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2 years ago

Given: Circle X with radius r and circle

Mathematics

1 answer:

valina [46]2 years ago

8 0

Answer:

The given parameters are:

Circle X

Radius = r

Circle Y

Radius = s

Step-by-step explanation:

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Help finding derivative

marusya05 [52]

$\bf \displaystyle \cfrac{d}{dx}\left[ \int\limits_{\sqrt{x}}^{\frac{\pi }{2}}~[cos(t^2)]dt \right]\implies \cfrac{d}{dx}\left[ -\int\limits_{\frac{\pi }{2}}^{\sqrt{x}}~[cos(t^2)]dt \right]\\\\\\ \cfrac{d}{dx}\left[ -\int\limits_{\frac{\pi }{2}}^{x^{\frac{1}{2}}}~[cos(t^2)]dt \right]\\\\
-------------------------------\\\\
u=x^{\frac{1}{2}}\implies \cfrac{du}{dx}=\cfrac{1}{2\sqrt{x}}\\\\\\ \textit{and now, let's use the \underline{2nd fundamental theorem of calculus}}\\\\
-------------------------------\\\\$

$\bf \displaystyle \cfrac{d}{dx}\left[ -\int\limits_{\frac{\pi }{2}}^{u}~[cos(t^2)]dt \right]\impliedby \cfrac{df}{dx}=\cfrac{df}{du}\cdot \cfrac{du}{dx}
\\\\\\
\cfrac{df}{dx}=-cos(u^2)\cdot \cfrac{du}{dx}\implies \cfrac{df}{dx}=-cos(u^2)\cdot \cfrac{1}{2\sqrt{x}}
\\\\\\
\cfrac{df}{dx}=-cos[(\sqrt{x})^2]\cdot \cfrac{1}{2\sqrt{x}}\implies \cfrac{df}{dx}=-\cfrac{cos(x)}{2\sqrt{x}}$

6 0

3 years ago

Aubrey's scarf is 4 inches more than half the length

mina [271]

Answer

Tyrone's scarf is 15 inches long

Step-by-step explanation:

34-4= 30

30/2= 15

5 0

4 years ago

Find the length of DE. Round to the nearest hundredth. (Picture included)

LenKa [72]

Notice the picture
we have, the opposite side
the angle
and we want the hypotenuse

so recall your SOH CAH TOA $\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad 
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}

\\ \quad \\\\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent} =$

which one has all that? low and behold, is Ms Sine,
so let's bother Ms Sine

$\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\implies sin(27^o)=\cfrac{18}{hypotenuse}
\\\\\\
hypotenuse=\cfrac{18}{sin(27^o)}$

make sure your calculator is in Degree mode, since the angle here is in degrees, as opposed to Radian mode

8 0

3 years ago

7/8 times 1/3 times 2/5

allsm [11]

Answer:

7/60

Step-by-step explanation:

7/8 times 1/3 is 7/24.

Then, 7/24 times 2/5 is 7/60

When multiplying fractions you just multiply across. For example, 7/8 times 1/3. 7 times 1 is 7 and 8 times 3 is 24. So, 7/8 times 1/3 is 7/24.

Hope this helps :)

4 0

3 years ago

The equation of line CD is Y=3X -3. Write an equation of a line perpendicular to line CD in slope intercept form that contains p

OLga [1]

(I'm learning this right now!)

y = 3x - 3
If a line is perpendicular to another line, they have negative reciprocal slopes.
So you would use the slope -1/3.

Use y - y₁ = m(x - x₁) to get an equation in slope intercept form.
Plug the numbers in.

y - 1 = -1/3(x - 3)
y - 1 = -1/3x + 1
y = -1/3x + 2

An equation of a line perpendicular to line CD is y = -1/3x + 2.

8 0

3 years ago