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3 years ago

Write the equation of the line in slope-intercept form using y=mx+b

Mathematics

1 answer:

Ierofanga [76]3 years ago

3 0

Answer:

y= -5x + 2

Step-by-step explanation:

the slope is heading downwards, and down five units for each one across (hence m=5) and the y-intercept is 2 (hence the 2)

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A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three s

makvit [3.9K]

Answer:

The dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

Step-by-step explanation:

Let the length of garden be x

Let the breadth of garden be y

Area of Rectangular garden = $Length \times Breadth = xy$

We are given that the area of the garden is 122 square feet

So, $xy=122$ ---A

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft

So, cost of brick along length x = 20 x

On the other three sides by a metal fence costing $10/ft.

So, Other three side s = x+2y

So, cost of brick along the other three sides= 10(x+2y)

So, Total cost = 20x+10(x+2y)=20x+10x+20y=30x+20y

Total cost = 30x+20y

Substitute the value of y from A

Total cost = $30x+20(\frac{122}{x})$

Total cost = $\frac{2440}{x}+30x$

Now take the derivative to minimize the cost

$f(x)=\frac{2440}{x}+30x$

$f'(x)=-\frac{2440}{x^2}+30$

Equate it equal to 0

$0=-\frac{2440}{x^2}+30$

$\frac{2440}{x^2}=30$

$\sqrt{\frac{2440}{30}}=x$

$9.018 =x$

Now check whether it is minimum or not

take second derivative

$f'(x)=-\frac{2440}{x^2}+30$

$f''(x)=-(-2)\frac{2440}{x^3}$

Substitute the value of x

$f''(x)=-(-2)\frac{2440}{(9.018)^3}$

$f''(x)=6.6540$

Since it is positive ,So the x is minimum

Now find y

Substitute the value of x in A

$(9.018)y=122$

$y=\frac{122}{9.018}$

$y=13.528$

Hence the dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

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3 years ago

What is the amplitude of the sinusoidal function?<br><br> Enter your answer in the box.

Firdavs [7]

Answer: 5

----------------------------------------------------------

On the curve, the highest point has a y coordinate of y = 6
The lowest point on the curve has a y coordinate of y = -4

Subtracting the y values gets us: 6 - (-4) = 6 + 4 = 10
Cut that result in half: 10/2 = 5
The amplitude is 5. This is the vertical distance from the midline (y = 1) to either the highest point or the lowest point.

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3 years ago

A rectangular prism has a length of 412 millimeters, a width of 412 millimeters, and a height of 6 millimeters. Sally has a stor

Dominik [7]

Multiply the length*width*height to get the volume of the prism then, take out the difference between the volumes
Volume of the prism= 1018464
Then just subtract

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3 years ago

A house has increased in value by 37% since it was purchased. If the original value was $720, 000, what is the value after the i

STALIN [3.7K]

Answer:$986,4000

Step-by-step explanation:

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2 years ago

What is the LCD of 3/4 and 5/6

Elena-2011 [213]

Answer:

19/12 or 1/7/12

Step-by-step explanation:

find what is common in both denominators. in this case 12 can be divisible.
3x3/4x3 + 5x2/6x2
9/12+10/12=19/12=1/7/12

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3 years ago

Read 2 more answers

Write the equation of the line in slope-intercept form using y=mx+b​

Write the equation of the line in slope-intercept form using y=mx+b