Answer:
$16,725.21
Step-by-step explanation:
To get the cost of the copper used for the sculpture, we must first determine the volume of the object which is given as a cone
Recall that the volume V of a cone
= 1/3Pir^2h
where r is the base radius and h is the height
Given that the sculpture is 67 inches tall, and its base has a radius of 15 inches, the volume of the sculpture
= 1/3 * 3.14 * 15^2 * 67
= 15,778.5 cubic inch
If copper costs 1.06$ per cubic inch, then the cost of the copper for the sculpture
= 15,778.5 * 1.06
= $16,725.21
Answer:
~1.29 inches
Step-by-step explanation:
C = 2πr
C = 3r + 4.25
2πr = 3r + 4.25
2πr - 3r = 4.25
r(2π-3) = 4.25
r = 4.25/(2π-3) ≈ 1.29
Answer:
for #1 it's 1, 4, 5, 6
for #2 it's both lines have the same slope
for #3 it's both lines have a different y-intercept
Step-by-step explanation:
#1 explanation: all of them have the y-intercept of -8
ex. y = 3x (- 8) y = 5x (-8) y = 2x (-8) y = (1/3)x (-8)
#2 explanation: both have a slope of (1/4)
#3 explanation: y = (1/4)x there is not y-intercept that we know of and y = (1/4)x - 5 the y-intercept is at -5 therefore the y-intercepts are different
(x - d) + x + (x + d) = 12 --> Create an equation using the first piece of information - "Three consecutive terms... have a sum of 12"
x - d + x + x + d = 12 --> Simplify the left side of this equation (d cancels out)
3x = 12 --> Divide both sides by 3
<u>x = 4
</u>
Use the value of x (x = 4) to find the value of d. To do this, set up another equation using the second piece of information.
(x - d) * (x + d) * x = - 80 --> "Three consecutive terms... have... a product of -80". Then, substitute the value of x (4) into this equation.
(4 - d) * (4 + d) * 4 = - 80 --> Multiply out the sets of brackets, the * 4 is dealt with afterwards
4(16 - 4d + 4d - d²) = - 80 --> Simplify the expression inside the brackets
4(16 - d²) = - 80 --> Multiply out these brackets by the 4
64 - 4d² = - 80 --> Subtract 64 from both sides
- 4d² = - 144 --> Divide both sides by - 4
d² = 36 --> Square root both sides
<u>d = 6
</u>Now, find the values of the terms of the sequence by using substituting the values of x and d into the expressions given.
<u>
</u><u />1. x - d = 4 - 6 = <u>- 2
</u><u></u>2.<u> x = 4</u>
3. x + d = 4 + 6 = <u>10
</u>
The three terms are - 2, 4, 10.
<u>
</u>
