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3 years ago

Find dy/dx. x^2y+xy^2=6

1 answer:

3 0

We are asked to evaluate dx/dy of the function x^2y+xy^2=6
we use implicit differentiation here:
2xy dx + 2xy dy = 0we can cancel 2xy from both terms in the left-hand side such that what is left is dx/dy = 0

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HELP PLEASE! Will give the Brainliest if shown work!!

scZoUnD [109]

Answer:

$\large\boxed{Q1.\ A_{\triangle PQR}=90\ cm^2}\\\\\boxed{Q2.\ V\approx321\ m^3}$

Step-by-step explanation:

$Q1.\\\\\text{If}\ \triangle ABC\sim\triangle PQR\ \text{then the quotient of the areas is equal}\\\text{the square of the similarity scale}\ k.\\\\\text{The sides}\ AB\ \text{and}\ QP\ \text{are corresponding}.\ \text{Calculate the scale:}\\\\k=\dfrac{4}{6}=\dfrac{4:2}{6:2}=\dfrac{2}{3}\\\\\text{The area of }\ \triangle ABC=40\ cm^2.\\\\\text{Let the area of}\ \triangle PQR=x,\ \text{then}\\\\\dfrac{40}{x}=\left(\dfrac{2}{3}\right)^2\\\\\dfrac{40}{x}=\dfrac{4}{9}\qquad\text{cross multiply}\\\\4x=(9)(40)\qquad\text{divide both sides by 4}\\\\x=(9)(10)\\\\x=90\ cm^2$

$Q2.\\\\\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{We have the diameter}\ 2R=8.5\ m\to R=\dfrac{8.5}{2}\ m=4.25\ m.\\\\\text{Substitute:}\\\\V=\dfrac{4}{3}\pi(4.25)^3=\dfrac{4}{3}\pi(76.765625)=(4)(25.588541)\pi=102.354164\pi\\\\\pi\approx3.14\\\\V=(102.354164)(3.14)\approx321\ m^3$

8 0

3 years ago

Read 2 more answers

What is the equation of the line that passes through the point (4,3) and has a slope<br> of 1?

Mamont248 [21]

Answer (<u>assuming it can be in point-slope form)</u>:

$y-3 = 1(x-4)$

Step-by-step explanation:

Use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line. Substitute real values for $m$ , $x_1$ , and $y_1$ in the formula.

Since $m$ represents the slope, substitute 1 in its place. Since $x_1$ and $y_1$ represent the x and y values of a point the line intersects, substitute the x and y values of (4,3) in its place. Substitute 4 for $x_1$ and 3 for $y_1$ . This gives the following equation and answer in point-slope form:

$y-3 = 1(x-4)$

5 0

3 years ago

The triangle shown is an equilateral triangle. An equilateral triangle has sides lengths a. What is the area of the equilateral

slava [35]

Answer:

The answer is c on edge. 1/2a squared sin 60 degrees.

Step-by-step explanation:

just got it right on edge.

5 0

3 years ago

Read 2 more answers

Does anyone know how to solve this math equation?

garik1379 [7]

Answer:

x = 8; y = -6

Step-by-step explanation:

We have a system of equations.

$\dfrac{3(x - 2)}{2} - \dfrac{y - 2}{4} = 11$

$\dfrac{2(x + 2)}{5} - \dfrac{y}{3} = 6$

First, let's multiply both sides of each equation by the LCM of both denominators of that equation to eliminate all denominators.

First equation:

$8 \times \dfrac{3(x - 2)}{2} - 8 \times \dfrac{y - 2}{4} = 8 \times 11$

$12(x - 2) - 2(y - 2) = 88$

$12x - 24 - 2y + 4 = 88$

$12x - 2y = 108$

$6x - y = 54$

The equation above is the simplified first equation.

Second equation:

$\dfrac{2(x + 2)}{5} - \dfrac{y}{3} = 6$

$15 \times \dfrac{2(x + 2)}{5} - 15 \times \dfrac{y}{3} = 15 \times 6$

$6(x + 2) - 5y = 90$

$6x + 12 - 5y = 90$

$6x - 5y = 78$

The equation above is the simplified second equation.

The simplified system of equations is:

$6x - y = 54$

$6x - 5y = 78$

The x term of both equations is 6x. If we multiply both sides of the second equation by -1 to get a first term of -6x, then when it is added to 6x, the x terms are eliminated.

Now we rewrite the first simplified equation as it is. Below it, we write the second equation multiplied by -1 on both sides. Then we add the equations.

$6x - y = 54$

$-6x + 5y = -78$