Given:
The given polynomial is
When it divided by (x+1) gives remainder 0 and when divided by (x-2) gives remainder of 45.
To find:
The values of m and n.
Solution:
According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is P(c).
Let the given polynomial be P(x).
When it divided by (x+1) gives remainder 0. So, P(-1)=0.
...(i)
When P(x) is divided by (x-2) gives remainder of 45. So, P(2)=0
...(ii)
Multiply 2 on both sides of (i).
...(iii)
Subtract (iii) from (ii).
Putting m=5.5 in (i), we get
Therefore, the values of m and n are 5.5 and -21.5 respectively.
<span>You need (8-6) 2 extra gallons to take a bath. With sixty people bathing, you'll need 60*2=120 extra gallons to meet the extra demand for water. Alternatively, you could note that 60 bathers*8 gallons per bath=480 gallons of water would be used for 60 baths and 60*6=360 needed for showers. The difference would be 480-360=120 gallons.</span>
You would get $3 every year.
That is because since you got $18 in 6 years you would need to divide 6 into 18 and you would get $3 every year
Answer:
619.13 feet
Step-by-step explanation:
Please find the attachment.
Let x represent the distance between doghouse to the foot of the tower.
We have been given that from the top of a vertical tower, 331 feet above the surface of the earth, the angle of depression to a doghouse is 28 degrees 8'. We are asked to find the distance between doghouse to the foot of the tower.
First of all, we will convert our given angle into degrees as it is given in degrees and minutes.
We will divide 8 by 60 to convert 8 minutes into degrees as:
The doghouse, tower and angle of depression forms a right triangle with respect to ground, where, 331 feet is opposite side and x is adjacent side to angle 28.13 degrees.
Upon rounding to nearest hundredth, we will get:
Therefore, the doghouse is 619.13 feet far from the foot of the tower.
