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3 years ago

Need help with this please

Mathematics

1 answer:

Crazy boy [7]3 years ago

8 0

Answer:

1. 2(k + 3)

2. 3. 75 + k

Step-by-step explanation:

1. 2x + 6

Since, 2 is a common factor of 2 and 6, we can take that common outside.

So, 2x + 6 = 2(x + 3)

Note that in the initial expression, this 2 was distributed to arrive at 2x + 6.

2. (1.5 + k) + 2.25

This is simple addition. We can simply remove the brackets to have:

1.5 + k + 2.25

Since, the like terms can be added, we will have:

1.5 + 2. 25 + k

= 3. 75 + k

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Convert 8 mililiters to fluid ounces use 1 ml~0.034 fl.oz.

Andrews [41]

So for this, we will be using dimensional analysis to convert it as such:

$\frac{8\ mL}{1}*\frac{0.034\ fl\ oz}{1\ mL}=\frac{0.272}{1}=0.272\ fl\ oz$

In short, 8 mL is 0.272 fl oz.

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2 years ago

Also what is the answer to 10=2x-3+4x+5

balandron [24]

I hope you get this for whatever reason you asked this

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3 years ago

What dimensions of the box maximize the volume of the box?<br><br> please help thank you so much!

bonufazy [111]

so, let's recall that the volume of a rectangular prism, namely a box, is Lwh, just the product of its dimensions, length, width and height.

now, check the 1st picture below. we know the original paperboard is a 16x14, so the width, as you see in the picture is w = 8 - x, its length is L = x, and its height is 14 -(x/2) - (x/2).

$\bf V(x)=\stackrel{L}{(x)}\stackrel{w}{(8-x)}\stackrel{h}{\left( 14-\cfrac{x}{2}-\cfrac{x}{2} \right)}\implies V(x)=(8x-x^2)(14-x) \\\\\\ V(x)=112x-8x^2-14x^2+x^3\implies V(x)=x^3-22x^2+112x$

now, let's find the critical points, by setting the derivative to 0, and then we'll do a first-derivative test.

$\bf \cfrac{dV}{dx}=3x^2-44x+112\implies 0=3x^2-44x+112 \\\\\\ \textit{plugging those values in the quadratic formula}\qquad x\approx \begin{cases} 11.39\\ 3.28 \end{cases}$

now, if we plot those two points, we get 3 regions, and then we check each of those regions to see what's the value of the first derivative.

check the 2nd picture below, that'd be the first derivative test, as you can see from the arrows, the slope increases and then decreases at 3.28, namely that critical point is the maximum, so the Volume maximizes at x = 3.28.

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2 years ago

WILL GIVE BRAINLIEST !!<br><br> Find the inverse function.

REY [17]

Answer:

$f^{-1}(x)=(x-1)^3$

Step-by-step explanation:

$y=\sqrt[3]{x} +1\\\\exchanging \ x \ and\ y\\\\x=\sqrt[3]{y} +1\\\\finding \ y\\\\\sqrt[3]{y}=x-1\\\\y=(x-1)^3$

3 0

2 years ago

Which of the following functions are solutions of the differential equation y'' + y = sin(x)? (Select all that apply.) y = âˆ’ 1

Svetach [21]

The function that is the solution of the differential y" + y = sin(x) is: y(x) = -1/2(x cos x)

<h3>What is a function?</h3>

A function is an expression, rule, or law in mathematics that describes a connection between one factor (the independent variable) and another variable (the dependent variable).

<h3>What is the proof of the above function?</h3>

Take a look at the the following differential equation:

y" + y = sin (x)

The auxiiliary equation is

m² + 1 = 0

m² + 1-1 = -1

m² + 0 = -1

m² = -1

m = ±√-1

m = ±i

So, the complimentary function is yₐ (x) = c₁ cos x + c₂ sin x

Let the particular integral be:

yₙ (x) = A cos x + B sin x

yₙ '(x) = - A sin x + B cos x

yₙ ''(x) = - A cos x + B cos x

yₙ ''(x) = - (A cos x + B cos x)

After we have substituted yₙ (x); and yₙ''(x) in the given differential equation

y'' + y = sin (x)

= - (A cos x + B cos x) + (A cos x + B cos x) = sin(x)

0 = sin (x)

If we take the particular integral to be:
yₙ (x) = x(A cos x + B cos x)

yₙ '(x) = x(-A sin x + B cos x) + A cos x + B cos x

yₙ ''(x) = x(-A cos x - B sin x) - A sin x + B cos x + -A sin x + B cos x

Substitute yₙ (x), yₙ''(x) into the stated differential equation

y'' + y = sin (x)

x (-Acosx - Bsin x) - Asinx + Bcosx + (-Asinx + Bcosx) - x (Acosx + Bsin x) = sin (x)

-Axcosx - Bxsin x - Asinx + Bcosx -Asinx + Bcosx - Axcosx + Bxsin x = sin (x)

-2Asinx + 2Bcosx = sin(x)

Compare the coefficients of like terms on both sides of the equation

-2A = 1, B = 0

A = -1/2, B = 0

Substitute A = -1/2, B =0 into the assumed solution.

yₙ(x) = x((-1/2)cosx + (0) sinx)

= -1/2xcosx +0

= -(1/2)xcosx

Now, the general solution for the given differential equation is:

y(x) = yₓ(x) +yₙ (x)

y (x) - c₁cosx + c₂sin x -1/2x cosx

Hence, the solution is:

y(x) = -1/2xcosx

Learn more about function at;
brainly.com/question/25638609
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Full Question:

Which of the following functions are solutions of the differential equation y'' + y = sin x? (Select all that apply.)

A) y = 1 2 x sin x

B) y = cos x

C) y = x sin x − 5x cos x

D) y = − 1 /2 x cos x

E) y = sin x

4 0

1 year ago