Please help
According to Cavalieri's principle,
A) the volume of the sphere is equal to the volume of the cones.
B) the volume of the sphere is equal to the volume of the cylinder.
C) the volume of the sphere is equal to two times the volume of the cones.
D) the volume of the sphere is equal to the volume of the solid between the cones and the cylinder.
Answers
Answer:
Step-by-step explanation:
The answer is d.
Answer:
d
Step-by-step explanation:
Related Questions
Simplify each expression. Use positive exponents.
(x–2y–4x3) –2,
Answers
(x^-2y^-4x³)^-2
We can combine the x terms inside the brackets using the concept;
x ^a × x^b = x^(a+b)
Therefore,
(x^-2)(x^3) = x^(3-2) = x^!
Thus we get;
(xy^-4)^-2
Using the concept
(x^a)^b = x^(ab)
Therefore
= x ^(-2×1) y^(-2×-4)
=x^-2y^8
But using the concept; x^-a = 1/x^a
Thus, x^-2y^8 = y^8/x²
Hence the simplified equation is;
= y^8/x²
1 .
Factor 13x⋅(x−3)+10⋅(x−3)
2.
Factor 17t⋅(17t−9)−12⋅(17t−9)
Answers
Solve for x. Simplify completely.
x^2-9=55
Answers
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work. Sn: 12 + 42 + 72 + . . . + (3n - 2)2 = n(6n^2-3n-1)/2
Answers
[tex]S_1 = 12 \\ S_2 = 54 \\ S_3 = 126 \\ S_n = 15n^2 - 3n [/tex]
Explanation:
[tex]S_1 = 12 \\ S_2 = 12 +42 = 54 \\ S_3 = 12 + 42 + 72 = 126[/tex]
To calculate for [tex]S_n[/tex], note that the series is an arithmetic series because each term is equal to the preceding term plus a constant, which is 30 (called common difference).
We let
[tex]a_1 = \text{ first term} = 12 \\ a_2 = \text{ second term} = 42 \\ a_3 = \text{ third term} = 72\\. \\. \\. \\a_n = n\text{th term}[/tex]
Since [tex]S_n[/tex] is an arithmetic series, [tex]a_1, a_2, a_3, ... , a_n[/tex] is an arithmetic sequence and so the formula for the nth term is given by
[tex]a_n = a_1 + d(n - 1) \\ a_n = 12 + 30(n - 1) \\ \boxed{a_n = 30n - 18}[/tex]
Where d = common difference = 30
Now, since [tex]S_n[/tex] is an arithmetic series, we can use the formula for the sum of the arithmetic series, which is given by
[tex]S_n = \frac{n}{2} (a_1 + a_n) \\ \\ = \frac{n}{2} (12 + 30n - 18) \\ \\= \frac{n}{2} (30n - 6) \\ \\ = \frac{30n^2 - 6n}{2} \\ \\ \boxed{S_n = 15n^2 - 3n}[/tex]
Jake forgot to replace the cap on a bottle of deodorant. The deodorant began to evaporate at the rate of 12% per day. If the original amount of deodorant in the bottle was 30 grams, which of the following graphs best represents the amount of deodorant f(x) that would remain in the bottle after x days?
graph of function f of x equals 30 multiplied by 0.88 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis
graph of function f of x equals 50 multiplied by 0.82 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis
Answers
f(x) = 30(0.88)^x
Answer:
1. Graph of function f of x equals 30 multiplied by 0.88 to the power of x
Step-by-step explanation:
We are given that,
Original amount of deodorant in the bottle = 30 grams
The rate of evaporation = 12% = 0.12
That is, we see that the deodorant is decreasing as the number of days increases.
So, the function form of the decrease in the amount of deodorant is given by,
[tex]f(x)=30(1-0.12)^x[/tex], where x is the number of days.
i.e. [tex]f(x)=30(0.88)^x[/tex], where x is the number of days.
Hence, the graph representing the amount of deodorant after x number of days is,
1. Graph of function f of x equals 30 multiplied by 0.88 to the power of x
Suppose that y varies inversely with x. Write a function that models the inverse function. X= 15 when y= 2
Answers
A circle is drawn within a square as shown.
What is the best approximation for the area of the shaded region?
Use 3.14 to approximate pi.
21.5 cm²
78.5 cm²
100 cm²
178.5 cm2
Answers
square10×10= 100
circle πr^2= π(10/2)^2=78.54
100-78.54=21.46≈ 21.5cm2
u should practice more, otherwise future mathematics will kill u XD
Answer:
21.5 I TOOK THE TEST
Step-by-step explanation:
IS THIS CORRECT!!!!!!!!!!!!!
Answers
We have then:
x: number of devices.
Y: plan charge
For the current plan we have:
[tex]y = 175 [/tex]
For the new plan we have:
[tex]y = 4.5x + 94 [/tex]
Since we want the new plan to be smaller than the current plan, then we have:
[tex]175\ \textgreater \ 4.5x + 94 [/tex]
From here, we clear the value of x:
[tex]4.5x \ \textless \ 175 - 94 x \ \textless \ 81 / 4.5 x \ \textless \ 18[/tex]
Answer:
x <18
Note: The graph is correct
The graph is the region (-∞,18)
i.e. the shaded region to the left of 18 and open circle at 18.
Step-by-step explanation:It was given that the cost of the current plan is: $ 175 per month.
Also, the flat rate of new plan is: $ 94
Also, cost of 1 device is: $ 4.50
cost of x device is: $ 4.50x
Total cost of the new plan for x devices is: $ (94+4.50x)
Now we are asked to find the inequality such that the total cost of new plan is less than the current plan i.e.
94+4.50x < 175
i.e. 4.50x < 175-94
i.e. 4.50x < 81
i.e. x<18
Hence,the graph would be a line to the left of 18 with open circle at 18, since the inequality is strict.
Does anyone know these two answers?
Answers
The vertical line and the horizontal line are perpendicular to each other, so they form right angles.
x + 61 = 90
x = 90 - 61
x = 29
Problem 2:
Vertical angles are congruent. They have the same measure.
m<1 = m<2 = 93 deg
Question #1
(90-61)= 29
x=29
Question #2
Vertical angles are across from each other. This would show us that we would have to subtract.
360-93=(267).
(267)÷ (3)= 89.
But then, we would have t understand that these vertical angles could always be congruent which would mean that they're the same size (93)
The product of two consecutive even integers is 528. find the integers
Answers
4x^2 + 4x = 528
4x^2 + 4x -528 = 0
x^2 + x -132 = 0
Using quadratic formula
x = 11
Therefore, the integers are
22 and 24
Jon is launching rockets in an open field. The path of the rocket can be modeled by the quadratic function h(t) = -16t^2 + 96t, where h(t) is the height in feet any time t in seconds. After how many seconds will the rocket reach a height of 80 feet for the second time
Answers
We set the equation equal to 80 feet:
80= -16t² + 96t
When solving quadratics, we want it equal to 0, so we subtract 80 from both sides:
80-80= -16t² + 96t - 80
0= -16t² + 96t - 80
We use the quadratic formula to solve:
[tex]t=\frac{-96\pm \sqrt{96^2-4(-16)(-80)}}{2(-16)} \\ \\t=\frac{-96\pm \sqrt{9216-5120}}{-32} \\ \\t=\frac{-96\pm \sqrt{4096}}{-32} \\ \\t=\frac{-96\pm 64}{-32} \\ \\t=\frac{-96+64}{-32} \text{ or } 0=\frac{-96-64}{-32} \\ \\t=1 \text{ or } t=5[/tex]
F left parenthesis x right parenthesis equals 9 x cubed plus 2 x squared minus 5 x plus 4 and g left parenthesis x right parenthesis equals 5 x cubed minus 7 x plus 4. what is f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis? show all of your steps and write your final answer in factored form.
Answers
When we subtract polynomials we combine like terms:
(9x³+2x²-5x+4)-(5x³-7x+4)
9x³-5x³=4x³
2x²- 0 = 2x²
-5x--7x=-5x+7x=2x
4-4=0
This gives us
4x³+2x²+2x
Each of these is divisible by 2, and each has an x, so we factor those out:
2x( )
4x³/2x = 2x²:
2x(2x² )
2x²/2x=x:
2x(2x²+x )
2x/2x = 1:
2x(2x²+x+1)
Which of the following functions corresponds to the sinusoid shown?
4 sin 3x
-3 cos 4x
-4 cos 3x
3 sin 2x
Answers
Justification:
1) The amplitude of the function of the graph is [4 - (-4) ] / 2 = [4+4] / 2 = 8/2 = 4.
2) Therofore the coefficient that multiplies the trigonometric function is 4.
3) That leaves you the first and the third options:
4sin(3x) and - 4cos(3x).
4) The y intercept of the graph, f(0), is - 4.
Check f(0) for both 4 sin(3x) and 4 cos(3x)
4sin(0) = 0 => this is not the function
- 4cos(0) = -4 => this is the function and thw answer to the question.
The sculpture consists of five identical prisms. JD says the surface area of the sculpture is 44 times the surface area of one prism. Which statement about JD's method is true?
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we know that
(see the attached figure n 2 to understand the problem)
[the surface area of one prism]=2*[x*x]+2*[x*y]+2*[x*y]----> 2x²+4xy
[the surface area of the sculpture]=2*[5*x*y]+2*[3*x*x]+2*[3*x*y]--> 6x²+16xy
now
JD says the surface area of the sculpture is 4 times the surface area of one prism
[the surface area of the sculpture]=4*(2x²+4xy)---> 8x²+16xy
we compare the value that JD says with the real value
(8x²+16xy) > (6x²+16xy)
the value that JD says is greater in comparison with the real value
This is because JD should also subtract the areas of eight hidden surfaces.
the answer is
JD should also subtract the areas of eight hidden surfaces
Kathy is a repair technician for a phone company. each week, she receives a batch of phones that need repairs. the number of phones that she has left to fix at the end of each day can be estimated with the equation p=108−23d, where ppp is the number of phones left and ddd is the number of days she has worked that week. what is the meaning of the value 108108108 in this equation?
Answers
[tex]p=108-23d[/tex]
p = number of phones left to repair
108 = initial amount at the start of week
23 = number of phones repaired each day
d = number of days she worked that week
In the equation p=108−23d, the value 108 represents the total number of phones that Kathy receives each week for repair.
Explanation:In the given equation p=108−23d, the number 108 represents the total number of phones that Kathy receives each week for repair.
This means that at the start of her work week, before she begins to fix any phones, she has 108 phones that need repairs.
As each day passes (represented by d), the number of phones that Kathy has left to fix decreases by 23, which is the number of phones she is able to repair in one day.
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A line that is parallel to y=12 has slope m=
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any parallel line to y = 12, like the red one and the green one there, will have the same slope as y = 12, what is the that slope anyway?
well, let's pick any two points y = 12 passes by, hmmmmm say 2, 12 and 4, 12
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 2 &,& 12~) % (c,d) &&(~ 4 &,& 12~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{12-12}{4-2}\implies \cfrac{0}{2}\implies 0[/tex]
Find the hypotenuse of a right triangle if the legs are: 5 and 12
Answers
In this case a would be 5 and b would be 12. If you add these into the equation and then square root your answer, that should be the hypotenuse of the triangle. Hope I helped, have a nice day :)
Tickets to a movie cost $7.25 for adults and $5.50 for students. a group of friends purchased 8 tickets for $52.75. how many adult tickets did they purchase?
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Sean has 3 times as many vegetable plants as Liz and Sejuan combined. Liz has 3 vegetable plants, and Sejuan has 2 vegetable plants. How many vegetable plants does Sean have?
Which statements about this word problem are true? Check all that apply.
This is an example of a part-whole problem.
This is an example of a comparison problem.
Addition then multiplication can be used to solve the problem.
Subtraction then division can be used to solve the problem.
Division then multiplication can be used to solve the problem.
Answers
This is a comparison problem in mathematics where addition and multiplication are used. Liz and Sejuan together have 5 vegetable plants and since Sean has 3 times what both of them have combined, Sean has 15 vegetable plants.
Explanation:The problem at hand is about a comparison of the number of vegetable plants between Sean, Liz and Sejuan. It's an example of a comparison problem where addition and multiplication are used to find the solution. First, you need to find the total number of plants that Liz and Sejuan have by adding their plants together (3 + 2). We get a result of 5. Then, we know that Sean has 3 times as many plants as Liz and Sejuan together, so you multiply the combined total by 3 (5 * 3). The result is 15, so Sean has 15 vegetable plants.
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A cab driver told Bernice her fare came to a total of $7.75. She pays with a $10 bill. How much change should she get?
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helpppppppppppppppppppppppppppppp
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first option: Harulo is correct because the angle is coterminal with 3π / 4 and the reference angle is π / 4.
Explanation:
1) 19 π/4 = 4π + 3 π/4, which is 4 complete turns and 3/4 of turn.
2) 3 π/4 is in the third quadrant, so the reference angle is π - 3 π/4 = π/4
3) sin (π/4) = sin (3π/4) = (√2) / 2
4) csc (π/4) = 1 / [ sin (3π/4) ] = 1 / [ (√2) / 2 ] = 2 / (√2) = √2, which shows the validity of the statement and csc(19π/4) = √2.
what is 83/4 as an mixed number
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think of 83 as 80 + 3
80/4 = 20
3/4= 3/4
20+3/4 = 20 3/4 thats your mixed number or 20 and 3/4 twenty and three fourths
A mixed number is a number that consists of a whole number and a fraction.
The numerator of a fraction is how many of the denominator there are, and the denominator is thr whole (total amount).
In this improper fraction, the whole is 4, and the numerator is greater than the denominator.
The question is, how many wholes of 4 can be made with that numerator?
First, divide the numerator by the denominator to find the whole number.
83 ÷ 4 = 20.75
This means that the whole number is 20.
Next, multiply this whole number by the denominator, and then subtract that from the original numerator to find the new numerator.
83 - (4 × 20) = 3
Finally, place the new numerator over the old denominator.
ANSWER:
83/4 = 20 3/4 as a mixed number.
A patient needs 0.024grams of a sulfa drug. There are 8-mg tablets in stock. how many tablet should be given?,
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Paige bought 34 yards of yarn at the store and 2⁄9 of the yarn was blue. How many yards of blue yarn did Paige buy?
Answers
(2/9) * (100) = 22.22222222%
Making the following rule of three we have:
34 ----> 100%
x ------> 22.22222222%
Clearing x we have:
x = ((22.22222222) / (100)) * (34)
x = 7.555555555
x = 7.6
Answer:
Paige did buy 7.6 yards of blue yarn
Answer:
the right answer is 7 5/9 yards.
Step-by-step explanation:
Please help me! I'm so lost t-t!!
Factor completely.
x^2−8x+15
Enter your answer in the box.
Answers
x² - 8x + 15
x -5
x -3
(x-5)(x-3)
x = 5, 3
hope this helps
The difference of two numbers is 44 1 /2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.
Answers
The difference of two numbers is 44 1/2.
If the smaller of the two numbers increases 7 times
the difference will be 10 3/14.
Find the numbers?
x - y = 44 1/2
x - 7y = 10 3/14
6y = 34 2/7
y = 40/7
x = 703/14
Have a nice day
Required numbers as per the given condition are [tex]50\frac{3}{14}[/tex] and [tex]5\frac{5}{7}[/tex].
What is a number?" A number is defined as the count of any given quantity."
According to the question,
[tex]'x'[/tex] represents the greater number
[tex]'y'[/tex] represents the smaller number
As per the given condition equation we have,
[tex]x- y = 44\frac{1}{2} \\\\\implies x-y = \frac{89}{2}[/tex] ______[tex](1)[/tex]
[tex]x-7y =10 \frac{3}{14} \\\\\implies x-7y = \frac{143}{14}[/tex] ______[tex](2)[/tex]
Subtract equation [tex](2)[/tex] from [tex](1)[/tex] to get the required numbers,
[tex]6y = \frac{89}{2} -\frac{143}{14} \\\\\implies 6y = \frac{623-143}{14}\\ \\\implies 6y = \frac{480}{14}\\ \\\implies y = \frac{40}{7}\\ \\\implies y = 5\frac{5}{7}[/tex]
Substitute the value of [tex]'y'[/tex] in [tex](1)[/tex] we get,
[tex]x= \frac{89}{2}+ \frac{40}{7} \\\\\implies x = \frac{623+80}{14} \\\\\implies x= \frac{703}{14}\\ \\\implies x= 50\frac{3}{14}[/tex]
Hence, required numbers as per the given condition are [tex]50\frac{3}{14}[/tex] and [tex]5\frac{5}{7}[/tex].
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Two times a number minus 8 is less than 5.
Answers
2x-8<5
The lowest altitude of an altocumulus cloud is about 3^8 feet. The highest altitude of an altocumulus cloud is about 3 times the lowest altitude. What is the hugest altitude of an altocumulus cloud? Write your answer as a power.,
Answers
The highest altitude of an altocumulus cloud is [tex]3^{9}[/tex] feet.
The lowest altitude mentioned is [tex]3^{8}[/tex] feet. To find the highest altitude, we should multiply the lowest altitude by 3. Therefore, the highest altitude will be
3 x [tex]3^{8}[/tex]
which can also be written as
[tex]3^{1}[/tex]x [tex]3^{8}[/tex]
Applying the rule of exponents where you add the exponents when you multiply the bases that are the same, we get the highest altitude as [tex]3^{9}[/tex] feet.
1. picture
2.picture
3.which graph represents f(x)=4sin(2πx)?
4. A cosine function has a period of 3, a maximum value of 20, and a minimum value of 0. The function is a reflection of its parent function over the x-axis.
Which function could be the function described?
5. A sinusoidal function whose frequency is 3, maximum value is 15, minimum value is −3 has a y-intercept of 6.
Which function could be the function described?
f(x)=9sin(6πx)+3
f(x)=9sin(3x)+3
f(x)=9sin(x3)+6
f(x)=9sin(6πx)+6
Answers
See the attached image. Specifically see figure 1.
==============================================
Problem 2
See the attached image. Specifically see figure 2.
==============================================
Problem 3
Answer: bottom right corner
------------------------
f(x) = 4*sin(2pi*x)
f(x) = a*sin(b*x)
a = 4 is the amplitude
b = 2pi
T = 2pi/b = 2pi/2pi = 1 is the period
The graph that has a period of 1 and amplitude 4 is the bottom row of choices. We can rule out the graph on the left because sine starts off increasing as you move away from the origin and go from left to right.
==============================================
Problem 4
Answer: f(x) = -10cos(2pi*x/3)
------------------------
T = period = 3
b = 2pi/T = 2pi/3
amplitude = (max - min)/2
amplitude = (20-0)/2
amplitude = 10
y = 10 is the midline since d = (20+0)/2 = 10
f(x) = a*cos(bx)+d
f(x) = -10*cos(2pi*x/3)+10
Note: the value of 'a' is negative because of the reflection over the x axis
==============================================
Problem 5
Answer: Choice D
f(x) = 9*sin(6pi*x)+6
------------------------
min = -3
max = 15
midline: d = (max + min)/2 = (15-3)/2 = 6
amplitude: a = (max - min)/2 = (15+3)/2 = 9
f = frequency = 3
T = period = 1/f = 1/3
b = 2pi/T = 2pi/(1/3) = 6pi
f(x) = a*sin(bx)+d
f(x) = 9*sin(6pi*x)+6
==============================================
The graph is shown in the figures.
Sinusoidal functionIt is a function that repeats itself after a regular interval of time.
How to calculate?1. Graph of g(t) = 4sin(3t) + 2 is shown below.
2. Graph of f(x) = 3cos(2x) - 1 is shown below.
3. Graph D represents the f(x) = 4sin(2[tex]\rm \pi[/tex]x) because the value of sine maximum and the minimum are 1 and -1 so the value of f(x) is maximum and the minimum is 4 and -4.
4. The maximum and minimum value of f(x) 20 and 0. and period is 3. then our f(x) will be
[tex]f(x) = 10\ cos(\dfrac{2\pi }{3}x ) +10[/tex]
5. For this D is the correct option. because maximum and minimum values, as well as frequency, satisfy the equation.
Thus, the graph is shown in figures.
More about the sinusoidal function link is given below.
https://brainly.com/question/12078395
You have a balance of $15,300 on your credit card with an 18% interest rate (1.5% per month). You pay $200 this month. Did your balance go up or down?
Will fan and medal
Answers
If balance is negative you charged $229.5 and you will add $200. So total balance will go down.
First, calculate the interest that will accumulate for 1 month on your current balance.
15300 * 0.015 = 229.5
Right now, we can stop since it's obvious that $229.50 of interest is greater than the $200.00 you're paying for that month. The new balance on your card will be:
$15,300 + $229.50 - $200 = $15,329.50