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3 years ago

Simplify the polynomial expressions by combining like terms, and then multiply the resulting

Mathematics

1 answer:

dimaraw [331]3 years ago

6 0

Answer:

The simplified expression is

20x^2 - 33x - 27

Step-by-step explanation:

(6x - 9 - 2x)(8 + 5x - 5)

We must first rewrite the expression as a product of two binomials.

This can be done by adding like terms

(6x - 9 - 2x)(8 + 5x - 5)

We have,

(4x-9)(5x+3)

Multiplying the resulting binomial expression

(4x-9)(5x+3)

(20x^2+12x-45x-27)

Add the like terms

20x^2-33x-27

The simplified expression is

20x^2 - 33x - 27

Twenty x squared minus thirty-three x minus twenty-seven

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Factor the polynomial by its greatest common monomial factor. 3b^5+15b^4−18b^7

Natasha2012 [34]

Answer:

Step-by-step explanation:

3b⁵ + 15b⁴ - 18b⁷ = 3b⁵ + [3*5*b⁴] - [6*3*b⁷]

=3b⁴*( b + 5 - 6b³)

3 0

3 years ago

Calculus 3 help please.

Reptile [31]

I assume each path $C$ is oriented positively/counterclockwise.

(a) Parameterize $C$ by

$\begin{cases} x(t) = 4\cos(t) \\ y(t) = 4\sin(t)\end{cases} \implies \begin{cases} x'(t) = -4\sin(t) \\ y'(t) = 4\cos(t) \end{cases}$

with $-\frac\pi2\le t\le\frac\pi2$ . Then the line element is

$ds = \sqrt{x'(t)^2 + y'(t)^2} \, dt = \sqrt{16(\sin^2(t)+\cos^2(t))} \, dt = 4\,dt$

and the integral reduces to

$\displaystyle \int_C xy^4 \, ds = \int_{-\pi/2}^{\pi/2} (4\cos(t)) (4\sin(t))^4 (4\,dt) = 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt$

The integrand is symmetric about $t=0$ , so

$\displaystyle 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \,dt$

Substitute $u=\sin(t)$ and $du=\cos(t)\,dt$ . Then we get

$\displaystyle 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^1 u^4 \, du = \frac{2^{13}}5 (1^5 - 0^5) = \boxed{\frac{8192}5}$

(b) Parameterize $C$ by

$\begin{cases} x(t) = 2(1-t) + 5t = 3t - 2 \\ y(t) = 0(1-t) + 4t = 4t \end{cases} \implies \begin{cases} x'(t) = 3 \\ y'(t) = 4 \end{cases}$

with $0\le t\le1$ . Then

$ds = \sqrt{3^2+4^2} \, dt = 5\,dt$

and

$\displaystyle \int_C x e^y \, ds = \int_0^1 (3t-2) e^{4t} (5\,dt) = 5 \int_0^1 (3t - 2) e^{4t} \, dt$

Integrate by parts with

$u = 3t-2 \implies du = 3\,dt \\\\ dv = e^{4t} \, dt \implies v = \frac14 e^{4t}$

$\displaystyle \int u\,dv = uv - \int v\,du$

$\implies \displaystyle 5 \int_0^1 (3t-2) e^{4t} \,dt = \frac54 (3t-2) e^{4t} \bigg|_{t=0}^{t=1} - \frac{15}4 \int_0^1 e^{4t} \,dt \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} e^{4t} \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} (e^4 - 1) = \boxed{\frac{5e^4 + 55}{16}}$

$\begin{cases} x(t) = 3(1-t)+t = -2t+3 \\ y(t) = (1-t)+2t = t+1 \\ z(t) = 2(1-t)+5t = 3t+2 \end{cases} \implies \begin{cases} x'(t) = -2 \\ y'(t) = 1 \\ z'(t) = 3 \end{cases}$

with $0\le t\le1$ . Then

$ds = \sqrt{(-2)^2 + 1^2 + 3^2} \, dt = \sqrt{14} \, dt$

and

$\displaystyle \int_C y^2 z \, ds = \int_0^1 (t+1)^2 (3t+2) \left(\sqrt{14}\,ds\right) \\\\ ~~~~~~~~ = \sqrt{14} \int_0^1 \left(3t^3 + 8t^2 + 7t + 2\right) \, dt \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 t^4 + \frac83 t^3 + \frac72 t^2 + 2t\right) \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 + \frac83 + \frac72 + 2\right) = \boxed{\frac{107\sqrt{14}}{12}}$

8 0

1 year ago

The sum of two numbers is 59 and the difference is 15 . what are the numbers?

UkoKoshka [18]

Write a system of equation based on the number
For an instance, the two numbers are a and b.
"The sum of two numbers is 59" can be written as follows.
⇒ a + b = 59 (first equation)
"The difference is 15" can be written as follows.
⇒ a - b = 15 (second equation)

Solve the system of equation by elimination/substitution method.
First, eliminate b to find the value of a.
a + b = 59
a - b = 15
--------------- + (add)
2a = 74
a = 74/2
a = 37

Second, substitute 37 as a in one of the equations
a + b = 59
37 + b = 59
b = 59 - 37
b = 22

The numbers are 37 and 22

5 0

3 years ago

You are driving to a conference in Cleveland and have already traveled 100 miles. You still have 50 more miles to go. When you a

Alborosie

Answer:

150 miles

Step-by-step explanation:

If you go 50 more miles after you have gone 100, you have traveled a total of ...

100 + 50 = 150 . . . miles

6 0

3 years ago

Read 2 more answers

What is the sum of 1-2 and V-18? † O42 O 421 O 52 05/21

frutty [35]

Answer:

B) 421

Step-by-step explanation:

√2 + √-18

√2 + √9·-2

√2 + 3√-2

(3 +1 )(√2 ·√-2) = 2i

4 · 2i

3 0

3 years ago