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1 year ago

Question Progress 10 Homework Progress 17/ x: y = 2:3 Which is the correct equation? A 2x = 3y B 2y = 3x C y = x - 1 D y = x + 1

Mathematics

1 answer:

gtnhenbr [62]1 year ago

3 0

Answer: 2y = 3x

Reason:

The equation x:y = 2:3 is the same as saying x/y = 2/3

Cross multiply to get 3x = 2y which flips to 2y = 3x

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3 regions are defined in the figure find the volume generated by rotating the given region about the specific line

anastassius [24]

The volume generated by rotating the given region $R_{3}$ about OC is $\frac{4}{g} \pi$

<h3>Washer method</h3>

Because the given region ( $R_{3}$ ) has a look like a washer, we will apply the washer method to find the volume generated by rotating the given region about the specific line.

solution

We first find the value of x and y

$y=2(x)^{\frac{1}{4} }$

$x=(\frac{y}{2} )^{4}$

$y=2x$

$x=\frac{y}{2}$

$\int\limits^a_b {\pi } \, (R_{o^{2} } - R_{i^{2} } ) dy$

$R_{o} = x = \frac{y}{2}$

$R_{i} = x= (\frac{y}{2}) ^{4}$

$a=0, b=2$

$v= \int\limits^2_o {\pi } \, [(\frac{y}{2})^{2} - ((\frac{y}{2}) ^{4} )^{2} ) dy$

$v= \pi \int\limits^2_o= [\frac{y^{2} }{4} - \frac{y^{8} }{2^{8} }} ] dy$

$v= \pi [\int\limits^2_o {\frac{y^{2} }{4} } \, dy - \int\limits^2_o {\frac{y}{2^{8} } ^{8} } \, dy ]$

$v=\pi [\frac{1}{4} \frac{y^{3} }{3} \int\limits^2_0 - \frac{1}{2^{8} } \frac{y^{g} }{g} \int\limits^2_o\\v= \pi [\frac{1}{12} (2^{3} -0)-\frac{1}{2^{8}*9 } (2^{g} -0)]\\v= \pi [\frac{2}{3} -\frac{2}{g} ]\\v= \frac{4}{g} \pi$

A similar question about finding the volume generated by a given region is answered here: brainly.com/question/3455095

6 0

1 year ago

Write the quadratic equation whose roots are -3 and 3 and whose leading coefficient is 5. (Use the letter x to represent the var

Bumek [7]

A(x - x₁)(x - x₂) = 0
a=5, x₁=-3, x₂ = 3

so:
5(x-(-3))(x-3)=0
5(x+3)(x-3)=0
5(x²-9) = 0
5x² - 45 = 0 ← answer

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3 years ago

LaTanya leaves her house at 12:30pm and bikes at 12 mi/h to marta’s House she stays at marta’s House for 90mij both girls walk b

babymother [125]

Answer:

2.9 mi

Step-by-step explanation:

The time difference t between 12.30pm and 3.30pm is 3h.

Let the distance to Marat's house be s.

The equation to calculate velocity v is given by:

v = distance / time.

Now you can write an equation for the time difference t and use the two velocities and the 90 min(= 1.5h) she stays:

3 = s/12 + 1.5 + s/2.3

Solve this equation for s:

(1/12 + 10/23)* s = 1.5

s = 2.9

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3 years ago

Ann made 100 cookies this week. She baked 4 more than three times the total she made last week. How many cookies did she bake la

drek231 [11]

304

100x3=300 300+4=304

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2 years ago

How many solutions are there to the following system of equations?

sweet [91]

$4x-8y=0 \\
\underline{-3x+8y=-7} \\
4x-3x=0-7 \\
x=-7 \\ \\
4x-8y=0 \\
4 \times (-7)-8y=0 \\
-28-8y=0 \\
-8y=28 \\
y=\frac{28}{-8} \\
y=-\frac{7}{2} \\ \\
 \left \{ {{x=-7} \atop {y=-\frac{7}{2}}} \right.$

There is one solution to this system of equations. The answer is B.

6 0

3 years ago

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