what is the maximum number of cubes with side lengths of 1/2 cm that can fit into a right rectangular prism with base dimensions of 12 1/2 cm by 8 1/2cm and a height of 9 1/2cm?

Answer:

[tex]\iint_D 8y^2 \ dA = \dfrac{88}{3}[/tex]

Step-by-step explanation:

The equation of the line through the point [tex](x_o,y_o)[/tex] & [tex](x_1,y_1)[/tex] can be represented by:

[tex]y-y_o = m(x - x_o)[/tex]

Making m the subject;

[tex]m = \dfrac{y_1 - y_0}{x_1-x_0}[/tex]

∴

we need to carry out the equation of the line through (0,1) and (1,2)

i.e

y - 1 = m(x - 0)

y - 1 = mx

where;

[tex]m= \dfrac{2-1}{1-0}[/tex]

m = 1

Thus;

y - 1 = (1)x

y - 1 = x ---- (1)

The equation of the line through (1,2) & (4,1) is:

y -2 = m (x - 1)

where;

[tex]m = \dfrac{1-2}{4-1}[/tex]

[tex]m = \dfrac{-1}{3}[/tex]

∴

[tex]y-2 = -\dfrac{1}{3}(x-1)[/tex]

-3(y-2) = x - 1

-3y + 6 = x - 1

x = -3y + 7

Thus: for equation of two lines

x = y - 1

x = -3y + 7

i.e.

y - 1 = -3y + 7

y + 3y = 1 + 7

4y = 8

y = 2

Now, y ranges from 1 → 2 & x ranges from y - 1 to -3y + 7

∴

[tex]\iint_D 8y^2 \ dA = \int^2_1 \int ^{-3y+7}_{y-1} \ 8y^2 \ dxdy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \int ^{-3y+7}_{y-1} \ y^2 \ dxdy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( \int^{-3y+7}_{y-1} \ dx \bigg) dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [xy^2]^{-3y+7}_{y-1} \bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [y^2(-3y+7-y+1)]\bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ([y^2(-4y+8)] \bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( -4y^3+8y^2 \bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [\dfrac{ -4y^4}{4}+\dfrac{8y^3}{3} \bigg ]^2_1[/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -y^4+\dfrac{8y^3}{3} \bigg ]^2_1[/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -2^4+\dfrac{8(2)^3}{3} + 1^4- \dfrac{8\times (1)^3}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -16+\dfrac{64}{3} + 1- \dfrac{8}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{64-8}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{56}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{-45+56}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{11}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA = \dfrac{88}{3}[/tex]

Answer:

A: the 5.62 kilograms should be negative, since he is losing weight.

B: -5.62 + 1.4 is -4.22, which is how many kilograms Patrick lost in total.

Hope this helps :)

Answer:

x = {-12, 12}

Step-by-step explanation:

Given:

A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis.

To find:

The volume of the figure.

Solution:

Points A(0,0) and C(0,9) lies on the y-axis. Length of AC is 9 units.

Points A(0,0) and B(6,0) lies on the x-axis. Length of AB is 6 units.

If a triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis, then it will form a cone with radius 6 units and height 9 units.

Volume of a cone is

[tex]V=\dfrac{1}{3}\pi r^2h[/tex]

where, r is radius of the base and h is vertical height of the cone.

Putting r=6 and h=9, we get

[tex]V=\dfrac{1}{3}\pi (6)^2(9)[/tex]

[tex]V=\pi (36)(3)[/tex]

[tex]V=108\pi[/tex]

Therefore, the volume of the figure is [tex]108\pi[/tex] sq. units.

Answer:

Step-by-step explanation:

the median would be 2,2 just the middle number/numbers if it has 1 # thats the median if it has 2 thats still the median

7 numbers middle is 6226

A.4

took the test

╰(*°▽°*)╯(☞ﾟヮﾟ)☞

Answer:

the answer is a i got a hundred on that tes a year ago

Step-by-step explanation:

Step-by-step explanation:

slope = y2 - y1

__________

x2 - x1

slope = (-10 -2) / (-16 - 4)

slope = -12/-20

slope = 3/5

Step-by-step explanation:

the correct answer is 6

Answer:

6

Step-by-step explanation:

Step 1:

2x + 9 = 21           Equation

Step 2:

2x = 12       Subtract 9 on both sides

Step 3:

x = 12 ÷ 2      Divide

Answer:

x = 6

Hope This Helps :)

Answer:

4

Step-by-step explanation:

Function of the graph shown: y=3x+4

Answer:

51:120

Step-by-step explanation:

since 120 is length in mm, it is the y value

since 50 is width in mm it is the x value

51mm:120mm

Answer:

21.5625

Step-by-step explanation:

So You would divide 258.75 / 12 = 26.5625

The radius of container is 2.6 inch.

The amount of space occupied by a three dimensional figure as measured in cubic units.

[tex]volume of cylinder= \pi r^{2} h[/tex]

where,

r is the radius

h is the height

According to the given question

shape of the container is cylindrical.

Height of the container, h = 12 inches

Volume of container = 258.75 cubic inches

for the radius of the container

volume of container = [tex]\pi r^{2}h[/tex]

258.75 = 3.14×[tex]r^{2}[/tex]×12

258.75 =37.68×[tex]r^{2}[/tex]

[tex]\frac{258.75}{37.68} =r^{2}[/tex]

[tex]6.9=r^{2}[/tex]

⇒ [tex]r = \sqrt{6.9} =2.62inch[/tex] = 2.6 inch

Hence, the radius of container is 2.6 inch.

Learn more about the volume of cylinder here:

https://brainly.com/question/16134180

#SPJ2

Answer:

Wth.. Okay. The probablility is probably low, seeing as there is 25 questions. So I guess like .2? Not sure.

Answer:

The answer is nine :)

Step-by-step explanation:

Answer: .12 grams of butter per cupcake

Step-by-step explanation:

1/12=x/100 this is what i found but this may or may not be the right answer but I am pretty sure that it is. Sorry if this doesn't help.

Answer: d) $1,432.50​

Step-by-step explanation:

Sales price = $35

25% rush charge = 35 * 25% = $8.75

Rush charge is taxable = (35 + 8.75) * 8% = $3.5

Total purchase price per unit = 35 + 8.75 + 3.5 = $47.25

Total cost = Total Purchase + Shipping

= (47.25 * 30) + 15

= $1,432.50

Answer: 59 1/2

Step-by-step explanation:

Answer:

The new elevation is -92 [tex]\frac{1}{8}[/tex] ft.

Step-by-step explanation:

-75 [tex]\frac{3}{4}[/tex] = -75[tex]\frac{6}{8}[/tex]

-75 [tex]\frac{6}{8}[/tex] + -16 [tex]\frac{3}{8}[/tex] = -91 [tex]\frac{9}{8}[/tex] = 92 [tex]\frac{1}{8}[/tex]

Answer:

25%

Step-by-step explanation:

28-21=7

7/28=×/100

7×100=700

700÷28=25

Answer:

7

Step-by-step explanation:

Okay so, 28-21 =07 right

7 as a percent is 700% and the limit is 100%

so 700%/100%= 7

Answer:

18

Step-by-step explanation:

basic math :/

Answer:

Oh, it's y=3x-4.

Because it's slope is 3 and it crosses through -4 on the y axis, we know that that would be the equation.

Good luck with the assignment man, let me know of anymore questions. :)

Answer:

None

Step-by-step explanation:

y=(2x)^(1/3)-7    wrong

y= -2(3x)^(1/6) wrong

y=-x^(1/2)+5 wrong

y=(x+2)^(1/4) wrong

Answer:

Step-by-step explanation:

Math answers to fraction 1498 divided by 30 can be calculated as follows.

1498/30 math problems division = 49.9333333333. Therefore 49.9333333333 to 2 decimal places= 49.93

1498/30 divided by 2 » (1498/30) ÷ 2 » 49.9333333333 ÷ 2 = 24.9666666667

Answer:

V≈1130.97cm³

Step-by-step explanation:

crown n add me plzz

Answer:

20 Mystery DVD’s

Step-by-step explanation:

32/8=4

4*5=20

Answer:

There are 20 Mystery DVD's.

Step-by-step explanation:

Since the ratio of Drama to Mystery is 8:5, then we can conclude that 32:x is another equivalent form of the ratio, given that 32 represents drama, and x represents the unknown number of mystery.  

Set up the ratios as 8/5 as one fraction, and 32/x as another, but make them equal each other.  Cross multiply the numerators and denominators, then you will get 8x=160

divide both sides to solve for x.

x=20

Answer:

with?

Step-by-step explanation:

Answer:

1. -5a

Step-by-step explanation:

The definition of combining like terms is adding their coefficients, for example: 2x + 3x = (2+3)x = 5x.

So for this one, -21a+16a = (-21+16)a = -5a.

Answer:

I believe it is the first answer

Step-by-step explanation:

-50 because it is being translated down 50, and the sloped are equal

Answer:

slope is 1/6

Step-by-step explanation:

Answer:

This quadratic equation has 2 solutions.

Step-by-step explanation:

I assume the '?' in your question is meant to be power 2 (²), or else it would not be a quadratic equation. You could write it using the superscript version of 2.

We can solve this equation by expressing it in the form: ax² + bx + c

x² + 9x= -8

x² + 9x + 8 = 0

Now if you know the discriminant, you can simply plug in your values of a, b, and c to see how many solutions there are.

In this case, you would not need the discriminant as there are whole-number factors and hence this can simply be factorised.

x² + 9x + 8 = 0

(x + 8)(x + 1) = 0

For this equation to be true (= 0), x can equal -8 OR -1.

Hence, this quadratic equation has 2 solutions.