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3 years ago

Which of the following laws is described in the situation below?

Mathematics

2 answers:

egoroff_w [7]3 years ago

5 0

I think that it is law of detachment but I'm not 100%

fredd [130]3 years ago

5 0

The answer is the answer.

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Use fundamental theorem of calculus to find derivative of the function LOOK AT PHOTO

kykrilka [37]

Let c > 0. Then split the integral at t = c to write

$f(x) = \displaystyle \int_{\ln(x)}^{\frac1x} (t + \sin(t)) \, dt = \int_c^{\frac1x} (t + \sin(t)) \, dt - \int_c^{\ln(x)} (t + \sin(t)) \, dt$

By the FTC, the derivative is

$\displaystyle \frac{df}{dx} = \left(\frac1x + \sin\left(\frac1x\right)\right) \frac{d}{dx}\left[\frac1x\right] - (\ln(x) + \sin(\ln(x))) \frac{d}{dx}\left[\ln(x)\right] \\\\ = -\frac1{x^2} \left(\frac1x + \sin\left(\frac1x\right)\right) - \frac1x (\ln(x) + \sin(\ln(x))) \\\\ = -\frac1{x^3} - \frac{\sin\left(\frac1x\right)}{x^2} - \frac{\ln(x)}x - \frac{\sin(\ln(x))}x \\\\ = -\frac{1 + x\sin\left(\frac1x\right) + x^2\ln(x) + x^2 \sin(\ln(x))}{x^3}$

8 0

2 years ago

Jernel has to figure out the area of her square garage. she knows that one side of the garage is equal to the length of her rabb

Setler [38]

10*10= 100

if 100 equals 1 side, then x = 4 sides

since there are 4 sides on a square you multiply 100 by 4

your answer is 400 units²

Hope this helps!!!

please rate, thank, and mark as brainliest!!!! :)

8 0

4 years ago

Consider the line which passes through the point P(−1,-3,5), and which is parallel to the line x=1+7t, y=2+2t, z=3+4t Find the p

bija089 [108]

The given line is parameterized by

x(t) = 1 + 7t

y(t) = 2 + 2t

z(t) = 3 + 4t

and points in the same direction as the vector

d/dt (x(t), y(t), z(t)) = (7, 2, 4)

So, the line we want has parameteric equations

x(t) = -1 + 7t

y(t) = -3 + 2t

z(t) = 5 + 4t

Solve for t when one of x, y, or z is equal to 0 - this will tell you for which value of t the line cross a given plane. Then determine the other coordinates of these intersections.

• x = 0, which corresponds to the y-z plane:

0 = -1 + 7t ⇒ 7t = 1 ⇒ t = 1/7

y(1/7) = -3 + 2/7 = -19/7

z(1/7) = 5 + 4/7 = 39/7

⇒ intersection = (0, -19/7, 39/7)

• y = 0 (x-z plane):

0 = -3 + 2t ⇒ 2t = 3 ⇒ t = 3/2

x(3/2) = -1 + 21/2 = 19/2

z(3/2) = 5 + 12/2 = 11

⇒ intersection = (19/2, 0, 11)

• z = 0 (x-y plane):

0 = 5 + 4t ⇒ 4t = -5 ⇒ t = -5/4

x(-5/4) = -1 - 35/4 = -39/4

y(-5/4) = -3 - 10/4 = -11/2

⇒ intersection = (-39/4, -11/2, 0)

8 0

2 years ago

500,000,000,000 in scientific notation

Alex Ar [27]

500,000,000,000 in scientific notation:
First you count to 0 zeros behind the 5 which is 11 zeros.
the scientific notation of 500,000,000,000 is:

₁₁
Answer: 5 x 10

I hop this helps :)

5 0

3 years ago

Read 2 more answers

What is the equation of the quadratic graph with a focus of (6, 0) and a directrix of y = −10 ?

Mademuasel [1]

Answer:

$(x-6)^{2}=20(y+5)^{2}$

Step-by-step explanation:

The standard for for the equation of a parabola is $(x-h)^{2}=4p(y-k)$

The focus is given as $(h, k+p)$

The directrix is given by $y=k-p$

Comparing focus given as $(6,0)$ to formula of focus $(h,k+p)$ , we see that $h=6$ and $k+p=0$
Comparing directrix given as $y=-10$ to formula of directrix $y=k-p$ , we can write $k-p=-10$

We can use the two system of equations [ $k+p=0$ and $k-p=-10$ ] to solve for $k$ and $p$ .

Adding the two equations gives us:

$2k=-10\\k=\frac{-10}{2}\\k=-5$

Using this value of $k$ , we can find $p$ by plugging this value in either equation. Let's put it in Equation 1. We have:

$k-p=-10\\-5-p=-10\\-5+10=p\\p=5$

Now, that we know $h=6$ , $k=-5$ , and $p=5$ , we can plug these values in the standard form equation to figure out the parabola's equation. Doing so and rearranging gives us:

$(x-6)^{2}=4(5)(y-(-5))^{2}\\(x-6)^{2}=20(y+5)^{2}\\$

This is the equation of the parabola with focus $(6,0)$ and directrix $y=-10$

3 0

3 years ago

Read 2 more answers