Answer:
yes; 2 m = 200 cm
Step-by-step explanation:
The SI prefix "centi-" signifies 1/100. That is 300 cm = 300/100 m = 3 m.
If the ceiling is 3 meters high, a sculpture that is 2 meters tall will have no difficulty fitting into the room.
calculus, question 5 to 5a
5. Let [tex]x = \sin(\theta)[/tex]. Note that we want this variable change to be reversible, so we tacitly assume 0 ≤ θ ≤ π/2. Then
[tex]\cos(\theta) = \sqrt{1 - \sin^2(\theta)} = \sqrt{1 - x^2}[/tex]
and [tex]dx = \cos(\theta) \, d\theta[/tex]. So the integral transforms to
[tex]\displaystyle \int \frac{x^3}{\sqrt{1-x^2}} \, dx = \int \frac{\sin^3(\theta)}{\cos(\theta)} \cos(\theta) \, d\theta = \int \sin^3(\theta) \, d\theta[/tex]
Reduce the power by writing
[tex]\sin^3(\theta) = \sin(\theta) \sin^2(\theta) = \sin(\theta) (1 - \cos^2(\theta))[/tex]
Now let [tex]y = \cos(\theta)[/tex], so that [tex]dy = -\sin(\theta) \, d\theta[/tex]. Then
[tex]\displaystyle \int \sin(\theta) (1-\cos^2(\theta)) \, d\theta = - \int (1-y^2) \, dy = -y + \frac13 y^3 + C[/tex]
Replace the variable to get the antiderivative back in terms of x and we have
[tex]\displaystyle \int \frac{x^3}{\sqrt{1-x^2}} \, dx = -\cos(\theta) + \frac13 \cos^3(\theta) + C[/tex]
[tex]\displaystyle \int \frac{x^3}{\sqrt{1-x^2}} \, dx = -\sqrt{1-x^2} + \frac13 \left(\sqrt{1-x^2}\right)^3 + C[/tex]
[tex]\displaystyle \int \frac{x^3}{\sqrt{1-x^2}} \, dx = -\frac13 \sqrt{1-x^2} \left(3 - \left(\sqrt{1-x^2}\right)^2\right) + C[/tex]
[tex]\displaystyle \int \frac{x^3}{\sqrt{1-x^2}} \, dx = \boxed{-\frac13 \sqrt{1-x^2} (2+x^2) + C}[/tex]
6. Let [tex]x = 3\tan(\theta)[/tex] and [tex]dx=3\sec^2(\theta)\,d\theta[/tex]. It follows that
[tex]\cos(\theta) = \dfrac1{\sec(\theta)} = \dfrac1{\sqrt{1+\tan^2(\theta)}} = \dfrac3{\sqrt{9+x^2}}[/tex]
since, like in the previous integral, under this reversible variable change we assume -π/2 < θ < π/2. Over this interval, sec(θ) is positive.
Now,
[tex]\displaystyle \int \frac{x^3}{\sqrt{9+x^2}} \, dx = \int \frac{27\tan^3(\theta)}{\sqrt{9+9\tan^2(\theta)}} 3\sec^2(\theta) \, d\theta = 27 \int \frac{\tan^3(\theta) \sec^2(\theta)}{\sqrt{1+\tan^2(\theta)}} \, d\theta[/tex]
The denominator reduces to
[tex]\sqrt{1+\tan^2(\theta)} = \sqrt{\sec^2(\theta)} = |\sec(\theta)| = \sec(\theta)[/tex]
and so
[tex]\displaystyle 27 \int \tan^3(\theta) \sec(\theta) \, d\theta = 27 \int \frac{\sin^3(\theta)}{\cos^4(\theta)} \, d\theta[/tex]
Rewrite sin³(θ) just like before,
[tex]\displaystyle 27 \int \frac{\sin(\theta) (1-\cos^2(\theta))}{\cos^4(\theta)} \, d\theta[/tex]
and substitute [tex]y=\cos(\theta)[/tex] again to get
[tex]\displaystyle -27 \int \frac{1-y^2}{y^4} \, dy = 27 \int \left(\frac1{y^2} - \frac1{y^4}\right) \, dy = 27 \left(\frac1{3y^3} - \frac1y\right) + C[/tex]
Put everything back in terms of x :
[tex]\displaystyle \int \frac{x^3}{\sqrt{9+x^2}} \, dx = 9 \left(\frac1{\cos^3(\theta)} - \frac3{\cos(\theta)}\right) + C[/tex]
[tex]\displaystyle \int \frac{x^3}{\sqrt{9+x^2}} \, dx = 9 \left(\frac{\left(\sqrt{9+x^2}\right)^3}{27} - \sqrt{9+x^2}\right) + C[/tex]
[tex]\displaystyle \int \frac{x^3}{\sqrt{9+x^2}} \, dx = \boxed{\frac13 \sqrt{9+x^2} (x^2 - 18) + C}[/tex]
2(b). For some constants a, b, c, and d, we have
[tex]\dfrac1{x^2+x^4} = \dfrac1{x^2(1+x^2)} = \boxed{\dfrac ax + \dfrac b{x^2} + \dfrac{cx+d}{x^2+1}}[/tex]
3(a). For some constants a, b, and c,
[tex]\dfrac{x^2+4}{x^3-3x^2+2x} = \dfrac{x^2+4}{x(x-1)(x-2)} = \boxed{\dfrac ax + \dfrac b{x-1} + \dfrac c{x-2}}[/tex]
5(a). For some constants a-f,
[tex]\dfrac{x^5+1}{(x^2-x)(x^4+2x^2+1)} = \dfrac{x^5+1}{x(x-1)(x+1)(x^2+1)^2} \\\\ = \dfrac{x^4 - x^3 + x^2 - x + 1}{x(x-1)(x^2+1)^2} = \boxed{\dfrac ax + \dfrac b{x-1} + \dfrac{cx+d}{x^2+1} + \dfrac{ex+f}{(x^2+1)^2}}[/tex]
where we use the sum-of-5th-powers identity,
[tex]a^5 + b^5 = (a+b) (a^4-a^3b+a^2b^2-ab^3+b^4)[/tex]
please help! (math)
Which expression is equivalent to the one below?
-1/2(10+1/4)
Answer:
B
Step-by-step explanation:
-½(10+¼)
-½*10 + -½*¼
-5 + -⅛
-5-⅛
Don't forget a positive and negative makes a negative
30
According to a survey at a local mall, 32% of the shoppers jog at least 3 days per week. Sam
asked 15 people at the mall whether they jog at least 3 days per week, and 8 people said yes.
Based on the survey, how many people should Sam have expected to say yes?
A
3
B 5
С
7
D 10
to know the most imnortant reason that neonle choose their brand of
Using the binomial distribution, it is found that Sam should have expected 5 people to say yes.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The expected value is given by:
E(X) = np.
In this problem:
15 people were sampled, hence n = 15.32% of the shoppers jog at least 3 days per week, hence p = 0.32.Hence, the expected value for the number of people that say yes is given by:
E(X) = np = 15 x 0.32 = 5.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
A flower garden is shaped like a circle. Its diameter is 40yd. A ring-shaped path goes around the garden. Its outer edge is a circle with diameter 48yd.
The gardener is going to cover the path with sand. If one bag of sand can cover 6yd^2, how many bags of sand does the gardener need? Note that sand comes only by the bag, so the number of bags must be a whole number. (Use the value 3.14 for pi number .)
Answer:
About 5 bags of sand
Step-by-step explanation:
1. Create Equation
[(48x3.14)-(40x3.14)]/6
2. Solve
[(48x3.14)-(40x3.14)]/6
[150.72-125.6]/6
25.12/6
Now if you use a calculater you will get
4.1866666667
So lets just round the number to 5 instead of
4 beacuse if we round it to 4 it won't be enough
to cover the whole path.
so your answer is 5
Select ALL of the expressions that are equivalent to 4√5.
A. 2√20
B. 6^1/2-5^1/2
c. 3*5^1/2+5^1/2
D.4*5^1/2
E.2√10
F.3*5^1/2
Answer:
A, C, D
All 3 of those simplfiy to 4√5
Given the complex number z_1=3\big(\cos \frac{14\pi}{15} +i\sin \frac{14\pi}{15}\big)z 1 =3(cos 15 14π +isin 15 14π ) and z_2=3\sqrt{3}\big(\cos \frac{11\pi}{15} +i\sin \frac{11\pi}{15}\big)z 2 =3 3 (cos 15 11π +isin 15 11π ), express the result of z_1z_2z 1 z 2 in rectangular form with fully simplified fractions and radicals.
The product of z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15) in rectangular form with fully simplified expressions is z₁ · z₂ = 7.794 - i · 13.5.
How to determine the product of two complex numbers
Let be two numbers of the form z = a + i · b, where i = √-1, the product of two of these numbers in rectangular form is described by the following formula:
z₁ · z₂ = (a + i · b) · (c + i · d) = (a · c - b · d) + i · (a · d + b · c) (1)
If we know that a = 3 · cos 14π/15, b = 3 · sin 14π/15, c = 3√3 · cos 11π/15, d = 3√3 · sin 11π/15, then the result in rectangular form is:
z₁ · z₂ = 7.794 - i · 13.5
The product of z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15) in rectangular form with fully simplified expressions is z₁ · z₂ = 7.794 - i · 13.5. [tex]\blacksquare[/tex]
Remark
The statement presents typing mistakes and is poorly formatted, the correct form is introduced below:
Given the complex number z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15), express the result of z₁ · z₂ in rectangular form with fully simplified fractions and radicals.
To learn more on complex numbers, we kindly invite to check this verified question: https://brainly.com/question/10251853
I NEED HELP ON THIS QUESTION (I will give a Brainlist to the best one no links please.)
HELPPPPPP PLEASEEE PLEASEEEEEEEEEEEEEEEEEE
Answer:
31.63495408
Step-by-step explanation:
Find area of trinagles and semicurucles and then add up
Answer:
31.625 ft²Step-by-step explanation:
It is assumed we need to find the area of shaded figure.The figure comprises of two semicircles and a triangle.
The two semicircles add to one full circle with the diameter of 5 ft.
Area of circle
A = πr² = 3.14*(5/2)² = 19.625 ft²Area of triangle
A = 1/2bh = 1/2(6)(4) = 12 ft²Total area
19.625 + 12 = 31.625 ft²I NEED HELP ASAP
QUESTION BELOW
Answer:
Circumference ≈ 50.27
Area ≈ 201.06
Step-by-step explanation:
The circumference of a circle is [tex]2\pi r[/tex] while the area of the circle [tex]\pi r^{2}[/tex]
Since the diameter is the radius multiplied by 2, the radius of the circle is 8. So substituting 8 for r, the circumference is 2 × [tex]\pi[/tex] × 8, which is approximately 50.27 (rounded to the nearest hundredth) and the area of the circle would be [tex]\pi[/tex] × 8². 8² is 64 so 64 times pi is approximately 201.06 (rounded to the nearest hundredth)
If you owned 2,000 shares of Exxon Mobile stock, how much dividend did you receive? Use the stock table below to find
your answer.
Name
Exxon Mobil
Symbol
XOM
Close
$82.80
Day Range
$82.47-$83.23
52-Week Range $80.30-$95.55
Volume
7,513,630
P/E
34.50
Dividend
$3.08
Dividend Yield
3.7%
EPS
$2.40
Answer:
$6,160
Step-by-step explanation:
The total amount of dividend received is the product of the number of shares and the dividend per share:
(2000 shares) × ($3.08/share) = $6,160.00 . . . dividend received
Write the standard equation of the circle with the center (-14,-5) that passes through the point (-7,5).
equation: (x + 14)² + (y + 5)² = 149
Given:
centre : (-14,-5)point (-7,5)=============
Formula's:
(x-h)² + (y-k)² = r²centre : (h, k)radius : rdistance between points : [tex]\sf \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]Find the radius:
[tex]\rightarrow \sf \sqrt{(-7-(-14))^2 + (5-(-5))^2}[/tex]
[tex]\sf \rightarrow \sqrt{\left(-7+14\right)^2+\left(5+5\right)^2}[/tex]
[tex]\sf \rightarrow \sqrt{149}[/tex]
Equation of circle:
(x-h)² + (y-k)² = r²(x-(-14))² + (y-(-5))² = (√149)²(x + 14)² + (y + 5)² = 149Graph for clarification:
Answer:
[tex]\sf (x+14)^2+(y+5)^2=149[/tex]
Step-by-step explanation:
Standard equation of a circle: [tex]\sf (x-a)^2+(y-b)^2=r^2[/tex]
(where (a, b) is the center and r is the radius of the circle)
Substitute the given center (-14, -5) into the equation:
[tex]\sf \implies (x-(-14))^2+(y-(-5))^2=r^2[/tex]
[tex]\sf \implies (x+14)^2+(y+5)^2=r^2[/tex]
Now substitute the point (-7, 5) into the equation to find r²:
[tex]\sf \implies ((-7)+14)^2+(5+5)^2=r^2[/tex]
[tex]\sf \implies (7)^2+(10)^2=r^2[/tex]
[tex]\sf \implies 149=r^2[/tex]
Final equation:
[tex]\sf (x+14)^2+(y+5)^2=149[/tex]
Determine the correct answer to the following
system of equations:
=
3x – y = 2
-2x + 4y = -8
Answer:
(0,-2)
Step-by-step explanation:
one way to solve...
3x - y = 2 --> *4
-2x + 4y = -8
multiply the first equation by 4
12x - 4y = 8
-2x + 4y = -8
-----------------
10x = 0
x = 0
y = -2
this method is called elimination
another way to solve...
3x - y = 2 simplify for y to get y = 3x - 2
-2x + 4y = -8 substitute y into this equation to solve for x
-2x + 4(3x - 2) = -8
-2x + 12x - 8 = -8
10x = 0
x = 0
y = -2
substitution
alsoo if there are options, just plug in the numbers to the correct variables
Answer:
3xy=2 2x4y=8
3x2=6x8=48x8
Helpp. Mee\\\..........
Answer:
may not be exact
1- surveying every fifth student who walks in
2-randomly selected people of both genders
3-asking 8 random students from each second period
4-asking 4 girls and 4 boys from each~~
5-randomly choosing a page and counting the words
Step-by-step explanation:
1-explanation; the first one is skewed two 7th graders, the third one is skewed to volleyball players, the fourth one is skewed to eight graders
Tim has a checking account with $1,200 remaining after paying bills after several months. He wants to earn interest on
this money rather than keep extra money he does not need for monthly bills in his checking account. Over the next
year, he thinks he might need to withdraw $100 one or two times. His bank requires $250 to open a regular savings
account, $500 for a one-year CD, $750 for a two-year CD, and $1,000 to open a money market account. Decide which
choice would be the best for his situation
Assuming He wants to earn interest on this money rather than keep extra money he does not need. The choice that would be the best for his situation is $250 to open a regular savings.
What is regular savings account?A regular savings account is a saving acount that enables you to save and earn interest based on the amount saved because it is an interest bearing account.
Although this account gives you interest but the interest rate is low. Since Tim has $1200 in his checking account assuming he withdraw $100 twices, Tim will have $1,000 ($1,200-$200).
Now if he open a regular saving with $250 he will have $750 left ($1,000-$250) with which he can earn interest with.
Inconclusion the choice that would be the best for his situation is $250 to open a regular savings.
Learn more about regular account here:https://brainly.com/question/25787382
1.Measurement of segment QR is 2Measurement of segment TS is 3.Measurement if segment QT is
4 The vallue of x is 5 the value of y is
In a parallelogram, opposite sides are of equal measure.
QR = TS
find x
5(x) - 1 = 2(x) + 55(x) - 2(x) = 5 + 13(x) = 6x = 21)
QR:5(x) - 15(2) - 110 - 192)
QR = TS = 9Find value of y:
QT = RSy + 8 = 3(y) - 2y - 3(y) = -2 - 8-2(y) = -10y = 53)
QT:
y + 85 + 8134)
if x = 5
means the diagram is enlarged.
scale factor = 5/2 = 2.5then y will be:
2.5 * 5 = 12.5We need x and y
Opposite sides of a parallelogram are equal
QR=TS5x-1=2x+53x=6x=2And
RS=QT3y-2=y+82y=10y=5Hence
QR=TS=5x-1=5(2)-1=9RS=QT=y+8=5+8=13#3
Segment QT is 4
so
y+8=4y=4+8y=12Another way
x is 5old x is 2So
scale factor:-
k=5/2=2.5Find y
y=5ky=5(2.5)y=12.516. An online magazine charges $45,000 for a 3-month contract for a banner ad
displayed above its weekly feature article. The magazine has 120,000
subscribers and gets 195,000 hits per day. What is the banner's cost per
subscriber if a banner ad was taken for a year?
Answer:
$1.50
Step-by-step explanation:
There are 4 3-month periods in a year.
$45,000 per 3 months period × 4 = $180,000 cost
$180,000 ÷ 120,000 subscribers = $1.50
The banner ad costs about $1.50 per subscriber
a rope is tied to the top of a 4-meter building its other end is tied to the ground 1 meter away form the building. what is an equation for the ropes height y at distance x from the building in standard from a x-4y=4 b 4x-y =4 c 4x+y=4d x-4y=-4
Let the equation be
[tex] \rightarrow y = mx + c[/tex]
y = height of the bulidingx = distance from buildingm = slope of equation[tex] \huge\rightarrow \: m = \frac{y' - y}{x' - x} \\ [/tex]
(x,y) =(1,0)(x'y') =(0,4)[tex] \huge\rightarrow \: m = \frac{4 - 0 }{0 \: - 1} = - 4 \\ [/tex]
m = -4y = mx+cy = -4x+cx= 0,y = 4 4= -4 x 0 + cc= 4hence ,our equation would be,
[tex]\huge \rightarrow 4x + y = 4[/tex]
Find the distance between the two points in simplest radical form (5,2)and (-3,-5)
Answer:
[tex]\sqrt{113}\\[/tex]
Step-by-step explanation:
[tex]distance= \sqrt{(5-[-3])^2+(2-[-5])^2}\\\\distance= \sqrt{(8)^2+(7)^2}\\\\distance= \sqrt{64+49}\\\\distance= \sqrt{113}\\[/tex]
Which of the following q values satisfies: 6-3q≤1
Q=0
Q=1
=
Q=2
Answer:
Q = 2
Step-by-step explanation:
6-3(2) = 0
0 ≤ 1
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
Consider this dilation.
(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b) What is the scale factor? Explain and show your work.
ANSWER BOTH PARTS YOU MAY GET EXTRA POINTS!
Step-by-step explanation:
1) if the initial figure ABCD, then the figure A'B'C'D' is reduction of the initial one.
2) the scale factor is 0.5: the ratio of all the corresponded coordinates is 2:1 [D(8;4) - D'(4;2); C(4;0)-C'(2;0); B(0;-2)-B'(0;-1) and A(-4;4)-A'(-2;2)].
Mark the quadrilaterals ABcD and A'B'C'D'
The image is reduced in size hence it's reduction
Take 2 sides two calculate scale factor
AD=12unitsA'D'=6unitsScale factor:-
6/121/2Find the value of y.
Answer:
this is your answer hope u like it
3^x= 3*2^x
solve this equation✂️
Step-by-step explanation:
this is what i get , i hope this will help you
eter and Area
5
Annita is sewing a lace edge around a rectangular quilt. She will need 160 inches of lace to do the entire quilt. If the quilt is 46
inches wide, how long is the quilt?
A. 32 inches
B. 34 inches
C. 80 inches
D.
68 inches
Reset
Submit
Answer:
b 34
Step-by-step explanation:
its 34 because if you do 46×2 because of the both sides you will get 92 then subtract 92 from 160 and you will get 68 then do 68÷2 to find out the second side and you will get 34
What is the value of h?
21 + h = 345
Answer:
324
Step-by-step explanation:
21 + h = 345
group like terms
h = 345 - 21
h = 324
Answer:
h=324
Step-by-step explanation:
21+h = 345
(Substituting the equation)
h=345 - 21
h= 324
!!PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!
Please help me with Part C of this question
Answer:
14-18 minutes
Step-by-step explanation:
Part a is 32 inches per minute
part b is 252 inches per minute
The question asks the change in elevation fastest, in part b 252 is greater than 32 so 14-18 minutes is the answer.
Answer:
14-18 minutes
Step-by-step explanation:
Part a is 32 inches per minute and part b is 252 inches per minute
this question asks the change in elevation fastest, in part b 252 is greater than 32 so 14-18 minutes is the answer.
Use the following statement to answer parts a) and b). One hundred raffle tickets are sold for $3 each. One prize of $500 is to be awarded. Winners do not have their ticket costs of $3 refunded to them. Raul purchases one ticket.
a) Determine his expected value.
b) Determine the fair price of a ticket.
Using the expected value of a discrete distribution, it is found that:
a) His expected value is of -$2.5.
b) The fair price of a ticket is of $0.5.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, the distribution for the net value of the ticket is:
P(X = 497) = 1/1000.P(X = -3) = 999/1000.Item a:
The expected value is given by:
[tex]E(X) = 497\frac{1}{1000} - 3\frac{999}{1000} = -2.5[/tex]
His expected value is of -$2.5.
Item b:
With an unknown ticket price, the distribution is:
P(X = 500 - x) = 1/1000.P(X = -x) = 999/1000.The game is fair if E(X) = 0, hence:
[tex]\frac{500 - x}{1000} - \frac{999x}{1000} = 0[/tex]
0.5 - x = 0
x = 0.
The fair price of a ticket is of $0.5.
More can be learned about the expected value of a discrete distribution at https://brainly.com/question/24855677
Seven more than a number is less than 18
Answer:
The first thing to do is translate the sentence into mathematical notation.
"no more than" means "less than or equal to" which is written as ≤
"seven less than a number" means we are subtracting 7 from a number. We don't know what the number is, so we can use a variable (like n) for the number. So "seven less than a number" becomes n - 7.
The whole thing becomes 12 ≤ n - 7.
To solve for n, we can add 7 to both sides.
19 ≤ n.
19 is less than or equal to n, which means the smallest (minimum) value of the number is 19.
We could also do it without an inequality:
If 12 is 7 less than a number, then the number is 19, because 19-7=12. If we chose a smaller number, like 18, then 7 less than 18 is smaller than 12, which is not allowed (12 is no more than 7 less than the number). So the smallest possible value of the number is 19.
Let the number be p.
Next, "seven times p" can be written like so:-
[tex]\pmb{7p}[/tex]
This expression is less than 18:-
[tex]\bigstar{\boxed{\pmb{7p < 18}}}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
Help I don't understand this math. Whoever gets the right answer gets Brainlist! :)
Do part B please! :)
Answer:
1=32
2=44
3=56
4=70
Step-by-step explanation:
if need working please ask
Write 8.6 × 10–3 as a basic numeral.
Answer:
[tex]8.6\times 10^{-3}=0.0086[/tex]
Step-by-step explanation:
Which decimal is greater: 0.347 or 0.437?
Answer:
0.437
Step-by-step explanation:
Decimals are read the same as whole numbers, starting with the first digit, which is the largest, to the right. So, to find the larger decimal you need to look at the first digit. If this digit is the same then continue to the right until there is a difference in the number. In this case, the first digit is different. Therefore, whichever has the larger first digit must be the greater one. Since 4 > 3, 0.437 must be greater than 0.347.