Which one should I choose.

What is the solution of √x^2+49=x+5

Alexandra [31]

Answer:

x=12/5

Step-by-step explanation:

6 0

4 years ago

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Let a and b be real numbers. Find all vectors (2,a,b) orthogonal to (1, -5, -4). What are all the vectors that are orthogonal to

malfutka [58]

Answer:

B) vector of the form (2,r, (2-5r)/4)

Step-by-step explanation:

(2,b,c) is orthogonal to (1,-5,-4) if

2*1-5b-4c=0, i.e,

5b+4c=2

We have equation with two variables, so we know that we wil have infinity lot solutions.

Let’s b be some real number r, so we have:

4c=2-5r, i.e,

c=(2-5r)/4.

So there is infinite lot of othogonal vectors of the form: (2, r, (2-5r)/c)) where r is any real number.

7 0

3 years ago

Find the area of the surface generated by revolving the curve xequals=StartFraction e Superscript y Baseline plus e Superscript

artcher [175]

Solution :

$x=f(y) = \frac{e^y + e^{-y}}{2} , \ \ \ \ \ 0 \leq y \leq \ln 2$

$\frac{dx}{dy} = \frac{e^y + e^{-y}}{2}$

$\left(\frac{dx}{dy}\right)^2 = \frac{e^{2y} - 2 + e^{-2y}}{4}$

$1+\left(\frac{dx}{dy}\right)^2 = 1+\frac{e^{2y} - 2 + e^{-2y}}{4} = \frac{e^{2y} + 2 + e^{-2y}}{4}$

$= \left(\frac{e^y + e^{-y}}{2}\right)^2$

$\sqrt{1+\left(\frac{dx}{dy}\right)^2} = \sqrt{\left(\frac{e^y + e^{-y}}{2}\right)^2}=\frac{e^y + e^{-y}}{2}$

$S = \int_{y=a}^b 2 \pix \sqrt{1+\left(\frac{dx}{dy}\right)^2 } \ dy$

$=\int_{0}^{\ln2} 2 \pi \left(\frac{e^y+e^{-y}}{2}\right) \left(\frac{e^y+e^{-y}}{2}\right) \ dy$

$=\frac{\pi}{2}\int_{0}^{\ln 2}(e^y+e^{-y})^2 \ dy = \frac{\pi}{2}\int_{0}^{\ln 2}(e^{2y}+e^{-2y}+2) \ dy$

$=\frac{\pi}{2} \left[ \frac{e^{2y}}{2} + \frac{e^{-2y}}{-2} + 2y \right]_2^{\ln 2}$

$=\frac{\pi}{2} \left[ \left(\frac{e^{2 \ln 2}}{2} + \frac{e^{-2\ln2}}{-2} + 2 \ln2 \right) - \left( \frac{e^0}{2} + \frac{e^0}{-2}+0\right) \right]$

$=\frac{\pi}{2}\left[ \frac{e^{\ln4}}{2} - \frac{e^{\ln(1/4)}}{2} + \ln 4 - \left( \frac{1}{2} - \frac{1}{2} + 0 \right) \right]$

$=\frac{\pi}{2} \left[\frac{4}{2} -\frac{1/4}{2} + \ln 4 \right]$

$=\frac{\pi}{2} \left[ 2-\frac{1}{8} + \ln 4 \right]$

$=\left( \frac{15}{8} + \ln 4 \right) \frac{\pi}{2}$

Therefore, $S = \frac{15}{16} \pi + \pi \ln 2$

3 0

3 years ago

What is the measurement of angle x plz help me !

Ilia_Sergeevich [38]

x = 60, since its n equilateral triangle

4 0

3 years ago

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Jill filled up the gas tank in her new hybrid car.Jill put 10.3 gallons of gas in her car and she has driven 473.8 miles. Determ

mafiozo [28]

Jill put 10.3 gallons of gas into her car. She drove for 473.8 miles.

So we have to find how many miles per gallon she drove.

473.8 into 10.3 = 46

To make sure= 10.3 x 46 = 473.8

So Jill drove 46 miles per gallon.

5 0

3 years ago