If f(x) = 52, what is the value of f(-6), to the nearest hundredth (if necessary)?

Which of the following sets are subspaces of R3 ?

Ratling [72]

Answer:

The following are the solution to the given points:

Step-by-step explanation:

for point A:

$\to A={(x,y,z)|3x+8y-5z=2} \\\\\to for(x_1, y_1, z_1),(x_2, y_2, z_2) \varepsilon A\\\\ a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)$

$=3(aX_l +bX_2) + 8(ay_1 + by_2) — 5(az_1+bz_2)\\\\=a(3X_l+8y_1- 5z_1)+b (3X_2+8y_2—5z_2)\\\\=2(a+b)$

The set A is not part of the subspace $R^3$

for point B:

$\to B={(x,y,z)|-4x-9y+7z=0}\\\\\to for(x_1,y_1,z_1),(x_2, y_2, z_2) \varepsilon B \\\\\to a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)$

$=-4(aX_l +bX_2) -9(ay_1 + by_2) +7(az_1+bz_2)\\\\=a(-4X_l-9y_1+7z_1)+b (-4X_2-9y_2+7z_2)\\\\=0$

$\to a(x_1,y_1,z_1)+b(x_2, y_2, z_2) \varepsilon B$

The set B is part of the subspace $R^3$

for point C: $\to C={(x,y,z)|x$

In this, the scalar multiplication can't behold

$\to for (-2,-1,2) \varepsilon C$

$\to -1(-2,-1,2)= (2,1,-1)$ ∉ C

this inequality is not hold

The set C is not a part of the subspace $R^3$

for point D:

$\to D={(-4,y,z)|\ y,\ z \ arbitrary \ numbers)$

The scalar multiplication s is not to hold

$\to for (-4, 1,2)\varepsilon D\\\\\to -1(-4,1,2) = (4,-1,-2)$ ∉ D

this is an inequality, which is not hold

The set D is not part of the subspace $R^3$

For point E:

$\to E= {(x,0,0)}|x \ is \ arbitrary) \\\\\to for (x_1,0 ,0) ,(x_{2},0 ,0) \varepsilon E \\\\\to a(x_1,0,0) +b(x_{2},0,0)= (ax_1+bx_2,0,0)\\$

The $x_1, x_2$ is the arbitrary, in which $ax_1+bx_2$ is arbitrary

$\to a(x_1,0,0)+b(x_2,0,0) \varepsilon E$

The set E is the part of the subspace $R^3$

For point F:

$\to F= {(-2x,-3x,-8x)}|x \ is \ arbitrary) \\\\\to for (-2x_1,-3x_1,-8x_1),(-2x_2,-3x_2,-8x_2)\varepsilon F \\\\\to a(-2x_1,-3x_1,-8x_1) +b(-2x_1,-3x_1,-8x_1)= (-2(ax_1+bx_2),-3(ax_1+bx_2),-8(ax_1+bx_2))$

The $x_1, x_2$ arbitrary so, they have $ax_1+bx_2$ as the arbitrary $\to a(-2x_1,-3x_1,-8x_1)+b(-2x_2,-3x_2,-8x_2) \varepsilon F$

The set F is the subspace of $R^3$

5 0

2 years ago

A lamp shade has a radius of 9 inches. What is the circumference of the top of the shade? Use 3.14 to approximate pi. Round your

horsena [70]

Circumference is diameter times pi, diameter is radius times 2. The answer should be 57 inches.

7 0

3 years ago

Read 2 more answers

Identify each number as rational or irrational.

ratelena [41]

Step-by-step explanation:

sorry answer ia not clear

3 0

2 years ago

What the correct answer do not want the wrong answer please

Crank

Answer:

388.5yd²

Step-by-step explanation:

We have Triangle TUV

In the question, we are given already

Angle U = 32°

Angle T = 38°

Angle V = ???

Side t = 31yd

Side u = ?

Side v = ?

Area of the triangle= ?

Step 1

We find the third angle = Angle V

Sum of angles in a triangle = 180°

Third angle = Angle V = 180° - (32 + 38)°

= 180° - 70°

Angle V = 110°

Step 2

Find the sides u and v

We find these sides using the sine rule

Sine rule or Rule of Sines =

a/ sin A = b/ Sin B

Hence for triangle TUV

t/ sin T = u/ sin U = v/ sin V

We have the following values

Angle T = 38°

Angle U = 32°

Angle V = 110°

We are given side t = 31y

Finding side u

u/ sin U= t/ sin T

u/sin 32 = 31/sin 38

Cross Multiply

sin 32 × 31 = u × sin 38

u = sin 32 × 31/sin 38

u = 26.68268yd

u = 26.68yd

Finding side x

v / sin V= t/ sin T

v/ sin 110 = 31/sin 38

Cross Multiply

sin 110 × 31 = v × sin 38

v = sin 110 × 31/sin 38

v = 47.31573yd

v = 47.32yd

To find the area of triangle TUV

We use heron formula

= √s(s - t) (s - u) (s - v)

Where S = t + u + v/ 2

s = (31 + 26.68 + 47.32)/2

s = 52.5

Area of the triangle = √52.5× (52.5 - 31) × (52.5 - 26.68 ) × (52.5 - 47.32)

Area of the triangle = √150967.6032

Area of the triangle = 388.5454973359yd²

Approximately to the nearest tenth =388.5yd²

5 0

3 years ago

Which equation would you use to find x?

Nitella [24]

You would use B to find X

8 0

3 years ago