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3 years ago

Can I get the answer please. If you get it right, the reward is a BRAINLIEST

Mathematics

1 answer:

liraira [26]3 years ago

7 0

Answer:

66.75m

Step-by-step explanation:

Area of Triangle: 4.5m

$\frac{bh}{2}$

height is 4.5m

base is 2m

overall height is 10m so 10-3.5-5= height of triangle

overall base is 10.75m so 10.75-3.25-2.5-3= base of triangle

Area of the smallest rectangle: 13.5m

base is 3m (provided)

height is 4.5m (same as triangle)

Area of the medium sized rectangle: 16.25m

base is 2.5m (provided)

height is 6.5

overall height is 10m so 10-3.5= the height of this rectangle

Area of largest rectangle: 32.5

base is 3.25m (provided)

heigh is 10m (provided)

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3 years ago

Report Error Suppose $P(x)$ is a polynomial of smallest possible degree such that: $\bullet$ $P(x)$ has rational coefficients $\

motikmotik

Answer:

We want a polynomial of smallest degree with rational coefficients with zeros in $\sqrt{7}$ , $1 - \sqrt{6}$ and -3. The last root gives us the factor (x+3). Hence, our polynomial is

$P(x) =(x+3)q(x)$

where $q$ is a polynomial with rational coefficients and roots $\sqrt{7}$ and $1 - \sqrt{6}$ . The root $\sqrt{7}$ gives us a factor $x-\sqrt{7}$ , but in order to obtain rational coefficients we must consider the factor $x^2-7$ .

An analogue idea works with $1 - \sqrt{6}$ . For convenience write $x - 1 + \sqrt{6} = ( x - 1) + \sqrt{6}$ . This gives the factor $(x-1)^2-6$ . Hence,

$P(x) = (x+3)(x^2-7)((x-1)^2-6)=x^5+x^4-18x^3-22x^2+77x+105$

Notice that $P(-1)=24$ . So, in order to satisfy the last condition we divide by 3 the whole polynomial, without altering its roots. Finally, the wanted polynomial is

$P(x) =(1/3)x^5+(1/3)x^4-6x^3-(22/3)x^2+(77/3)x+35$

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 $x-\sqrt7$ will introduce in the expression, we need to multiply by its conjugate $x+\sqrt7$ . Hence, we will obtain $x^2-7$ 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.