'(x)-9f(x)}{x^{10}}'}$

Step-by-step explanation:

Use the division formula for derivatives:

$y=\dfrac{a}{b}$ → $y' = \dfrac{a'b - ab'}{b^2}$

$y=\dfrac{f(x)}{x^9}\\\\a=f(x)\qquad b=x^9\\\\a'=f(x)\qquad b'=9x^8\\\\y'=\dfrac{a'b-ab'}{b^2}\\\\y'=\dfrac{x^9f'(x)-9x^8f(x)}{(x^9)^2}\\\\.\ =\dfrac{x^9f'(x)-9x^8f(x)}{x^{18}}\\\\\text{factor out }x^{8}: y'=\dfrac{xf'(x)-9f(x)}{x^{10}}$

Note: You can also move the denominator to the top (it will have a negative exponent) and use the multiplication formula for derivatives.

5 0

3 years ago

Hi, please help me out with this math problem.

GalinKa [24]

9514 1404 393

Answer:

x - 4

Step-by-step explanation:

The expression simplifies to ...

$\sqrt{x^2-8x+16}=\sqrt{(x-4)^2}=|x-4|$

For x ≥ 4, the argument of the absolute value function is non-negative, so it remains unchanged. The simplified expression is ...

x - 4 . . . . for x ≥ 4

6 0

3 years ago

A factory makes 4250 bars of chocolate. There were three kinds of chocolate bars - creamy, milky and

mariarad [96]

Answer:

2525

Step-by-step explanation:

1. Draw a block diagram to illustrate the different types of chocolate bars. (In this diagram, the creamy chocolate bars are shown as orange blocks, the milky chocolate bars as blue blocks and the white chocolate bars as red blocks.)

2. Since the number of creamy chocolate bars was 5 times the number of milky chocolate bars, we can replace one orange block (creamy) with 5 blue blocks (milky).

Since the number of white chocolate bars was 715 more than the number of milky chocolate bars, we replace one red block with one blue block + 715.

3. Looking at the block diagram, find the number of milky chocolate bars (blue block)

4250 – 715 = 3535

7 blue blocks = 3535

1 blue block = 3535 ÷ 7 = 505

The number of milky chocolate bars made was 505.

4. Calculate the number of creamy chocolate bars.

The number of creamy chocolate bars was 5 times the number of milky chocolate bars = 5 × 505 = 2525

8 0

4 years ago