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3 years ago

Solve the inequality of -4p < 2/3

1 answer:

4 0

Just divide both sides by -4. Since you are dividing with a negative number, you will also have to flip the greater than sign.

p > -1/6

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HELPPP PLEASE 50 POINTSS

victus00 [196]

Answer:

184

Step-by-step explanation:

edmund as a 2 by 2 cube

so samuel has a cuboid twice as long

2 x 2 = 4

3 times as wide

3 x 2 = 6

and 4 times as high

2 x 4 = 8

8 x 6 x 4 = 192 small cubes

but we are trying to find how much more samuel got

so 192 - 8 = 184

3 0

3 years ago

Solve the following: 4x3 = 2x + 7

Yuri [45]

Answer:

If you meant 4x to the third power, than x = 1.34

8 0

2 years ago

Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

3 years ago

Put the following equation of a line into slope-intercept form 4x+3y=-21

s2008m [1.1K]

Answer: Y=( $\frac{4}{3}$ ) x-7

Step-by-step explanation:

8 0

3 years ago

Please help me i don't know what to do please show your work

Diano4ka-milaya [45]

<h3>Distributive Property</h3>

The distributive property lets you group or ungroup terms using parentheses. It lets you multiply an external factor by every term in parentheses, expressing the result as a sum:

... a(b + c) = ab + ac . . . . . . factor a multiplies the terms b and c

and it lets you remove a common factor from different terms, putting that factor outside parentheses:

... ab + ac = a(b + c)

The letters a, b, c here can stand for any number or expression.

<h3>Homework</h3>

20. To do this problem, you need to eliminate the parentheses using the distributive property. Then, "collect terms," which is another application of the distributive property. The external factor outside the parentheses is (-2/3). Multiply that by each term in parentheses, and add the results.

After that, recognize that c is a factor of two of the terms. Add their coefficients to simplify that sum to one term.

$-\dfrac{2}{3}(12c-9)+14c=\left(-\dfrac{2}{3}\right)(12c)+\left(-\dfrac{2}{3}\right)(-9)+14c=-8c+6+14c\\\\=c(-8+14)+6\\\\=6c+6$

22. You are to evaluate the expression with x=2 two ways: as is, and after you simplify it by combining like terms.

As is:

$-8x+5-2x-4+5x\\=-8(2)+5-2(2)-4+5(2)\\=-16+5-4-4+10\\=-9$

Simplified:

$-8x+5-2x-4+5x\\=x(-8-2+5)+(5-4)=-5x+1\\=-5(2)+1=-10+1\\=-9$

I prefer simplifying the expression first. The number of calculations and chances for error are reduced.

23. It is convenient to check for equivalence after simplifying both expressions.

First Expression:

$8x^2+3\left(x^2+y\right)=8x^2+3x^2+3y=11x^2+3y$

Second Expression:

$7x^2+7y +4x^2-4y=(7+4)x^2+(7-4)y=11x^2+3y$

The simplified forms of the expressions are identical, so we conclude the expressions are equivalent.

25. The area of a rectangle is the product of its length and width. Here, you are asked to simplify the product of (3+x) ft and 3 ft.

$((3+x)\,\text{ft})(3\,\text{ft})=(3\,\text{ft})\cdot (3\,\text{ft})+(x\,\text{ft})\cdot (3\,\text{ft})=9\,\text{ft}^2+3x\,\text{ft}^2\\\\=(3x+9)\,\text{ft}^2$

In the last form of this expression, we have used "standard form" which has the degree of the variable decreasing in terms left to right. The units are factored out to make the expression a bit less cumbersome.

3 0

3 years ago

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