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The <em><u>correct answer</u></em> is:
3 inches.
Explanation:
We will use the Rational Roots Theorem to solve this.
First we can divide both sides of the equation by 4 in order to simplify it:
In order to solve this, we want the polynomial set equal to 0. To do this, subtract 105 from both sides:
The Rational Roots Theorem says that if p/q is a root of the polynomial, then p is a factor of the constant term and q is a factor of the leading coefficient. The constant term is -105. Drawing a factor tree, we find that the factors of this number are 1, -1, 3, -3, 5, -5, 7, -5, 15, -15, 21, -21. The leading coefficient is 1; its only factor is 1. This means p/q must be a whole number, and can be any of the factors of 105.
Using synthetic division, we try 1 in the box:
<u>1 |</u> 1 -18 80 -105
_______<u> 1</u>__<u> -17</u>___<u>63</u>__
1 -17 63 -42
Since there is a remainder, this is not a root. Trying -1,
<u>-1 |</u> 1 -18 80 -105
_______<u>-1</u>__<u> 19 </u>_<u>-99</u>_
1 -19 99 -204
This is not a root; in fact, it shows us that none of the negatives will be a factor, as the absolute values increase as we complete the synthetic division.
Trying 3,
3 | 1 -18 80 -105
________<u>3</u>__<u>-45</u>___<u>105</u>_
1 -15 35 0
Since there is no remainder, 3 is a root, and is the answer we are looking for.
Answer:
1. " second picture"
2. The graph of h(x) is shown below.
Step-by-step explanation:
The given function is
h(x)=7\sin xh(x)=7sinx
The general form of sine function is
f(x)=a\sin(bx+c)+df(x)=asin(bx+c)+d
Where, a is amplitude, b is period, c is phase shift and d is vertical shift.
So, the amplitude of the given function is 7, period is 1, phase shift is 0 and vertical shift is 0.
It means the minimum value of function is -7 and maximum value is 7.
Put x=0 in the given function.
h(x)=7\sin (0)=7(0)=0h(x)=7sin(0)=7(0)=0
Put x=-\frac{\pi}{2}x=− 2ππ in the given function.
h(x)=7\sin (-\frac{\pi}{2})=-7(1)=-7h(x)=7sin(−2π )=−7(1)=−7
Put x=\frac{\pi}{2}x= 2π in the given function.
h(x)=7\sin (\frac{\pi}{2})=7(1)=7h(x)=7sin( 2π )=7(1)=7
Therefore the points on the function are (0,0), (-\frac{\pi}{2},-7),(\frac{\pi}{2},7)(− 2π ,−7),( 2π,7) .
The graph of function is shown below.
"Hope this helps"
