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2 years ago

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Miguel and Maria are washing the windows in their home. Together, they can complete the task in 1.5 hours. If Maria can wash win

dows twice as fast as Miguel, how many minutes would it take her to wash them by herself? In your answer, include the equation you used to solve the problem.

2 answers:

snow_tiger [21]2 years ago

8 0

Answer:

2 hours 15 minutes

2.25 hours.

Step-by-step explanation:

Let Maria's time by herself = x minutes

Let Miguel's time by himself = 2x minutes

You have to be careful how you set this equation up. Start with the right. The 1 represents the Job to be done. It takes 90 minutes.

The left hand side = 1/x which is the amount of time Maria (x) takes to do the job by herself. She doesn't do the job by herself.

Miguel helps her, so the portion he does is represented by 1/2x. Because he's helping, her time is cut back; he's doing some of the work.

1/x + 1/(2x) = 1/90 minutes

(2 + 1)/(2x) = 1/90 minutes

3/(2x) = 1/90 minutes

270 = 2x

x = 135 minutes.

It would take her 135 minutes to do the windows alone. That's 2 hours and 15 minutes.

Crazy boy [7]2 years ago

4 0

Answer:For this case, the first thing we must do is define variables.

x: amount of time Miguel uses to complete the task.

y: amount of time Maria uses to complete the task.

We write the system of equations:

x + y = 60

y = (1/2) x

Solving the system we have:

x = 40 minutes

y = 20 minutes

Answer:

it take her to wash them by herself about:

y = 20 minutes

Step-by-step explanation:

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Pablo generates the function f (x) = three-halves (five-halves) Superscript x minus 1 to determine the xth number in a sequence.

kondor19780726 [428]

Answer:

f(x + 1) = Five-halves f(x) (A)

Question:

The complete question as found in brainly( ID:13525864) is stated below.

Pablo generates the function f(x) = three-halves (five-halves) Superscript x minus 1 to determine the xth number in a sequence.

Which is an equivalent representation?

f(x + 1) = Five-halvesf(x)

f(x) = Five-halvesf(x + 1)

f(x + 1) = Three-halvesf(x)

f(x) = Three-halvesf(x + 1)

Step-by-step explanation:

f(x) = (3/2)(5/2)^(x-1)

Where 3/2 = three-halves and 5/2 = (five-halves)

To determine an equivalent representation, let's assign values to x to see the outcome and compare it with the options.

f(x) = (3/2)(5/2)^(x-1)

For x = 1

f(x) = (3/2)(5/2)^(1-1) = (3/2)(5/2)^(0)

f(x) =(3/2)(1) = 3/2

For x = 2

f(x) = (3/2)(5/2)^(2-1) = (3/2)(5/2)^(1)

f(x) =(3/2)(5/2)

So from the above assigned values

f(x=1) = 3/2

f(x=2) = f(x + 1) = f(1 + 1)

f(x + 1) = (3/2)(5/2)

Since f(x) = 3/2

f(x+1) = (3/2)(5/2) = f(x) × 5/2 = 5/2f(x)

From the options, an equivalent representation: f(x + 1) = Five-halves f(x)

(A)

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2 years ago

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SVETLANKA909090 [29]

Answer:

D, E, F are correct

Step-by-step explanation:

I know this because the square root of 196 is 14, the square root of 80 is 8.94427191 and if you square that you'll get 80. The square root of 16 is 4. So that is why A, B, C are wrong because they are all rational. Pi is infinite so it is irrational, the square root of 12 cannot be multiplied by itself to make 12 so it is irrational, and 7 divided by 18 is 3.8 and the 8 goes on for infinity.

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1 year ago

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Let D be the smaller cap cut from a solid ball of radius 8 units by a plane 4 units from the center of the sphere. Express the v

natima [27]

Answer:

Step-by-step explanation:

The equation of the sphere, centered a the origin is given by $x^2+y^2+z^2 = 64$ . Then, when z=4, we get

$x^2+y^2= 64-16 = 48$ .

This equation corresponds to a circle of radius $4\sqrt[]{3}$ in the x-y plane

c) We will use the previous analysis to define the limits in cartesian and polar coordinates. At first, we now that x varies from $-4\sqrt[]{3}$ up to $4\sqrt[]{3}$ . This is by taking y =0 and seeing the furthest points of x that lay on the circle. Then, we know that y varies from $-\sqrt[]{48-x^2}$ and $\sqrt[]{48-x^2}$ , this is again because y must lie in the interior of the circle we found. Finally, we know that z goes from 4 up to the sphere, that is , z goes from 4 up to $\sqrt[]{64-x^2-y^2}$

Then, the triple integral that gives us the volume of D in cartesian coordinates is

$\int_{-4\sqrt[]{3}}^{4\sqrt[]{3}}\int_{-\sqrt[]{48-x^2}}^{\sqrt[]{48-x^2}} \int_{4}^{\sqrt[]{64-x^2-y^2}} dz dy dx$ .

b) Recall that the cylindrical coordinates are given by $x=r\cos \theta, y = r\sin \theta,z = z$ , where r corresponds to the distance of the projection onto the x-y plane to the origin. REcall that $x^2+y^2 = r^2$ . WE will find the new limits for each of the new coordinates. NOte that, we got a previous restriction of a circle, so, since $\theta[\tex] is the angle between the projection to the x-y plane and the x axis, in order for us to cover the whole circle, we need that [tex]\theta$ goes from 0 to $2\pi$ . Also, note that r goes from the origin up to the border of the circle, where r has a value of 4\sqrt[]{3}. Finally, note that Z goes from the plane z=4 up to the sphere itself, where the restriction is \sqrt[]{64-r^2}. So, the following is the integral that gives the wanted volume

$\int_{0}^{2\pi}\int_{0}^{4\sqrt[]{3}} \int_{4}^{\sqrt[]{64-r^2}} rdz dr d\theta$ . Recall that the r factor appears because it is the jacobian associated to the change of variable from cartesian coordinates to polar coordinates. This guarantees us that the integral has the same value. (The explanation on how to compute the jacobian is beyond the scope of this answer).

a) For the spherical coordinates, recall that $z = \rho \cos \phi, y = \rho \sin \phi \sin \theta, x = \rho \sin \phi \cos \theta$ . where $\phi$ is the angle of the vector with the z axis, which varies from 0 up to pi. Note that when z=4, that angle is constant over the boundary of the circle we found previously. On that circle. Let us calculate the angle by taking a point on the circle and using the formula of the angle between two vectors. If z=4 and x=0, then y=4 $\sqrt[]{3}$ if we take the positive square root of 48. So, let us calculate the angle between the vector $a=(0,4\sqrt[]{3},4)$ and the vector b =(0,0,1) which corresponds to the unit vector over the z axis. Let us use the following formula

$\cos \phi = \frac{a\cdot b}{||a||||b||} = \frac{(0,4\sqrt[]{3},4)\cdot (0,0,1)}{8}= \frac{1}{2}$

Therefore, over the circle, $\phi = \frac{\pi}{3}$ . Note that rho varies from the plane z=4, up to the sphere, where rho is 8. Since $z = \rho \cos \phi$ , then over the plane we have that $\rho = \frac{4}{\cos \phi}$ Then, the following is the desired integral

$\int_{0}^{2\pi}\int_{0}^{\frac{\pi}{3}}\int_{\frac{4}{\cos \phi}}^{8}\rho^2 \sin \phi d\rho d\phi d\theta$ where the new factor is the jacobian for the spherical coordinates.

d ) Let us use the integral in cylindrical coordinates

$\int_{0}^{2\pi}\int_{0}^{4\sqrt[]{3}} \int_{4}^{\sqrt[]{64-r^2}} rdz dr d\theta=\int_{0}^{2\pi}\int_{0}^{4\sqrt[]{3}} r (\sqrt[]{64-r^2}-4) dr d\theta=\int_{0}^{2\pi} d \theta \cdot \int_{0}^{4\sqrt[]{3}}r (\sqrt[]{64-r^2}-4)dr= 2\pi \cdot (-2\left.r^{2}\right|_0^{4\sqrt[]{3}})\int_{0}^{4\sqrt[]{3}}r \sqrt[]{64-r^2} dr$

Note that we can split the integral since the inner part does not depend on theta on any way. If we use the substitution $u = 64-r^2$ then $\frac{-du}{2} = r dr$ , then

$=-2\pi \cdot \left.(\frac{1}{3}(64-r^2)^{\frac{3}{2}}+2r^{2})\right|_0^{4\sqrt[]{3}}=\frac{320\pi}{3}$

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What is 660/120 as a fraction simplified

Alex Ar [27]

I think the answer to your question is 11/2

5 0

2 years ago

The sale price S (in dollars) of an item is given by the formula S=L−rL, where L is the list price (in dollars) and r is the dis

ser-zykov [4K]

The sale price S (in dollars) of an item is given by the formula

S=L−rL , where L is the list price (in dollars) and r is the discount rate.

Since, S = L -rL

rL = L -S

r = $\frac{L-S}{L}$

r = $1-\frac{S}{L}$

Since, the listed price of the shirt is $30, we have to find the discount rate.

Therefore, r = $1-\frac{S}{30}$ is the discount rate.

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2 years ago

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