Box #1:
Dimensions are x, 3x, and x³.
Base area, A = x*(3x) = 3x².
Volume, V = (3x²)*(x³) = 3x⁵.
The volume is a 5-th order polynomial. It has only one term, which is the leading term.

Box #2:
Dimensions are x, (4x-1), and x³.
Base area, A = x*(4x-1) = 4x² - x.
Volume, V = (4x² - x)*(x³) = 4x⁵ - x⁴.
The volume is a 5-th order polynomial. It has two terms.
It could be written as
V(x) = 4x⁵ - x⁴ + 0x³ + 0x² + 0x¹ + 0x⁰.
Only terms involving x⁵ and x⁴ have non-zero coefficients.

3 0

3 years ago

Read 2 more answers

Solve the following surd given below <br>(1-√5)÷(1+√5)

Shkiper50 [21]

$\dfrac{1-\sqrt 5}{1+\sqrt 5}\\\\\\=\dfrac{\left( 1- \sqrt 5\right)\left( 1- \sqrt 5\right)}{\left( 1+ \sqrt 5\right)\left( 1- \sqrt 5\right)}\\\\\\=\dfrac{\left( 1-\sqrt 5)^2}{1^2 - \left(\sqrt 5 \right)^2}\\\\\\=\dfrac{1+\left(\sqrt 5 \right)^2 -2 \sqrt 5\cdot 1}{1-5}\\\\\\=\dfrac{1+5-2\sqrt 5}{-4}\\\\\\=-\dfrac{6-2\sqrt 5}{4}\\\\\\=-\dfrac{2\left(3-\sqrt 5 \right)}{4}\\\\\\=-\dfrac{3-\sqrt 5}{ 2}\\\\\\=\dfrac{\sqrt 5 -3}{2}$

4 0

2 years ago

Find the acute angle formed by line 2y=x+1

givi [52]

Answer:

26.57°

Step-by-step explanation:

$2y = x + 1 \\ y = \frac{1}{2} x + 1 \\ equating \: it \: with \\ y = mx + b \\ slope \: m = \frac{1}{2} \\ \because \: \tan \theta = m \\ \therefore \: \tan \theta = \frac{1}{2} = 0.5 \\ \therefore \: \theta = {tan}^{ - 1} (0.5) \\\therefore \: \theta = {tan}^{ - 1} ( \tan \: 26.565051177 \degree) \: \\ \\ \huge \red{ \boxed{\therefore \: \theta = 26.57 \degree}}$

6 0

3 years ago

When dividing decimals, in which situation might you use a trailing zero?

kiruha [24]

Answer:

Option C

Step-by-step explanation:

When dividing a number by another number that is not completely divisible, for example 10÷4 we start by getting 2 as the divider then remainer from 10-(2*4)=2. The remainder being 2 is not divisible by 4, we introduce a decimal and trailing zero. 20÷4=5 hence the answer of 10÷4 will be 2.5 because it had a remainder and we introduced a trailing zero.

3 0

4 years ago