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3 years ago

Find the inverse of the following

Mathematics

2 answers:

spin [16.1K]3 years ago

7 0

Answer:

Inverse should be (-2y^2 + 4)/(ln 3)

Step-by-step explanation:

Find Y, for reversed roles/position of X and Y. Cancel out square root with ^2. Cancel out -2 by multiplying. Then, add 4 to both sides to cancel them out. Finally, nature log it and divide it to isolate X.

Andrei [34K]3 years ago

3 0

Answer:
Use this site
It helps a lot
:)

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An amount of $18,000 is borrowed for 10 years at 8.25% interest, compounded annually. If the loan is paid in full at the end of

cricket20 [7]

218 dollars will have to be paid back

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3 years ago

Question 4

laiz [17]

Answer:

I just solved a question similar to this

Let's understand it

It's saying she got 660 or it is that her weekly pay is 660

So now let weekly pay which is P be 660

Hence the formulae is given

It's 480 + 18 (h – 30) = 660

Now its just boring calculation

If you mark it brainleist I will do the calculation for you wink wink

Never mind

480 + 18 (h – 30) = 660

18 (h – 30) = 660-480

18 (h – 30) = 120

(h – 30) = 120/18

(h – 30) = 6.6

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5 0

3 years ago

8y=28-4x <br> 6x+8y=6<br> find the solution to the system of equations

sesenic [268]

first equation equivalent to

4x+8y=28

substract with second equation

-2x=22

divide with -2

x=-11

substitute to first equation

8y=28-4(-11)

8y=72

divide with 8

y=9

so the solution is (-11,9)

8 0

4 years ago

Which of the following graphs best represents the solution to the pair of equations below? y = −x + 6 y = 2x − 3 A coordinate pl

spayn [35]

Answer:

The lines are

i) y=-x+6

ii) y=2x-3

The solution of the system of equations is found by equalizing the 2 equations:

-x+6=2x-3

-2x-x=-6-3

-3x=-9

x=-9/(-3)=3

substitute x=3 in either i) or ii):

i) y=-3+6=3

ii) y=2(3)-3=6-3=3

(the result is the same, so checking one is enough)

This means that the point (3, 3) is a point which is in both lines, so a solution to the system.

In graphs, this means that the lines intersect at (3, 3) ONLY

Answer: The graph where the lines intersect at (3, 3)

6 0

3 years ago

Find equations of the spheres with center(3, −4, 5) that touch the following planes.a. xy-plane b. yz- plane c. xz-plane

postnew [5]

Answer:

(a) (x - 3)² + (y + 4)² + (z - 5)² = 25

(b) (x - 3)² + (y + 4)² + (z - 5)² = 9

Step-by-step explanation:

The equation of a sphere is given by:

(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ---------------(i)

Where;

(x₀, y₀, z₀) is the center of the sphere

r is the radius of the sphere

Given:

Sphere centered at (3, -4, 5)

=> (x₀, y₀, z₀) = (3, -4, 5)

(a) To get the equation of the sphere when it touches the xy-plane, we do the following:

i. Since the sphere touches the xy-plane, it means the z-component of its centre is 0.

Therefore, we have the sphere now centered at (3, -4, 0).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;

$d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}$

$d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}$

$d = \sqrt{(0)^2+ (0)^2 + (-5)^2}$

$d = \sqrt{(25)}$

d = 5

This distance is the radius of the sphere at that point. i.e r = 5

Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 5²

(x - 3)² + (y + 4)² + (z - 5)² = 25

Therefore, the equation of the sphere when it touches the xy plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 25

(b) To get the equation of the sphere when it touches the yz-plane, we do the following:

i. Since the sphere touches the yz-plane, it means the x-component of its centre is 0.

Therefore, we have the sphere now centered at (0, -4, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;

$d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}$

$d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}$

$d = \sqrt{(-3)^2 + (0)^2+ (0)^2}$

$d = \sqrt{(9)}$

d = 3

This distance is the radius of the sphere at that point. i.e r = 3

Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 3²

(x - 3)² + (y + 4)² + (z - 5)² = 9

Therefore, the equation of the sphere when it touches the yz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 9

(b) To get the equation of the sphere when it touches the xz-plane, we do the following:

i. Since the sphere touches the xz-plane, it means the y-component of its centre is 0.

Therefore, we have the sphere now centered at (3, 0, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;

$d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}$

$d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}$

$d = \sqrt{(0)^2 + (4)^2+ (0)^2}$

$d = \sqrt{(16)}$

d = 4

This distance is the radius of the sphere at that point. i.e r = 4

Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 4²

(x - 3)² + (y + 4)² + (z - 5)² = 16

Therefore, the equation of the sphere when it touches the xz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 16

3 0

3 years ago