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2 years ago

Find the coordinates of the image of point R(4, –1) rotated 270 percent about the origin.

Mathematics

1 answer:

NeX [460]2 years ago

8 0

(4,-1) turns into (1,4) because the equation for that is (x,y)->(y•-1,x)

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The temperature function (in degrees Fahrenheit) in a three dimensional space is given by T(x, y, z) = 3x + 6y - 6z + 1. A bee i

madam [21]

You're looking for the extreme values of $T(x,y,z)=3x+6y-6z+1$ subject to $x^2+y^2+z^2=9$ . The Lagrangian is

$L(x,y,z,\lambda)=3x+6y-6z+1+\lambda(x^2+y^2+z^2-9)$

with critical wherever the partial derivatives vanish:

$L_x=3+2\lambda x=0\implies x=-\dfrac3{2\lambda}$

$L_y=6+2\lambda y=0\implies y=-\dfrac3\lambda$

$L_z=-6+2\lambda z=0\implies z=\dfrac3\lambda$

$L_\lambda=x^2+y^2+z^2-9=0$

Substituting the first three solutions into the last equation gives

$\dfrac9{4\lambda^2}+\dfrac9{\lambda^2}+\dfrac9{\lambda^2}=9$

$\implies\lambda=\pm\dfrac32$

$\implies x=1,y=2,z=-2\text{ or }x=-1,y=-2,z=2$

At these points, we have

$T(1,2,-2)=28$

$T(-1,-2,2)=-26$

so the highest temperature the bee can experience is 28º F at the point (1, 2, -2), and the lowest is -26º F at the point (-1, -2, 2).

6 0

2 years ago

Graph the linear equation.

NNADVOKAT [17]

Go one box left from the 0 an 3 down

8 0

2 years ago

C is the midpoint of ab. Ac = 5x-13, cb = 4x+7. What is the length of ac

krek1111 [17]

AC in this problem will equal 87. If the (units) is where you put the put units like feet, inches if there is units.

3 0

2 years ago

Will Mark brainliest if correct.

Serhud [2]

Answer:

SF = 7/3

Step-by-step explanation:

Like the problem hint says, you want to put the new coordinate over the old one to find the scale factor. We'll use both x and y.

-7/-3 = 7/3

14/6 = 7/3

Therefore, the scale factor is 7/3.

4 0

2 years ago

A bag contains 10 counters

juin [17]

44%

6/10 = 3/5

3/5 x 1/10 = 3/50

3/50 x 1/10 = 3/500

3/500 / 2/6 = 44/100

7 0

2 years ago