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2 years ago

5

Maria was preparing the oven to bake brownies. The recipe's direction was to pre-heat the oven to 350 F but her oven thermometer

was in C. What should be the thermometer reading before Maria puts the baking pan full of the brownie mix in the oven?

1 answer:

Akimi4 [234]2 years ago

7 0

176.667 C, round accordingly.

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13 If B is the midpoint of AC, and AC = 8x – 20,<br><br> find BC.<br><br> 3x-1<br><br> А в

Papessa [141]

Answer:

BC = 26

Step-by-step explanation:

Given that:

B is the midpoint of AC

Then AC = AB + BC

AC = 8x - 20 and AB = 3x - 1

Then,

8x - 20 = (3x - 1) + BC

8x - 20 - (3x - 1) = BC

8x - 20 - 3x + 1 = BC

5x - 19 = BC

But AB = BC

5x - 19 = 3x - 1

5x - 3x = - 1 + 19

2x = 18

x = 9

Hence,

Since BC = AB = 3x - 1

3(9) - 1

27 - 1

= 26

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2 years ago

In a bike race: Julie came in ahead of Roger. Julie finished after James. David beat James but finished after Sarah. In what pla

mel-nik [20]

write it out in the order they give

Julie , Roger

James , Julie, Roger

David, James, Julie, Roger

Sarah, David, James, Julie, Roger

David is in 2nd place

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2 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,

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

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2 years ago

How many grams of salicylic acid should be added to 75 g of a polyethylene glycol ointment to prepare an ointment containing 6%

Alla [95]

Answer:

4.79 g

Step-by-step explanation:

mass of salicylic acid = ??

Mass of polyethylene = 75 g

% w/w concentration = 6% w/w

Let the mass of salicylic acid be x

Let the mass of solution = 75 + x

from

% w/w = mass of solute/ mass of solution * 100

Hence concentration of salicylic is;

6 = (x/75 + x) * 100

6/100 = x/75 + x

0.06 (75 + x) = x

4.5 + 0.06x =x

4.5 = x-0.06x

x = 4.5/0.94

x= 4.79 g

6 0

2 years ago

Write the equivalent fraction, the reduced fraction, and the decimal equivalent for 45%. Jenny solved this problem and her work

svp [43]

Answer:

Jenny did not make any mistake.

Step-by-step explanation:

From the information given:

We are asked to do three things.

To find the equivalent fraction of 45%, The reduced fraction of 45%, The decimal fraction of 45%

The equivalent fraction of 45% = $\mathbf{\dfrac{45}{100}}$

The reduced fraction means to divide $\mathbf{\dfrac{45}{100}}$ to its lowest value.

i.e. dividing both the numerator and denominator by 5, we have:

$\mathbf{\dfrac{9}{20}}$

The decimal fraction of 45% = 0.45

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2 years ago

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