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3 years ago

8

A painter spends three hours working on a painting. A sculptor spends 2 2/3 as long working on a sculpture. How long does the sc

ulptor work?

1 answer:

Aleksandr [31]3 years ago

8 0

Answer:

Step-by-step explanation:

8 because 2 and 2/3 times 3 equals 8/3 times 3 and the threes cancel out and there is a 8 left.

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At a fabric store, fabrics are sold by the yard. A dressmaker spent $36.35 on 4.25 yards of silk and cotton fabrics for a dress.

vaieri [72.5K]

Given:

The system of equations that represent the constraints for the given situation is

$x+y=4.25$

$16.90x+4y=36.35$

To find:

The solution of given system of equations.

Solution:

We have,

$x+y=4.25$ ...(i)

$16.90x+4y=36.35$ ...(ii)

Multiply equation (i) by 4.

$4x+4y=17$ ...(iii)

Subtracting (iii) from (ii), we get

$16.90x+4y-(4x+4y)=36.35-17$

$16.90x+4y-4x-4y=19.35$

$12.90x=19.35$

Divide both sides by 12.90.

$x=\dfrac{19.35}{12.90}$

$x=1.5$

Put this value in (i).

$1.5+y=4.25$

$y=4.25-1.5$

$y=2.75$

The solution of system of equations is x=1.5 and y=2.75. It means, the yards of silk are 1.5 and yards of cotton are 2.75.

5 0

3 years ago

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

Just do b d f h and j

Andrew [12]

Answer:

b) 1.383

d) 2733

f) 41.429

h) 6317

j) 87.889

Step-by-step explanation:

4 0

3 years ago

Solve this problem plzzz

damaskus [11]

Here is how to solve it with long division and synthetic division.

7 0

3 years ago

Differentiating a Logarithmic Function In Exercise, find the derivative of the function.

sp2606 [1]

Answer:

$\dfrac{d(f(x))}{dx} = \dfrac{2}{x}$

Step-by-step explanation:

We are given the following function in the question:

$f(x) = \ln (3x^2)$

We have to derivate the given function.

Formula:

$\dfrac{d(\ln x)}{dx} = \dfrac{1}{x}\\\\\dfrac{d(x^n)}{dx} = nx^{n-1}$

The derivation takes place in the following manner

$f(x) = \ln (3x^2)\\\\\dfrac{d(f(x))}{dx} = \displaystyle\frac{d(\ln(3x^2))}{dx}\\\\=\frac{1}{3x^2}\times \frac{d(3x^2)}{dx}\\\\= \frac{1}{3x^2}\times (6x)\\\\=\frac{6x}{3x^2}\\\\=\frac{2}{x}$

$\dfrac{d(f(x))}{dx} = \dfrac{2}{x}$

5 0

3 years ago