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3 years ago

Simplify: (7x4 – 7x3 + 7x2 + 2x) + (-5x4 + 7x3 + 5x2 – 9)

Mathematics

1 answer:

ikadub [295]3 years ago

8 0

Answer:

Step-by-step explanation:

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What is 35/75 reduced to

Sedbober [7]

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3 years ago

Read 2 more answers

2 points) Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One

Stells [14]

$y'=(t+y)^2-1$

Substitute $u=t+y$ , so that $u'=y'$ , and

$u'=u^2-1$

which is separable as

$\dfrac{u'}{u^2-1}=1$

Integrate both sides with respect to $t$ . For the integral on the left, first split into partial fractions:

$\dfrac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)=1$

$\displaystyle\int\frac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm dt=\int\mathrm dt$

$\dfrac12(\ln|u-1|-\ln|u+1|)=t+C$

Solve for $u$ :

$\dfrac12\ln\left|\dfrac{u-1}{u+1}\right|=t+C$

$\ln\left|1-\dfrac2{u+1}\right|=2t+C$

$1-\dfrac2{u+1}=e^{2t+C}=Ce^{2t}$

$\dfrac2{u+1}=1-Ce^{2t}$

$\dfrac{u+1}2=\dfrac1{1-Ce^{2t}}$

$u=\dfrac2{1-Ce^{2t}}-1$

Replace $u$ and solve for $y$ :

$t+y=\dfrac2{1-Ce^{2t}}-1$

$y=\dfrac2{1-Ce^{2t}}-1-t$

Now use the given initial condition to solve for $C$ :

$y(3)=4\implies4=\dfrac2{1-Ce^6}-1-3\implies C=\dfrac3{4e^6}$

so that the particular solution is

$y=\dfrac2{1-\frac34e^{2t-6}}-1-t=\boxed{\dfrac8{4-3e^{2t-6}}-1-t}$

3 0

3 years ago

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?

iogann1982 [59]

ANSWER

$\pm1,\pm11,\pm \frac{1}{5} \pm \frac{11}{5}$

EXPLANATION

The given function is;

$f(x) = 5 {x}^{2} - 7x + 11$

The constant term is 11.

The coefficient of the leading term is 5.

The factors of 11 are ±1,±11

The factors of 5 are ±1,±5

According to the Rational roots Theorem,

the potential roots are obtained by expressing the factors of the constant term over the coefficient of the leading term.

$\pm1,\pm11,\pm \frac{1}{5} \pm \frac{11}{5}$

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3 years ago

What is a scale factor?

Blababa [14]

Answer:

Here is some helpful information from my mini lessons.

Step-by-step explanation:

If two objects have the same shape, they are called "similar." When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles shown are similar, compare their corresponding sides. Here you'll learn that the ratio of the perimeters of similar figures is equal to their scale factor and that the ratio of their areas is equal to the square of their scale factor. If two polygons are similar, then the ratio of the lengths of any two corresponding sides is called the scale factor. This means that the ratio of all parts of a polygon is the same as the ratio of the sides.

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3 years ago

A cable company charges $70 per month for cable service to existing customers. Find a linear equation representing the relations

aleksley [76]

Answer:

y = 70x

Step-by-step explanation:

5 0

2 years ago

Simplify: (7x4 – 7x3 + 7x2 + 2x) + (-5x4 + 7x3 + 5x2 – 9)​

Simplify: (7x4 – 7x3 + 7x2 + 2x) + (-5x4 + 7x3 + 5x2 – 9)