Answer:
1. k=0
2. yes, result is still a polynomial.
3. yes, f and g must have the same degree to have deg(f+g) < deg(f) or deg(g)
Step-by-step explanation:
1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x)
for k=0 any polynomial f(x) will reduce f(k) to the constant term.
2. If we multiply a polynomial by a constant, is the result a polynomial?
Yes, If we multiply a polynomial by a constant, the result is always a polynomial.
3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?
Yes.
If
deg(f+g) < deg(f) and
deg(f+g) < deg(g)
then it means that the two leading terms cancel out, which can happen only if f and g have the same degree.
Answer: An article was sold at a 20% discount, at Rs. 400. What was its marked price?
Let M denotes the required marked price of the given article.
Hence from above data we get following relation,
(1 - 20/100)*M = 400
or (4/5)*M = 400
or M = (5/4)*400 = 500 (Rs) [Ans]
Step-by-step explanation:
Looking at the question, we can see we have 5 different numbers that can go in any order.
<u>5</u> * <u>4</u> * <u>3</u>
The above is basically saying there are 5 different numbers that can be multiplied by 4 other numbers. Those 2 can be multiplied by 3 different ones, leaving us with a 3 digit positive integer.
5 * 4* 3 = 60
R=(3V4<span>Home: Kyle's ConverterKyle's CalculatorsKyle's Conversion Blog</span>Volume of a Sphere CalculatorReturn to List of Free Calculators<span><span>Sphere VolumeFor Finding Volume of a SphereResult:
523.599</span><span>radius (r)units</span><span>decimals<span> -3 -2 -1 0 1 2 3 4 5 6 7 8 9 </span></span><span>A sphere with a radius of 5 units has a volume of 523.599 cubed units.This calculator and more easy to use calculators waiting at www.KylesCalculators.com</span></span> Calculating the Volume of a Sphere:
Volume (denoted 'V') of a sphere with a known radius (denoted 'r') can be calculated using the formula below:
V = 4/3(PI*r3)
In plain english the volume of a sphere can be calculated by taking four-thirds of the product of radius (r) cubed and PI.
You can approximated PI using: 3.14159. If the number you are given for the radius does not have a lot of digits you may use a shorter approximation. If the radius you are given has a lot of digits then you may need to use a longer approximation.
Here is a step-by-step case that illustrates how to find the volume of a sphere with a radius of 5 meters. We'll u
π)⅓
The equivalent expression to given expression is 1/3.
<h3>What is Equivalent Expression?</h3>
Equivalent expressions are defined as algebraic expressions which give the same resulting expression. An algebraic expression (or) a variable expression is defined as a combination of terms by the operations such as addition, subtraction, multiplication, division.
Here, given expression
= 
= 
= 1/3
Thus, the equivalent expression to given expression is 1/3.
Learn more about equivalent expression from:
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