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Dimas [21]
3 years ago
13

Write the standard equation of a circle that passes through (1, −6) with center (7, −2).

Mathematics
1 answer:
Eduardwww [97]3 years ago
7 0

Answer:

D: (x – 7)2 + (y + 2)2 = 52

Step-by-step explanation:

Circle: (x -h)² + (y - k)² = r²    center (h , k)    r: radius

(1 , -6) on the circle: radius   √(1 - 7)² + (-6 - (-2))² = √36 + 16 = √52

(x -7)² + (y +2)² = (√52)² = 52

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How to Find a Greatest Common Factor in a Polynomial?
Lina20 [59]

Answer:

To find the greatest common factor of a polynomial, first take all of the coefficients and list out their factors. After doing this, we can identify the greatest number that appears in each of the lists.

From there we will look for the lowest exponent for every variable. We'll use that number in our final answer. Remember, when doing this, that if the variable doesn't appear in a term, then the exponent is assumed to be 0.

4 0
3 years ago
Three forces act on an object. Two of the forces are at an angle of 95◦ to each other and have magnitudes 35 N and 7 N. The thir
Cerrena [4.2K]

We want to find \vec F_4 such that the object needs is in equilibrium:

\vec F_1+\vec F_2+\vec F_3+\vec F_4=\vec0

We're told that F_1=35\,\mathrm N, F_2=7\,\mathrm N, and F_3=9\,\mathrm N. We also know the angle between \vec F_1 and \vec F_2 is 95º, which means

\vec F_1\cdot\vec F_2=F_1F_2\cos95^\circ=245\cos95^\circ

\vec F_3 is perpendicular to both \vec F_1 and \vec F_2, so \vec F_1\cdot\vec F_3=\vec F_2\cdot\vec F_3=0.

If we take the dot product of \vec F_1 with the sum of all four vectors, we get

\vec F_1\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0

\vec F_1\cdot\vec F_1+\vec F_1\cdot\vec F_2+\vec F_1\cdot\vec F_3+\vec F_1\cdot\vec F_4=0

{F_1}^2+\vec F_1\cdot\vec F_2+0+\vec F_1\cdot\vec F_4=0

\implies\vec F_1\cdot\vec F_4=-\left({F_1}^2+\vec F_1\cdot\vec F_2\right)

We can do the same thing with \vec F_2 and \vec F_3:

\vec F_2\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0

\implies\vec F_2\cdot\vec F_4=-\left(\vec F_1\cdot\vec F_2+{F_2}^2\right)

\vec F_3\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0

\implies\vec F_3\cdot\vec F_4=-{F_3}^2

Finally, if we do this with \vec F_4, we get

\vec F_4\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0

\implies{F_4}^2=-\left(\vec F_1\cdot\vec F_4+\vec F_2\cdot\vec F_4+\vec F_3\cdot\vec F_4\right)

\implies{F_4}^2=-\left(-\left({F_1}^2+\vec F_1\cdot\vec F_2\right)-\left(\vec F_1\cdot\vec F_2+{F_2}^2\right)-{F_3}^2\right)

\implies F_4=\sqrt{{F_1}^2+{F_2}^2+{F_3}^2+2(\vec F_1\cdot\vec F_2)}

\implies\boxed{F_4\approx36.2\,\mathrm N}

7 0
2 years ago
4.9÷9.8 how do you come up with the answer
Naddika [18.5K]
All you need to do is divide it 4.9/9.8 which would equal 0.5
3 0
2 years ago
In a 45-45-90, what is the ratio of the length of one leg to the length of the other leg
butalik [34]

Answer:

1:1

Step-by-step explanation:

In such a triangle, the legs are of equal length (but are shorter than the hypotenuse).  Thus, the ratio in question is 1:1.

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2 years ago
What are the common factors that Greg found?
Arada [10]
<span>The answer is:  1, 2, 7, 14 .
</span>_____________________________________________________
Explanation:
________________________________________________
FIrst, list all the factors of 42 (positive integers):
________________________________________________________
1, 42
2, 21, 
3, 14,
6, 7
_________________________________________________
     Then list all the factors of 28 (positive integers):
____________________________________________________
<span>     1, 28
     2, 14,
     4, 7
</span>_____________________________________________________
        Now, list all numbers that occur for BOTH the factors of "28" AND the factors of "42"
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        1, 2, 7, 14
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      The answer is:  1, 2, 7, 14 .
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3 years ago
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