A 25.8 gallon fish tank is 5/6 full. How many gallons will it take to fill the tank?

To fit between two windows, the width of a bookshelf must be no greater than 6 1/2feet. Mrs.aguilar purchases a bookshelf that i

MArishka [77]

I need points sorry

6 0

3 years ago

Find the total mass of the triangular region shown below. All lengths are in cm, and the density of the region is sigma(x) = 1 +

anastassius [24]

Answer:

3 grams

Step-by-step explanation:

We are going to take the mass of a bunch of little strips below the triangle "roof." To do this, we must figure out what formula for the mass we'll use, in this case, we'll use:

Mass of strip = denisty * area = (1+x)*y*deltax grams

now, because the "roof" of the triangle contains two different integrals (it completely changes direction), we will use TWO integrals!

**pretend ∈ is the sum symbol

Mass of left part = lim x->0 ∈ (1+x)*y*deltax = inegral -1 to 0 of (1+x)*3*(x+1) = 3 * integral -1 to 0 of (x^2 + 2x + 1) = 3 * 1/3 = 1

Mass of left part = lim x->0 ∈ (1+x)*y*deltax = inegral 0 to 1 of (1+x)*3*(-x+1) = 3 * integral 0 to 1 of (-x^2 + 1) = 3 * 2/3 = 2

Total mass = mass left + mass right = 1 + 2 = 3 grams

8 0

3 years ago

I’m struggling to answer this question on my test, can someone explain it to me?

Flauer [41]

Correct answer is Option A: 18/48 = 21/56

You’ll have to divide the numerator by the denominator of each fraction to see whether they have the same quotient:

18/48 = 0.375
21/56 = 0.375

The other options are not proportional.

B) 20/28 = 15/18:

20/28 = 0.714
15/18 = 0.833

Thus, 20/28 ≠ 15/18

C). 3/5 = 13/10
3/5 = 0.6
13/10 = 1.3

Hence, 3/5 ≠ 13/10

D) 7/10 = 10/7
7/10 = 0.7
10/7 = 1.43

Thus, 7/10 ≠ 10/7

These solutions prove that the correct answer is A) 18/48 = 21/56

Please mark my answers as the Briainliest if you find my explanations helpful :)

4 0

3 years ago

Help please:))

Blababa [14]

Answer:

a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.

Remember that for a cylinder of radius R and height H the volume is:

V = pi*R^2*H

And the surface will be:

S = 2*pi*R*H + pi*R^2

where pi = 3.14

Here we know that the volume is 1000cm^3, then:

1000cm^3 = pi*R^2*H

We can rewrite this as:

(1000cm^3)/pi = R^2*H

Now we can isolate H to get:

H = (1000cm^3)/(pi*R^2)

Replacing that in the surface equation, we get:

S = 2*pi*R*H + pi*R^2

S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2

S = 2*(1000cm^3)/R + pi*R^2

So we want to minimize this.

Then we need to find the zeros of S'

S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0

So we want to find R such that:

2*pi*R = (2000cm^3)/R^2

2*pi*R^3 = 2000cm^3

R^3 = (2000cm^3/2*3.14)

R = ∛(2000cm^3/2*3.14) = 6.83 cm

The radius that minimizes the surface is R = 6.83 cm

With the equation:

H = (1000cm^3)/(pi*R^2)

We can find the height:

H = (1000cm^3)/(3.14*(6.83 cm)^2) = 6.83 cm

(so the height is equal to the radius)

b) The surface equation is:

S = 2*pi*R*H + pi*R^2

replacing the values of H and R we get:

S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2

c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.

Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.

3 0

3 years ago

a stack of cards is placed next to a ruler, and the height of stack measured to be 3/4inches. how thick is one card

4vir4ik [10]

Total thickness of the stack of cards = 3/4 inch or 0.75 inch

In a full stack of cards, there are 52 cards.

Hence, the thickness of 52 cards = 0.75 inch.

To find the thickness of one card, we divide the total thickness with the total number of cards.

Thickness of one card = $\frac{0.75}{52} = 0.014423 inch$

1 inch = 2.54 cm

0.014423 inch is approximately equal to 0.34 cm.

Answer = 0.34 cm

7 0

3 years ago