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4 years ago

How are all triangles the same

Mathematics

2 answers:

True [87]4 years ago

7 0

Their angles add up to 360 degrees no matter what triangle.

Elina [12.6K]4 years ago

4 0

They are all the same because If two of their angles are equal, then the third angle must also be equal, because angles of a triangle always add to make 180°.

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Please help me with this question!!

nata0808 [166]

Answer:

(4, 3)

Step-by-step explanation:

x = (-2 + 10)/2 = 4

y = (3+3)/2 = 3

(4,3)

6 0

3 years ago

Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of

kifflom [539]

Looks like we have

$\vec F(x,y,z)=z^2x\,\vec\imath+\left(\dfrac{y^3}3+\sin z\right)\,\vec\jmath+(x^2z+y^2)\,\vec k$

which has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(z^2x)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial z}=z^2+y^2+x^2$

By the divergence theorem, the integral of $\vec F$ across $S$ is equal to the integral of $\nabla\cdot\vec F$ over $R$ , where $R$ is the region enclosed by $S$ . Of course, $S$ is not a closed surface, but we can make it so by closing off the hemisphere $S$ by attaching it to the disk $x^2+y^2\le1$ (call it $D$ ) so that $R$ has boundary $S\cup D$ .

Then by the divergence theorem,

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(x^2+y^2+z^2)\,\mathrm dV$

Compute the integral in spherical coordinates, setting

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

so that the integral is

$\displaystyle\iiint_R(x^2+y^2+z^2)\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^1\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{2\pi}5$

The integral of $\vec F$ across $S\cup D$ is equal to the integral of $\vec F$ across $S$ plus the integral across $D$ (without outward orientation, so that

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\iint_D\vec F\cdot\mathrm d\vec S$

Parameterize $D$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=-u\,\vec k$

Then we have

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^1\left(\frac{u^3}3\sin^3v\,\vec\jmath+u^2\sin^2v\,\vec k\right)\times(-u\,\vec k)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^1u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac\pi4$

Finally,

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\left(-\frac\pi4\right)=\boxed{\frac{13\pi}{20}}$

6 0

4 years ago

10 POINTS AND WILL GIVE BRAINLIEST

lisov135 [29]

$35,000 times 20% you figure that out you get $7,000 so the core value of the car $35k-7,000 after four years is 7,000 is the value after four years

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4 years ago

Solve for x. Find the exact answer by simplifying the radical.<br> 3<br> 24

zvonat [6]

Download the app named connects works everytime i swear

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3 years ago

A manufacturing process has a? 70% yield, meaning that? 70% of the products are acceptable and? 30% are defective. if threethree

Setler79 [48]

1. Assume the manufacturer produced 100 products.

2. 70 are acceptable and 30 are defective.

3. the first product has a probability of 70/100 to be selected from the acceptable ones. The second 69/99 (one is removed from the good ones) and the third one 68/98

4. so P(pick 3 consecutive acceptable products)= $\frac{70}{100}* \frac{69}{99}* \frac{68}{98}= \frac{7*69*68}{10*99*98}=$ =0.339

5. If familiar to the Combination formula C(n, r)= $\frac{n!}{r!(n-r)!}$ :

P(picking 3 acceptable out of 100)=n(picking 3 acceptable)/n(picking 3)=C(70, 3)/C(100/3)= $\frac{70!}{3!67!}/\frac{100!}{3!97!}=\frac{70*69*68*67!}{3!67!}/\frac{100*99*98*97!}{3!97!}= \frac{70*69*68}{3!}/\frac{100*99*98}{3!}= \frac{70*69*68}{100*99*98}$ = 0.339

7 0

4 years ago