An imaginary number is not a real number

vesna_86 [32]

Answers:

Problem #1: Option C, 166 yards cubed

Problem #2: Option A, 10

Step-by-step solution:

The first problem may seem a lot more confusing that it really is and this actually happened to me when I looked at it. Just because the cylinder is slanted that actually doesn't change any of the volume that we would have if it was straight up with the same diameter and height.

Using what we know about cylinders, let us plug all the information inside of the formula to determine the volume of the cylinder. However, before doing that we need to determine the radius of the circle from the diameter that was given.

Divide the diameter by two to get the radius

$Radius = \frac{Diameter}{2}$

$Radius = \frac{5.2\ yd}{2}$

$Radius = 2.6\ yd$

Plug in the values

$V_{cylinder} = (\pi * radius^2)*height$

$V_{cylinder} = (\pi * (2.6\ yd)^2)*7.8\ yd$

Simplify the exponent

$V_{cylinder} = (\pi * (2.6)^2 *(yd)^2)*7.8\ yd$

$V_{cylinder} = (\pi * 6.76\ yd^2)*7.8\ yd$

Simplify the expression

$V_{cylinder} = (21.237\ yd^2)*7.8\ yd$

$V_{cylinder} = 165.65\ yd^3$

Therefore, after simplifying the expression using the cylinder volume formula and the given information we were able to determine that the option that best fits the description of our answer is option C, 166 cube yards.

Now that we completed the first question, we can move onto the second question. In this question we are given a figure along with 3 numbers and one unknown, x, which we need to find the value of. We need to use the Secant-Secant Power Theorem to help determine our solution.

Make an expression to represent the scenario

$32(x + 32) = 28(20 + 28)$

We know have an expression which we can now simplify and get the value of the unknown easily. The first step would be to distribute the 32 and 28.

Distribute both sides

$32(x + 32) = 28(20 + 28)$

$(32 * x) + (32 * 32) = (28 * 20) + (28 * 28)$

$32x + 1024 = 560 + 784$

Simplify the expression

$32x + 1024 = 1344$

We now have a simple expression where we can now subtract both sides by 1024 to help isolate x with its coefficient.

Subtract 1024 from both sides

$32x + 1024 - 1024 = 1344 - 1024$

$32x = 1344 - 1024$

$32x = 320$

The final step that we have to help fully isolate x by itself is to divide both sides by 32 which would remove the coefficient from x.

Divide both sides by 32

$\frac{32x}{32} = \frac{320}{32}$

$x = \frac{320}{32}$

$x = 10$

After simplifying the expression completely, we are able to see that the best option that fits our description is option A, 10.

8 0

2 years ago

(3x + 5)º (6x + 13)°

Zigmanuir [339]

Answer: 18x2 + 69x + 65

Step-by-step explanation:

(3x + 5) (~6x + 13)

1. 3x(6x + 13) + 5(6x + 13)

2. 18x2 + 39x + 5(6x + 13)

3. 18x2 + 39x + 30 + 65

4. 18x2 + 69 + 65

6 0

3 years ago

Anyone know the answer to these?

pishuonlain [190]

Not math.

33. (c) A chain reaction is from extra neutrons making even more neutrons.

34. (a) E=mc² and all that; the missing mass becomes kinetic energy

6 0

4 years ago

Can you give me the answer

Mnenie [13.5K]

Answer: B

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A rectangular tank with a square base, an open top, and a volume of 10,976 ft cubed is to be constructed of sheet steel. Find

Marizza181 [45]

Answer:

Dimensions to minimize surface are is 28 ft x 28 ft x 14 ft

Step-by-step explanation:

The Volume of a box with a square base of say;x cm by x cm and height

h cm is;

V = x²h

Now, the amount of material used is directly proportional to the surface area, hence we will minimize the amount of material by minimizing the surface area.

The formula for the surface area of the box described is given by;

A = x² + 4xh

However, we need A as a function of

only x, so we'll use the formula;

V = x²h

V = x²h = 10,976 ft³

So,

h = 10976/x²

So,

A = x² + 4x(10976/x²)

A = x² + 43904/x

So, to minimize the area, it will be at dA/dx = 0.

So,

dA/dx = 2x - 43904/x² = 0

Factorizing out, we have;

2x³ = 43904

x³ = 43904/2

x³ = 21952

x = ∛21952

x = 28 ft

since, h = 10976/x²

h = 10976/28² = 14 ft

Thus,dimension to minimize surface are is 28 ft x 28 ft x 14 ft

7 0

4 years ago