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2 years ago

6

Successive discounts of 20% and 10% are taken on an item priced at $16. Describe how to find the sale price of the item and give

the sale price.

2 answers:

eimsori [14]2 years ago

7 0

Answer:

Find 20% of $16: (0.2)(16) = $3.20 Subtract $3.20 from $16: 16 - $3.20 = $12.80 Take 10% of $12.80: (0.1)(12.80) = $1.28 Subtract $1.28 from $12.80: $12.80 - $1.28 = $11.52 literally the dude here has it right

Step-by-step explanation:

icang [17]2 years ago

5 0

<span>Successive discounts of 20% and 10% are taken on an item priced at $16.
=> Let's find out how much is the discount in all.
=> 16 dollars * .20 = 3.2 dollars
=> 16 - 3.2 = 12.8 dollars.
then another 10% discount,
=> 12.8 * .10 = 1.28 dollars
=> 12.8 - 1.28 = 11.52 dollars is not the price minus the discounts,</span>

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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

-2(x - 2) - 4x = 3(x + 1) - 9x

Sonbull [250]

$\huge\boxed{\text{no solution}}$

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Add $6x$ on both sides of the equation. $4=3$

This statement is false, so this equation has $\boxed{\text{no solution}}$ .

4 0

2 years ago

A tank contains 24 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let

LenKa [72]

Answer:

a) $V(t) = 24 - 2t$

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Step-by-step explanation:

The volume of the tank in terms of the time can be described by the following equation:

$V(t) = V(0) - at$

In which V(0) is the initial volume and a is the hourly decrease rate.

a. Write a formula that expresses v in terms of t.

The tank initially contains 24 gallons of water, which means that $V(0) = 24$

Drains at a constant rate of 2 gallons per hour, so $a = 2$

Then

$V(t) = V(0) - at$

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$V(3) = 24 - 2*3 = 18$

$V(6) = 24 - 2*6 = 12$

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2 years ago

Christopher runs a farm stand that sells apples and bananas. Yesterday Christopher sold 35 pounds of apples and 34 pounds of ban

AVprozaik [17]

Answer:

Pound of Apples = 2$

Pound of Banana = 2.75$

Step-by-step explanation:

Data

Yesterday Christopher sold 35 pounds of apples (35A) and 34 pounds of bananas (34B) for a total revenue of $163.5 (=163.50)

Today he sold 15 pounds of apples (15A) and 17 pounds of bananas (17B) for a total revenue of $76.75. (=76.75)

Now well, we have a system of the equation

35A+34B=163.50

15A+17B=76.75

we must eliminate A or B, As you can see 34 is twice 17, so we multiply on both sides of the equation so as not to alter it

35A+34B=163.50 35A+34B=163.50

15A+17B=76.75 (-2) ⇒ <u>-30A-34B=-153.50</u>

5A-0B = 10

5A=10 ⇒ A=10/5 ⇒ A=2

and B:

35(2)+34B=163.5 ⇒ 70+34B=163.5 ⇒ 34B=163.5-70

34B=93.5 = 93.5/34

B=2.75

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2 years ago

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stiv31 [10]

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2 years ago

Read 2 more answers