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Degger [83]
3 years ago
6

What is the distance between points A(-3,4) and B(1,-2)?

Mathematics
1 answer:
SashulF [63]3 years ago
6 0

Answer:

7.211103

Step-by-step explanation:

For:

(X1, Y1) = (-3, 4)

(X2, Y2) = (1, -2)

Distance Equation Solution:

d=(1−(−3))2+(−2−4)2−−−−−−−−−−−−−−−−−−−√

d=(4)2+(−6)2−−−−−−−−−−√

d=16+36−−−−−−√

d=5–√2

d=7.211103

:)

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Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.
lora16 [44]
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.


The sum x^2+y^2 can be written as: x^2+y^2=(x+y)^2-2xy, 
<span>
from the binomial expansion formula: </span>(x+y)^2=x^2+2xy+y^2.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>

</span>x^2+y^2=(x+(-3x+18))^2-2x(-3x+18)=(-2x+18)^2+6x^2-36x=4x^2-72x+18^2+6x^2-36x=10x^2-108x+18^2.

This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.


At x=5.4, the expression 10x^2-108x+18^2, which is equivalent to x^2+y^2, takes it smallest value.

Substituting, we would find 10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324=32.4 This is the smallest value of the expression. 


For x=5.4, y=-3x+18=-3(5.4)+18=1.8.



Answer:   (5.4, 1.8)
8 0
3 years ago
I need help today like right now
Artyom0805 [142]
W area you just add the sides. or multiply the. if you add the it is 24
5 0
2 years ago
How to solve this? Don't just give me the answer help me learn this.
Sphinxa [80]

Answer:

I'm not entirely sure but I think that what is says is that it wants you to find the value of x in (4x+28) to make it 116 degrees because it is that same angle. So what you do is you get (4x+28)=116 and you do this because they are the same angle so you use 116 and get it to solve x. Since I'm lazy, then I go to this website and type the equation in: m a t h w a y . c o m but without all of the spaces, I had to do that so it would let me answer this, but I'll do it the real way this time. (4x+28)=116  Their is a rule in math that as long as you do something to one side of the equal sign in the equation, you have to do it to the other and it will still work. So, you minus 28 from both sides so that you can get rid of it and you now have 4x=88. Now you should know this part but you divide 4 from both sides to make so x is alone. Now you have x=22 because you divided 4 from each side. So their is your answer: x=22.

Step-by-step explanation: If you have the answer key that you can check from to make sure you got it right because I know some teachers let you do that, then you should make sure that is right, but I am pretty sure it is.


6 0
3 years ago
The surface area of a sphere is decreasing at the constant rate of 3π sq. cm/sec . At what rate is the volume of the sphere decr
olga nikolaevna [1]
Whooh



SA=4pir²
take derivitive
dSA/dt=8pir dr/dt

and do the volume as well
V=(4/3)pir³
dV/dt=4pir² dr/dt

we need to solve for dV/dt
to do taht we need dr/dt
so

dSA/dt=8pir dr/dt
given dSA/dt=3pi cm/sec
r=2
3pi=8pi2 dr/dt
3=16 dr/dt
3/16=dr/dt

now do the volume
dV/dt=4pir² dr/dt
r=2
dr/dt=3/16
dV/dt=4pi2² (3/16)
dV/dt=16pi(3/16)
dV/dt=3pi

nice
the volume of the sphere is decreasing at 3pi cm/sec as well
3 0
3 years ago
Which equation is equivalent to 3[x+3(4x-5)]=15x-24
Klio2033 [76]
3[x+3(4x-5)]=15x-24; x+12x-15=5x-8 (divide both sides by 3); 8x=7 (move all the x's to one side), x=7/8
7 0
3 years ago
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