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Reptile [31]
2 years ago
6

Find the perimeter of the figure to the nearest hundredth.

Mathematics
1 answer:
Pavlova-9 [17]2 years ago
4 0

Answer:

60.00 in^2

Step-by-step explanation:

First focus on the area ABOVE the dotted line.  The shape here is that of a trapezoid.  The two leg lengths are 12 in and 18 in (18 in is the diameter).  At the far right of this trapezoid we can picture a triangle of base 3 in, height h and hypotenuse 5 in.  Using the Pythagorean Theorem, we get h = 4 in.

This 4 in measurement is the width of the trapezoid.  Thus, we are now ready to apply the formula for the area of a trapezoid:  A = (average length of legs)*(width).

Here that area comes out to

       12 in + 18 in

A = --------------------- * 4 in = 15 in*4in = 60 in^2, or (to the nearest hundredth)

                 2                                           60.00 in^2

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I am having trouble with this relative minimum of this equation.<br>​
Norma-Jean [14]

Answer:

So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach.  You have to let me know if you want this done another way.

Here are some rules I'm going to use:

(f+g)'=f'+g'       (Sum rule)

(cf)'=c(f)'          (Constant multiple rule)

(x^n)'=nx^{n-1} (Power rule)

(c)'=0               (Constant rule)

(x)'=1                (Slope of y=x is 1)

y=4x^3+13x^2-12x-56

y'=(4x^3+13x^2-12x-56)'

y'=(4x^3)'+(13x^2)'-(12x)'-(56)'

y'=4(x^3)'+13(x^2)'-12(x)'-0

y'=4(3x^2)+13(2x^1)-12(1)

y'=12x^2+26x-12

Now we set y' equal to 0 and solve for the critical numbers.

12x^2+26x-12=0

Divide both sides by 2:

6x^2+13x-6=0

Compaer 6x^2+13x-6=0 to ax^2+bx+c=0 to determine the values for a=6,b=13,c=-6.

a=6

b=13

c=-6

We are going to use the quadratic formula to solve for our critical numbers, x.

x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}

x=\frac{-13 \pm \sqrt{169+144}}{12}

x=\frac{-13 \pm \sqrt{313}}{12}

Let's separate the choices:

x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}

Let's approximate both of these:

x=0.3909838 \text{ or } -2.5576505.

This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.

The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

f(x)=4x^3+13x^2-12x-56

f'(x)=12x^2+26x-12

f''(x)=24x+26

So if f''(a) is positive then we have a minimum at x=a.

If f''(a) is negative then we have a maximum at x=a.

Rounding to nearest tenths here:  x=-2.6 and x=.4

Let's see what f'' gives us at both of these x's.

24(-2.6)+25

-37.5  

So we have a maximum at x=-2.6.

24(.4)+25

9.6+25

34.6

So we have a minimum at x=.4.

Now let's find the corresponding y-value for our relative minimum point since that would complete your question.

We are going to use the equation that relates x and y.

I'm going to use 0.3909838 instead of .4 just so we can be closer to the correct y value.

y=4(0.3909838)^3+13(0.3909838)^2-12(0.3909838)-56

I'm shoving this into a calculator:

y=-58.4654411

So the approximate relative minimum is (0.4,-58.5).

If you graph y=4x^3+13x^2-12x-56 you should see the graph taking a dip at this point.

3 0
3 years ago
What's 13 and 14 thx a lot!
Mumz [18]
13) B. 8.47,8.67,8.7
14) A

Just ask for explanation if u need it

Hope that helped :)


8 0
2 years ago
Read 2 more answers
Students at Dessau Middle School can have fun with math at their first Olympic Math Game Night. It is scheduled for 6 to 8 p.m.
galina1969 [7]

Answer:

great essay lol

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
3x – 7(4 + 2x) = –x + 2 Answer?? Idk how to do this
lesantik [10]
<u>3x-7(4+2x)=-x+2</u> first step is to distribute the -7 into the (4+2x) this is done by multiplying the -7 to the 4 and them doing the same for the 2x
<u>3x-28-14x=-x+2</u> next you combine like terms as in all the x's you do this by adding the -14x and the 3x together
<u>-11x-28=-x+2 </u> next you put all the x's on one side
<u>+x         +x</u>
<u>-10x-28=2</u> <u />next you add 28 to both sides to combine your final like terms
      <u>+28 +28 
-10x=30</u> the last step is to divide -10x and 30
<u>/-10x /-10x
</u><u>x=-3</u>
6 0
3 years ago
Read 2 more answers
Which of these strategies would eliminate a variable in the system of equations? \begin{cases} 2x - 5y = 13 \\\\ -3x + 2y = 13 \
Elena-2011 [213]

Answer and Step-by-step explanation:

Given the system of equations:

2x – 5y = 13

–3x + 2y = 13

We can decide to eliminate either x or y in order to solve the simultaneous equations.

1. To eliminate x:

Multiply the first equation by the coefficient of x in the second equation and multiply the second equation by the coefficient of x in the first equation. By doing this the coefficients of x in the equations would be the same and subtracting them to be equal to zero becomes easy, thus eliminating that variable.

The coefficient of x in the second equation is –3, if we multiply the first equation by it we have:

–6x+15y = –39

The coefficient of x in the first equation is 2, if we multiply the second equation by it we have:

–6x+4y = 26

Subtracting the resulting equations we have:

11y = –65 and x is eliminated.

2. To eliminate y:

Multiply the first equation by the coefficient of y in the second equation and multiply the second equation by the coefficient of y in the first equation. By doing this the coefficients of y in the equations would be the same and subtracting them to be equal to zero becomes easy, thus eliminating that variable.

The coefficient of y in the second equation is 2, if we multiply the first equation by it we have:

4x–10y = 26

The coefficient of y in the first equation is –5, if we multiply the second equation by it we have:

15x–10y = –65

Subtracting the resulting equations we have:

–11x = 91 and y is eliminated.

4 0
2 years ago
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