Help me salve 2x+17=5x-10

A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria

goldfiish [28.3K]

Answer:

wire for square to maximize total area = 23 m

Wire to minimize total area = 2.019 m

Step-by-step explanation:

For the square, let's say the total length of the square is "y" m.

Thus, length of one side is = y/4

And area of the square = (y/4) = y²/16

Since the wire is 23 m, then total length of equilateral triangle is; 23 - y.

Thus, length of one side of equilateral triangle = (23 - y)/3

Using trigonometric ratio, we can find the height of the triangle and thus area.

Area of triangle = (√3)/4) × ((23 - y)/3)²

Area of triangle = (√3)/36)(23 - y)²

So, total area of square and triangle is;

A_total = (y²/16) + (√3)/36)(23 - y)²

Now, extremizing this function by derivatives, we have;

dA/dy = (y/8) - (√3)/18)(23 - y)

d²A/dy² = ⅛ + (√3)/18)

So, d²A/dy² > 0

Now,let's find the maximum or minimum of the function.

So, we equate dA/dy to zero.

Thus;

(y/8) - (√3)/18)(23 - y) = 0

y/8 = (√3)/18)(23 - y)

(y/8) + (√3)/18)y = 23((√3)/18)

Multiply through by 8 to give;

y + 0.0962y = 2.2132

1.0962y = 2.2132

y = 2.2132/1.0962

y = 2.019 m

2.019 will be a minimum because d²A/dy² > 0

The maximum will occur at a boundary of the allowed values. Thus, the absolute maximum is for y = 23.

Note that a square has more area than a triangle and as such it is normal for the square to get the largest area over the triangle and therefore we will have to use all of the wire to construct the square.

6 0

3 years ago

Please????????????????

Alenkasestr [34]

For the first question, simply make a right angle triangle with the following dimensions.

The angle of elevation or the angle from the ground between the first floor and ground is 60 degrees.

The height between the 2 floors is 26 feet.

Solve for the hypotenuse, or the diagonal length between the first and second floors.

Then for the second question, divide the length in feet by the rate to find the time it takes for the object to move.

4 0

3 years ago

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I need 5 brainliest answers anyone wanna give me a free one also dont reporttttt

Arada [10]

Answer:

Ok tell me what you need so I can help

7 0

3 years ago

URGENT: PLEASE HELP!

vazorg [7]

To solve this problem, we are going to set up an equation. However, first we need to convert the percentages to decimals by dividing by 100.

15% = 0.15 , 7.5% = 0.075

Now, we should substitute in our given information into our equation and let our unknown value be equal to the variable x.

0.15(500) = 0.075x

Then, we should simplify our equation by multiplying together the two factors on the left side of the equation.

75 = 0.075x

Finally, we should divide both sides of the equation by 0.075 to get the variable x alone.

x = 1000

Therefore, your answer is 1000.

Hope this helps!

4 0

3 years ago

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Write the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x

Solnce55 [7]

Answer:

The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is $\mathbf{y=-\frac{2}{3}x+3 }$

Step-by-step explanation:

We need to Write the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x

The equation in slope-intercept form is: $y=mx+b$ where m is slope and b is y-intercept.

Finding Slope:

The both equations given are parallel. So, they have same slope.

Slope of given equation y= - 2/3x is m = -2/3

This equation is in slope-intercept form, comparing with general equation $y=mx+b$ where m is slope , we get the value of m= -2/3

So, slope of required line is: m = -2/3

Finding y-intercept

Using slope m = -2/3 and point (-3,5) we can find y-intercept

$y=mx+b\\5=-\frac{2}{3}(-3)+b\\5=2+b\\ b=5-2\\b=3$

So, we get b = 3

Now, the equation of required line:

having slope m = -2/3 and y-intercept b =3

$y=mx+b\\y=-\frac{2}{3}x+3$

The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is $\mathbf{y=-\frac{2}{3}x+3 }$

5 0

3 years ago

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