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3 years ago

-3<3x less than or equal to 9 on an number line

Mathematics

1 answer:

liraira [26]3 years ago

7 0

-3 < 3x ≤ 9
-1 < x ≤ 3

hope it helps

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The law of cosines reduces to the Pythagorean theorem whenever the triangle is acute. true or false

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Is the given point interior, exterior, or on the circle (x + 2)2 + (y - 3)2 = 81? R(6, 3)

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Hello :
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3 years ago

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Researchers estimate that 15 out of every 25 customers at a store make purchases with a credit card. If the store has 600 custom

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Answer:

360

Step-by-step explanation:

Number of customers who make purchases with a credit card

=15 out of every 25= $\frac{15}{25}=\frac{3}{5}$

The fraction 3/5 represents the part of the customer that makes purchases with credit cards.

Therefore if there are 600 customers tomorrow, 3/5 of them will use a credit card.

$\frac{3}{5} X 600=360$

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3 years ago

If 3x^2 + y^2 = 7 then evaluate d^2y/dx^2 when x = 1 and y = 2. Round your answer to 2 decimal places. Use the hyphen symbol, -,

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Taking $y=y(x)$ and differentiating both sides with respect to $x$ yields

$\dfrac{\mathrm d}{\mathrm dx}\bigg[3x^2+y^2\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[7\bigg]\implies 6x+2y\dfrac{\mathrm dy}{\mathrm dx}=0$

Solving for the first derivative, we have

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x}y$

Differentiating again gives

$\dfrac{\mathrm d}{\mathrm dx}\bigg[6x+2y\dfrac{\mathrm dy}{\mathrm dx}\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[0\bigg]\implies 6+2\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2+2y\dfrac{\mathrm d^2y}{\mathrm dx^2}=0$

Solving for the second derivative, we have

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=-\dfrac{3+\left(\frac{\mathrm dy}{\mathrm dx}\right)^2}y=-\dfrac{3+\frac{9x^2}{y^2}}y=-\dfrac{3y^2+9x^2}{y^3}$

Now, when $x=1$ and $y=2$ , we have

$\dfrac{\mathrm d^2y}{\mathrm dx^2}\bigg|_{x=1,y=2}=-\dfrac{3\cdot2^2+9\cdot1^2}{2^3}=\dfrac{21}8\approx2.63$

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3 years ago