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Burka [1]
3 years ago
9

Which of the following is the solution to |x+8|=1?

Mathematics
2 answers:
bija089 [108]3 years ago
7 0

The solution to |x+8|=1 is  -7,-9

Explanation:

Given :

|x+8|=1

To Find:

The solution to |x+8|=1

Solution:

Now, we know the Properties of modulus function as  

|x|  = x          if x>0

|x|= -x           if x<0

Similarly property will be followed in the given question as

Case 1:  if x>-8  

Then the given equation will become as  

|x+8|= x+8=1

After solving the equation , we will get

x= -7

Similarly,  

Case2: if x<-8

Then the given equation will become as  

|x+8|= -(x+8)=1

After solving the equation , we will get  

x= -9

Hence,  the possible values of x are -7,-9

KonstantinChe [14]3 years ago
6 0

Answer:

-7 OR -9

Step-by-step explanation:

8-7 in the inside

Absolute value of 1 is 1

OR

8-9 in the inside for -1

Absolute value of -1 is 1

Absolute value signs makes everything positive

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The circumference of the circle is increasing at a rate of 0.5 meters per minute. What's the rate of change of the area of the c
morpeh [17]

Answer:

The rate of change of the area of the circle when the radius is 4 meters = 2 meters²/minute ⇒ answer 4

Step-by-step explanation:

* Lets revise the chain rule in the derivative

- If dy/da = m and dx/da = n, and you want to find dy/dx

∴ dy/dx = dy/da ÷ dx/da = m ÷ n = m/n

* In our problem we have

- The rate of increasing of the circumference dC/dt = 0.5 meters/minute

- We need the find the rate of change of the area of the circle

 when the radius is 4 meters

- The common element between the circumference and the area

 of the circle is the radius of the circle

* We must to find dC/dr and dA/dr and use the chain rule to

 find dA/dr

- Find the rate of change of the radius dr/dt

∵ C = 2πr

- Find the derivative of C with respect to r

∴ dC/dr = 2π ⇒ (1)

∵ dC/dt = 0.5 meters/minute ⇒ (2)

- Divide (1) by (2) to get dr/dt by using chain rule

∵ dC/dt ÷ dC/dr = 0.5 ÷ 2π

∴ dC/dt × dr/dC = 0.5 × 1/2π ⇒ cancel dC together and change

   0.5 to 1/2

∴ dr/dt = 1/2 × 1/2π = 1/4π ⇒ (3)

- Find the rate of change of the area dA/dt

∵ A = πr²

- Find the derivative of A with respect to r

∴ dA/dr = 2πr

∵ r = 4

∴ dA/dr = 2π(4) = 8π ⇒ (4)

- Multiply (4) by (3) to get dA/dt by using chain rule

∵ dA/dr × dr/dt = 8π × 1/4π ⇒ divide 8 by 4 and cancel π

∴ dA/dt = 2 meters²/minute

* The rate of change of the area of the circle when the radius is

  4 meters = 2 meters²/minute

3 0
3 years ago
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