[tex]V = 864\pi[/tex]
Step-by-step explanation:
Since one of the boundaries is y = 0, we need to find the roots of the function [tex]f(x)=-2x^2+6x+36[/tex]. Using the quadratic equation, we get
[tex]x = \dfrac{-6 \pm \sqrt{36 - (4)(-2)(36)}}{-4}= -3,\:6[/tex]
But since the region is also bounded by [tex]x = 0[/tex], that means that our limits of integration are from [tex]x=0[/tex] (instead of -3) to [tex]x=6[/tex].
Now let's find the volume using the cylindrical shells method. The volume of rotation of the region is given by
[tex]\displaystyle V = \int f(x)2\pi xdx[/tex]
[tex]\:\:\:\:\:\:\:= \displaystyle \int_0^6 (-2x^2+6x+36)(2 \pi x)dx[/tex]
[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \int_0^6 (-2x^3+6x^2+36x)dx[/tex]
[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \left(-\frac{1}{2}x^4+2x^3+18x^2 \right)_0^6[/tex]
[tex]\:\:\:\:\:\:\:= 864\pi [/tex]
Suppose that two balanced, six sided dice are tossed repeatedly and the sum of the two uppermost faces is determined on each toss. (a) What is the probability that we obtain a sum of 3 before we obtain a sum of 7
Answer:
[tex]\frac{(2/36)}{(1-(28/36))} = 1/4[/tex]
Step-by-step explanation:
Respond to each of the four questions.
Describe the steps to graphing a linear equation. Be sure to provide an example to illustrate your description.
Describe the steps to graphing a quadratic equation. Be sure to provide an example to illustrate your description.
Describe how to solve a linear equation. Be sure to provide an example to illustrate your description.
Describe how to solve a quadratic equation. Be sure to provide an example to illustrate your description.
Answer:hello
Step-by-step explanation:
1+1
help
Does this graph represent a function? Why or why not?
A- no because it fails the vertical line test
B- yes because it passes the vertical line test
C-yes because it passes the horizontal line test
D- no because it fails the horizontal line test
Answer: No, it fails the vertical line test.
Step-by-step explanation:
Choose which triangle goes into the right category.
Answer:
obtuse cant be a right angle
Step-by-step explanation:
in order to be obtuse you have to be more than 90 dagrees
Which of the following are not polynomials?
Answer:
A, C and D are not polynomials
Step-by-step explanation:
A because the variable has a negative power.
C because the variable is in the denominator
D because the variable has a root.
When a variable has a root, it's power is 1/2 which does not count as an ideal polynomial. You might be wondering then that why E is a polynomial?
E is a polynomial because because the root is not on the variable but on the constant.
B and E are polynomials while A,C and D are not.
Please mark me as brainliest.
How do I do this equation
This question requires the manipulation of the Ideal Gas formula. By moving the variables around, you'll get :
V = nRT/P
n = PV/RT
the angle of elevation of the top of the mast from a point 53m to its base on level ground is 61°. find the height of the mast to the nearest meter
the answer Is 95.61465. If you approximate you get 10.
I didn't understand this to be honest I thought I had to find what jm and lm were together and then subtract from the whole total...but ended up being wrong. whats the correct answer?
Answer:
The correct answer is 3x-2
Step-by-step explanation:
It gives you the expression for JM and LM, and it asks for JL. Therefore, if you take away LM from JM, you are left with JL. You must subtract 2x-6 from 5x-8.
∴5x-8-(2x-6)
Do not forget to distribute the negative since you are subtracting, so instead of subtracting 6 from 8, you will be adding 6 to 8 because two negatives make a positive.
Please help me >_< will give out brainliest
====================================================
Explanation:
We have an octagon because there are n = 8 sides. The diagram below shows one way to number the sides so you can count them efficiently (without missing any or double counting any).
----------------
Plug n = 8 into the formula below
S = 180(n-2)
S = 180(8-2)
S = 180(6)
S = 1080
The 8 interior angles add up to 1080 degrees.
John runs a computer software store. Yesterday he counted 125 people who walked by the store, 58 of whom came into the store. Of the 58, only 21 bought something in the store. (Round your answers to two decimal places.)
(a) Estimate the probability that a person who walks by the store will enter the store.
(b) Estimate the probability that a person who walks into the store will buy something.
(c) Estimate the probability that a person who walks by the store will come in and buy something.
(d) Estimate the probability that a person who comes into the store will buy nothing.
Answer:
a) 0.46 = 46% probability that a person who walks by the store will enter the store.
b) 0.36 = 36% probability that a person who walks into the store will buy something.
c) 0.17 = 17% probability that a person who walks by the store will come in and buy something.
d) 0.64 = 64% probability that a person who comes into the store will buy nothing.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
(a) Estimate the probability that a person who walks by the store will enter the store.
58 out of 125. So
[tex]p = \frac{58}{125} = 0.46[/tex]
0.46 = 46% probability that a person who walks by the store will enter the store.
(b) Estimate the probability that a person who walks into the store will buy something.
58 walked, 21 bought. So
[tex]p = \frac{21}{58} = 0.36[/tex]
0.36 = 36% probability that a person who walks into the store will buy something.
(c) Estimate the probability that a person who walks by the store will come in and buy something.
21 came in and bought out of 125 that walked by. So
[tex]p = \frac{21}{125} = 0.17[/tex]
0.17 = 17% probability that a person who walks by the store will come in and buy something.
(d) Estimate the probability that a person who comes into the store will buy nothing.
0.36 probability that a person buys something, so 1 - 0.36 = 0.64 = 64% probability that a person who comes into the store will buy nothing.
Which rule describes the composition of transformations that maps ABC to A”B’C”
convert 65 kg into gram .
Answer:
65000
Step-by-step explanation:
65x 1000
1000 because 1kg= 1000
A robot that makes _/6 of a boat per day will make 5 boats in 6 days
I need help with this question
9514 1404 393
Answer:
x = 22, y = 123
Step-by-step explanation:
The sum of angles in a triangle is 180°.
(2x +13)° +57° +3x° = 180°
5x +70 = 180 . . . . . . . . . . . . . collect terms, divde by °
5x = 110 . . . . . . . . . . . subtract 70
x = 22 . . . . . . . . divide by 5
__
Angles in a linear pair are supplementary.
y° + 57° = 180°
y = 123 . . . . . . . . divide by °, subtract 57
What transformation was not done to the linear parent function, f(x) = x, to
get the function g(x) = – } (x + 5) + 7?
A. Reflected over the x-axis
B. Vertically compressed by a factor of 2
O c. Shifted right 5 units
D. Shifted up 7 units
Answer:
C.
Step-by-step explanation:
The function shifted left five units instead of right five units.
There's no vertical compression in the equation provided, but that's probably just a typo since there's a random bracket that I assume was supposed to be a fraction.
3/8 + 1/4 + 1/2 - 2/3 =
Answer:
[tex]\frac{11}{24}[/tex]
Step-by-step explanation:
3/8 + 1/4 + 1/2 - 2/3
- > 1/4 = 2/8
3/8 + 2/8 + 1/2 - 2/3
5/8 + 1/2 - 2/3
- > 1/2 = 4/8
5/8 + 4/8 - 2/3
9/8 - 2/3
- > LCM of 8,3: 24
- > 9/8 = 27/24
- > 2/3 = 16/24
27/24 - 16/24
11/24
Hope this helps you.
i’ll give brainliest to right answer please hurry
Answer:
Scientific notation uses exponential notation. When a number is written in scientific notation, the exponent tells you if the term is a large or a small number. A positive exponent indicates a large number and a negative exponent indicates a small number that is between 0 and 1.
Answer:
Look at the exponitial factor. If it is like 10^2 or like 10^10 the number is very big because it is raised to a very big power. Oppisitely, when it is rasied to a negative number, the number producted will have many decimal places. For example 10^-1 is literaly 0.1.
Step-by-step explanation:
Yes I got u
How many vertices (corners) does a cube have?
How many faces does a rectangular prism have?
How many edges does a rectangular prism have?
How many edges does a square-based pyramid have?
How many vertices (corners) does a square-based pyramid have?
How many faces does a triangular prism have?
How many vertices (corners) does a triangular prism have?
kb 2021
Answer:
The answer is below
Step-by-step explanation:
a) A cube is a three dimensional solid with 6 square faces.
A cube has 8 vertices
b) A rectangular prism is a three dimensional solid with two parallel rectangular bases.
A rectangular prism has 6 faces.
c) A rectangular prism is a three dimensional solid with two parallel rectangular bases.
A rectangular prism has 12 edges.
d) A square-based pyramid is a pyramid with a square base.
A square-based pyramid has 8 edges
e) A triangular prism is a three dimensional solid with two parallel triangular bases.
A triangular prism has 5 faces.
f) A triangular prism is a three dimensional solid with two parallel triangular bases.
A triangular prism has 6 vertices.
O EXPONENTAL AND LOGARITHMIC FUNCTIONS
Finding the initial or final amount in a word problem on...
An initial amount of money is placed in an account at an interest rate of 2% per year, compounded continuously. After two years, there is $1269.79 in the
account. Find the initial amount placed in the account. Round your answer to the nearest cent.
Answer:
$ 1220.00
Step-by-step explanation:
1269.79 = A [tex]e^{.02 * 2}[/tex]
1269.79 /A = [tex]e^{.04}[/tex]
ln(1269.79 /A) = .04 ln(e)
ln(1269.79 /A) = .04
1269.79 /A = [tex]e^{.04}[/tex]
1269.79 /A = 1.0408
A = 1269.79 / 1.0408
$ 1220.00
Alex thinks of a number. he squares it, then takes away five .Next multiplies it by 4 ,takes away seven, divides it by three ,and finally adds six his answer is nine what number did he start with
Answer:
3
Step-by-step explanation:
start with the ending answer and go backwards
Answer:
3.
Step-by-step explanation:
.
Geometry please someone help i cant fail this class
The total number of labor hours for a construction project by week x is given by: Week 1 4 7 10 13 16 19 Total hours 25 158 1254 5633 9280 10,010 10,100 Look at its scatter plot, an appropriate model for this data is:
Answer:
Logistic model
Step-by-step explanation:
A scatter plot is a mathematical representation or diagram which is used to shoe the relation between two given variables. It uses the Cartesian coordinates which is used to display the values for a typically two variables for the given set of data.
In the context, a scatter plot is made between two variables. The two variables are the total number of hours and the number of weeks.
From the graph shown, we can say that model is a logistic model as the shape of the graph is S shaped.
Therefore, the appropriate model for the data given is logistic model.
Casey and Malik can paint a room in 6 hours if they work together. If Malik were to work by himself, it would take him 4 hours longer than it would take Casey working by himself. How long would it take Casey to paint the room by himself if Malik calls in sick? Round to 2 decimal places.
Answer:
It would take 10 hours for Casey to paint the room by himself.
Step-by-step explanation:
Given that Casey and Malik can paint a room in 6 hours if they work together, and if Malik were to work by himself, it would take him 4 hours longer than it would take Casey working by himself, to determine how long would it take Casey to paint the room by himself if Malik calls in sick the following calculation must be performed:
6 x 2 = 12
12 x 2 = 24
(24 - 4) / 2 = 10
Therefore, it would take 10 hours for Casey to paint the room by himself.
Which angle is complementary to angle CFD ?
Answer:
∠DFE
Step-by-step explanation:
Complementary angles are angles that have a sum of 90°. Since there is a box on angle ∠CFB, we can infer that ∠CFE is also 90°. This is because the two are supplementary (equal 180°). Therefore, ∠DFE is the other part of ∠CFD that would complete the 90° pair.
Which of the following equations describes this graph?
A. y=(x-1)^2-
B. y=(x-3)^2+2
C. y=(x+1)^2-2
D. y=(x-2)^2+3
Answer:
The choose (A)
y=(x-1)²-2
A regular polygon has each interior angle is 156°, what is the number of sides of the polygon? A. 14 C. 16 B. 15 D. 17
Answer:
option B is correct
interior angle of given polygon =156
exterior angle of polygon=180 - 156 =24
as we know that sum of exterior angle of any polygon is 360 degree
so number of sides of regular polygon=360/24=15
Answer:
option B. 15
Step-by-step explanation:
Sum of interior angles of a polygon with n sides = ( n - 2 ) x 180°
Therefore each interior angle,
[tex]\frac{n - 2}{n} \times 180^\circ[/tex]
Given the interior angles = 156°
That is ,
[tex](\frac{n-2}{n}) \times 180 = 156\\\\\frac{n-2}{n} = \frac{156}{180}\\\\1- \frac{2}{n} = \frac{156}{180}\\\\1 - \frac{156}{180} = \frac{2}{n}\\\\\frac{180-156}{180} = \frac{2}{n}\\\\\frac{24}{180} = \frac{2}{n}\\\\24 \times n = 2 \times 180\\\\n = \frac{2 \times 180}{24} =\frac{180}{12} = 15[/tex]
1. The area of a square is less than 25cm2. What can we say about
a. The length of one of its sides?
b. Its perimeter?
Step-by-step explanation:
Let us take a nominal square of area 25 cm².
It's length of one of it's sides will be √25 = 5 cm².It's perimeter will be 5*4 = 20 cm.So, in this question, we can say that:-
a. The length of one of its sides will be less than 5 cm.
b. Its perimeter will be less than 20 cm.
Hope it helps :)
Step-by-step explanation:
area= 25cm squared
length of one side = 5cm as 5*5 =25
perimeter= 5*4= 20cm
But since the area is less than 25cm squared
we can say that the length of one side is less than 5cm and we can also say that the length of the perimeter is less than 20cm.
Hope this helps.
URGENT PLS HELP
Given f(y)=2y^2 - 4y, and h(x)= x^2 - 1, determine f(h(x))
Answer:
f(h(x)) = 2•(x²-1)² -4•(x²-1)
if TS is a midsegment of PQR find TS
Answer:
B. 7
Step-by-step explanation:
Recall: according to thee Mid-segment Theorem of a triangle, the Mid-segment of a triangle is half the length of the base of the triangle
Base length of the traingle, RQ = 14 (given)
Mid-segment = TS
Therefore,
TS = ½(RQ)
Plug in the value
TS = ½(14)
TS = 7
what is the range of the funcion y=x^2
Answer:
Range = [0, infinity)
Step-by-step explanation:
Minimum point of the graph is at (0,0) and it is a u shaped graph. Hence, range is 0 inclusive to infinity