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2 years ago

I need to know this question for edge

Mathematics

1 answer:

Rus_ich [418]2 years ago

4 0

Answer:

first function:

$f(x) = \dfrac{2 - 10}{2 - 0} x + 10 = \\ - 4x + 10$

second one:

$g(x) = \cfrac{ - 4 - 2}{2 - 0} x + 2 = \\ - 3x + 2$

now the intersection:

-4x+10=-3x+2

x=8

then y

y = -4×8+10 = -22

so it's

(8,-22)

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Write the equation of the sphere in standard form. x^2 + y^2 + z^2 + 2x − 4y − 6z = 22

madam [21]

The equation $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ in standard form looks like $(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$ .

Given equation of sphere be $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ .

We are required to express the given equation in the standard form of the equation of sphere.

Equation is basically relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation,quadratic equation, cubic equation or many more depending on the powers of variables. The standard form of the equation of sphere looks like $x^{2} +y^{2} +z^{2} =r^{2}$ .

The given equation is $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ .

We have to break 22 which is in right side into various parts according to the left side of the equation.

$x^{2} +y^{2} +z^{2} +2x-4y-6z=-1-4-9+36$

$x^{2} +y^{2} +z^{2} +2x-4y-6z+1+4+9=36$

$x^{2} +1+2x+y^{2}+4-4y+z^{2} +9-6z=36$

$x^{2} +(1)^{2} +2*1*x+y^{2} +(2)^{2} -2*2y+z^{2} +(3)^{2} -2*3z=36$

$(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$

Hence the equation $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ in standard form looks like $(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$ .

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1 year ago

A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work pro

olchik [2.2K]

Answer:

0.756

Step-by-step explanation:

It is given that a machine has four components, A, B, C, and D.

$P(A)=P(B)=0.93, P(C)=0.95,P(D)=0.92$

If these components set up in such a manner that all four parts must work for the machine to work properly.

We need to find the probability that the machine works properly. It means we have to find the value of $P(A\cap B\cap C\cap D)$ .

If two events X and Y are independent, then

$P(X\cap Y)=P(X)\times P(Y)$

Assume the probability of one part working does not depend on the functionality of any of the other parts.

$P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)$

Substitute the given values.

$P(A\cap B\cap C\cap D)=0.93\times 0.93\times 0.95\times 0.92$

$P(A\cap B\cap C\cap D)=0.7559226$

$P(A\cap B\cap C\cap D)\approx 0.756$

Therefore, the probability that the machine works properly is 0.756.

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3 years ago

8x−5x+4−x=Ax+8. Anyone know

lora16 [44]

Answer:

a = $\frac{2x-4}{x}$

x = $\frac{4}{-a+2}$

Step-by-step explanation:

Let's solve for a.

8x−5x+4−x=ax+8

Step 1: Flip the equation.

ax+8=2x+4

Step 2: Add -8 to both sides.

ax+8+−8=2x+4+−8

ax=2x−4

Step 3: Divide both sides by x.

Let's solve for x.

8x−5x+4−x=ax+8

Step 1: Add -ax to both sides.

2x+4+−ax=ax+8+−ax

−ax+2x+4=8

Step 2: Add -4 to both sides.

−ax+2x+4+−4=8+−4

−ax+2x=4

Step 3: Factor out variable x.

x(−a+2)=4

Step 4: Divide both sides by -a+2.

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2 years ago

What is the diameter of the circle that has a radius of 6

pav-90 [236]

Answer:

12 units

Step-by-step explanation:

The radius is half of the diameter, so we need to double 6 to get 12.

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