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3 years ago

15

The distance from c to d?

1 answer:

myrzilka [38]3 years ago

4 0

Pretty sure it’s
A. 7 units.

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Find the indefinite integral using the substitution provided.

Nady [450]

Answer: $7\text{Ln}\left(e^{2x}+10\right)+C$

This is the same as writing 7*Ln( e^(2x) + 10) + C

=======================================================

Explanation:

Start with the equation $u = e^{2x}+10$

Apply the derivative and multiply both sides by 7 like so

$u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\$

The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)

This way we can do the following substitutions:

$\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\$

Integrating leads to

$\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\$

Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.

To verify the answer, you can apply the derivative to it and you should get back to the original integrand of $\frac{14e^{2x}}{e^{2x}+10}$

4 0

2 years ago

Mulitply (2-2)(3x+4) using distributive property

Sati [7]

8x.......................

3 0

3 years ago

The length of a rectangle is 1 foot less than 3 times the width. The area is 310 ft². Find the dimensions of the rectangle.

sattari [20]

The dimension would be 10, i think

brainly pleaseee

4 0

3 years ago

Can someone pls help me solve this question!!!!!!!

KiRa [710]

Total of 90 fish:

c + p = 90

Charlie gave 1/4 c to Peter. Now

Charlie has c - (1/4) c

Peter has p + (1/4) c

Peter gave 2/5 of his to Charlie. Now

Peter has p + (1/4) c - 2/5( p + (1/4) c )

Charlie has c - (1/4) c + 2/5( p + (1/4) c )

And then they had equal number:

c - (1/4) c + 2/5( p + (1/4) c ) = p + (1/4) c - 2/5( p + (1/4) c )

Let's do the easy subtractions then multiply by 20 to clear the fractions,

(3/4) c + 2/5( p + (1/4) c ) = 3/5( p + (1/4) c )

15c + 8p + 2c = 12p + 3c

14c = 4p

7c = 2p

c + p = 90

2c + 2p = 180

2c + 7c = 180

9c = 180

c = 20

p = 70

Answer: Charlie started with 20, Peter with 70

Check:

Initially C:20, P:70

1/4(20)=5 to P

C:15, P:75

(2/5) 75 = 30 to C

C:45, P45

Good

3 0

3 years ago

Prove or disprove that the point (√5, 12) is on the circle centered at the origin and containing the point (-13, 0). Show your w

pav-90 [236]

Using the equation of the circle, it is found that since it reaches an identity, the point (√5, 12) is on the circle.

<h3>What is the equation of a circle?</h3>

The equation of a circle of center $(x_0, y_0)$ and radius r is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

In this problem, the circle is centered at the origin, hence $(x_0, y_0) = (0,0)$ .

The circle contains the point (-13,0), hence the radius is found as follows:

$x^2 + y^2 = r^2$

$(-13)^2 + 0^2 = t^2$

$r^2 = 169$

Hence the equation is:

$x^2 + y^2 = 169$

Then, we test if point (√5, 12) is on the circle:

$x^2 + y^2 = 169$

$(\sqrt{5})^2 + 12^2 = 169$

25 + 144 = 169

Which is an identity, hence point (√5, 12) is on the circle.

More can be learned about the equation of a circle at brainly.com/question/24307696

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6 0

3 years ago