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3 years ago

Work out and simplify where possible 5/18 + 4/9

Mathematics

1 answer:

Fittoniya [83]3 years ago

3 0

Answer:

0.73

Step-by-step explanation:

$\\ \frac{5}{18 } + \frac{4}{9}$

$\\ = \frac{5 + 8}{18}$

$\\ = \frac{13}{18}$

$\\ = 0.73$

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Find an equation of the sphere with point P such that the distance from P to A(−2, 6, 2) is twice the distance from P to B(4, 3,

Sveta_85 [38]

Answer:

$3*x^{2} - 36*x + 3*y^{2} -12*y + 3*z^{2} -4*z + 62 = 0$

Step-by-step explanation:

The distance from a point $P = (x,y,z)$ to another point $A = (a,b,c)$ is given by $((x-a)^{2} + (y-b)^{2} + (z-c)^{2})^{1/2}$ .

So, if the distance from P to A is twice the distance from P to B, we have an equality given by:

$((x+2)^{2} + (y-6)^{2} + (z-2)^{2})^{1/2} = 2*((x-4)^{2} + (y-3)^{2} + (z+1)^{2})^{1/2}$

If we power by 2 both sides of the equality to remove the square roots, we have:

$(x+2)^{2} + (y-6)^{2} + (z-2)^{2} = 4 * ((x-4)^{2} + (y-3)^{2} + (z+1)^{2})$

And solving every parenthesis and operating the similar terms, we have:

$(x^{2} + 4*x + 2) - 4*(x^{2} - 8*x + 16) + (y^{2} - 12 * y + 36) - 4*(y^{2} -6*y + 9) + (z^{2} -4*z+4) - 4*(z^{2}+2*z+1) = 0$

Operating and multiplying both sides by -1:

$(3*x^{2} - 36*x +62) + (3*y^{2} -12*y + 0) + (3*z^{2} -4*z + 0) = 0$

Giving as result:

$3*x^{2} - 36*x + 3*y^{2} -12*y + 3*z^{2} -4*z + 62 = 0$

The sphere can be seen here: https://www.wolframalpha.com/input/?i=3*x%5E2+-+36*x+%2B+3*y%5E2+-12*y+%2B+3*z%5E2+-4*z+%2B+62+%3D+0

7 0

4 years ago

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Lapatulllka [165]

Answer:

Step-by-step explanation:

3 0

3 years ago

Really confused on how to approach this problem.

kkurt [141]

Step-by-step explanation:

For this Q, you should draw a triangle to help you with the values.

cos x =

$\frac{ \sqrt{2} }{2}$

csc x =

$\frac{2}{ \sqrt{2} }$

tan x = sin x/ cos x

= 1

cot x = 1

sec x =

$\frac{ \sqrt{2} }{2}$

x = 45 degrees

6 0

3 years ago

Use the distance formula to calculate the distance between the following two points:

Harrizon [31]

Answer:

d = 11 units if rounded to nearest whole number

Step-by-step explanation:

Distance formula:

d=√((x_2-x_1)²+(y_2-y_1)²)

Your ordered pairs (-1, 1) and (4, 11)

d=√((4-(-1))²+(11-1)²)

d=√((4+1))²+(10))²)

d=√((5)²+ 100)

d = √125

d = 11.18

d = 11 units if rounded to nearest whole number

4 0

3 years ago

1+4=5 2+5=12 3+6=21 5+8= ?

Lady bird [3.3K]

Answer:

Step-by-step explanation:

(1×4)+1=5

(2×5)+2=12

(3×6)+3=21

(5×8)+5=45

right?

7 0

3 years ago