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3 years ago

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a school buys 200 calculators at a special price. x of them were scientific calculators at R 89 a piece and the rest were financ

ial calculators at R 599 a piece. an expression in terms of x,for the total number of calculators bought is?

1 answer:

garri49 [273]3 years ago

3 0

We have 200 calculators and x are scientific. That means (200-x) are financial.

Total cost = 89x + 599(200-x)

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X+½x+7y=0 what is the value of y=?

Ganezh [65]

Answer:

$\frac{-3x}{14}$

Step-by-step explanation:

$x+\frac{1}{2}x+7y = 0\\$

$1.5x + 7y = 0$

$7y = -1.5x$

$y = \frac{-1.5x}{7}$

$= \frac{-3x}{14}$

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of <em>f</em> :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of <em>g</em> :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

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$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So <em>f</em> has a minimum of -7 and a maximum of 299.

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3 years ago

Circle A has a diameter of approximately 20 inches and an area of approximately 300 in2.

Katena32 [7]

Answer:

4. About 2,700 in2

Step-by-step explanation:

The area of a circle ( $A$ ), measured in square inches, is directly proportional to the square of its diameter ( $d$ ), measured in inches. That is:

$A \propto d^{2}$

$A = k\cdot d^{2}$

Where $k$ is the constant of proportionality, dimensionless.

In consequence, the following relationship between circles A and B is obtained:

$\frac{A_{B}}{A_{A}} = \frac{d_{B}^{2}}{d_{A}^{2}}$

The area of the circle B is now cleared:

$A_{B} =\left(\frac{d_{B}}{d_{A}} \right)^{2}\cdot A_{A}$

Given that $d_{A} = 20\,in$ , $d_{B} = 60\,in$ and $A_{A} = 300\,in^{2}$ , then:

$A_{B} = \left(\frac{60\,in}{20\,in} \right)^{2}\cdot (300\,in^{2})$

$A_{B} = 2700\,in^{2}$

Therefore, the correct answer is 4.

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3 years ago

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Vlad1618 [11]

Answer:

Slope=4

x−intercept=−

4

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=−4

b−intercept=

1

16

=16.0000

Step-by-step explanation:

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3 years ago