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3 years ago

Find the volume of the cement block in the figure shown. Please help :)

Mathematics

1 answer:

Alexxandr [17]3 years ago

6 0

9514 1404 393

Answer:

1240 in³

Step-by-step explanation:

The overall dimensions of the block are ...

10 in by 11 in by 17 in

The volume of that space is ...

V = LWH = (10 in)(11 in)(17 in) = 1870 in³

The volume of each of the three identical holes is similarly found:

V = (10 in)(3 in)(7 in) = 210 in³

Then the volume of the block is the overall volume less the volume of the three holes:

= 1870 in³ - 3(210 in³) = 1240 in³

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You are planning to make an open rectangular box from a 25-in.-by-49-in. piece of cardboard by cutting congruent squares from

Darya [45]

Answer:

The dimensions of the box are 38.48 x 14.48 x 5.26 in.

Step-by-step explanation:

We will have a piece of cardboard with squares of side x cut from the corners to make a open box.

The volume of the box can be written as:

$V=A\cdot B\cdot x\\\\V=(49-2x)\cdot (25-2x)\cdot x\\\\V=x\cdot (4x^2-2x*(49+25)+49*25)\\\\V=4x^3-148x^2+1225x$

To calculate the maximum volume, we derive and equal to zero

$dV/dx=12x^2-296x+1225=0$

We apply the quadratic equation to know the roots of the equation

$x=\frac{-b\pm\sqrt{b^24ac}}{2a}\\\\x=\frac{296\pm\sqrt{296^2-4*12*1225}}{2*12} =\frac{296\pm\sqrt{87616-58800}}{24}= \frac{296\pm\sqrt{28816}}{24}\\\\x=\frac{296\pm169.75}{24}= 12.333\pm7.073\\\\\\x_1=12.333+7.073=19.406\\\\x_2=12.333-7.073=5.26$

The first solution is physically impossible, as the side that is cut would be bigger than 25.

So the real solution is for x=5.26 in.

Then, the dimensions of the box are:

$A=49-2x=49-2*5.26=49-10.52=38.48\\\\B=25-2x=25-10.52=14.48$

8 0

3 years ago

What is the answer to x/3+8=-2

Bingel [31]

Answer:

x = - 30

Step-by-step explanation:

x/3 + 8 = - 2 subtract 8 from both sides of the equation

x/3 = -2 - 8 = -10 now multiply both sides by 3

x = -30

3 0

2 years ago

I don’t get this pls helppppppp!!!!!!!!!!!!

MrRa [10]

Answer:

1) f(x)<x+4

f(x)>-x-3

f(x)<5

$ANSWER: (-3,4)$

2)2.5>0+2

2.5<0+3

2.5<0+5

$ANSWER: (0,2.5)$

HOPE IT HELPS

HAVE A GREAT DAY!!

8 0

3 years ago

find 2 consecutive integers such that three times the square of the first is equal to seven more than five times the second

melamori03 [73]

Answer:

Step-by-step explanation:

We are looking for two numbers, $N$ and $N + 1$ . From the problem statement, we can setup the following equation:

$3N^{2} = 5(N + 1) + 7$

$3N^{2} = 5N + 5 + 7$

$3N^{2} - 5N - 12 = 0$

$(3N + 4)(N - 3)$

$N = \frac{-4}{3}, 3$

Because 3 is the only integer solution, the answer is 3 and 4.

5 0

3 years ago

martin pidio 1/8 de kg de clavos de 1/2 pulgada si la bascula es digital y pesa en kilogramos ¿cuantos tienes q marcar en este c

love history [14]

Martin will have to mark 0.125 on the

Let the original weight of the scale be 1kg. Hence we can say the original mark for 1kg weight is 1 that is:

1kg = 1 ................ 1

Since we are to calculate where to mark for a 1/8 kg weight, we can write;

1/8 kg = x ..................2

Divide both expressions

$\frac{1}{1/8}= \frac{1}{x}\\\\Cross \ multiply\\8= \frac{1}{x} \\x = \frac{1}{8}$

This means Martin will have to mark 0.125 on the scale.

Learn more here: https://brainly.lat/tarea/13002863

3 0

2 years ago