Answer:
A) [tex]\int\frac{2x^2}{3}dx=\frac{2x^3}{9}+C[/tex]
B) [tex]\int(5-x)^{23}dx=-\frac{(5-x)^{24}}{24}+C[/tex]
Step-by-step explanation:
A)
So we have the integral:
[tex]\int\frac{2x^2}{3}dx[/tex]
First, remove the constant multiple:
[tex]=\frac{2}{3}\int x^2\dx[/tex]
Use the power rule, where:
[tex]\int x^ndx=\frac{x^{n+1}}{x+1}[/tex]
Therefore:
[tex]\frac{2}{3}\int x^2\dx\\=\frac{2}{3}(\frac{x^{2+1}}{2+1})[/tex]
Simplify:
[tex]=\frac{2}{3}(\frac{x^{3}}{3})[/tex]
And multiply:
[tex]=\frac{2x^3}{9}[/tex]
And, finally, plus C:
[tex]=\frac{2x^3}{9}+C[/tex]
B)
We have the integral:
[tex]\int(5-x)^{23}dx[/tex]
To solve, we can use u-substitute.
Let u equal 5-x. Then:
[tex]u=5-x\\du=-1dx[/tex]
So:
[tex]\int(5-x)^{23}dx\\=\int-u^{23}du[/tex]
Move the negative outside:
[tex]=-\int u^{23}du[/tex]
Power rule:
[tex]=-(\frac{u^{23+1}}{23+1})[/tex]
Add:
[tex]=-(\frac{u^{24}}{24})[/tex]
Substitute back 5-x:
[tex]=-(\frac{(5-x)^{24}}{24})[/tex]
Constant of integration:
[tex]=-\frac{(5-x)^{24}}{24}+C[/tex]
And we're done!
1 mile to yards, as a fraction..
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Since 3 feet is a yard, one foot is 1/3.
So that is the answer.
Answer:
1/3
1 mile to yards as a fraction would probably be 1/3. I'm not so sure...
A lorry driver charges $1800 to carry 60 tonnes of weight. How much will he charge for carrying 80 tonnes at the same rate
Answer:
$2400
Step-by-step explanation:
60 tonnes = $1800
80 tonnes = $?
= 1800 × 80/60
= $2400
Step-by-step explanation:
$2400 to Carry 80tonnes of weight
if you run for 4 hours at 8miles an hour and walk 8 hours at 2 miles an hour, how far will you you have gone at the end of 12 hours?
Answer:
48 miles
Step-by-step explanation:
run -- 4 hrs at 8 mph = 4 • 8 = 32 miles
walk -- 8 hrs at 2 mph = 8 • 2 = 16 miles
32 + 16 = 48 miles
Twice the sum of six "x" and seventy eight.
Answer:
2(6x+78)
Unless it's the exact number. You hadn't specified what x is.
Find the slope (-4,8) and (-3,-6)
Answer:
-14
Step-by-step explanation:
[tex] \boxed{gradient = \frac{y1 - y2}{x1 - x2} } [/tex]
Using the above formula, slope
[tex] = \frac{8 - ( - 6)}{ - 4 - ( -3 )} \\ = \frac{8 + 6}{ - 4 + 3} \\ = \frac{14}{ - 1} \\ = - 14[/tex]
Solve the linear equation. 3x = 24 x = ?
Answer:
3x =24
x = 24 -3
x = 21 (ans)
Answer:
X=8
Step-by-step explanation:
3x=24
divide each side by 3 to isolate x
x=8
Answer please quick
Answer:
1 metric ton is = to 1000 kilograms
Factorise P(2m+n)+(q-r)(2m-n)
Answer:
2Pm+Pn+2qm-qn-2rm+rn
Step-by-step explanation:
Can someone help me pls!
This question is about how transformations can affect graphs.
First, we'll want to get rid of that -4 on the function of F.
So we can reflect the function over the y-axis and then compress it by a factor of 4 to make the graph [tex]x^2[/tex].
Then we can move the graph over to the left 3 because the c value is positive, meaning that we move the graph over to the left.
Finally, we can move the function of by [tex]\frac{2}{3}[/tex] because the d value is positive, meaning that we move the graph up.
Hope this helps.
頑張って!
Acellus
x = [?]°
1040
1170
X
124°
1000
Hint: Sum = (n-2)180
Answer:
x = 95°
Step-by-step explanation:
The sum of the interior angles of any polygon is
sum = 180° (n - 2)
Here n = 5, thus
sum = 180° × 3 = 540°
Sum the given angles in the polygon and equate to 540
104° + 117° + 100° + 124° + x = 540°, that is
445° + x = 540° ( subtract 445° from both sides )
x = 95°
After your yearly checkup, the doctor has some bad news and some good news. The bad news is that you tested positive for a serious disease, and the test is 99% accurate( i.e. that probability of testing positive given that you have the disease is .99, as is the probability of testing negative given that you don’t have the disease). The good news is that this is a rare disease, striking only one in 10,000 people. What are the changes that you actually have the disease?
Answer:
0.009804
Step-by-step explanation:
We are given;
probability of testing positive given that you have the disease is 0.99
Also, probability of not testing positive and not having the disease is 0.99
We are also told that it is a rare disease and so strikes only 1 in 1000 people = 0.0001
Let's denote positive test by T+, negative test by T¯, having the disease by D+, not having the disease by D¯.
So, we can now denote all the values in probability we have written earlier.
Thus:
P(T+ | D+) = 0.99
P(T¯ | D¯) = 0.99
P(D+) = 0.0001
Thus, P(D¯) = 1 - P(D+) = 1 - 0.0001 = 0.9999
Now, let's find probability of testing positive;
P(T+) = (P(T+ | D+) × P(D+)) + (P(T+ | D¯) × P(D¯))
Now, (P(T+ | D¯) is not given but by inspection, we can infer from the values given that it is 0.01
Thus;
P(T+) = (0.99 × 0.0001) + (0.01 × 0.9999)
P(T+) = 0.010098
Chances that one has the disease would be gotten from Baye's theorem;
P(D+ | T+) = (P(T+ | D+) × P(D+))/P(T+) = (0.99 × 0.0001)/0.010098 = 0.009804
Which of the following is a statistical question? A. What state were you born in? B. How tall is Ms. Lin? C. What are the ages of the students in your class? D. What is the formula for the circumference of a circle?
Answer:
C
Step-by-step explanation:
makes sense
How I do this?
3x+4y=11
X-2y=-3
Answer:
[tex]\huge\boxed{x=1,\ y=2\to(1,\ 2)}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}3x+4y=11\\x-2y=-3&\text{multiply both sides by (-3)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x+4y=11\\-3x+6y=9\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\ \ \ \ 10y=20\qquad\text{divide both sides by 10}\\.\qquad\qquad\boxed{y=2}\\\\\text{subtitute it to the second equation:}\\x-2(2)=-3\\x-4=-3\qquad\text{add 4 to both sides}\\\boxed{x=1}[/tex]
Dimensional analysis: How many atoms are in a kilogram of silver, if there are 6.02 x 10^23 atoms per mole and silver weighs 107.9 grams/mole?
Answer:
5.58×10²⁴ atoms.
Step-by-step explanation:
From the question given above, the following data were obtained:
1 mole of silver = 107.9 g
Number of atoms in 1 mole of silver = 6.02×10²³ atoms.
Number of atoms in a kilogram of silver =.?
Next, we shall convert 1 kg of silver to grams (g). This can be obtained as follow:
1 kg = 1000g
Therefore, 1 kg of silver is equivalent to 1000g.
Finally, we shall determine the number of atoms in 1 kg (i.e 1000 g) of silver as follow:
107.9 g of silver contains 6.02×10²³ atoms.
Therefore, 1000 g of silver will contain = (1000 × 6.02×10²³) / 107.9 = 5.58×10²⁴ atoms.
Thus, a kilogram of silver contains 5.58×10²⁴ atoms.
Given the formula below, solve for x. y - y1 = m(x-x1)
Answer:
y-3 = 2/9 (x-8)
Step-by-step explanation:
BRAINLY I NEED HELP ASAPPPP!!
After game 6, her mean number of points scored per game is 9.
How many points did Maya score in game 6?
A. 4
B. 8
C. 9
D. 10
Answer:
b
Step-by-step explanation:
8
Angles Find the values of x and y
Answer:
15 23
Step-by-step explanation:
Answer:
Step-by-step explanation:
11x - 6 + 15x - 8 = 90
26x - 14 = 90
26x = 104
x = 4
11(4) - 6 = 44 - 6 = 38
13y - 14 + 38= 180
13y + 24 = 180
13y = 156
y = 12
13(12) - 14 = 156 - 14=142
What is the value of x?
3
6
10
12
Answer:
value of x is 6.
please follow me.
Your answer would be B- 6. Hope this helps you!!
How do you do this question?
Answer:
y' = -4eˣ sin⁵(eˣ)
Step-by-step explanation:
Part 1 of the Fundamental Theorem of Calculus simply says that the definite integral of a function is equal to the antiderivative evaluated between the limits.
∫ₐᵇ f(x) dx = F(b) − F(a), where F(x) = ∫ f(x) dx.
y = ∫ₑₓ⁰ 4 sin⁵(t) dt
To integrate, use Pythagorean identity.
y = 4 ∫ₑₓ⁰ (1 − cos²(t))² sin(t) dt
Ignoring the limits for the moment, let's say u = cos(t) and du = -sin(t) dt.
y = 4 ∫ (1 − u²)² (-du)
y = -4 ∫ (1 − 2u² + u⁴) du
y = -4 (u − ⅔u³ + ⅕u⁵) + C
y = -4 (cos(t) − ⅔ cos³(t) + ⅕ cos⁵(t)) + C
Evaluate between t = eˣ and t = 0.
y = -4 (cos(0) − ⅔ cos³(0) + ⅕ cos⁵(0)) + C − [-4 (cos(eˣ) − ⅔ cos³(eˣ) + ⅕ cos⁵(eˣ)) + C]
y = -4 (1 − ⅔ + ⅕) + 4 (cos(eˣ) − ⅔ cos³(eˣ) + ⅕ cos⁵(eˣ))
Now take derivative with respect to x.
y' = 0 + 4 (-sin(eˣ) eˣ − 2 cos²(eˣ) (-sin(eˣ) eˣ) + cos⁴(eˣ) (-sin(eˣ) eˣ))
y' = -4eˣ sin(eˣ) (1 − 2 cos²(eˣ) + cos⁴(eˣ))
y' = -4eˣ sin(eˣ) (1 − cos²(eˣ))²
y' = -4eˣ sin⁵(eˣ)
This can be more easily calculated using the Second Fundamental Theorem of Calculus.
How do you do this question?
Step-by-step explanation:
F(x) = ∫ₐˣ t⁷ dt
F(x) is the area under f(t) between t=a and t=x. When x=a, the width of the interval is 0, so the area is zero.
F(6) = 0, so a = 6.
F(x) = ∫₆ˣ t⁷ dt
F(6) = ∫₆⁶ t⁷ dt
F(6) = 0
Homer and Bart plan to buy one computer for $499.00 strictly for gaming purposes. Games cost $49.99 each. Part A: Define each variable and write an algebraic expression to describe how much they will spend before sales tax, based on purchasing the computer and the number of games. Part B: If they purchase one computer and five games, how much do they spend before sales tax? Part C: Homer and Bart have friends. They want to purchase extra controllers. Each controller costs $24.99. Use an algebraic expression to describe how much they spend in total (before sales tax) when they purchase one computer, when they purchase any number of games, and when they purchase any number of extra controllers. Part D: What would be the total cost, before sales tax, if Homer and Bart purchase one computer, four games, and three extra controllers?
Answer:
use 499.00+the number of games times 49.99Step-by-step explanation:
Please brailiest
HELP ASAP PLEASE Question 1 Part A What inference can be made about the "Using Our Imaginations" section in the Newsela article "Health Benefits of Reading, Writing, Are Not Just for Patients"? Part B Which evidence best supports the answer in Part A? “Reading stories is a chance for children and adults to talk about the complicated parts of life.”
The answer to the first one is A and the second one is D
(I took the test)
Answer:
Fist one:
A
Second one:
D
Step-by-step explanation:
→!Hope this helps I toke the test!←What are the correct intermediate steps of the following data set when it is being sorted with the bubble sort? 15, 20, 10, 18
A. 15,10,20,18 -- 15,10,18,20 -- 10,15,18,20
B. 10, 20,15,18 -- 10,15,20,18 -- 10,15,18,20
C. 15,20,10,18 -- 15,10,20,18 -- 10,15,20,18 -- 10,15,18,20
D. 15,18,10,20 -- 10,18,15,20 -- 10,15,18,20 -- 10,15,18,20
Answer:
A. 15,10,20,18 -- 15,10,18,20 -- 10,15,18,20
Step-by-step explanation:
Bubble sorting can be defined as a technique or methodology whereby numbers that are not in their proper order are sorted into proper order that is from smallest to highest( increasing to decreasing order).
The method of bubble sorting involves the shuffling or swapping of adjacent numbers until the numbers are well sorted or arranged.
In the above question, we were given, a set of numbers:
15, 20, 10, 18
Step 1
20 is adjacent to 10
20 > 10
hence we swap
= 15,10,20,18
Step 2
From, 15,10, 20,18
20 is adjacent to 18
20 > 18
hence we swap
= 15,10,18,20
Step 3
From step 2, which gave us 15,10,18,20
15 us adjacent to 10
15 > 10
We swap
= 10,15,18,20
Hence,
15, 20, 10, 18 -- 15,10,20,18 -- 15,10,18,20 -- 10,15,18,20
Therefore, Option A is the correct option.
The correct intermediate steps of data 15, 20, 10, 18 set when it is being sorted with the bubble sort is; Choice A: 15,10,20,18 -- 15,10,18,20 -- 10,15,18,20.
Definition;
Bubble sort, otherwise termed the sinking sort, is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order.
With emphasis on the word adjacent, it is evident Choice A is the correct intermediate steps of the data set 15, 20, 10, 18 when it is being sorted with the bubble sort.
Read more:
https://brainly.com/question/15148294
Find the sum. r/r^2-q^2 + 5/r+q
Answer:
The answer is:
[tex]\frac{6r-5q}{r^2-q^2}[/tex]
which agrees with the last answer option (D) in the list.
Step-by-step explanation:
In order to add rational expressions, we need to express them with the same denominator. Therefore we examine what factors there are in the first denominator, which happens to be a difference of squares which is readily factored out as:
[tex]r^2-q^2=(r+q)\,(r-q)[/tex]
the second denominator consists of only one of these factors: [tex](r+q)[/tex], then in order to express both rational expressions with the same common denominator, we multiply numerator and denominator of the second fraction by the factor: [tex](r-q)[/tex]
Then we get two expressions that can be easily added as shown below:
[tex]\frac{r}{(r+q)\,(r-q)} +\frac{5\,(r-q)}{(r+q)\,(r-q)} =\frac{r+5(r-q)}{(r+q)(r-q)} =\frac{r+5r-5q}{(r+q)\,(r-q)} =\frac{6r-5q}{r^2-q^2}[/tex]
13w-8w =20 ??????????
Answer:
w = 4
Step-by-step explanation:
13w-8w =20
Combine like terms
5w = 20
Divide each side by 5
5w/5 = 20/5
w = 4
Answer:
w=4
Step-by-step explanation:
13w-8w=20
5w=20
w=4
please help o.o ¯\_(ツ)_/¯¯\_(ツ)_/¯¯\_(ツ)_/¯¯\_(ツ)_/¯¯\_(ツ)_/¯(┬┬﹏┬┬)(┬┬﹏┬┬)(┬┬﹏┬┬)Simplify 3x - 4 - 5x = 6 + 4x + 2
Bring all the X to the left side and all the numbers to the right side. ( remember to flip the signs )
3x - 4 - 5x = 6 + 4x + 2
3x - 5x - 4x = 6 + 2 + 4
-6x = 12
6x = -12
x = -2
Math Math Math Math Math
Answer:
see below
Step-by-step explanation:
sqrt(2)+ sqrt(98)
sqrt(2) + sqrt( 2*49)
sqrt(2) + 7sqrt(2)
8 sqrt(2)
Answer:
[tex]\sqrt{2}[/tex]+ [tex]\sqrt{98}[/tex]
[tex]\sqrt{2}[/tex]+ [tex]\sqrt{2}[/tex] *49
[tex]\sqrt{2}[/tex] + 7[tex]\sqrt{2}[/tex]
8 [tex]\sqrt{2}[/tex]
evaluate the numerical expression. 8 X {[(7 + 4) X 2] - [(11 - 7) X 4]}
Answer:
48
Step-by-step explanation:
To solve this we need to do the operations in the brackets first. We should start with the innermost brackets. Then, we work our way outwards. To show my working out I will use an asterisk (*) for multiplication to not confuse X as a variable.
8*{[(7 + 4) * 2] - [(11 - 7) * 4]}
= 8*{[(11) X 2] - [(4) X 4]}
= 8*{[22] - [16]}
= 8*{6}
= 48
Given the set A=(2,5) and B=(5,7,9) find the following: AnB
a
5
b
2.9
n
2,5,7,9
7,9
d
Greetings from Brasil....
The intersection of two sets is given by the elements that are common - present in both - to the sets.
A = {2; 5}
B = {5; 7; 9}
Element in both sets = 5.... So
A ∩ B = {5}What is the slope of the line?
La pendiente de una recta es la tangente del ángulo que forma la recta con la dirección positiva del eje de abscisas. En funciones no lineales, la razón de cambio varía a lo largo de la curva. La derivada de la función en un punto dado es la pendiente de la línea tangente en dicho punto.
F:V 7w7