1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Masja [62]
3 years ago
11

Which one is the answer

Mathematics
1 answer:
MAVERICK [17]3 years ago
3 0

Answer:

I don't know Sorry

   

Step-by-step explanation:

You might be interested in
a canoe rental company offers two trips along the river. Neil and Gabriela choose the longer trip. If they split the cost of the
jek_recluse [69]
Neil and gabriela  will both pay half. Or 50%.
8 0
3 years ago
Read 2 more answers
Find the exact area of the surface obtained by rotating the curve about the x-axis. y = 1 + ex , 0 ≤ x ≤ 9
tekilochka [14]

The surface area is given by

\displaystyle2\pi\int_0^9(1+e^x)\sqrt{1+e^{2x}}\,\mathrm dx

since y=1+e^x\implies y'=e^x. To compute the integral, first let

u=e^x\implies x=\ln u

so that \mathrm dx=\frac{\mathrm du}u, and the integral becomes

\displaystyle2\pi\int_1^{e^9}\frac{(1+u)\sqrt{1+u^2}}u\,\mathrm du

=\displaystyle2\pi\int_1^{e^9}\left(\frac{\sqrt{1+u^2}}u+\sqrt{1+u^2}\right)\,\mathrm du

Next, let

u=\tan t\implies t=\tan^{-1}u

so that \mathrm du=\sec^2t\,\mathrm dt. Then

1+u^2=1+\tan^2t=\sec^2t\implies\sqrt{1+u^2}=\sec t

so the integral becomes

\displaystyle2\pi\int_{\pi/4}^{\tan^{-1}(e^9)}\left(\frac{\sec t}{\tan t}+\sec t\right)\sec^2t\,\mathrm dt

=\displaystyle2\pi\int_{\pi/4}^{\tan^{-1}(e^9)}\left(\frac{\sec^3t}{\tan t}+\sec^3 t\right)\,\mathrm dt

Rewrite the integrand with

\dfrac{\sec^3t}{\tan t}=\dfrac{\sec t\tan t\sec^2t}{\sec^2t-1}

so that integrating the first term boils down to

\displaystyle2\pi\int_{\pi/4}^{\tan^{-1}(e^9)}\frac{\sec t\tan t\sec^2t}{\sec^2t-1}\,\mathrm dt=2\pi\int_{\sqrt2}^{\sqrt{1+e^{18}}}\frac{s^2}{s^2-1}\,\mathrm ds

where we substitute s=\sec t\implies\mathrm ds=\sec t\tan t\,\mathrm dt. Since

\dfrac{s^2}{s^2-1}=1+\dfrac12\left(\dfrac1{s-1}-\dfrac1{s+1}\right)

the first term in this integral contributes

\displaystyle2\pi\int_{\sqrt2}^{\sqrt{1+e^{18}}}\left(1+\frac12\left(\frac1{s-1}-\frac1{s+1}\right)\right)\,\mathrm ds=2\pi\left(s+\frac12\ln\left|\frac{s-1}{s+1}\right|\right)\bigg|_{\sqrt2}^{\sqrt{1+e^{18}}}

=2\pi\sqrt{1+e^{18}}+\pi\ln\dfrac{\sqrt{1+e^{18}}-1}{1+\sqrt{1+e^{18}}}

The second term of the integral contributes

\displaystyle2\pi\int_{\pi/4}^{\tan^{-1}(e^9)}\sec^3t\,\mathrm dt

The antiderivative of \sec^3t is well-known (enough that I won't derive it here myself):

\displaystyle\int\sec^3t\,\mathrm dt=\frac12\sec t\tan t+\frac12\ln|\sec t+\tan t|+C

so this latter integral's contribution is

\pi\left(\sec t\tan t+\ln|\sec t+\tan t|\right)\bigg|_{\pi/4}^{\tan^{-1}(e^9)}=\pi\left(e^9\sqrt{1+e^{18}}+\ln(e^9+\sqrt{1+e^{18}})-\sqrt2-\ln(1+\sqrt2)\right)

Then the surface area is

2\pi\sqrt{1+e^{18}}+\pi\ln\dfrac{\sqrt{1+e^{18}}-1}{1+\sqrt{1+e^{18}}}+\pi\left(e^9\sqrt{1+e^{18}}+\ln(e^9+\sqrt{1+e^{18}})-\sqrt2-\ln(1+\sqrt2)\right)

=\boxed{\left((2+e^9)\sqrt{1+e^{18}}-\sqrt2+\ln\dfrac{(e^9+\sqrt{1+e^{18}})(\sqrt{1+e^{18}}-1)}{(1+\sqrt2)(1+\sqrt{1+e^{18}})}\right)\pi}

4 0
4 years ago
17 is added to a number, the result is 37 less than twice the number. Find the number
vesna_86 [32]

Answer:

x=6.67

Step-by-step explanation:

17+x=37-2x

17+x-x=37-2x-x

17=37-3x

17-37=37-37-3x

-20=-3x

-20/-3=-3x/3

6.666667=x

3 0
4 years ago
the sum of two numbers is 94. their difference is 14. write a system of equations that describes this situation. solve by elimin
lisov135 [29]

Answer:

0A + B = 3AB

10 / B = 3 - (1/A)

10/B is between 2 and 3.

B = 5, A = 1

Step-by-step explanation:

67

4 0
3 years ago
Can u pls help me with this question
yan [13]
18.1 i have to keep typing bc it’s required to be 20 characters long so ignore this
6 0
3 years ago
Other questions:
  • HELP FAST URGENTLY!!!
    12·1 answer
  • All solutions to y=2x^4+5x^3+38x^2+125x-300
    11·1 answer
  • Maia's calculator displays a number as 9.125 E10. What is this number in standard form?
    12·2 answers
  • List five numbers that hav 3,5,and 7 as prime factors
    10·1 answer
  • Solve by factoring:<br> 5t=t ^2
    13·1 answer
  • The perimeter of a rectangle is 34 units. it's width is 6.5 units. Write an equation to determine the length of the rectangle
    5·1 answer
  • PLEASE HELP IM TIMED!
    15·1 answer
  • Last month, a car dealership sold 376 new cars.
    15·1 answer
  • Find the measures of the interior angles.
    14·1 answer
  • In 2018 there were 238 Republicans and 201 Democrats in the House of Representatives. Find the percentage of Democrats in the Ho
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!