[tex]\displaystyle \int x \cos x ~dx\\\\=x\displaystyle \int \cos x ~dx- \displaystyle \int \left(\dfrac{d}{dx} x \displaystyle \int \cos x ~dx \right) dx\\\\=x\sin x - \displaystyle \int\left( \sin x \right) dx\\ \\=x \sin x - (-\cos x) +C\\\\=x \sin x + \cos x +C[/tex]
1. When you go to a party or other gathering you shake hands with many people. The following is a formula that will predict how many hand shakes take place if every person shakes hands with every other person only once.
s = n(n - 1)/ 2
where S is the total number of hand shakes and n is the total number of people at the party.
(a) Express this formula in words.
(b) How many hand shakes will occur if there are 12 people present?
Answer:
s = 66
Step-by-step explanation:
S = number of shakes
N = number of people
(N-1) = takes yourself out of the equation
÷ 2 = shaking hands with everyother person
so when 12 people present:
s = 12(12-1) /2
s = 12(11) /2
s = 132 /2
s = 66
Answer:
This is called an exponential function, values are inserted to variables where applicable, aka, n = total number of people at the party, if there are only 12 people, (b:) insert into function where 'n' appears: (12(12-1)/2 = 66. This means 66 handshakes will occur if there are 12 people present.
the diagonal of a rectangular garden measures 111/4m while it's width measures 63/4m . Calculate the perimeter of the garden
Answer:
Step-by-step explanation:
The diagonal of a rectangular garden forms a hypotenuse with the width and length sides. We can use the Pythogorean Theorem to calculate the remaining side.
Let W, L, and H stand for the Width, Length, and Hypotenuse, all in meters.
W^2 + L^2 = H^2
Enter the data:
(63/4)^2 + L^2 = (111/4)^2
248.06 + L^2 = 770.06
L^2 = 522
L = 22.847 meters
Perimeter is 2W + 2L
Perimeter = 2(63/4) + 2(22.847)
Perimeter = 77.19 meters
PLS ANSWER FAST FOR MY TEST!! There were three ant hills in Mrs. Brown's yard. The first ant hill had 4,867,190 ants. The second ant hill had 6,256,304 ants, and the third ant hill had 3,993,102 ants. Choose the best estimate of the number of ants in Mrs. Brown's yard.
Answer:
my best estimate would be 15,116,600
Step-by-step explanation:
,
help pplease i need help
Answer:
15/2 min/m
Step-by-step explanation:
Minuters per meter = min/m
4.5 min/(3/5) m
4.5 x 5/3 = 7.5
7.5 = 15/2
Hope this helps!
Write an expression that can be used to produce vector g from vectors e and f Explain how
you determined that expression.
Answer:
Step-by-step explanation:
vector e is (-1,5),f is (3,-4),g is (2,1)
2i+j=x(-i+5j)+y(3i-4j)
2=-x+3y (multiply by 5)
10=-5x+15y
1=5x-4y
add
11=11y
y=1
2=-x+3(1)
x=3-2=1
2i+j=1(-i+5j)+1(3i-4j)
Ticket for football final selling well, on Thursday 4/7 of the tickets are sold, on Friday 1/4 of the tickets are sold, What fractions of tickets are available on Saturday?
Answer:
5/28
Step-by-step explanation:
1/1 represents the whole amount of tickets.
4/7 are sold on Thursday.
an additional 1/4 are did on Friday.
fraction of available tickets on Saturday are therefore
1/1 - 4/7 - 1/4 = 4/1 - 16/7 - 1/1 = 28/1 - 16/1 - 7/1 = 5/1
that means out of 28 equal parts of the total number of tickets 16+7 = 23 parts have been sold.
so, there are only 5 out of the total 28 parts available on Saturday, and the fraction of available tickets is therefore 5/28.
we could have also tried to bring both fractions to the same denominator, and found that this is 28.
and then
4/7 + 1/4 = 4/4 × 4/7 + 7/7 × 1/4 =
= 16/28 + 7/28 = 23/28
and the whole is 28/28.
so we have 28/27 - 23/28 = 5/28 left.
surprise, surprise, it is the same result ...
Can some help me I will mark u brilliant
Answer:
The answer is C
Step-by-step explanation:
The formula of a circle is pie radius ^2. Its asking for the surface area. So I got C because you do pie 18^2 and gets you approximately 1017. Although A also says 18 as the radius, it says meters. After you solve a surface area problem you do square meters or square units. For volume you have to use units cubed or units ^3. Make sure to always do this or your teacher might count you as wrong.
Answer:
Let's first try to find the radius before finding the diameter because when you find the radius, you double it to get the diameter.
To find the radius, use the area for a circle formula and plug in the values you know so far, so the formula is;
A = π[tex]r^{2}[/tex]
What we know:
1,017 is the area.Plug that area in our equation:-
A = π[tex]r^{2}[/tex]
1,017 = 3.14[tex]r^{2}[/tex]
Solve for r;
÷3.14 ÷3.14
324(approximate) = [tex]r^{2}[/tex]
√324 = r
18 = r, the radius is around 18 square meters (do not mistake the unit for some other unit).
Therefore, your answer is C.Another alternative way;Plug in your options' numbers into the equation;
A = π[tex]r^{2}[/tex]
And by looking at the options, we can see the only number here being used is 18, so we use 18 in the formula for the area of a circle to check if it'll result in 1,017 as the area.
Also: Notice if it says diameter or radius when using this solution, you are looking for the radius first.
2 books are removed at random from a set of 2 mysteries, 1 biography, and 1 romance. What is the probability that the 2 books consist of 1 mystery and 1 biography? Draw a tree diagram to help you find the answer.
1/3
1/6
1/4
5/12
I did the problem and I know that 1/4 and 5/12 are wrong
Answer:
1/6
Step-by-step explanation:
Check the attachment.
Find the solutions to the equation below.
Check all the apply.
16x^2 - 64 = 0
A. x = 4
B. x = 2
C. x = -64
D. x = -2
E. x = -4
F. x = -8
Answer:
x = 2
x = - 2
Step-by-step explanation:
⇒ 1: Common Factor
16x² - 64 = 016(x² - 4) = 0⇒ 2: Use the sum-product pattern
16 (x² - 4) = 016 (x² + 2x - 2x - 4) = 0⇒ 3: Common factor from the two pairs
16((x² + 2x) + (-2x - 4) = 016(x(x+2)-2(x+2))=0I dont feel like adding more details.
- rewrite in factored form
16(x(x+2)-2(x+2))=0
16(x-2)(x+2)=0
- create seperate equations
16(x-2)(x+2)=0
x-2=0
x+2=0
- solve
*rearrange and isolate the variable to find each solution
x = -2
x = 2
Answer:
B.x=2
Step-by-step explanation:
[tex]16x ^{2} - 64 = 0[/tex]
[tex]16x ^{2} = 64[/tex]
[tex]4 ^{2} {x}^{2} = {4}^{3} [/tex]
[tex] {x}^{2} = \frac{4 ^{3} }{4 ^{2} } [/tex]
[tex]x^{2} = 4[/tex]
[tex] \sqrt{x ^{2} } = \sqrt{4} [/tex]
[tex]x = 2[/tex]
The following graph is a function. True or False
Answer:
TRUE
Step-by-step explanation:
Do the pencil test . It doesnt have repeating X's.
Answer:
It is actually True so when you do it press true
A line passes through the point (-4,9) and has a slope of -3/2. Write an equation in slope intercept form for this line
Answer:
y = -3/2x + 3
Step-by-step explanation:
slope-intercept form: y - y₁ = m (x - x₁)
y - 9 = -3/2 ( x + 4)
y = -3/2 x - 6 + 9
y = -3/2x + 3
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
The total mass of 8 cereal boxes is 4 kilograms. What is the mass of each box of cereal in grams?
Answer:
500 grams
Step-by-step explanation:
we can conclude that the mass of each box is 0.5 kg by dividing 4 by 8
0.5 kg is 500 grams
Simplify the expression.
c^-6 d^4/c^-16 d^14
Answer:
[tex]\red{\frac{ {c}^{10}}{{d}^{10} } }[/tex]
Step-by-step explanation:
[tex] \huge \: \frac{ {c}^{ - 6} {d}^{4}}{ {c}^{ - 16} {d}^{14} } \\ \\ = \huge \: \frac{ {c}^{16 - 6}}{{d}^{14 - 4} } \\ \\ = \huge \: \red{\frac{ {c}^{10}}{{d}^{10} } }[/tex]
Help picture below problem 15
Answer:
B. Pentagon
Step-by-step explanation:
A Pentagon is a polygon with 5 sides like this one.
Hope that helps!
The sum of three numbers is 10. The sum of twice the first number, 4 times the second number, and 5 times the third number is 33. The difference between 6 times the first number and the second number is 28. Find the three numbers.
Answer:
5 2 3Step-by-step explanation:
The given relations allow us to write three equations in the three unknown values. We can let x, y, z represent the three numbers, in order.
__
x +y +z = 10 . . . . . . . the sum of the three numbers is 10
2x +4y +5z = 33 . . . . . designated sum is 33
6x -y = 28 . . . . . . . . 6 times the first is 28 more than the second
__
There are many ways to solve a system of equations like this. Perhaps one of the easiest is to enter the equations as an augmented matrix in your calculator, and let it do the work. (Some calculators will solve the equations directly.)
The three numbers are 5, 2, and 3.
_____
Additional comment
The third equation lets you write an expression for y in terms of x:
y = 6x -28
Substituting this into the first two equations, we get ...
x +(6x -28) +z = 10 ⇒ 7x +z = 38
2x +4(6x -28) +5z = 33 ⇒ 26x +5z = 145
Subtracting the second from 5 times the first of these equations gives ...
5(7x +z) -(26x +5z) = 5(38) -(145)
9x = 45 . . . . . the y-variable is eliminated
x = 5
Use equations from above to find z and y.
z = 38 -7x = 3
y = 6(5) -28 = 2
Simplify the expression. 16 • 4–4
a)256
b)–256
c)1/16
d)–4,096
Answer: C) 1/16
Hope this helps :)
The half-life of radon is 385 days. What fraction of a sample with no atoms remains at the end of 77 days?
Step-by-step explanation:
calculate the missing angle 'a'
9:57
Answer
Hence in 77 days 107. will decay Remain = 90%
Explanation
Given: half life = 385 half-life
To find: what fraction remains after 22 days
Solution.
Let total amount = 100%.
time taken for decaying Si%. = 385
In time of 72 days = 305 77
= 5
→ Remarwiny = 50 = 10%.
Hence in 72 days 1-7. will decay Remain = 90%.
. Question 3 Terrance made a list of his expenses. He is creating a check off matrix to organize when his bills are due. A check off matrix is a table without dollar amounts. You can use a matrix to indicate what time of the year an expense will occur Help Terrance complete his check off matrix by placing an X in the correct cells of the table according to his list of expenses, mortgage payment monthly • Utilities, monthly • Insurance quarterly • Internet monthly cell phone monthly . car loan: semiannually lawn care: monthly, April-September • food: monthly day care every other month beginning with February gym membership: annually. July . в тухх, m. AL 10pt Oct Dec Nov Feb Mar Sep Jul Jun Aug May Jan x Expense mortgage payment X X X x x X x insurance y internet cellphone car loan 1 x Iawn care X x X x food X day Care rym membership
=====================================================
Explanation:
The first two rows are already done. They have X's for every month to indicate a monthly payment regularly throughout the year without any extra conditions/requirements.
The third row will have exactly 4 copies of X in it. Two of them are already placed for January and April. The other two payments are in July and October. Notice the months are spaced 3 apart and how 12/4 = 3.
The fourth row will have X's across every cell in the same way the first row does since the internet bill is monthly. The same applies to the cell phone bill and food rows.
Something like the car loan will only have 2 copies of X in that row. Semiannual means twice a year, aka every 6 months. One copy of X is already placed for us in this row. This is in January (month 1). Six months later in month 1+6 = 7 (July) is when the next car loan payment occurs.
Lawn care will have X's only for the months of April through September; any other month won't have an X.
Day care will have X's for February, April, June, August, October, December. We start with February and alternate each month to fill out the rest of the year. This is due to the phrasing "every other month".
The gym membership will have one X for July only, since it's an annual payment.
What is the equation
of the line that passes through the point (-2, -3) and has a
slope of -1?
Answer:
Step-by-step explanation:
Hello:
an equation for the line is : y =mx +b (m: is a slope )
given : m = -1
the equation is : y = -x+b
through the point (-2,-3) :-3 =-(-2)+b....... b=-5
the equation is : y = -x-5
how to find the area of a triangle with a base of 4 1/2 and a height of 2 2/3
Answer:
The area is 4.
Step-by-step explanation:
hope this helps.
Which expression is not equivalent to 2\3 x 4?
Answer:
8/3
Step-by-step explanation:
Consider the line y=7x-1.
Find the equation of the line that is perpendicular to this line and passes through the point (-2, 4).
Find the equation of the line that is parallel to this line and passes through the point (-2, 4).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Answer:
Step-by-step explanation:
For which values of x is the expression undefined
Answer:
7, -9
Reasoning:
When x is 7 or -9, the denominator equates to zero, making the expression undefined because nothing can be divided by zero.
16 The three models below are each shaded to represent a different fraction.
What is the sum of the fractions represented by the shaded parts of the
models?
Answer:
C
Step-by-step explanation:
3/5 + 2/5 + 4/5 = 1 4/5 or 9/5
Answers are c !!!
Step-by-step explanation:
if you added them you would get c I think hope this helps!!
[tex]Find } \sum r^{2} \cdot{ }^{20} C_{r}\end{equation}[/tex]
Options:
(a) [tex]$2^{20}$[/tex]
(b) [tex]$2^{21}$[/tex]
(c) [tex]$210 \times 2^{19}$[/tex]
I bet the sum you're referring to is supposed to be
[tex]\displaystyle \sum_{r=0}^{20} r^2 \times {}^{20}C_r[/tex]
or equivalently,
[tex]\displaystyle \sum_{r=0}^{20} r^2 \binom{20}r[/tex]
where [tex]\binom nk = \frac{n!}{k!(n-k)!}[/tex] is the binomial coefficient.
Recall the binomial series,
[tex](1+x)^\alpha = \displaystyle \sum_{r=0}^\infty \binom\alpha r x^r[/tex]
which is valid for |x| < 1. (Note that if r > α, the binomial coefficient is defined to be zero, so there really are only α many terms when α is a whole number.)
Differentiating both sides with respect to x gives
[tex]\alpha (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^{r-1}[/tex]
Multiply both sides by some arbitrary x in |x| < 1 :
[tex]\alpha x (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^r[/tex]
Repeat:
[tex]\alpha (1+x)^{\alpha-1} + \alpha(\alpha-1) x(1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^{r-1}[/tex]
[tex]\alpha x (1+x)^{\alpha-1} + \alpha(\alpha-1) x^2 (1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^r[/tex]
Let α = 20, and let x approach 1 from below. The right side converges to the sum we want, while the left side converges to
[tex]20 \times 2^{19} + 20\times19\times 2^{18} = (20 + 10\times19)\times2^{19} = \boxed{210\times2^{19}}[/tex]
What’s the slope of the line that passes through (10,2) and (5,9)
Answer:
y = -1.4x + 16
Step-by-step explanation:
the slope is -1.4x
Use the slope formula:-
[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]
Plug in the values:-
[tex]\displaystyle\frac{9-2}{5-10}[/tex]
Simplify:-
[tex]\displaystyle\frac{7}{-5}= -\frac{7}{5}[/tex]
[tex].~~~~~~~\uparrow\sf{Slope}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
What are the seven principles of entrepreneurial finance? List them?
Answer: 1) Real, human and financial capital must be rented from owners, 2) Risk and expected reward go hand in hand, 3) While accounting is the language of business, cash is the currency, 4) New venture financing involves search, negotiation and privacy, 5) A venture’s financial objective is to increase value, 6) It is dangerous to assume that people act against their own self-interests, 7) Venture character and reputation can be assets or liabilities.
Fill in the blanks below with the correct units. (a) John's desk is about 2 ? long. (b) Milan used a fork that had a mass of about 28 ? . (c) Rita poured about 10 ? of medicine onto a spoon.
Answer:
Blank 1. is 2 feet
Blank 2. is 28 grams
Blank 3. is 8 mililiters
Step-by-step explanation:
Help picture below problem 6
Answer:
i think that B..is a right answer
Answer:
An octagon is a polygon with eight sides.
Step-by-step explanation:
Octa or Octo means eight. Like an octopus. They call it an octopus because it has eight limbs.
A stop-sign is an examle of an octagon.
Hope that helps!
Which shows the solution to the
inequality? 6(x - 2) +21 < 39
A x < 5
C x>3
B X >5
D x < 3
Answer:
A
Step-by-step explanation:
multiply the 6 with the numbers in the bracket
6x -12 + 21 < 39
addition(-12+21 =9)
6x + 9 < 39
grouping
6x < 39-9
6x < 30
divide both sides by the coefficient of x
6x/6 < 30/6
x < 5