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DaniilM [7]
3 years ago
7

Examine the following figure.

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
4 0
Blank a : does
blank b : two

hope this helps and if you can plz mark brainliest! :)
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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, -,
S_A_V [24]
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
3 0
3 years ago
Determine all the factors for the following expression(Note: you will need to use the Rational Root Theorem more than one time)
Aleks [24]
ANSWER

Possible rational roots: <span><span>±1,±2,±3,±4,±6,±12</span><span>±1,±2,±3,±4,±6,±12</span></span>

Actual rational roots: <span><span>1,−1,2,−2,−3</span></span>

<span><span>see attachments for all steps.</span></span>

4 0
3 years ago
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Step-by-step explanation:

First, you need to find what 7.5% of $2,200 is,

(2200/100)7.5=165

then to find how much interest has accumulated over 3 1/4 year you need to multiply the one-year interest rate by the 3.25

(165)3.25=536.25

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3 years ago
Growth or decay pls answer
algol13

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Step-by-step explanation:

6 0
2 years ago
4<br> Select the correct answer.<br> Which of these mappings is a function?
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Step-by-step explanation:

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