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Korolek [52]
2 years ago
14

How many shovels of sand need to be added to two shovels of cement?

Mathematics
1 answer:
Alborosie2 years ago
4 0

Answer:

8 sand shovels

Step-by-step explanation:

1 cement needs 4 sand shovels

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Olivia made 14 outfits for her dolls. Each outfit used 3/5 of fabric. If she started with 10 3/4 yards of fabric, how much did s
Zepler [3.9K]

Answer:

0.1 yards of fabric

Step-by-step explanation:

Data provided in the question:

Number of outfits made for the doll = 14

Fabric used in each outfit = \frac{3}{5} yards of fabric

Starting fabric available = 10 × \frac{3}{4} or \frac{30}{4} yards

Now,

The total fabric used in making the outfits of 14 dolls

= 14 × \frac{3}{5} yards of fabric

= \frac{42}{5} yards of fabric

Therefore,

The fabric left after making the outfits

= Fabric available in the start - Fabric used  in making the outfits

= \frac{30}{4} yards - \frac{42}{5} yards

= \frac{30\times5-42\times4}{4\times5} yards

=  \frac{150-168}{20} yards

= \frac{2}{20} yards

= 0.1 yards of fabric

5 0
3 years ago
Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of
GenaCL600 [577]

Close off the hemisphere S by attaching to it the disk D of radius 3 centered at the origin in the plane z=0. By the divergence theorem, we have

\displaystyle\iint_{S\cup D}\vec F(x,y,z)\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec F(x,y,z)\,\mathrm dV

where R is the interior of the joined surfaces S\cup D.

Compute the divergence of \vec F:

\mathrm{div}\vec F(x,y,z)=\dfrac{\partial(xz^2)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial k}=z^2+y^2+x^2

Compute the integral of the divergence over R. Easily done by converting to cylindrical or spherical coordinates. I'll do the latter:

\begin{cases}x(\rho,\theta,\varphi)=\rho\cos\theta\sin\varphi\\y(\rho,\theta,\varphi)=\rho\sin\theta\sin\varphi\\z(\rho,\theta,\varphi)=\rho\cos\varphi\end{cases}\implies\begin{cases}x^2+y^2+z^2=\rho^2\\\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi\end{cases}

So the volume integral is

\displaystyle\iiint_Rx^2+y^2+z^2\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^3\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{486\pi}5

From this we need to subtract the contribution of

\displaystyle\iint_D\vec F(x,y,z)\cdot\mathrm d\vec S

that is, the integral of \vec F over the disk, oriented downward. Since z=0 in D, we have

\vec F(x,y,0)=\dfrac{y^3}3\,\vec\jmath+y^2\,\vec k

Parameterize D by

\vec r(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath

where 0\le u\le 3 and 0\le v\le2\pi. Take the normal vector to be

\dfrac{\partial\vec r}{\partial v}\times\dfrac{\partial\vec r}{\partial u}=-u\,\vec k

Then taking the dot product of \vec F with the normal vector gives

\vec F(x(u,v),y(u,v),0)\cdot(-u\,\vec k)=-y(u,v)^2u=-u^3\sin^2v

So the contribution of integrating \vec F over D is

\displaystyle\int_0^{2\pi}\int_0^3-u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac{81\pi}4

and the value of the integral we want is

(integral of divergence of <em>F</em>) - (integral over <em>D</em>) = integral over <em>S</em>

==>  486π/5 - (-81π/4) = 2349π/20

5 0
3 years ago
Help please 31-33 I'm very confused
Alexxandr [17]
I'm not going to dignify this question with a response. xD
5 0
3 years ago
A car rental agency charges ​$33 per day to rent a car and ​$11.95 per day for a global positioning system​ (GPS). Customers are
harkovskaia [24]

(a) b = (33+11.95)d + 55.5

(b) The bill for a 5 day rental is $280.25

Step-by-step explanation:

Given,

Rent of car per day = $33

Rent of GPS per day = $11.95

Cost of gas = $3.70 per gallon

Cost of 15 gallons = 3.70*15 = $55.5 per tank

a) Write a function rule for the total bill b as a function of the days d the car is rented.

Let,

d be the number of days.

Total bill = (Rent of car per day + Rent of GPS per day )* Number of days + Cost of tank

b = (33+11.95)d + 55.5

b) What is the bill for a 5 day​ rental?

Putting d=5 in above function

b = (33+11.95)*5+55.5\\b=(44.95)*5+55.5\\b=224.75+55.5\\b=280.25

The bill for a 5 day rental is $280.25

Keywords: function, addition

Learn more about addition at:

  • brainly.com/question/9738996
  • brainly.com/question/9729310

#LearnwithBrainly

5 0
3 years ago
Solve for x: 4x^2 + 2(2x + 2)^2 = 100
balu736 [363]
Would it be 4(1)^2+2(2(1)+2)^2=100
8 0
3 years ago
Read 2 more answers
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