Answer:
We want a polynomial of smallest degree with rational coefficients with zeros in 
, 
and -3. The last root gives us the factor (x+3). Hence, our polynomial is
where 
is a polynomial with rational coefficients and roots and . The root gives us a factor 
, but in order to obtain rational coefficients we must consider the factor 
.
An analogue idea works with . For convenience write 
. This gives the factor 
. Hence,
Notice that 
. So, in order to satisfy the last condition we divide by 3 the whole polynomial, without altering its roots. Finally, the wanted polynomial is
Step-by-step explanation:
We must have present that any polynomial it's determined by its roots up to a constant factor. But here we have irrational ones, in order to eliminate the irrational coefficients that a factor of the type 
will introduce in the expression, we need to multiply by its conjugate 
. Hence, we will obtain that have rational coefficients. Finally, the last condition is given with the intention to fix the constant factor. Usually it is enough to evaluate in the point and obtain the necessary factor.
The answer is
<span>a) 1000=-16t^2+1700, implies t² = -700 /-16, and t= 6.61s
b) </span><span>970= -16t^2+1700, </span><span>implies t² = -730 /-16, and t=6.75s
c)
reasonable domain of h
h is polynomial function, so its domain is R, (all real number)
its range
the inverse of h is h^-1 = sqrt (1700- t / 16), and its domain is </span>
<span><span><span>1700- t / 16>=0, so t <1700,
the range of h is I= ]-infinity, 1700]</span> </span> </span>
Answer:
a. $60
Step-by-step explanation:
We will use simple interest formula to solve our given problem.
, where
A= Amount after t years.
P= Principal amount.
r= Interest rate in decimal form.
t= Time in years.
Let us find amount of loans repayable after 12 months for taking two amounts of $2000 and $1000.
As $2000 and $1000 are less than 2500, so the rate of loan will be 10%.
12 months = 1 year.
Now let us find amount repayable after 12 months for borrowing $1000.
Adding these amounts we will get total repayable amount after 12 months for borrowing $2000 and $1000 separately.
Now let us find repayable amount after 12 months for taking 1 loan. As $3000 is between $2501 and $7500, so rate of loan will be 8%.
Now let us find difference between both repayable loan amounts.
Therefore, the customer should have saved $60, if he had taken out one loan for $3000 and option a is the correct choice.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Whether dividing constant terms or polynomials, we always have definitive terms when it comes to division. Suppose we say, 10x divided by 2. The dividend is the 10x and the divisor is the 2. In other words, the dividend is the number to be divided by the divisor, to obtain the answer called the quotient.
When dividing polynomials, your main goal is to be able to divide the dividend evenly into the <em>divisor</em>. For example, we divide x²+2x+1 by x+1. The first thing you're going to focus is, what term will completely divide the first term of the polynomial? That would be x. Why? Because when you multiply x with x+1, the product is x²+x. When you subtract this from the polynomial, the x² will cancel out. All you have to do is subtract x from 2x, yielding x. Then, you carry down the last term of the equation: +1. You do the steps again. The term that will completely divide x+1 by x+1 is 1. When you subtract the two, you will come up with zero. That means there is no remainder. The polynomial is divisible by the divisor.
x + 1
------------------------------------
x+1| x²+2x+1
- x²+x
----------------------
x +1
- x +
------------
0
