This is assuming that p is not in the denominator. To make it more clear that p is not in the denominator, I recommend you write (1/3)p.
Taking 1/3 of a number is the same as dividing by 3.
Example:
27/3 = 9
27*(1/3) = 9
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
y = 6x − x2, y = 8; about x = 2
Answer:
[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]
Step-by-step explanation:
Given that:
y = 6x - x² , y = 8 about x = 2
To find the volume of the region bounded by the curves about x = 2; we have the radius of the cylindrical shell to be x - 1, the circumference to be 2 π (x -2 ) and the height to be 6x - x² - 8
6x - x² - 8
6x - x² - 8 = 0
-x² + 6x - 8 = 0
x² - 6x + 8 = 0
(x -4) (x - 2 ) = 0
So;
x = 2 , x = 4
Thus, the region bound of the integral are from a = 2 and b = 4
Therefore , the volume of the solid can be computed as :
[tex]V = \int \limits ^b _a \ 2x \times f(x) \ dx[/tex]
[tex]V = \int \limits ^4_2 2 \pi (x -2) (6x -x^2 -8) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 (6x^2 - x^3 -8x -12 x - 2x^2 +16) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 (8x^2 -x^3-20x +16) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 ( -x^3+8x^2-20x +16) \ dx[/tex]
[tex]V = 2 \pi [\dfrac{ -x^7}{4}+\dfrac{8x^3}{3} -\dfrac{20x^2}{2} +16x]^4_2[/tex]
[tex]V = 2 \pi [\dfrac{ -(4^4-2^4)}{4}+\dfrac{8(4^3-2^3)}{3} -\dfrac{20(4^2-2^2)}{2} +16(4-2) ]^4_2[/tex]
[tex]V = 2 \pi [\dfrac{ -(256-16)}{4}+\dfrac{8(64-8)}{3} -10(16-4)} +16(2) ][/tex]
[tex]V = 2 \pi [\dfrac{ 4}{3}][/tex]
[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]
Jemma has 24 balls. Out of the 24 balls, 12 are yellow, 4 are pink, and the rest are red. What is the ratio of the number of red balls to the number of balls that are either yellow or pink? arrowRight
Answer:
1 :2
Step-by-step explanation:
12 are yellow, 4 are pink
To find the number of red
24 -12 -4 = 8
There are 8 red balls
We want the ratio of
red: yellow or pink
8 : 12+4
8 :16
Divide each side by 8
8/8 : 16/8
1 :2
Answer:1:2
Step-by-step explanation: 12 yellow + 4 pink= 16
24 balls total minus 16 =8 red balls so 8:16=1:2
Please someone help me
Answer:
r = 0.046212737
Step-by-step explanation:
A = 14,400 (what your investment originally is)
P = 7,200 (what you want your investment to be)
n = 365 (interest is compounded daily)
t = 15 (15 years)
Plug all of these numbers into the equation, then solve for r
14,400 = 7,200(1 + r/365)^365 · 15
Divide 7,200 on both sides --> 2 = (1 + r/365)^365 · 15
365 · 15 = 5475 --> 2 = (1 + r/365)^5475
5475√(2) = 1 + r/365 (root 5475 both sides to cancel out the exponent)
(5475√(2)) - 1 = r/365 (subtract one from both sides)
((5475√(2)) - 1) · 365 = r (multiply both sides by 365 to isolate r)
Type the left side into the calculator to get r --> 0.046212737.
Hope this helps!
PLEASE HELP ME!! I WILL GIVE BRAINLIEST!!
Find the output, y, when the input, x, is -5.
Answer:
[tex]\boxed{y = -2}[/tex]
Step-by-step explanation:
Hey there!
To find y when x is -5 we go to -5 on the x-axis.
When at -5 find where the blue line is vertical to -5,
which is -2.
Hope this helps :)
attachment help for question c no explanation only answer thank you
Answer:
Tablets.
Step-by-step explanation:
You didn't want an explanation so....here you go....no explanation.
Hope that helps and maybe earns a brainliest.
Have a great day!
Plzz help I’ll mark brainliest
Answer:
6cot 50
Step-by-step explanation:
Tan 50=6/x
x= 6/(tan 50)
x= 6cot 50°
Answer:
? = 6 cot 50
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 50 = 6 /?
? tan 50 = 6
? = 6 / tan 50
We know that 1 / tan 50 = cot 50
? = 6 cot 50
Match each function formula with the corresponding transformation of the parent function y = 3x
1. y = -3^ x Translated up by 1 unit 2.
2.y = 3^ -x Reflected over the y-axis 3.
3.y = 3 ^x - 2 Translated right by 2 units 4.
4. y = 3 ^x + 1 Translated down by 2 units 5.
5. y = 3^ x + 1 Translated left by 1 unit 6.
6. y = 3 ^x - 2 Reflected over the x-axis
Everything is exponents of the three except the -2 at the end and the 4th one is also +1 not an exponent
Answer:
1. y = -3^ x Translated up by 1 unit 2.
2.y = 3^ -x Reflected over the y-axis 3.
3.y = 3 ^x - 2 Translated right by 2 units 4.
4. y = 3 ^x + 1 Translated down by 2 units 5.
5. y = 3^ x + 1 Translated left by 1 unit 6.
6. y = 3 ^x - 2 Reflected over the x-axis
Step-by-step explanation:
One of the solutions of the system of equations shown in the graph has an x-value of -4. What is its corresponding integer y-value? -1 -3 0 3
Answer:
Solution: (-4,-3)
Step-by-step explanation:
We need to complete the solution set of given graph.
We are given two graph one straight line and one parabola. We can see in graph both intersect at two points.
At x=-4 and x=-1
We can easily find the value of y corresponding to the value of x using given graph.
At x=-4,
First we draw a vertical line at x=-4 and see where it cut graph. From that point draw a horizontal line and see where y-axis cut.
The value of at x=-4 would be -3
Please see the attachment and see the vertical and horizontal line.
Thus, The Solution is (-4,-3)
Drag each object to show whether distance is proportional to time in the situation represented.
Answer: please find the answer in the explanation.
Step-by-step explanation:
1.) The distance is not proportional to time. Because the distance was constant from time = 3 seconds to 10 seconds.
2.) A person running down a field to score a touchdown. Not enough information.
3. A dog jogging at a constant speed for 20 minute. The distance is proportional to time because of the constant speed.
4.) The distance is proportional to time because their is increase in distance covered and increase in time taken.
5.) A truck passing through the 4 cities at a constant speed. The distance is proportional to time because the speed is constant.
6.) A horse running around a race track. Distance is not proportional to time because this is not a linear motion.
Please help! Dad will murder me if I don't have this done by the time he gets home! 100 points for whoever solves this!
Answer:
3(4)to the 3
Step-by-step explanation:
Factor the following expression completely:
32
z
4
+
8
z
3
−
4
z
2
Answer:
40z + 5
Step-by-step explanation:
I'm assuming you need to factor 32z + 4 + 8z + 3 - 4 + 2
32z + 8z ( since they both have the same variable ) = 40z4 + 3 - 4 + 2 ( since they have to variables ) = 5Hope this helped
Answer:
The factored expression for the given equation is 4(8z⁴ + 2z³ - z²)
Step-by-step explanation:
In the problem, we a re given an equation.
32z⁴ + 8z³ - 4z²
We can factor out this equation by finding the common factor between all of the coefficients which are 32, 8, and 4.
A common factor between them is 4 because each number can be easily divided by 4. Each number is also a multiple of 4. So, when we are factoring, we will divide each number by 4 because 4 will be on the outside of the parentheses in the final answer.
4(8z⁴ + 2z³ - z²)
So, this is your factored expression from the given equation.
I know how to do it but right now I'm cooking and have no time please say if the first part is right and the second part will be much appreciated!
Part A is correct. We have x+15 as the length and x+3 as the width. Convention usually has the width be the smaller of the two.
------------------
Part B will have you replace x with 8 and simplify
length = x+15 = 8+15 = 23
width = x+3 = 8+3 = 11
the rectangle is 23 yards by 11 yards, so the area is 23*11 = 253 square yards
Answer:
Below
Step-by-step explanation:
As we see the area is expressed as second degree polynomial
We have already a side wich is (x+15)
● x^2 +18x + 45 = w × (x+15)
● w = (x^2 +18x+45)/(x+15)
Using the eucledian division we get:
● w = x+3
Since x^2 +18x +45 = (x+15) × (x+3)
So your answer was right
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's calculate the dimensions if x= 8 yards
● the length
x+15 = 8+15 = 23 yards
● the width
x+3 = 8 + 3 = 11 yards
● the area
(x+15)×(x+3) = 23 × 11 = 253 yards^2
what is the first step to solving this problem: 3x-10=2(x+3)
Answer:
x = 16
Step-by-step explanation:
3x - 10 = 2(x+3)
First step is solve this:
2(x+3) = 2*x + 2*3 = 2x + 6
then:
3x - 10 = 2x + 6
3x - 2x = 6 + 10
x = 16
Check:
3*16 - 10 = 2(16+3)
48 - 10 = 2*19 = 38
Answer:
x = 16
Step-by-step explanation:
you start off by isolating the variable
