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3 years ago

What is the antiderivative of secx-tanx

Mathematics

2 answers:

Leto [7]3 years ago

7 0

Answer:

tan

(

)

sec

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)

sec

(

)

Step-by-step explanation:

Ivenika [448]3 years ago

6 0

Step-by-step explanation:

∫ (sec x − tan x) dx

∫ sec x dx + ∫ -tan x dx

∫ (sec²x + sec x tan x) / (sec x + tan x) dx + ∫ (-sin x / cos x) dx

ln(sec x + tan x) + ln(cos x) + C

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What is the simplified form of x+5/3x+4 + x+4/x+3

alina1380 [7]

$x + \frac{5}{3}x + 4 + x + \frac{4}{x} + 3 \\ x + \frac{5x}{3}+ 4 + x + \frac{4}{x}+ 3 \\ (x + \frac{5x}{3} + x) + (4 + 3) + \frac{4}{x} \\ x = \frac{11x}{3} + 7 + \frac{4}{x}$

3 0

3 years ago

Solve the inequality

GenaCL600 [577]

-1 < c + 2 < 3....subtract 2 from all sections
-1 - 2 < c + 2 - 2 < 3 - 2...simplify
-3 < c < 1
==============================
32 > 16 - 4g > 12....subtract 16 from all sections
32 - 16 > 16 - 16 - 4g > 12 - 16....simplify
16 > -4g > -4 ...now divide all sections by -4, and change inequality signs
16/-4 < (-4/-4)g < -4/-4...simplify
-4 < g < 1
============================
6y + 1 > = 10
6y > = 10 - 1
6y > = 9
y > = 9/6 which reduces to 3/2 or 1 1/2

-3/2y > = 9 ....multiply both sides by -2/3, cancelling the -3/2 on the left...and change the inequality sign
y < = 9 * -2/3
y < = -18/3 which reduces to - 6

so y > = 9/6(or 1 1/2) or y < = -6

3 0

3 years ago

the half life of c14 is 5730 years. Suppose that wood found at an archeological excavation site contains about 35% as much C14 a

Furkat [3]

Answer:

The wood was cut approximately 8679 years ago.

Step-by-step explanation:

At first we assume that examination occured in 2020. The decay of radioactive isotopes are represented by the following ordinary differential equation:

$\frac{dm}{dt} = -\frac{m}{\tau}$ (Eq. 1)

Where:

$\frac{dm}{dt}$ - First derivative of mass in time, measured in miligrams per year.

$\tau$ - Time constant, measured in years.

$m$ - Mass of the radioactive isotope, measured in miligrams.

Now we obtain the solution of this differential equation:

$\int {\frac{dm}{m} } = -\frac{1}{\tau}\int dt$

$\ln m = -\frac{1}{\tau} + C$

$m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$ (Eq. 2)

Where:

$m_{o}$ - Initial mass of isotope, measured in miligrams.

$t$ - Time, measured in years.

And time is cleared within the equation:

$t = -\tau \cdot \ln \left[\frac{m(t)}{m_{o}} \right]$

Then, time constant can be found as a function of half-life:

$\tau = \frac{t_{1/2}}{\ln 2}$ (Eq. 3)

If we know that $t_{1/2} = 5730\,yr$ and $\frac{m(t)}{m_{o}} = 0.35$ , then:

$\tau = \frac{5730\,yr}{\ln 2}$

$\tau \approx 8266.643\,yr$

$t = -(8266.643\,yr)\cdot \ln 0.35$

$t \approx 8678.505\,yr$

The wood was cut approximately 8679 years ago.

5 0

3 years ago

If you answer this i will give you the BRAINLIEST Pls answer Asap

Eva8 [605]

Answer:

You know that negative 3 1/2 is the lowest number so you would put that first. The greatest number would be the coldest in Celsius, and 1/20 would be the last question (the sea level) if calculations are correct, you would get full credit.

5 0

2 years ago

What is the following product?

jenyasd209 [6]

Answer:

$10\sqrt{3}$

Step-by-step explanation:

$\sqrt{30} .\sqrt{10} \\= \sqrt{300} \\=\sqrt{100*3} \\= 10 \sqrt{3}$

6 0

3 years ago