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Paladinen [302]

2 years ago

15

What is the rate of change of the function?

2 answers:

scoundrel [369]2 years ago

7 0

Answer:

rate of change = 3

Step-by-step explanation:

to find the rate of change $\frac{y1 - y2}{x1 - x2}$

(0,-4) (1,-1)

$\frac{-4+1}{0-1}$ = $\frac{-3}{-1}$ = 3

allochka39001 [22]2 years ago

5 0

Answer:

3

Step-by-step explanation:

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Udrey used compensation to mentally solve the subtraction problem 5.35−0.07

Licemer1 [7]

The last step you need to do is 5.25+0.03, because you took away 0.03 more than what the question asked so you need to add the 0.03 back, which gets you the final result of 5.28.

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3 years ago

Find the area of the composite shape

jekas [21]

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½ * 6 ft * 7 ft = 21 sq ft

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4 0

2 years ago

Show that ( 2xy4 + 1/ (x + y2) ) dx + ( 4x2 y3 + 2y/ (x + y2) ) dy = 0 is exact, and find the solution. Find c if y(1) = 2.

fredd [130]

$\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

$\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

so the ODE is indeed exact and there is a solution of the form $F(x,y)=C$ . We have

$\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)$

$\dfrac{\partial F}{\partial y}=4x^2y^3+\dfrac{2y}{x+y^2}=4x^2y^3+\dfrac{2y}{x+y^2}+f'(y)$

$f'(y)=0\implies f(y)=C$

$\implies F(x,y)=x^2y^3+\ln(x+y^2)=C$

With $y(1)=2$ , we have

$8+\ln9=C$

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$\boxed{x^2y^3+\ln(x+y^2)=8+\ln9}$

8 0

2 years ago

What is the volume of a hemisphere that

ch4aika [34]

<u>Given</u>:

Given that the diameter of the hemisphere is 12.6 cm

The radius of the hemisphere is given by

$r=\frac{d}{2}=\frac{12.6}{2}=6.3$

We need to determine the volume of the hemisphere.

<u>Volume of the hemisphere:</u>

Let us determine the volume of the hemisphere.

The volume of the hemisphere can be determined using the formula,

$V=\frac{2}{3} \pi r^3$

Substituting the values, r = 6.3 and π = 3.14, we have;

$V=\frac{2}{3} (3.14)(6.3)^3$

Simplifying the values, we have;

$V=\frac{2}{3} (3.14)(250.047)$

$V=\frac{1570.29516}{3}$

Dividing, we have;

$V=523.43172$

Rounding off to the nearest tenth, we get;

$V=523.4$

Thus, the volume of the hemisphere is 523.5 cm³

6 0

2 years ago