All categories

3 years ago

Multiply the polynomials. (2x2 + 6x + 6)(3x – 2)

Mathematics

1 answer:

gavmur [86]3 years ago

6 0

Answer:

$6x^{3}+16x^{2} +6x-12$

Step-by-step explanation:

To calculate the result of that mutiplication you have to firs evaluate the first term of the second function multipying the whole first function, woudl be like this:

$(3x)(2x^{2}+6x+6)= 6x^{3}+18x^{2} +18x$

Now that you have this, you multiply the second term from the second function to obtain:

$(-2)(2x^{2}+6x+6)= -4x^{2}-12x-12$

Now you just have to add both results:

$6x^{3}+18x^{2} +18x$

+ $-4x^{2}-12x-12$

And the result of the sum would be:

$6x^{3}+16x^{2} +6x-12$

You might be interested in

Solve, be sure to show each step under the original problem for any credit. 1 =k/12 +5

Naya [18.7K]

K = -48

1. subtract 5 from both sides
-4 = k/12

2. multiply 12 from both sides to get k alone
-48 = k

3 0

2 years ago

one hose can fill a goldfish pond in 14 minutes, and the two hoses can fill the same pond in 10 minutes, find how long it takes

likoan [24]

Answer:

Step-by-step explanation:

$\frac{1}{14} +\frac{1}{t} =\frac{1}{10}$

Solving this ^^ would equal t=35.

4 0

3 years ago

You are still debating about the two different computers. If you are paid $10.00/hour and your deductions are FICA (7.65%), fede

sattari [20]

Answer:

89 hours

Step-by-step explanation:

First solve all the deductions.

For each multiply the $10, which you are paid, and the percentage.

For FICA: $10 x 0.0765 = $0.77 per hr

For Fed tax: $10 x 0.12 = $1.2 per hr

For State tax: $10 x 0.08 = $0.8 per hr

Now subtract the remaining pay:

10 – 0.77 – 1.2 – 0.8 = $7.23

Time required = $640 / $7.23 per hr

Time required = 89 hrs

Final answer:

89 hours

8 0

3 years ago

What is the length of the curve with parametric equations x = t - cos(t), y = 1 - sin(t) from t = 0 to t = π? (5 points)

zzz [600]

Answer:

B) 4√2

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Parametric Differentiation

Integration

Integrals
Definite Integrals
Integration Constant C

Arc Length Formula [Parametric]: $\displaystyle AL = \int\limits^b_a {\sqrt{[x'(t)]^2 + [y(t)]^2}} \, dx$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \left \{ {{x = t - cos(t)} \atop {y = 1 - sin(t)}} \right.$

Interval [0, π]

Step 2: Find Arc Length

[Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]: $\displaystyle \left \{ {{x' = 1 + sin(t)} \atop {y' = -cos(t)}} \right.$
Substitute in variables [Arc Length Formula - Parametric]: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{[1 + sin(t)]^2 + [-cos(t)]^2}} \, dx$
[Integrand] Simplify: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx$
[Integral] Evaluate: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}$

Topic: AP Calculus BC (Calculus I + II)

Unit: Parametric Integration

Book: College Calculus 10e

4 0

2 years ago

Consider the following function G(x) = 2 (x-3) Find G(4) + G (5)

NNADVOKAT [17]

Answer: 6

Solution: 2(4-3) + 2(5-3) = 8-6+10-6=6

4 0

2 years ago