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3 years ago

6. At what intervals is the function g(x) shown below increasing and/or decreasing?

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

4 0

Decreasing [-8, -4] increasing [-1, 2]

(look at the slopes)

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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

-7-4p-(-5) pls answer

Evgesh-ka [11]

Answer:

-7-20p

Step-by-step explanation:

Did it in my head but generally first parentheses so -1 times by -5 is 5... still there so multiply 5 by -4p, after that no more simplifying to be done as you cant combine or simplify a number with a variable to one that doesn't have a variable.

7 0

2 years ago

Janet Fog's uncle, Pete Moore, promised her a gift of $30,000 upon her graduation from law school or $1500 every quarter for the

LenaWriter [7]

First calculate the future value of the annuity
The formula to find the future value of an annuity ordinary is
Fv=pmt [((1+r/k)^(kn)-1)÷(r/k)]
Fv future value?
PMT quarterly payment 1500
R interest rate 0.12
K compounded quarterly 4
N time 4 years
Fv=1,500×(((1+0.12÷4)^(4×4)
−1)÷(0.12÷4))
=30,235.32

Now compare the amount of the annuity with amount of the gift
30,235.32−30,000=235.32
So as you can see the amount of the annuity is better than the amount of the gift by 235.32

Second offer is better

Hope it helps!

5 0

4 years ago

I need help finding surface area

Papessa [141]

Use the formula A= abch
a= side
b= side
c= side
h= side

6 0

3 years ago

Read 2 more answers

Plz I need help help me plzzzz

Annette [7]

Answer:

4400

Step-by-step explanation:

15 percent is 660

this means 1 percent is 44

this means 100 percent is 4400

please give me brainliest!<3

5 0

3 years ago