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3 years ago

6

The diameter of a circle is 19 inches. If the diameter is extended 5 inches beyond the circle to point C, how long is the tangen

t segment from point C to the circle?

1 answer:

svetlana [45]3 years ago

5 0

The tangent segment from point C is 5 inches from the circle

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What 3 digit number has tens digit that is 5 more than the ones digit and a hundreds digit that is 8 less than the tens digit?

Darina [25.2K]

194 is your answer.
<span>Since you have a three digit number the hundredth digit is not zero. Then from the fact that h = t -8, t must be 9, then u = 9-5 or 4.</span>

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3 years ago

F=e−yi−xe−yj is conservative. find a scalar potential f and evaluate the line integral over any smooth path c connecting a(0,0)

Alexxx [7]

If $\mathbf F$ is conservative, then there is a scalar function $f$ such that

$\nabla f(x,y)=\mathbf F(x,y)\iff\dfrac{\partial f}{\partial x}\,\mathbf i+\dfrac{\partial f}{\partial y}\,\mathbf j=e^{-y}\,\mathbf i-xe^{-y}\,\mathbf j$

Setting the first components equal to one another, we can integrate both sides to find

$\dfrac{\partial f}{\partial x}=e^{-y}\implies f(x,y)=xe^{-y}+g(y)$

Differentiating both sides with respect to $y$ gives

$\dfrac{\partial f}{\partial y}=-xe^{-y}+\dfrac{\mathrm dg}{\mathrm dy}=-xe^{-y}$
$\implies\dfrac{\mathrm dg}{\mathrm dy}=0$
$\implies g(y)=C$

so that

$f(x,y)=xe^{-y}+C$

By the fundamental theorem of calculus, we have that

$\displaystyle\int_{\mathcal C}\mathbf F\cdot\mathrm d\mathbf r=\int_{\mathcal C}\nabla f\cdot\mathrm d\mathbf r=f(1,1)-f(0,0)=\frac1e$

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3 years ago

Which best describes the meaning of the term theorem?

timurjin [86]

The answer would be "B". A seems to be a "hypothesis". C is an axiom and D is a definition. I hope this was helpful.

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4 years ago

Brandy is making a peach pie for her grandmother for christmas. the diameter of the pie is 12 in. if three-fourths of the area o

Mariulka [41]

Roughly 84 square in

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3 years ago

What is the measure of ∠w, rounded to the nearest degree? 19° 19° 32° 32° 56° 56° 71° 71° a horizontally-aligned scalene triangl

ella [17]

Answer:

(d) 71°

Step-by-step explanation:

The desired angle in the given isosceles triangle can be found a couple of ways. The Law of Cosines can be used, or the definition of the sine of an angle can be used.

<h3>Sine</h3>

Since the triangle is isosceles, the bisector of angle W is an altitude of the triangle. The hypotenuse and opposite side with respect to the divided angle are given, so we can use the sine relation.

sin(W/2) = Opposite/Hypotenuse

sin(W/2) = (35/2)/(30) = 7/12

Using the inverse sine function, we find ...

W/2 = arcsin(7/12) ≈ 35.685°

W = 2×36.684° = 71.37°

W ≈ 71°

<h3>Law of cosines</h3>

The law of cosines tells you ...

w² = u² +v² -2uv·cos(W)

Solving for W gives ...

W = arccos((u² +v² -w²)/(2uv))

W = arccos((30² +30² -35²)/(2·30·30)) = arccos(575/1800) ≈ 71.37°

W ≈ 71°

7 0

2 years ago