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3 years ago

give the standard form, degree, leading coefficient and the constant term of the function h(x) = (2x+1)² (2x-3)

Mathematics

1 answer:

Softa [21]3 years ago

3 0

Answer:

The standard form is: $h(x) = 8x^3 - 4x^2 - 10x - 3$

The function is of the 3rd degree.

The leading coefficient is 8.

The constant term is -3.

Step-by-step explanation:

Placing in standard form:

To place in standard form, we solve the operations. So

$h(x) = (2x+1)^2(2x-3)$

$h(x) = (4x^2 + 4x + 1)(2x - 3)$

$h(x) = 8x^3 - 12x^2 + 8x^2 - 12x + 2x - 3$

$h(x) = 8x^3 - 4x^2 - 10x - 3$

Degree:

The degree is given by the highest power of x, which, in this exercise, is 3.

Leading coefficient:

The leading coefficient is the term that multiplies the highest power of x. In this exercise, the higher power of x is $x^3$ , which is multiplied by 8. So the leading coefficient is 8.

Constant term:

The constant term is the one which does not multiply a power of x. So in this exercise, it is -3.

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Solve each equation.<br> 1/3a = -5 a = ?<br> 12 - b = 12.5 b = ? <br> -0.1 = -10c c = ?

Rina8888 [55]

Answer:

a = -15, b = -.5, c = -1

Step-by-step explanation:

1/3a = -5 --> multiply each side with 3 --> a = -15

12 - b = 12.5 --> subtract 12 from both sides --> -b = .5 --> multiply each side with -1 to get b positive --> b = -.5

.1 = -10c --> multiply each side with -10 --> c = -1

8 0

3 years ago

Y+b=10???????????????

tatyana61 [14]

5+5=10

y=5
b=5
the answer is 5 plus 5

6 0

3 years ago

Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).

I am Lyosha [343]

Take the homogeneous part and find the roots to the characteristic equation:

$y''+4y=0\implies r^2+4=0\implies r=\pm2i$

This means the characteristic solution is $y_c=C_1\cos2x+C_2\sin2x$ .

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form $y_p=ax\cos2x+bx\sin2x$ . Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With $y_1=\cos2x$ and $y_2=\sin2x$ , you're looking for a particular solution of the form $y_p=u_1y_1+u_2y_2$ . The functions $u_i$ satisfy

$u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx$
$u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx$

where $W(y_1,y_2)$ is the Wronskian determinant of the two characteristic solutions.

$W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2$

So you have

$u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx$
$u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x$

$u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx$
$u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x$

So you end up with a solution

$u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x$

but since $\cos2x$ is already accounted for in the characteristic solution, the particular solution is then

$y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x$

so that the general solution is

$y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x$

7 0

3 years ago

A rectangular Corn Hole area at the Recreation Center has a width of 5 feet and a length of 10 feet. If

inysia [295]

Answer:

2 feet

Step-by-step explanation:

Let

x ----> the uniform amount added to each side

we know that

The algebraic expression that represent this situation is

$(5+x)(10+x)=84$

solve for x

Apply distributive property

$50+ 5x+10x+x^2=84\\x^2+15x-34=0$

solve the quadratic c equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

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

in this problem we have

$x^2+15x-34=0$

$a=1\\b=15\\c=-34$

substitute in the formula

$x=\frac{-15\pm\sqrt{15^{2}-4(1)(-34)}} {2(1)}$

$x=\frac{-15\pm\sqrt{361}} {2}$

$x=\frac{-15\pm19} {2}$

$x=\frac{-15\pm19} {2}=2$

$x=\frac{-15\pm19} {2}=-17$

therefore

The solution is x=2 ft

8 0

3 years ago

At lunch 3 1/4 small pizzas were equally divided amping students. If each student ate 1/4 of a pizza, how many students were fed

Vilka [71]

Answer:

13 students were fed

Step-by-step explanation:

now first in order to count we will have to turn 3 1/4 into a whole number which means we will have to multiply the denomintor by 3 and add it to the numerator which is 1

4 x 3= 12 ..... 12 + 1 = 13

13/4 and the denominator always stays the same

and now to count we will have to divide 13/4 divided by 1/4

now instead of dividing you can just multiply them by switching the denominator and numerator 1/4 to 4/1

13/4 x 4/1

52/4

5 0

3 years ago

give the standard form, degree, leading coefficient and the constant term of the function h(x) = (2x+1)² (2x-3)​

give the standard form, degree, leading coefficient and the constant term of the function h(x) = (2x+1)² (2x-3)