Answer:
4:00 pm
Step-by-step explanation:
To find the time it takes Malik to finish his English essay, let's start by subtracting one hour.
5:30 minus 1 hour is 4:30.
Now, subtract 30 minutes.
4:30 minus 30 minutes is 4:00.
Malik started working on his English essay at 4:00 pm.
Hope that helps.
Need Help with these (Giving brainiest if you can solve these)
Answer: try using sine for this equasion
Step-by-step explanation:
use the cubic model y=x^3+x^2+x to estimate the value of y when x = 10. a 910 b. 110 c. 1210 d. 3150
Answer:
y = 1110
Step-by-step explanation:
In the above question, we are given the cubic model
y=x³ +x² + x
We are to solve for y when x = 10
Hence,
y = 10³ + 10² + 10
y = 1000 + 100 + 10
y = 1110
Therefore, the value of y when x is 10 using the cubic model of ' y =x³ +x² + x' is 1110.
In horse race betting, a trifecta bet is one in which you try to pick which horses will finish first, second, and third, in the correct order. If 8 horses are running in a race and you randomly place a trifecta bet, what is the probability of winning the bet
Answer:
The probability of winning the bet is 1/336
Step-by-step explanation:
We should understand that there is only one possible arrangement of the winning selection
Now, the horse that comes first can be selected in 8 ways given that all the horses have equal chances
The horse that comes second can be selected in 7 ways given that all the horses have equal chances
The horse that comes third can be selected in 6 ways given that all the horses have equal chances
Now the total number of ways of selection would be;
8 * 7 * 6 = 336
Since there is only one of the selections that is correct, the probability of making the correct choice is thus 1/336
A Canadian longitudinal study1 examined whether giving antibiotics in infancy increases the likelihood that the child will be overweight later in life. The study included children and found that of the children had received antibiotics during the first year of life. Test to see if this provides evidence that more than of Canadian children receive antibiotics during the first year of life. Show all details of the hypothesis test, including hypotheses, the standardized test statistic, the -value, the generic conclusion using a significance level, and a conclusion in context.
1. Clearly state the null and alternative hypotheses.
2. Calculate the test statistic and p-value.
3. What is the conclusion?
4. Do we have evidence to conclude that more than 70% of Canadian infants receive antibiotics?
A. Yes
B. No
Answer:
1. [tex]H_{0}[/tex] : p = 0.70 , [tex]H_{a}[/tex] : p > 0.70
2. Test Statistic : 0.54 , P value : 0.2946
3. Fail to reject null Hypothesis
4. No.
Step-by-step explanation:
1. Null hypothesis is 70% of children receive antibiotics.
Alternative hypothesis is more than 70% of children receive antibiotics.
2. Test statistic is calculated as;
z = [tex]\frac{p (1 - p)}{\sqrt{\frac{p (1-p}{n} )} }[/tex]
z = [tex]\frac{0.01}{0.0185}[/tex]
z = 0.54
3. p value is calculated as;
1 - right tailed probability
1 - 0.7054 = 0.2946
Simplify the polynomial, then evaluate for x=3 x^2+2x-3-2x^2+x+4
Answer:
The answer is
19Step-by-step explanation:
x² + 2x - 3 - 2x² + x + 4
Group like terms
That's
x² - 2x² + 2x + x - 3 + 4
Simplify
- x² + 3x + 1
when x = 3
We have
(-3)² + 3(3) + 1
9 + 9 + 1
18 + 1
19
Hope this helps you
3. The area of a rectangular deck, in square meters, is given by the polynomial 40p2 + 24p.
The deck is 8p meters wide.
a) Find the polynomial that represents the length of the deck.
b) Find the polynomial that represents the perimeter of the deck.
Answer:
Length = 5p + 3
Perimeter = 26p + 6
Step-by-step explanation:
Given
Area = 40p² + 24p
Width = 8p
Solving for the length of deck
Given that the deck is rectangular in shape.
The area will be calculated as thus;
Area = Length * Width
Substitute 40p² + 24p and 8p for Area and Width respectively
The formula becomes
40p² + 24p = Length * 8p
Factorize both sides
p(40p + 24) = Length * 8 * p
Divide both sides by P
40p + 24 = Length * 8
Factorize both sides, again
8(5p + 3) = Length * 8
Multiply both sides by ⅛
⅛ * 8(5p + 3) = Length * 8 * ⅛
5p + 3 = Length
Length = 5p + 3
Solving for the perimeter of the deck
The perimeter of the deck is calculated as thus
Perimeter = 2(Length + Width)
Substitute 5p + 3 and 8p for Length and Width, respectively.
Perimeter = 2(5p + 3 + 8p)
Perimeter = 2(5p + 8p + 3)
Perimeter = 2(13p + 3)
Open bracket
Perimeter = 2 * 13p + 2 * 3
Perimeter = 26p + 6
The same bedroom furniture set costs $1,500 in both Florida and Alabama. The table gives a breakdown of the taxes someone would pay when purchasing the furniture set in either state. Alabama Florida State of Alabama: 4.225% County Tax: 1.375% City Tax: 3.0% State of Florida: 6.5% County Tax: 1% City Tax: 1.625% Which statement is true? A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations.
Answer:
A: True
B, C and D: False
Step-by-step explanation:
We have a total sales tax for Alabama that is:
[tex]T_A=4.225+1.375+3=8.6[/tex]
The total sales tax for Florida is:
[tex]T_F=6.5+1+1.625=9.125[/tex]
The total sales tax is greater in Florida than in Alabama.
A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE
The sales tax difference in this purchase can be calculated as:
[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]
B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)
C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)
The amount of sales tax in Alabama is:
[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]
D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).
Solve the quadratic equation 4x2 – 2x = 9 using the quadratic formula
Answer:
x= 1 + or - sr37/4 got it from a sitr
Here you go.
I really hope I helped. Good luck.
TIMERBUATING
09:56
The figure is a parallelogram. One diagonal measures 28
units
Is the figure a rectangle? Explain
20
21
No, t is not a rectangle because the diagonals are
congruent
O No, it is not a rectangle because the sides of the
parallelogram do not meet at night angles.
o Yes, tis a rectangle because the diagonals are
congruent
O Yes, it is a rectangle because the sides of the
parallelogram do meet at right angles.
21
20
Save and Exit
Answer:
No, it is not a rectangle because the sides of the
parallelogram do not meet at night angles (B)
Step-by-step explanation:
The diagonal of the rectangle = 28
The two sides of the figure measures 20 and 21 units respectively.
To determine if the shape is a rectangle, we would apply Pythagoras theorem
hypotenuse² = opposite² + adjacent²
hypotenuse = diagonal = 28
The other two sides represent the opposite and adjacent
28² = 20² + 21²
784 = 400 + 441
784 ≠ 841
The square of the diagonal is not equal to the sum of the square of the other two sides (length and width). And as a result of this, the triangle isn't a right angled triangle and the sides of the parallelogram would not meet at right angles.
Therefore, the figure isn't a rectangle.
Option B: No, it is not a rectangle because the sides of the
parallelogram do not meet at night angles.
Now find the product (2+ sqrt 5)(2- sqrt 5). The product is ...
the answer is -1
Answer:
-1
Step-by-step explanation:
Thanks
The product of expression (2 + √5) (2 - √5) is,
⇒ (2 + √5) (2 - √5) = - 1
We have to given that,
An expression to simplify,
⇒ (2 + √5) (2 - √5)
Now, We can simplify it by using formula,
⇒ (a - b) (a + b) = a² - b²
Hence, We get;
⇒ (2 + √5) (2 - √5)
⇒ (2² - √5²)
⇒ 4 - 5
⇒ - 1
Therefore, The product of expression (2 + √5) (2 - √5) is,
⇒ (2 + √5) (2 - √5) = - 1
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Edgar accumulated $5,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for 2 years, how much will he owe on this debt in 2 years by compounding continuously? Round to the nearest cent.
Answer:
Loan amount due after 2 years =$7,387.28
Explanation:
The amount due on the loan would be equal to the total accrued interest plus the accumulated amount amount.
Note that, since Edgar did not pay any amount off the loan in the course of the 2 years, the interest due per quarter would be equal to the quarterly interest rate multiplied by the unpaid balance till date.
To determine the amount due, we would compound $5,000 at a quarterly interest rate of for 8 quarters. The formula below would suffice
Loan amount due = loan balance × (1+r)^(n)
Quarterly interest rate -20%/4 =5%, number of quarters - 2× 4 =8, loan balance - 5,000
Loan amount due = 5,000 × (1.05)^(8)
= 7,387.28
Loan amount due after 2 years =$7,387.28
Step-by-step explanation:
Answer:
7434.57
Step-by-step explanation:
An urn contains 3 one-dollar bills, 1 five-dollar bill and 1 ten-dollar bill. A player draws bills one at a time without replacement from the urn until a ten-dollar bill is drawn. Then the game stops. All bills are kept by the player. Determine: (A) The probability of winning $12. (B) The probability of winning all bills in the urn. (C) The probability of the game stopping at the second draw.
Hey there! I'm happy to help!
PART A
There are 3 $1 bills, 1 $5 bill, and 1 $10 bill. This gives us 5 total bills.
First, we want to find the probability of winning $12. Well, to win, you have to draw the $10 bill. You only have room for two dollars beforehand to equal $12 dollars after pulling out the ten. So, this is the probability of drawing two one dollar bills and the the ten. Let's calculate this below.
[tex]\frac{3}{5} *\frac{1}{2} *\frac{1}{3} =\frac{1}{10}[/tex]
Where did I get these numbers from? Well 3 of the 5 bills are $1, so the first probability is 3/5. Then, if we draw one of the $1 bills, there are only 2 of those left and 4 total bills, so the probability is then one half. Finally, there would be only 3 left and you need to pick the $10 bill, which is a probability of 1/3.
The probability of winning $12 is 1/10 or 10%.
PART B
Now, we want to find the probability of picking every single bill before the ten. This means that we pick the three one dollar bills and the five dollar bill before the ten.
To pick the first $1 bill, our probability is 3/5, and then for the second it is 1/2. For the third, there are three total cards and 1 $1 bill, so the probability is 1/3. Then we have a 1/2 chance of picking the $5 bill over the $10 bill, giving us this solution.
[tex]\frac{3}{5} * \frac{1}{2} * \frac {1}{3} * \frac{1}{2}= \frac{1}{20}[/tex]
The probability of winning all bills in the urn is 1/20 or 5%.
PART C
For this event, we want to get any bill that isn't the $10 and then we want the $10 on the second one.
Since there are 4 bills that aren't the $10, our first probability is 4/5. Then, we only have 4 left, with 1 being the $10, so our second probability is 1/4.
[tex]\frac{4}{5}*\frac{1}{4}=\frac{1}{5}[/tex]
The probability of the game stopping at the second draw is 1/5 or 20%.
Have a wonderful day! :D
The probability of winning $12 will be 0.15.
How to calculate probability?The game stops after drawing$10 bill. There can also be 2 draws of $2 and $10 to make $12.
Therefore, the probability of winning $12 will be calculated thus:
= Probability of getting $2 × probability of getting $10
= 3/5 × 1/4
= 0.15
The probability of winning all balls in the urn will be:
= 4/5 × 3/4 × 2/3 × 1/2
= 0.2
Lastly, the probability of the game stopping at the second draw will be:
= First draw × Second draw
= 4/5 × 1/4
= 0.2
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A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x+6y=7.50 10x+5y=8.75
Answer:
x = $0.50
y= $0.75
Step-by-step explanation:
1. Multiply the equations to have the same coefficients
5(6x + 6y = 7.5) → 30x + 30y = 37.5
3(10x + 5y = 8.75) → 30x + 15y = 26.25
2. Subtract the equations
30x + 30y = 37.5
- 30x + 15y = 26.25
15y = 11.25
3. Solve for y by dividing both sides by 15
y = 0.75
4. Plug in 0.75 for y into one of the equations
6x + 6(0.75) = 7.5
5. Simplify
6x + 4.5 = 7.5
6. Solve for x
6x = 3
x = 0.5
Answer:
The cost of one apple is $0.5
The cost of one orange is $0.75
Step-by-step explanation:
Given information
The cost of an apple = [tex]x[/tex]
The cost of an orange = [tex]y[/tex]
Equation to find the values are:
[tex]6x=6y=7.50\\10x+5y=8.75[/tex]
Now, convert the equations to have same coefficient as:
[tex]5(6x=6y=7.50)\\=30x+30y=37.5\\3(10x+5y=8.75)\\=30x+15y=26.25[/tex]
Now, on solving the above equation by subtracting one from another.
We get,
[tex]15y=11.25\\y=0.75[/tex]
Now , put the value of [tex]y[/tex] in one equation to find the value of [tex]x[/tex].
As,
[tex]6x+4.5=7.5\\x=0.5[/tex]
Hence,
The cost of one apple is $0.5
The cost of one orange is $0.75
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When a button is pressed, a computer program outputs a random even number greater than 0 less than 8. You press the button 4 times.
Can some help me with this?
Answer:
Well all even numbers between 0 and 8 are,
2, 4, 6, 8
Meaning if the button is pressed 4 times 2, 4, 6, or 8 will be outputted.
When press button 4 times. Then output of the program will be, [tex](2,4,6,2)[/tex]
Even number:Any number that can be exactly divided by 2 is called as an even number.
Given that, When a button is pressed, a computer program outputs a random even number greater than 0 less than 8.
Even numbers greater than 0 less than 8 are,
[tex]=2,4,6[/tex]
When press button 4 times. Then output of the program will be,
[tex]=(2,4,6,2)[/tex]
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Computing a two-independent sample t-test is appropriate when?
A) different participants are assigned to each group
B) the population variance is unknown
C) participants are observed one time
D) all of the above
Answer:
D) all of the above
Step-by-step explanation:
The two-independent sample t-test is used to evaluate the differences in the means of two independent groups to ascertain if there is indeed a difference in the population means. So, the population variance is unknown before this test is done. To carry out this type of test, the researcher should ensure that there are no similarities between participants in the two groups so that there would be no influences between the groups. The participants in the research should be randomly selected.
The participants are observed one time to ensure that the same conditions hold for both groups and that there is a balance in the research blueprint.
For f(x) = 4x + 1 and g(x) = x2 – 5, find (f – g)(x).
Answer:
(f – g)(x) = - x² + 4x + 6Step-by-step explanation:
f(x) = 4x + 1
g(x) = x² – 5
To find (f – g)(x) subtract g(x) from f(x)
That's
(f – g)(x) = 4x + 1 - ( x² - 5)
Remove the bracket
(f – g)(x) = 4x + 1 - x² + 5
Group like terms
(f – g)(x) = - x² + 4x + 1 + 5
We have the final answer as
(f – g)(x) = - x² + 4x + 6Hope this helps you
35=7x Equals What? Like this is os hard for me
Answer:
x=5
Step-by-step explanation:
35 = 7x
Divide each side by 7
35/7 = 7x/7
5 = x
What is the 13th term of this arithmetic sequence? 132, 135, 138, 141, …
a 168
b 172
c 176
d 179
Answer:
182
Step-by-step explanation:
The sequence has a common difference of +3.
Answer:
It's none of those. It's supposed to be 171.
Step-by-step explanation:
That's because in an arithmetic sequence it's a list of numbers with a definite pattern, and all you're doing is adding 3 to each number.
WILL MARK AS BRAINLIEST 4. Suppose there is a card game where you are dealt a hand of three cards. You have already learned that the total number of three-card hands that can be dealt from a deck of 52 cards is: 52C3=52!/49!3! 52C3=22100 Calculate the probability of getting a hand that has exactly two aces in it (A A X). Do this by finding out the number of possible hands that have exactly two aces, and then dividing by the total possible number of three-card hands that is stated above. Part A: Use the multiplication principle to tell the total number of three-card hands (permutations) that can be made with two aces. (2 points) Part B: In the answer from Part I, each two-ace hand got counted twice. For example, A A X got counted as a separate hand from A A X. Since order should not matter in a card hand, these are really the same hand. What is the actual number of two-ace hands (combinations) you can get from a deck of 52 cards?(2 points) Part C: Find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards. Write your answer as a fraction. (2 points)
Answer:
Part A- 6
Part B- 3
Part C- 3/22100
Step-by-step explanation:
Part A-
Use the permutation formula and plug in 3 for n and 2 for k.
nPr=n!/(n-k)!
3P2=3!/(3-2)!
Simplify.
3P2=3!/1!
3P2=6
Part B-
Use the combination formula and plug in 3 for n and 2 for k.
nCk=n!/k!(n-k)!
3C2=3!/2!(3-2)!
Simplify.
3C2=3!/2!(1!)
3C2=3
Part C-
It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.
I believe the answer is 3/22100
I honestly suck at probability but I tried my best.
A poll shows that 41% of voters in a city favor of a $0.0.1 tax increase. If 25 voters are selected at random, what is that exactly 15 of them will vote in favor of the initiative?
Answer:
The probability is 0.026 to 3 d.p
Step-by-step explanation:
To calculate this , we shall be using the Bernoulli approximation.
let P = percentage of voters supporting the increase = 41% = 41/100 = 0.41
q = percentage of voters not supporting = 100-41% = 59% = 59/100 = 0.59
Now we want to calculate that exactly 15 out of 25 will vote in favor
Mathematically that would be ;
25C15 p^15 q^10
= 25C15 0.41^15 0.59^10
= 0.025981307443 or simply 0.026 to 3 decimal places
Use the graph to solve the given system of equations, then enter your solution below. {x−3y=−3x+y=5
Answer:
Step-by-step explanation:
Given the system of equation x−3y=−3 and x+y=5, we can solve for x and y by solving the equation simultaneously using the substitution method.
x−3y=−3_____________ 1
x+y=5 ______________2
From equation 2; x = 5- y ________ 3
Substitute equation 3 into equation 1
Since x - 3y = -3
(5-y)-3y = -3
5-y-3y = -3
5-4y = -3
Subtract 5 from both sides of the equation
5-4y-5 = -3-5
-4y = -8
Divide both sides by -4
-4y/-4 = -8/-4
y = 2
Substitute y = 2 into equation 2 to get the value of y;
From equation 2, x+y = 5
x+2 = 5
Subtract 2 from both sides of the equation
x+2-2 = 5-2
x = 3
Hence the value of x and y from the graph will be 3 and 2 respectively.
A psychologist is studying the effects of lack of sleep on the performance of various perceptual-motor tasks. After a given period of sleep deprivation, a measurement of reaction time to an auditory stimulus was taken for each of 36 adult male subjects.The mean and standard deviation of the reaction times (in seconds) for the fifty adult male subjects were 1.82 seconds and 0.28 seconds respectively. Previous psychological studies have shown that the true mean reaction time for non-sleep-deprived male subjects is 1.70 seconds. Does the sample evidence indicate that the mean reaction time for sleep-deprived adult males is longer than that of non-sleep-deprived adult males.
A. H0:μ=1.82;Ha:μ<1.82
B. H0:μ=1.70;Ha:μ<1.70
C. H0:μ=1.82;Ha:μ>1.82
D. H0:μ=1.70;Ha:μ>1.70
E. None of the above
Answer:
D. [tex]H_{0}[/tex] : μ = 1.70, [tex]H_{a}[/tex] : μ > 1.70
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
Find the area of the polygon shown in the figure.
Answer:
Hey there!
Area for a triangle: 0.5bh, where b is the base, and h is the height.
Plugging in the values: 0.5(4)(8), or simplified to 16.
The area of the polygon is 16 units^2
Hope this helps :)
Answer:
[tex]\boxed{16 \: units^2}[/tex]
Step-by-step explanation:
Apply formula for area of a triangle.
Area of a triangle = [tex]\frac{1}{2} bh[/tex]
[tex]b:base\\h:height[/tex]
The base is 4 units. The height is 8 units.
[tex]\frac{1}{2} (4)(8)[/tex]
[tex]\frac{1}{2} (32)=16[/tex]
2. Tomás compró una bicicleta en $199.900. Primero, canceló la mitad y el resto en 7 cuotas de igual valor, con un interés total de $4000. ¿Cuánto es el valor de cada cuota?
Answer:
Cada cuota tendrá un valor de $14,850.
Step-by-step explanation:
Dado que Tomás canceló la mitad del valor de la bicicleta, la cual costaba $199.900, el valor pagado al inicio fue de $99,950 (199,900 / 2).
Luego, para el valor restante, Tomás suscribió a una financiación con un interés de $4,000, elevando el monto a pagar a $103,950, pagaderos en 7 cuotas. Por lo tanto, dichas cuotas tendrán cada una un valor de $14,850 (103,950 / 7).
prove identity trigonometric equation
[tex]2 \tan(x) = \frac{ \cos(x) }{ \csc(x - 1) } + \frac{ \cos(x) }{ \csc(x + 1) } [/tex]
Explanation:
The given equation is False, so cannot be proven to be true.
__
Perhaps you want to prove ...
[tex]2\tan{x}=\dfrac{\cos{x}}{\csc{(x)}-1}+\dfrac{\cos{x}}{\csc{(x)}+1}[/tex]
This is one way to show it:
[tex]2\tan{x}=\cos{(x)}\dfrac{(\csc{(x)}+1)+(\csc{(x)}-1)}{(\csc{(x)}-1)(\csc{(x)}+1)}\\\\=\cos{(x)}\dfrac{2\csc{(x)}}{\csc{(x)}^2-1}=2\cos{(x)}\dfrac{\csc{x}}{\cot{(x)}^2}=2\dfrac{\cos{(x)}\sin{(x)}^2}{\cos{(x)}^2\sin{(x)}}\\\\=2\dfrac{\sin{x}}{\cos{x}}\\\\2\tan{x}=2\tan{x}\qquad\text{QED}[/tex]
__
We have used the identities ...
csc = 1/sin
cot = cos/sin
csc^2 -1 = cot^2
tan = sin/cos
Find the work done by the force field F(x, y) = xi + (y + 5)j in moving an object along an arch of the cycloid r(t) = (t − sin(t))i + (1 − cos(t))j, 0 ≤ t ≤ 2π.
Integrate the force field along the given path (call it C):
[tex]W=\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=\int_0^{2\pi}\mathbf F(x(t),y(t))\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}\bigg((t-\sin t)\,\mathbf i+(6-\cos t)\,\mathbf j\bigg)\cdot\bigg((1-\cos t)\,\mathbf i+\sin t\,\mathbf j\bigg)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}(t-t\cos t+5\sin t)\,\mathrm dt=\boxed{2\pi^2}[/tex]
By direct calculation we will find that the work done is equal to 2π²
The formula to compute the work done is given by:
[tex]W = \int\limits^a_b {F(x(t), y(t))\cdot\frac{dr(t)}{dt} } \, dt[/tex]
Here we have:
[tex]r(t) = (t - sin(t))i + (1 - cos(t))j[/tex]
This means that:
[tex]x(t) = (t - sin(t))\\y(t) = (1 - cos(t))\\\\\frac{dr(t)}{dt} = (1-cos(t))i + sin(t)j = (1-cos(t), sin(t))[/tex]
And we know that 0 ≤ t ≤ 2π, so b = 0 and a = 2π
Replacing that in the work integral we get:
[tex]W = \int\limits^{2\pi}_0 {(t - sin(t), 1 - cos(t) + 5)\cdot(1-cos(t), sin(t))} \, dt \\\\W = \int\limits^{2\pi}_0 {(t - sin(t), 6 - cos(t))\cdot(1-cos(t), sin(t))} \, dt\\\\W = \int\limits^{2\pi}_0 {(-t*cos(t) +t-sin(t)+ cos(t)*sin(t)+ 6*sin(t) - cos(t)*sin(t) )} \, dt\\\\W = \int\limits^{2\pi}_0 {(-cos(t)*t + 5*sin(t) + t)} \, dt \\\\[/tex]
the sin(t) integral can be removed because it is equal to zero, so we get:
[tex]W = \int\limits^{2\pi}_0 {(-cos(t)*t + t)} \, dtW = [(-t*sin(t) - cos(t)) + \frac{t^2}{2} ]^{2\pi}_0\\\\W = -2\pi*sin(2\pi) - cos(2\pi) + 0*sin(0) + cos(0) + \frac{(2\pi)^2}{2} - \frac{(0)^2}{2}\\\\W = 2\pi^2[/tex]
If you want to learn more, you can read:
https://brainly.com/question/22599382
You are returning from Mexico and want to convert 5,00 pesos to US dollar . The rate of exchange that day is 1 pesos is 0.55 . How many dollars will you receive for your pesos ?
Hey there! I'm happy to help!
We see that 1 peso is equal to 0.55 U.S. dollars. So, the amount we will get in U.S dollars is the same as $5000×0.55 because 0.55 US dollars is equal to one peso!
5000×0.55=2750
Therefore, you will receive $2750.
Have a wonderful day!
Which situation is most likely to have a constant rate of change?
HELP
Answer:
the answer i would go with is A
Good luck on your Test :)
Step-by-step explanation:
B doesnt really have a constant rate of change as it depends on how many games happen and usually the longer an arena stays open has no correlation on how many people attend the games there
C has no real constant rate of change as it always ends up stopping after a little bit, and the change is usually not a constant one
D this could count, but since its a number that would go down if its not brought back up, its not a real constant rate of change, since it cant go below or above a certain range
so by process of elimination, A is the answer. also seeing as how its saying the distance with the number of times, that means that its an objective thing, as a track is a set distance, and the distance of a run or the track cant be affected by time or anything and could technically never end. so its a constant thing, meaning the longer the distance is, the higher the laps around the track are, and it could theoretically go on forever.
i hope this helped answer your question! :)
I got the 90 and 8.9 for them but it’s wrong. I really confused now. What is the right answer??? Can someone explain to me ASAP?!!!!
Answer:
[tex] A = 70.6 [/tex] ≈ 71°
[tex] x = 36.5 [/tex]
Step-by-step explanation:
Step 1: Use the Law of sine to find A
[tex] \frac{sin(A)}{38} = \frac{sin(44)}{28} [/tex]
Cross multiply:
[tex] sin(A)*28 = sin(44)*38 [/tex]
[tex] sin(A)*28 = 0.695*38 [/tex]
Divide both sides by 28:
[tex] \frac{sin(A)*28}{28} = \frac{0.695*38}{28} [/tex]
[tex] sin(A) = 0.9432 [/tex]
[tex] A = sin^{-1}(0.9432) [/tex]
[tex] A = 70.6 [/tex]
A ≈ 71°
Step 2: find the measure of the angle opposite side x
Angle opposite side x = 180 - (71+44) (sum of triangle)
= 180 - 115 = 65°
Step 3: find x using the law of sines
[tex] \frac{x}{sin(65)} = \frac{28}{sin(44)} [/tex]
[tex] \frac{x}{0.906} = \frac{28}{0.695} [/tex]
Multiply both sides by 0.906
[tex] x*0.695= 28*0.906 [/tex]
Divide both sides by 0.695
[tex] \frac{x*0.695}{0.695} = \frac{28*0.906}{0.695} [/tex]
[tex] x = \frac{28*0.906}{0.695} [/tex]
[tex] x = 36.5 [/tex]
In a four-digit number, the sum of the thousands and hundred digits is 3.
The tens digit is 4 times the hundreds digit.
The ones digit is seven more than the thousands digit.
No two digits are equal.
What is the four-digit number?
Answer: 2149
Step-by-step explanation: If the sum of the first two digits is 3, the choices must be 1 and 2 (or 2 and 1) In order to satisfy the other specifications, "the tens digit is 4 times the hundreds digit." the hundreds digit can't be 2 because that would make the tens dight 8. and the ones digit would also have to 8 in order to satisfy the "seven more than the thousands digit" which would be a 1. And that violates the condition, "No two digits are equal."
So the only possible combination is 2149
4 is 4 times 1
9 is 7 +2