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horsena [70]
3 years ago
8

1. A three-dimensional figure that has one vertex and one circular base is known as a:

Mathematics
1 answer:
user100 [1]3 years ago
7 0

Answer:

cone

Step-by-step explanation:

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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.

4 0
3 years ago
Find the valuesof integers x and y: x^(8)+16y^(8)=0
avanturin [10]

Answer:

x=0,

y=0

Step-by-step explanation:

x^8+16y^8=0\\(x^{2}) ^{4} +16(y^{2}) ^{4} =0\\x^2\geq 0,y^2\geq 0\\sum~ of ~two ~positive~ integers ~is~ zero~ if~ each=0\\so~x=0,~y=0

8 0
3 years ago
-3n^2-13n +1= 0<br> need this asap. i’m lost.
lesya692 [45]

Answer:

if you're trying to find the discriminant, then it's 181.

Step-by-step explanation:

6 0
3 years ago
I need help on number 3 please
Misha Larkins [42]

Answer:

\large\boxed{x=10}\\\\\boxed{40^o,\ 50^o,\ 90^o}

Step-by-step explanation:

We have the right triangle. The sum of the angles measured in the right triangle is 90 °. Therefore we have the equation:

4x+(6x-10)=90[/tex][tex]4x+6x-10=90  <em>                 add 10 to both sides</em>

10x=100           <em>divide both sides by 10</em>

x=10

The measure of angles:

Put the value of x to the eqpressions:

6x-10\to6(10)-10=60-10=50\\\\4x\to4(10)=40

5 0
3 years ago
In the figure below, G is between E and H, and F is the midpoint of EG. if FH=11 and FG=5 , find EH
Gemiola [76]
<span>F is the midpoint of EG
so EF =  FG  = 5
EG =  EF + FG = 5 + 5 = 10

</span>
EH = EF + FH = 5 + 11 = 16

answer
EH = 16
6 0
3 years ago
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