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3 years ago

5

You can mow a lawn in 2 hours with a ride on mower and your friend can mow a lawn in 3 hours with a hand mower. How much time wi

ll it take if both mow the same lawn

1 answer:

ololo11 [35]3 years ago

7 0

Answer:

Step-by-step explanation:

If you can mow a lawn in 2 hours, then you get 1/2 of the job done in 1 hour.

If your friend can mow the same lawn in 3 hours, then he can get 1/3 of the job done in 1 hour.

The equation for the time it would take for both of you to do the job together, then, is

$\frac{1}{2} +\frac{1}{3} =\frac{1}{x}$

where x is the number of hours it takes for both of you to do this job. Get rid of the denominators to solve for x. Do this by multiplying everything by the LCD, which is 6x.

$6x(\frac{1}{2} +\frac{1}{3} =\frac{1}{x} )$ which simplifies to

3x + 2x = 6 and

5x = 6

x = 6/5 or 1 1/5 hours

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

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

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

4 years ago

I have no idea how to solve??

kupik [55]

120 = (1/3)b(8) =

B = 120/ (1/3)8

B = 120/ 2 2/3

B = 45

3 0

3 years ago

Please help!!!!!!!!!!

pogonyaev

Answer:

By hypotenuse - side test (HL) the two triangles are congruent.

Step-by-step explanation:

In ∆ABC and ∆DCB

i) angleABC = angleDCB.....(each 90°)

ii) BC = BC .....( common side)

iii) AC = DB.....(given)

therefore by hypo-side test ∆ABC congruent ∆DCB

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d1i1m1o1n [39]

Answer:

-7/5

Step-by-step explanation:

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3 years ago

What is the greatest common factor of 42, 56, and 112

VashaNatasha [74]

Answer: gcf, hcf, gcd (42; 112) = 14 = 2 × 7: greatest (highest) common factor (divisor), calculated.

Step-by-step explanation:

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