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UkoKoshka [18]
3 years ago
14

Write the product and then write an equivalent expression. The multiplicative inverse of 2 and (4x +8)

Mathematics
1 answer:
lozanna [386]3 years ago
6 0

Answer:

The answer is

4 ( x + 2)

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3 years ago
The equation h=7sin(pi/21t)+28 can be used to model the height, h, in feet of the end of one blade of a windmill turning on an a
satela [25.4K]

Answer:

7 feet is the length of the blade of the windmill.

Step-by-step explanation:

We have the equation

h = 7 sin(pi/21t) + 28 ------ eq1

At time 't' = 0, the end of the blade is pointing to the right parallel to the ground meaning it is at the same height as the other end. (Ф = 0°)

So, by calculating the maximum height of this end at  Ф = 90°. we can calculate the length of the blade.

Now, we know that a general model equation of a circular simple harmonic motion is represented as :     y = A sinωt + k ----- eq2

Where A is the amplitude that is, maximum displacement from mean to maximum position.

ω is the angular frequency.

Comparing eq1 and eq2:

A = 7

so the difference in blades end height at Ф = 0° and Ф = 90° is 7 feet.

Hence, the length of the blade is 7 feet.

4 0
3 years ago
Read 2 more answers
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
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