In the accompanying diagram, a right circular cone is carved out of a solid foam cylinder and discarded. What is the volume of the foam remaining in the cylinder?
A. 150π cubic units
B. 125π cubic units
C. 100π cubic units
D. 50π cubic units
Answer:
100π cubic units is left
Step-by-step explanation:
πr²h - 1/3πr²h
π(5)²(6) - 1/3π(5)²(6)
150π - 50π = 100π
The volume of the foam is 100π cubic units remaining in the cylinder.
Given,
Radius of cone (r) = 5
Height of cone (h) = 6
What is the volume of a cone?The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.
∵ The volume of the cone (V )= 1/3πhr²
To determine the volume of the foam remaining in the cylinder
Subtract the volume of the cone into the volume of the cylinder
⇒ πr²h - 1/3πr²h
Substitute the values of h and r,
⇒ π(5)²(6) - 1/3π(5)²(6)
⇒ 150π - 50π
⇒ 100π
Hence, The volume of the foam is 100π cubic units remaining in the cylinder.
Learn more about the volume of the cone here:
brainly.com/question/1578538
#SPJ5
Someone lmk thank youuu
Answer:
please mark my answer brainliest
Step-by-step explanation:
=8 x cube + 27
=2 X whole cube + 3 whole cube
=(2x+3)(2 X whole square + 3 whole square -2× 2 X ×3 )
=(2x+3)(4x square +9-12x)
....thats all...if require more than use splitting midterm to get more appropriate answer
A triangle has vertices at (1,3),(2,-3), and (-1,-1). What is the approximate perimeter of the triangle? A. 16 B: 14 C: 15 D: 10
Answer:
B 14
explanation:
i did the math
The perimeter of the given triangle is 14 units, so the correct option is B.
How to get the perimeter of the triangle?
The perimeter of the triangle will be equal to the sum between the distances between the given points.
Remember that the distance between two points is (x₁, y₁) and (x₂, y₂) is:
[tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex]
For the pair of (1,3), (2,-3): the distance is:
[tex]d = \sqrt{(2 - 1)^2 + (-3 - 3)^2} = 6.08[/tex]
For the pair (1, 3) , (-1, -1) the distance is:
[tex]d = \sqrt{(-1 - 1)^2 + (-1 - 3)^2} = 4.5[/tex]
For the pair (2, -3) and (-1, -1) the distance is:
[tex]d = \sqrt{(2 - (-1))^2 + (-3 - (-1))^2} = 3.6[/tex]
Then the total perimeter, rounded to the next whole number is:
6.08 + 4.5 + 3.6 = 14
So the correct option is B.
If you want to learn more about triangles, you can read:
https://brainly.com/question/4289712
how do you break down 213 in times
Answer:2 hundred+1 tens+3 ones
Step-by-step explanation:
26.9 microgram/milliliter to hectograms/deciliter
Answer:
.0000269 hectograms/ deciliter
2.69 * 10^e-5 hectograms/ deciliter
Step-by-step explanation:
micro grams to hectograms
10^8 micrograms = 1 hectogram
milliliters to deciliter
100 milliliters = 1 deciliter
Using conversion factors
26.9 microgram 1 hectogram 100 milliliters
----------------------- * --------------------------- * ---------------------
milliliter 10^8 micrograms 1 deciliter
2690 hectograms
---------------------------
10^8 deciliters
.0000269 hectograms/ deciliter
2.69 * 10^e-5 hectograms/ deciliter
Classify the numbers as rational or irrational.
6
√2.6
√2+6
Step-by-step explanation:
[tex] \sqrt 2, \: \sqrt 2. 6 \: \& \: \sqrt 2 + 6[/tex] are irrational and 6 is the only rational number.
help me with these please
Step-by-step explanation:
(1) y = x e^(x²)
Take derivative with respect to x:
dy/dx = x (e^(x²) 2x) + e^(x²)
dy/dx = 2x² e^(x²) + e^(x²)
dy/dx = (2x² + 1) e^(x²)
Take derivative with respect to x again:
d²y/dx² = (2x² + 1) (e^(x²) 2x) + (4x) e^(x²)
d²y/dx² = (4x³ + 2x) e^(x²) + 4x e^(x²)
d²y/dx² = (4x³ + 6x) e^(x²)
Substitute:
d²y/dx² − 2x dy/dx − 4y
= (4x³ + 6x) e^(x²) − 2x (2x² + 1) e^(x²) − 4x e^(x²)
= 4x³ + 6x − 2x (2x² + 1) − 4x
= 4x³ + 6x − 4x³ − 2x − 4x
= 0
(2) y = sin⁻¹(√x)
sin y = √x
sin²y = x
Take derivative with respect to x:
2 sin y cos y dy/dx = 1
sin(2y) dy/dx = 1
dy/dx = csc(2y)
Take derivative with respect to x again:
d²y/dx² = -csc(2y) cot(2y) 2 dy/dx
d²y/dx² = -2 csc²(2y) cot(2y)
Substitute:
2x (1 − x) d²y/dx² + (1 − 2x) dy/dx
= 2 sin²y (1 − sin²y) (-2 csc²(2y) cot(2y)) + (1 − 2 sin²y) csc(2y)
Use power reduction formula:
= (1 − cos(2y)) (1 − ½ (1 − cos(2y))) (-2 csc²(2y) cot(2y)) + (1 − (1 − cos(2y))) csc(2y)
= (1 − cos(2y)) (1 − ½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cos(2y) csc(2y)
= (1 − cos(2y)) (½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cot(2y)
= (cos(2y) − 1) (1 + cos(2y)) csc²(2y) cot(2y) + cot(2y)
= (cos²(2y) − 1) csc²(2y) cot(2y) + cot(2y)
= -sin²(2y) csc²(2y) cot(2y) + cot(2y)
= -cot(2y) + cot(2y)
= 0
Jacob spent $35.40 to fill up 15 gallons of gas in his pick-up truck. How much does 6 gallons cost?
Answer:
$14.16 for 6 gallons.
Step-by-step explanation:
35.40/15 = 2.36
2.36*6 = 14.16
area of a triangle two sides of which are 18 cm and 12 cm
and the perimeter is 44 cm.
Answer:
≈ 83.9 cm²
Step-by-step explanation:
Given:
P = a+b+c = 44 cma = 18 cmb = 12 cmThen:
c= P -(a+b) = 44 -(18+12) = 14 cmArea of the triangle is found by using Herons formula:
A = √s(s-a)(s-b)(s-c),where s = P/2 = 44/2 = 22 cm
A = √22(22-18)(22-12)(22-14) = √22*4*10*8= √7040 ≈ 83.9 cm²Answer:
[tex]\huge \boxed{\mathrm{83.9 \ cm^2}}[/tex]
Step-by-step explanation:
Two sides of the triangle are given.
The perimeter is given.
We need to solve for the third side.
[tex]P=a+b+c[/tex]
[tex]P= \sf perimeter[/tex]
[tex]a,b,c= \sf side \ lengths[/tex]
[tex]44=18+12+c[/tex]
[tex]c=14[/tex]
The measure of the third side is 14 cm.
When three sides of the triangle are given, we can solve for the area using Heron’s formula.
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s=\sf semi \ perimeter[/tex]
[tex]\displaystyle s=\frac{P}{2} =\frac{44}{2} =22[/tex]
Plugging in the values and evaluating.
[tex]A=\sqrt{22(22-18)(22-12)(22-14)}[/tex]
[tex]A = 83.904708...[/tex]
The area of the triangle is approximately 83.9 cm².
reduce to simplest term 44/4
Answer:
11
Step-by-step explanation:
44/4 = 11
4/4 = 1
then:
44/4 = 11/1 = 11
Coleman uses his graphing calculator to find all of the solutions to the equation shown below.
23 + 3 = -24 + 4
What are ALL of the solutions to the equation, rounded to the nearest hundredth?
A.
x = 0.82 and 3.55
B. O x = -1.38 and 0.37
C.
x = 0.37 and 3.55
D.Ox=-1.38 and 0.82
Answer:
The correct option is;
D. x = -1.38 and 0.82
Please find attached the combined function chart
Step-by-step explanation:
The given equation is x³ + 3 = -x⁴ + 4
Plotting the equation using Excel, we have;
f(x) = x³ + 3, h(x) = -x⁴ + 4
x f(x) h(x)
-1.4 0.256 0.1584
-1.39 0.314381 0.26699
-1.38 0.371928 0.373261
-1.37 0.428647 0.477246
-1.36 0.484544 0.57898
Which shows an intersection at the point around -1.38
x f(x) h(x)
0.77 3.456533 3.64847
0.78 3.474552 3.629849
0.79 3.493039 3.610499
0.8 3.512 3.5904
0.81 3.531441 3.569533
0.82 3.551368 3.547878
0.83 3.571787 3.525417
Which shows the intersection point around 0.82
Therefore, the correct option is x = -1.38 and 0.82
From the graphing calculator the intersection point is given as
x = -1.3802775691 and 0.81917251339.
The calorie count of a serving of food can be computed based on its composition of carbohydrate, fat, and protein. The calorie count C for a serving of food can be computed using the formula C = 6h + 11f + 7p, where h is the number of grams of carbohydrate contained in the serving, f is the number of grams of fat contained in the serving, and p is the number of grams of protein contained in the serving. Solve this formula for f, the number of grams of fat contained in a serving of food.
Answer:
see below (I hope this helps!)
Step-by-step explanation:
C = 6h + 11f + 7p
Get all non-f terms on one side:
C - 6h - 7p = 11f
Divide by 11:
f = [tex]\frac{C - 6h - 7p}{11}[/tex]
Hello I was wondering if you can help me list these from least to greatest
Answer:
See below.
Step-by-step explanation:
Convert to decimal form
7 3/5 = 7.6
7 7/10 = 7.7
10 2/5 = 10.4
8 1/2 = 8.5
So the answer is
7 3/5 , 7 7/10, 8.3, 8.1/2, 10.2 10 2/5, 11.1.
Two years ago ,a woman was 7 times as old as her daughter,but in 3 years time ,she would be 2 times as old as the girl,how old are they now?.
Let present age of women and her daughter be x and y respectively.
According to the question,
Case 1 :
Two years ago,
Woman age = ( x - 2 ) years
Her daughter age = ( y - 2 ) years
Woman was 7 times old as her daughter. [ Given ]
x - 2 = 7 ( y - 2 )
=> x - 2 = 7y - 14
=> x - 2 + 14 = 7y
=> x + 12 = 7y ....( i )
Case 2 :
After Three years ,
Woman age = x + 3
Her daughter age = y + 3
she would be 4 times old as the girl. [ Given ]
x + 3 = 4 ( y + 3 )
=> x + 3 = 4y + 12
=> x = 4y + 12 - 3
=> x = 4y + 9....( ii )
Now,
★ Substituting the value of x = 4y + 9 from equation ( ii ) in equation ( i ),we get
x + 12 = 7y
=> 4y + 9 + 12 = 7y
=> 21 = 7y - 4y
=> 21 = 3y
=> 3y = 21
=> y = 21/3
=> y = 7
And,
x = 4y + 9
★ Substituting the value of y in equation ( ii ), we get
x = 4 × 7 + 9
x = 28 + 9
x = 37
Hence, the present age of women is 37 years and her daughter age is 7.
the current age of the daughter is 3 years old, and the current age of the woman is 9 years old.
Let's denote the current age of the daughter as "D" and the current age of the woman as "W".
From the given information:
1. Two years ago, the woman was 7 times as old as her daughter:
W - 2 = 7(D - 2)
2. In three years time, the woman would be 2 times as old as the girl:
W + 3 = 2(D + 3)
We now have a system of two equations with two unknowns. Let's solve this system of equations:
From equation 1, we can rewrite it as:
W = 7(D - 2) + 2
Substituting this expression for W in equation 2, we have:
7(D - 2) + 2 + 3 = 2(D + 3)
Simplifying the equation:
7D - 14 + 2 + 3 = 2D + 6
Combine like terms:
7D - 9 = 2D + 6
Subtract 2D from both sides:
7D - 2D - 9 = 6
Combine like terms:
5D - 9 = 6
Add 9 to both sides:
5D = 15
Divide both sides by 5:
D = 3
Now that we know the daughter's current age (D = 3), we can substitute it back into equation 1 to find the woman's age:
W = 7(D - 2) + 2
W = 7(3 - 2) + 2
W = 7(1) + 2
W = 7 + 2
W = 9
Therefore, the current age of the daughter is 3 years old, and the current age of the woman is 9 years old.
Learn more about Age here
https://brainly.com/question/17210425
#SPJ2
Marisha walks 8 miles in 5 days. If she walks at the same rate, how far
does Marisha walk in 40 days?
Answer:
56 miles
Step-by-step explanation:
The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is
true?
x2 + x = 42
x2 + 2x = 42
x²+x+42=0
x² + 2x + 42=0
Answer:
x2 + x = 42
Step-by-step explanation:
x = nhmber
x² = its square
then:
The sum of a number and its square is 42 is:
x² + x = 42
What is the solution to this equation 34(x+8)=12(x−6)
Answer:
x = - 172*11
Step-by-step explanation:
is -7 a rational number
When the solution of x2 + 9x - 9 is expressed as
9&
2
what is the value of r?
X
-btvb2 - 4ac
2a
117
O 54
045
09
answer
r = b²-4ac
= 81 + 36
= 117
you are building a new house and need to pour 1200 cubic feet of concrete for the foundation. the concrete truck delivers concrete by the cubic yard. how much concrete do you need to buy from the concrete company?
Answer:
400 cubic yards
Step-by-step explanation:
There are three cubic feet in each cubic yard
Each table below lists the squared residuals for a line of fit for a certain set of data points. Find the sum of the squared residuals for each potential line of fit, and then determine which potential line is the true line of best fit.
c.) Square of Residual
.200
.116
.16
D) Square of Residual
.0036
.0016
.009
Answer:
c
Step-by-step explanation:
Factoring Polynomials, please help.
Answer:
(x²)² + 2(9)x² + 9²
(x² + 9)²
Step-by-step explanation:
Given expression in the question is,
(x⁴ + 18x²+ 81)
We have to factorize this expression.
We know the formula of (a + b)² = a² + 2ab + b²
Comparing this formula with the given expression,
a = x²
b = 9²
By substituting these values in the given formula,
Therefore, (x⁴ + 18x²+ 81) = (x²)² + 2(9)x² + 9²
= (x² + 9)²
Clarence set his watch 16 seconds behind , and it falls behind 2 seconds every day . How many days behind has it been since Clarence last set his watch if the watch is 46 seconds behind
Answer:
15 days.
Step-by-step explanation:
46 - 16 = 30.
It falls 2 seconds behind each day so the number of required days
= 30 / 2 = 15.
Answer:
Step-by-step explanation:
15 days 16-40=30 the take 30/2= 15
0.07 is 10 times as great as ? A.0.1 B.0.7 C.0.001 D.0.007
Answer:
D. 0.007
Step-by-step Explanation:
0.07= 10 x
= 0.07/ 10
= 0.007
A store reduces the price of a jacket by 40%. The sale price of the jacket is marked as $30. What percent of the original price is the sale price? What was the original price of a jacket?
Answer:
-60%
-$50
Step-by-step explanation:
As the statement says that the price of the jacket was reduced by 40%, to determine the percent that the sale price represents from the original price, you have to subtract 40% from 100% that represents the original price:
100%-40%= 60%
This means that $30 represents 60% of the original price.
-To determine the original price of the jacket, you can use the rule of three:
$30 → 60%
x ← 100%
x=(100*30)/60= 50
According to this, the original price of a jacket was $50.
Homer Simpson entered a pie eating contest at the county fair. Homer was determined to win and went into training for 6 days. Each
day, he ate 4 more pies than the day before. Homer ate 150 pies while in training. How many pies did he eat each day?
Day 1: type your answer...
Day 2: type your answer....
Day 4: type your answer....
Day 3: type your answer....
type your answer...
Day 5: type your answer...
Day 6: type your answer...
Answer:
151923273135Step-by-step explanation:
He ate 15, 19, 23, 27, 31, 35 pies for each day.
What is addition?Addition in math is a process of combining two or more numbers.
Given that, Homer Simpson entered a pie eating contest at the county fair. Homer was determined to win and went into training for 6 days, each day, he ate 4 more pies than the day before. Homer ate 150 pies while in training.
Let he ate x pie for 1st day, then according to question,
1st day = x
2nd day = x+4
3rd day = x+8
4th day = x+12
5th day = x+16
6th day = x+20
He ate 150 pies for 6 days
Therefore, x+x+4+x+8+x+12+x+16+x+20 = 6x + 60 = 150
6x = 90
x = 15
Hence, he ate 15, 19, 23, 27, 31, 35 pies for each consecutive day.
For more references on addition, click;
https://brainly.com/question/14092461
#SPJ2
A parent rewards a child with 50 cents for each correctly solved mathematics problem and fines the child 30 cents for each incorrectly solved problem. If the child nets $22.00 after 100 problems. How many problems were solved correctly?
Answer:
65
Step-by-step explanation:
Let c = number of correct answer.
Let i = number of incorrect answers.
There are 100 questions, so
c + i = 100
The correct answers are worth 0.5c.
The incorrect answers are worth -0.3i (a negative value because 30 cents is taken away for each incorrect answer)
The total worth of the answers is 0.5c - 0.3i. The total worth of the answers is $22.00, so the second equation is
0.5c - 0.3i = 22
We have a system of two equations in 2 unknowns:
c + i = 100
0.5c - 0.3i = 22
We'll use the substitution method to solve the system of equations.
Solve the firt equation for c:
c = 100 - i
Now substitute 100 - i for c in the second equation.
0.5(100 - i) - 0.3i = 22
50 - 0.5i - 0.3i = 22
-0.8i = -28
i = 35
c = 100 - i
c = 100 - 35
c = 65
Answer: 65 problems were solved correctly.
7p − p = 18 2) −5n − 4n = −9
Answer:
[tex] \boxed{ \bold{ \sf{ \boxed{ p = 3}}}} [/tex][tex] \boxed{ \bold{ \sf{ \boxed{n = 1}}}}[/tex]
Step-by-step explanation:
1. [tex] \sf{7p - p = 18}[/tex]
Collect like terms
⇒[tex] \sf{6p = 18}[/tex]
Divide both sides of the equation by 6
⇒[tex] \sf{ \frac{6p}{6} = \frac{18}{6} }[/tex]
Calculate
⇒[tex] \sf{p = 3}[/tex]
2. [tex] \sf{ - 5n - 4n = - 9}[/tex]
Collect like terms
⇒[tex] \sf{ - 9n = - 9}[/tex]
Divide both sides of the equation by -9
⇒[tex] \sf{ \frac{ - 9n}{ - 9} = \frac{ - 9}{ - 9} }[/tex]
Calculate
⇒[tex] \sf{n = 1}[/tex]
Hope I helped!
Best regards!!
40 ➗ [24 - 4 x (2 + 3) ]
What is the value of this expression?
Answer: this is your answer
10
_____
6-5x
Answer:
1.7-20x OR 10/6-5x
Step-by-step explanation:
40÷(24-4x(2+3))
first you add the last set of ()
40÷(24-4x(5))
then you multiply by 4x
40÷(24-20x)
since you can't subtract those two you do this
40÷24-20x
divide 40 and 24
you get 1.66666667 then you round up
1.7-20x
ORyou put 40/24-20x
divide the top and the bottom by 4
(40÷4)/(24÷4) -(20x÷4)
and your answer will be
10/6-5x
Evaluate −12(−2). (1 point) 14 −14 −24 24
Answer:
24.
Step-by-step explanation:
−12(−2
= -12 * -2 ( Note - * - = +) so we have:
24 (answer).