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3 years ago

Please i really need helpThe perimeter of each shape is 3 units? True or False?

Mathematics

2 answers:

Verizon [17]3 years ago

6 0

The perimeter of each shape is false

Licemer1 [7]3 years ago

3 0

4(2.5x-3)=3(2x-2)
10x-12=6x-6
4x-12=-6
4x=6
x=1.5

2.5(1.5)-3= 0.75
2(1.5)-2=1

False

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NARA [144]

$x^3y^2+\sin(x\ln y)+e^{xy}=0$

Differentiate both sides, treating $y$ as a function of $x$ . Let's take it one term at a time.

Power, product and chain rules:

$\dfrac{\mathrm d(x^3y^2)}{\mathrm dx}=\dfrac{\mathrm d(x^3)}{\mathrm dx}y^2+x^3\dfrac{\mathrm d(y^2)}{\mathrm dx}$

$=3x^2y^2+x^3(2y)\dfrac{\mathrm dy}{\mathrm dx}$

$=3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}$

Product and chain rules:

$\dfrac{\mathrm d(\sin(x\ln y)}{\mathrm dx}=\cos(x\ln y)\dfrac{\mathrm d(x\ln y)}{\mathrm dx}$

$=\cos(x\ln y)\left(\dfrac{\mathrm d(x)}{\mathrm dx}\ln y+x\dfrac{\mathrm d(\ln y)}{\mathrm dx}\right)$

$=\cos(x\ln y)\left(\ln y+\dfrac1y\dfrac{\mathrm dy}{\mathrm dx}\right)$

$=\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}$

Product and chain rules:

$\dfrac{\mathrm d(e^{xy})}{\mathrm dx}=e^{xy}\dfrac{\mathrm d(xy)}{\mathrm dx}$

$=e^{xy}\left(\dfrac{\mathrm d(x)}{\mathrm dx}y+x\dfrac{\mathrm d(y)}{\mathrm dx}\right)$

$=e^{xy}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)$

$=ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}$

The derivative of 0 is, of course, 0. So we have, upon differentiating everything,

$3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}+\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}+ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}=0$

Isolate the derivative, and solve for it:

$\left(6x^3y+\dfrac{\cos(x\ln y)}y+xe^{xy}\right)\dfrac{\mathrm dy}{\mathrm dx}=-\left(3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}\right)$

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}}{6x^3y+\frac{\cos(x\ln y)}y+xe^{xy}}$

(See comment below; all the 6s should be 2s)

We can simplify this a bit by multiplying the numerator and denominator by $y$ to get rid of that fraction in the denominator.

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^3+y\cos(x\ln y)\ln y-y^2e^{xy}}{6x^3y^2+\cos(x\ln y)+xye^{xy}}$

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3 years ago

Abdul deposits $6000 into an account that pays simple interest at an annual rate of 2%. He does not make any more deposits. He m

Ierofanga [76]

Step-by-step explanation:

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3 0

3 years ago

I’m not sure how to solve “system of equations”

natka813 [3]

Hey there! :)

Answer:

(2, -2)

Step-by-step explanation:

-2x + y = -6

4x + 3y = 2

We can begin by setting the first equation equal to y:

-2x + y = -6

Add 2x to both sides:

y = 2x - 6

Plug this equation for y into the second equation:

4x + 3(2x - 6) = 2

Distribute:

4x + 6x - 18 = 2

Combine like terms:

10x = 20

x = 2

Plug the value of 'x' into an equation to solve for 'y':

-2(2) + y = -6

-4 + y = -6

y = -2

Therefore, the solution is (2, -2)

7 0

3 years ago

Which equation does not represent a quadratic function?

Kryger [21]

$\text{A quadratic function is in the form of } ~ f(x)=ax^2 +bx+c.\\\\\\y=x+5 ~ \text{is linear so it is not in a form of quadratic function.}$

3 0

3 years ago

One leg of a 45°-45°-90° triangle measures inches. What is the length of the hypotenuse?

Alika [10]

Answer:

each leg of the right triangle = 12√2

Step-by-step explanation:

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3 years ago

Please i really need helpThe perimeter of each shape is 3 units? True or False?​

Please i really need helpThe perimeter of each shape is 3 units? True or False?