Answer:
The correct answer is
C. 23.1
Step-by-step explanation:
i think this is correct
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]
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.
PLZZ HELPP!! Water is poured from a 1.5 L water bottle into an empty glass until both the glass and the bottle are 3/4 full. What is the volume of the glass?
Answer:
0.5 L
Step-by-step explanation:
volume of bottle: 1.5 L
amount of water = 1.5 L
volume of glass: x
3/4 full is the same as 0.75 full
vol of water in bottle + vol of water in glass = total vol of water
0.75(bottle) + 0.75(glass) = 1.5
0.75(1.5) + 0.75x = 1.5
0.75x = 0.375
x = 0.5
Clare has 150$ in her bank account. She buys a bike for 200$. What is Clares account balance now?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The amount left in the bank account is -$50.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount in the bank account = $150
Cost of the bike = $200
The amount left in the bank account.
= 150 - 200
= -$50
Thus,
The amount left in the bank account is -$50.
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Triangle ABC is dilated to form new triangle DEF. If angle A is congruent to angle D, what other information will prove that the two triangles are similar by the AA similarity postulate?
Angle B is congruent to angle E.
Side AB is congruent to side DE.
Angle C is congruent to angle D.
Side BC is congruent to side EF.
Answer:
Step-by-step explanation:
option A , angle B is congruent to angle E { SINCE IT IS AA POSTULATE
Answer:
B=E (b)
Step-by-step explanation:
-5+2(10b-2)=31 need help thanks!
Answer:
[tex]\Large \boxed{b=2}[/tex]
Step-by-step explanation:
-5+2(10b-2)=31
Expand brackets.
-5+20b-4=31
-9+20b=31
Add 9 on both sides.
20b=40
Divide both sides by 20
b=2
Answer:
b = 2Step-by-step explanation:
-5+2(10b-2)=31
Multiply the terms in the bracket
That's
- 5 + 20b - 4 = 31
Group like terms
Send the constants to the right side of the equation
That's
20b = 31 + 4 + 5
Simplify
20b = 40
Divide both sides by 20
We have the final answer as
b = 2Hope this helps you
which of these expressions are equivalent to p/3?
A. p-2/3
B. 1/3p
C. p-3
D. 3/p
E. 3p/p
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
A lab technician is dividing a cell that has a diameter of 4.32×10−4 4 . 32 × 10 - 4 millimeters. Each of the new cells has a diameter measuring exactly one half of the diameter of the original cell. Which is the diameter of a new cel
Answer:
Bottom right option
Step-by-step explanation:
To find this, we can calculate:
1/2 * 4.32 * 10⁻⁴
= (1/2 * 4.32) * 10⁻⁴
= 2.16 * 10⁻⁴
The diameter of a new cell is 2.16×10−⁴millimeters
First step is to calculate 4.32×10−⁴ to the original numbers
4.32×10−⁴ =0.000432
Second step is to determine the diameter of a new cell
New cell diameter=0.000432×1/2
New cell diameter=0.000216
New cell diameter=2.16×10−⁴millimeters
Inconclusion The diameter of a new cell is 2.16×10−⁴millimeters
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help me plz can somewon help me
Answer:
The answer is 6x10^-4.
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10 .
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
How to get this answer:
Place the decimal point after the 6 to get 6.0
The question is now "how do we go from 6.0 to get back to 0.0006?"
The answer is "move the decimal point 4 spots to the left". This movement of "move 4 left" means the exponent is -4. The negative because we moved to the left. The 4 indicates how many spaces we moved.
So we get the scientific notation value of [tex]6.0 \times 10^{-4}[/tex] which is the same as [tex]6 \times 10^{-4}[/tex] because 6.0 simplifies to 6
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
The coefficient of 8.2 N is
8
2
16
Answer:
2
Step-by-step explanation:
A coefficient is the number placed before the variable. The variable gets multiplied by the coefficient.
The format is not exactly clear with the expression in the question.
Assuming the expression is '8 * 2n', the coefficient would be 2.
'n' is getting multiplied by '2'.
'8' does not have a variable next to it, so it is just a term in the expression.
The product of 8 and 2 is 16. 16 is not in the expression.
If the expression was '8.2n', 8.2 would be the coefficient.
Brainilest Appreciated.
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:
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
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.
Use a number line to approximate the value of root 33
Let's think about the square root of 33 here for a second.
What two perfect squares surround 33?
The answer is 25 and 36.
Then, let's take the square root of both 25 and 36, which are 5 and 6. Therefore, since the square root of 25 and 36 are both nearest to the square root of 33, then the square root of 3 must be between 5 and 6.
The correct answer is A (or option 1): 5 < root 33 < 6
Hope this helps! :)
Answer:
a (the first choice)
Step-by-step explanation:
To start, you should think of square root values near 33 that you know the answer to. For example, the square root of 25 is 5, and the square root of 36 is 6. Therefore, you know that the square root of 33 is 5.something because it is in between 25 and 36.
PLEASE HELP WILL GIVE BRAINLY!!!!!!!
Which are the roots of the quadratic function f(q) = q^2 - 125? Select two options.
A) q= 5/5
B) q= -5/5
C) q= 3/5
D) q= -3/5
E) q= 25/5
Answer:
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Since there is no constant value. This must be a special case.
So,
(q+5[tex]\sqrt{5}[/tex])(q-5[tex]\sqrt{5}[/tex])
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
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:
PLS HELP ME WITH THIS QUESTION, ANYTHING REALLY HELPSS!!!!
Answer:
x = 75
Step-by-step explanation:
FGE is a straight line so it equals 180 degrees
FGA + AGC + CGE = FGE
x + 90 + 15 = 180
Combine like terms
x+ 105 = 180
Subtract 105 from each side
x = 180-105
x = 75
Answer:
x = 75º
Step-by-step explanation:
The Vertical Angle Theorem shows that:
∠CGE ≅ ∠DGF
So:
∠DGF = 15º
∠AGD = 90º
90º - 15º = 75º
x = 75º
If you apply the changes below to the absolute value parent function, f(x)=x, what is the equation of the new function? Shift 2 units to the right shift 3 units down
Answer:
f(x) = Ix - 2I -3
Step-by-step explanation:
f(x) = IxI
f(x) = Ix - 2I -3
The equation is f(x) = | x – 2 | + 3 Then the vertex of the absolute function will be at (2, 3).
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x – h | + k
If you apply the changes below to the absolute value parent function
f(x) = |x|
Then the equation of the new function will be
Shift 2 units to the right, shift 3 units down
f(x) = | x – 2 | + 3
Then the vertex of the absolute function will be at (2, 3).
More about the absolute function link is given below.
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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
please help me.... The question no.b and would like to request you all just give me correct answer.
Answer: see proof below
Step-by-step explanation:
You will need the following identities to prove this:
[tex]\tan\ (\alpha-\beta)=\dfrac{\tan \alpha-\tan \beta}{1+\tan \alpha\cdot \tan \beta}[/tex]
[tex]\cos\ 2\alpha=\cos^2 \alpha-\sin^2\alpha[/tex]
LHS → RHS
[tex]\dfrac{2\tan\ (45^o-A)}{1+\tan^2\ (45^o-A)}\\\\\\=\dfrac{2\bigg(\dfrac{\tan\ 45^o-\tan\ A}{1+\tan\ 45^o\cdot \tan\ A}\bigg)}{1+\bigg(\dfrac{\tan\ 45^o-\tan\ A}{1+\tan\ 45^o\cdot \tan\ A}\bigg)^2}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan\ A}{1+\tan\ A}\bigg)}{1+\bigg(\dfrac{1-\tan\ A}{1+\tan\ A}\bigg)^2}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{1+\bigg(\dfrac{1-2\tan\A+\tan^2 A}{1+2\tan A+\tan^2A}\bigg)}\\[/tex]
[tex]=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\dfrac{(1+2\tan A+\tan^2A)+(1-2\tan A+\tan^2 A)}{1+2\tan A+\tan^2A}}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\dfrac{2+2\tan^2A}{1+2\tan A+\tan^2A}}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{2\bigg(\dfrac{1+\tan^2A}{(1+\tan A)^2}\bigg)}\\\\\\=\dfrac{\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\bigg(\dfrac{1+\tan^2A}{(1+\tan A)^2}\bigg)}[/tex]
[tex]=\dfrac{1-\tan A}{1+\tan A}}\times \dfrac{(1+\tan A)^2}{1+\tan^2A}\\\\\\=\dfrac{1-\tan^2 A}{1+\tan^2 A}\\\\\\=\dfrac{1-\dfrac{\sin^2 A}{\cos^2 A}}{1+\dfrac{\sin^2 A}{\cos^2 A}}\\\\\\=\dfrac{\bigg(\dfrac{\cos^2 A-\sin^2 A}{\cos^2 A}\bigg)}{\bigg(\dfrac{\cos^2 A+\sin^2 A}{\cos^2 A}\bigg)}\\\\\\=\dfrac{\cos^2 A-\sin^2 A}{\cos^2 A+\sin^2 A}\\\\\\=\dfrac{\cos^2 A-\sin^2 A}{1}\\\\\\=\cos^2 A-\sin^2 A\\\\\\=\cos 2A[/tex]
cos 2A = cos 2A [tex]\checkmark[/tex]
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)
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!
Liam tried to define a translation. - Point A maps to point A' - Every point P maps to point P' such that PP' is parallel to AA' and points in the same direction as AA' Which counterexample shows that Liam's definition does not fully define a translation?
Answer:
B
Step-by-step explanation:
This is the correct answer.
From The diagrams shown here, the option that does not fully define a translation is B.
What is a translation in mathematics?
In mathematics, this is another word for a transformation. What the translation does is that it helps to move a shape in different ways without altering the appearance of the shape.
The translation in this question is option B given the definition that we have above.
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A grocery store recently sold a bag of peanuts for $0.76 and a bag of Pikachu's for $3.68 at the end of the day 50 bags of peanuts and Pikachu's were sold for a total of 128 point 52 how many bags of each were sold
Answer:
31 Pikachu bags were sold.
19 peanut bags were sold.
Step-by-step explanation:
Let's set up an equation of the total revenue of the day, where x is the number of Pikachu's sold.
We know that the number of Peanuts sold is 50-x (as the total needs to be 50)
We know that the total revenue is:
Number of Pikachus * Cost per Pikachus + Number of Peanuts * Cost per Peanuts
Using our definitions above:
Total Revenue = x * $3.68 + (50-x) * $0.76
We know that the revenue needs to be $128.52.
$128.52 = x * $3.68 + (50-x) * $0.76
Let's remove the $ signs.
128.52 = x * 3.68 + (50-x) * 0.76
Multiplying both 50 and -x with 0.76, "expanding" the parenthesis.
128.52 = x*3.68 + 50*0.76 - x*0.76
128.52 = x*3.68 + 38 - 0.76*x
Subtracting 38 from both sides
90.52 = 3.68*x - 0.76*x
We can simplify the right side.
90.52 = 2.92*x
We can divide both sides by 2.92:
31 = x
And flip it:
x = 31
So 31 Pikachus were sold (remember we claled that x), and as we know, the number of peanut bags sold is
50-x = 50-31 = 19
31 Pikachu bags were sold.
19 peanut bags were sold.
[tex] \LARGE{ \boxed{ \rm{ \pink{Solution:}}}}[/tex]
Let the number of peanut bags be x
Then, Number of pikachu bags = 50 - x
Given,
Cost of each peanut bag = $0.76Cost of each pikachu bag = $3.68Then,
⇛ Total cost he gets from peanut bag = $0.76 × x
⇛ Total cost he gets from pikachu bag = $3.68(50 - x)
According to question,
⇛ $0.76x+ $3.68(50 - x) = $128.52
Solving this equation,
⇛ 0.76x + 184 - 3.68x = 128.52 (Removed $ symbol)
⇛ 184 - 2.92x = 128.52
⇛ 184 - 128.52 = 2.92x
⇛ 55.48 = 2.92x
Flipping the equation,
⇛ 2.92x = 55.48
⇛ x = 55.48 / 2.92
⇛ x = 19
Then,
⇛ 50 - x = 50 - 19 = 31
[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: peanut \: bags = 19}}}}}[/tex]
[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: pikachu \: bags = 31}}}}}[/tex]
━━━━━━━━━━━━━━━━━━━━
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
colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?
Answer: 24
Step-by-step explanation:
Colleen painted 7 windows, some of which were her mother's.
Her dad painted 7+1 (8) windows, and that is twice as much as what her mother was supposed to do. Her mother was supposed to do 4 windows. That means Colleen's share was 3 windows.
If all the kids had to do an equal amount of windows, than each kid had to do 3 windows.
8+7+3+3+3=24
The total windows in the house are 21.
What is an algebraic expression?It is an expression contains a relation between different parameters (variables). It contains variable and constant values, along with algebraic operations.
In our given problem, the algebraic relation between different members work output and total windows can be expressed as:
Windows painted by colleen and her mother = 7
Windows painted by father = (Windows painted by colleen and her mother + 1)
= (7 + 1) = 8
∴ Windows painted by father = 8
Now, as given,
2 Windows painted by mother = Windows painted by father
∴ Windows painted by mother = [tex]\frac{8}{2}[/tex] = 4
and Windows painted by colleen = 7 - 4 = 3
Colleen and her 2 brothers paint equal windows;
∴ They painted 3 windows each.
The total windows in the house is equal to total painted windows by mother, father, colleen and her two brothers:
⇒ 4 + 8 + 3 x 3 = 12 + 9 = 21
Hence the total windows in the house are 21.
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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 :)
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!