A saving account balance is now less then $550 Write an inequality

Consider the function on the interval (0, 2π). f(x) = sin x + cos x (a) Find the open intervals on which the function is increas

Annette [7]

Answer:Increasing in x∈(0,π/4)∪(5π/4,2π) decreasing in(π/4,5π/4)

Step-by-step explanation:

given f(x) = sin(x) + cos(x)

f(x) can be rewritten as $\sqrt{2} [\frac{sin(x)}{\sqrt{2} }+\frac{cos(x)}{\sqrt{2} } ]..................(a)\\\\\ \frac{1}{\sqrt{2} } = cos(45) = sin(45)\\\\$

Using these result in equation a we get

f(x) = $\sqrt{2} [ cos(45)sin(x)+sin(45)cos(x)]\\\\= \sqrt{2} [sin(45+x)]..........(b)$

Now we know that for derivative with respect to dependent variable is positive for an increasing function

Differentiating b on both sides with respect to x we get

f '(x) = $f '(x)=\sqrt{2} \frac{dsin(45+x)}{dx}\\ \\f'(x)=\sqrt{2} cos(45+x)\\\\f'(x)>0=>\sqrt{2} cos(45+x)>0$

where x∈(0,2π)

we know that cox(x) > 0 for x∈[0,π/2]∪[3π/2,2π]

Thus for cos(π/4+x)>0 we should have

1) π/4 + x < π/2 => x<π/4 => x∈[0,π/4]

2) π/4 + x > 3π/2 => x > 5π/4 => x∈[5π/4,2π]

from conditions 1 and 2 we have x∈(0,π/4)∪(5π/4,2π)

Thus the function is decreasing in x∈(π/4,5π/4)

5 0

3 years ago

If h(x)=6-x, what is the value of (h ∘h)(10)

V125BC [204]

Good evening ,

______

Answer:

(h ∘h)(10)=10

______

Details:

If h(x)=6-x ,the value of (h ∘h)(10) = h(h(10)) = h(6-10) = h(-4)=6-(-4) =6+10 =10.

:)

8 0

3 years ago

Solve for x: 2xsquared+4x-16=0

sergejj [24]

2x² + 4x - 16 = 0
2(x²) + 2(2x) - 2(8) = 0
 2(x² + 2x - 8) = 0
 2 2
 x² + 2x - 8 = 0
 x = -(2) ± √((2)² - 4(1)(-8))
 2(1)
 x = -2 ± √(4 + 32)
 2
 x = -2 ± √(36)
 2
 x = -2 ± 6
 2
 x = -1 ± 3
 x = -1 + 3 U x = -1 - 3
 x = 2 x = -4

7 0

3 years ago

nine out of 20 teens said they eat breakfast every morning. What is a reasonable prediction for the number of teens out of 280 w

egoroff_w [7]

Answer:

126

Step-by-step explanation:

9 ÷ 20 = 0.45

280 × 0.45 = 126

7 0

4 years ago

Read 2 more answers

Jack measured 1 amp as the total current in a certain circuit when he applied 20 volts to the circuit. When he applied 60 volts,

Natali5045456 [20]

Answer:

The linear equation is V - IR =0

The total current is 2.5 amps

Step-by-step explanation:

According to ohms law, the voltage (V) applied is directly proportional to current (I)

Therefore, V = IR

V - IR = 0 (R is resistance)

When V = 20, I = 1

The 1st equation is 20 - R = 0

When V = 60, I = 3

The 2nd equation is 60 - 3R = 0

From the 1st equation, R = 20

Substiting R = 20, V = 50 into the linear relation V - IR = 0

50 - 20I = 0

50 = 20I

I = 50/20 = 2.5 amps

3 0

3 years ago