Answer:
v = 2u
Step-by-step explanation:
note that
2u = 2 (5, - 2 ) ← multiply each component by 2
= (10, - 4) = v , then
v = 2u
A cylindrical container 30cm in diameter holds approximately 30 litres of oil. how far does the oil level fall after 1 litre of oil has been used
The fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.
We assume the drop in the level of water to be d cm.
Since the container is cylindrical in shape, its volume is given as:
V = πr²h, where V is the volume, r is the radius, and h is the height.
In the question, we are given that the diameter of the can is 30 cm.
Hence its radius = 30/2 = 15 cm.
The capacity of the container is given to be 30 liters or 30*1000 = 30000 cm³.
The volume of the oil used = 1 liter or 1*1000 = 1000 cm³.
Thus, substituting V = 1000, r = 15, and h = d, in the formula of the volume, V = πr²h, we get:
1000 = π(15)²(d),
or, d = 1000/(225π) = 1.4147.
Thus, the fall in the water level is 1.4147 cm.
Therefore, the fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.
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Solve x ^ 2 - 3x = - 8 using the quadratic formula.
Answer: [tex]\frac{3 +- \sqrt{23}i}{2}[/tex] If using complex numbers, or undefined if using all real numbers
Step-by-step explanation:
Moving -8 to the left side of the eq by adding both sides by 8=
x^2-3x+8=0
The quad formula:[tex]\frac{-b +- \sqrt{b^2-4ac}}{2a}[/tex]
a=1 b=-3 c=8
Inserting a b c values into formula: [tex]\frac{-(-3) +- \sqrt{(-3)^2-4(1)(8)}}{2(1)}[/tex]
Simplifying: [tex]\frac{3 +- \sqrt{9-32}}{2}[/tex]
[tex]\frac{3 +- \sqrt{-23}}{2}[/tex] Since the square root of a negative number doesn't exist in the set of real numbers, the equation is undefined.
OR
[tex]\frac{3 +- \sqrt{23}i}{2}[/tex] Using complex numbers i, to replace the negative number created by subtracting 9-32.
After grabbing some food from the cafeteria, Ray trips causing his food to go up in the air before hitting the ground. The parabolic path of his food tray can be modeled by the function ℎ() = − 0. 2 , where h is 2 + 0. 4 + 1. 6 the height in meters after t seconds. a)
What is the maximum height of the tray?
If Ray manages to catch the tray at the same height from which the tray flew out of his hands, how long is it in the air?
The maximum height of the tray is 1.8 meters and the tray is in the air for 2 seconds
The maximum height of the trayThe distorted information (i.e. the function) in the question is:
h(t) = -0.2t^2 + 0.4t + 1.6
Differentiate the function
h'(t) = -0.4t + 0.4
Set to 0
-0.4t + 0.4 = 0
Subtract 0.4 from both sides
-0.4t = -0.4
Divide by -0.4
t = 1
Substitute t = 1 in h(t) = -0.2t^2 + 0.4t + 1.6
h(1) = -0.2(1)^2 + 0.4(1) + 1.6
Evaluate
h(1) = 1.8
Hence, the maximum height of the tray is 1.8 meters
Time spent in the airIn (a), we have:
t = 1
This represents the time to reach the maximum height.
The time spent in the air is:
T = 2t
This gives
T = 2 * 1
T = 2
Hence, the tray is in the air for 2 seconds
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Evaluate the expression 9 - z when z = 4.
Answer:
its 5 5+4=9
Step-by-step explanation:
Select the correct answer.
The graph of function f is shown.
Which statement about function f is true?
answers:
The function f has an inverse because it passes the vertical line test.
The function f does not have an inverse because it is not one-to-one.
The function f has an inverse because it is one-to-one.
The function f does not have an inverse because its domain is not .
Answer:
The function f has an inverse because it is one-to-one.
Step-by-step explanation:
The condition for a function to have an inverse is that every x coordinate maps to a single y - coordinate. As illustrated by the diagram attached in the second picture, every x value maps to one y value therefore satisfying the condition making the function have an inverse.
What is the slope of the line that passes through (0,5) and (10,0)?
Answer:
-1/2
Step-by-step explanation:
slope is change in y / change in x
change in y is -5 bc y decreases by 5
change in x is 10 bc x increases by 10
-5/10 simplifies to -1/2
I don’t understand this. Help me please!
Answer:
2
Step-by-step explanation:
So the midpoint of AB can be calculated by finding the length of AB, dividing it by 2 and then adding it to A. So the length of AB is equal to B-A or in general the difference between two values is |a-b| where the order doesn't matter, but assuming B is the right side (meaning it should be greater than A) the length should be B-A. in this case A = -5 and B = 3 so the length is 3 - (-5) = 8. The length is 8 so the midpoint is half of that which is 4, now adding 4 to the left side (A) you get -5 + 4 = -1. So the midpoint of AB lies at -1. Now the midpoint of AC can be found using the same process. 7 - (-5) = 12 => 12/2 = 6 => -5 + 6 = 1 so the midpoint of AC is at 1. Now to find how many units from the midpoint AB to AC you just subtract the midpoint of AB from AC. this gives you 1 - (-1) which is 2.
Find the quotient of the complex numbers. Express your answer in trigonometric form. SEE ATTATCHED
The quotient of the complex numbers is 3[cos(240)+ isin(240)] option (D) is correct.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have two complex number is given.
The quotient of the complex numbers:
[tex]= \rm \dfrac{12\left[cos\left(320\right)+isin\left(320\right)\right]}{4\left[cos\left(80\right)+isin\left(80\right)\right]}[/tex]
= 3[cos(320-80)+ isin(320-80)]
= 3[cos(240)+ isin(240)]
Thus, the quotient of the complex numbers is 3[cos(240)+ isin(240)] option (D) is correct.
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Damien and Anna are counting fish. They have 4 tanks with 4 fish and 5 tanks with 2 fish. They are planning to fill an order for 3 fish today. Which expression shows how many fish they will have in stock after the 3 are sold. 4×4+5×2−3 3−4×4+5×2 4+4×5+2−3 4×4×5×2−3
GIVEING BRAINLYEST!
Answer:
The answer is 4×4+5×2−3.
Step-by-step explanation:
This is because, in the original amount, they had 4 tanks with 4 fish and 5 tanks with 2 fish. 4x4 is 16 and 5x2 is 10. Then you add them together to get 26. But, you have to subtract 3 because of the order of 3 fish, which equals 23. The equation 4×4+5×2−3 shows that.
After using a compass and a straightedge to generate this figure, Jeremy claims AABC is an equilateral triangle inscribed in circle O.
How can Jeremy prove his claim?
A.He can show that the measures of arcs AB, AC, and BC are all equal to 60°.
B. He can show that the lengths of segments AB, AC, and BC are all equal to the length of the circle's radius.
C. He can show that the measures of arcs AB, AC, and BC are all equal to 120°.
D.He can show that the lengths of segments AB, AC, and BC are all equal to the length of the circle's diameter.
Answer: C. He can show that the measures of arcs AB, AC, and BC are all equal to 120°.
Step-by-step explanation:
Each angle of an equilateral triangle measures 60°, so by the inscribed angle theorem, each arc created by a pair of adjacent vertices will measure 120°.
i need answer
because this is hella hard and i m trying to cheat but apps trying to make your boy pay and i aint doing it lol
Answer:
C) 12 m
Step-by-step explanation:
b=(1-1/3).(1-1/3).(1-1/4).................(1-1/2004)
When the above complex expression has been simplified the solution to the above expression is = 2003/8016.
What is the formula for solving the above?The formula is given as:
1 - [tex]\frac{1}{n}[/tex] = [tex]\frac{n-1}{n}[/tex]
From the stated express, we have:
(1 - (1/2)) * (1 - (1/3)) * (1 - (1/4)) *( 1 - (1/2004))
→ ((2-1)/2) ((3-1)/3) ((4-1)/4) ((2004 -1)/2004)
→ (1/2) * (2/3) * (3/4) * (2003/2004)
→ [tex]\frac{ 1* 2003}{4*2004}[/tex]
= 2003/8016
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Answer:
When the above complex expression has been simplified the solution to the above expression is = 2003/8016.
What is the formula for solving the above?
The formula is given as:
1 - =
From the stated express, we have:
(1 - (1/2)) * (1 - (1/3)) * (1 - (1/4)) *( 1 - (1/2004))
→ ((2-1)/2) ((3-1)/3) ((4-1)/4) ((2004 -1)/2004)
→ (1/2) * (2/3) * (3/4) * (2003/2004)
→
= 2003/8016
Step-by-step explanation:
Select the two expressions equal to the area of this figure in square centimeters.
Answer:
1.(6*4) + (18*6) + (6*4)
1.(6*10) + (6*6) + (6*10)
Step-by-step explanation:
there are two ways to break this shape into three rectangles:
1.Top right rectangle, Top left rectangle, Bottom long rectangle
2. Left rectangle, Middle square, Right rectangle.
In the race Math , drivers must complete laps of miles each. Dave drove the first laps at mph and the last laps at mph. What was Dave's average speed for the race, in miles per hour
The average speed in approximately 184.62 miles per hour.
We have been given that in the race Math 600, drivers must complete 200 laps of 3 miles each. Dave drove the first 150 laps at 180 mph and the last 50 laps at 200 mph.
First of all, we will find the number of miles in 150 laps and 50 laps as:
150 X 3 miles = 450 miles
50 X 3 miles = 150 miles.
Now, we will find time taken to complete each distance as:
Time = 450/180 =2.5 hr
Time = 150/200 = 0.75 hr
Average speed = 184.62
The average speed in approximately 184.62 miles per hour.
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A horse 24 feet from the center of a merry-go-round makes 32 revolutions. In order to travel the same distance, how many revolutions would a horse 8 feet from the center have to make
Using proportions, the horse 8 feet from the center would have to make 96 revolutions.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
A horse 24 feet from the center of a merry-go-round makes 32 revolutions. If it is 8 feet and wants the same distance, how many revolutions will it need? The rule of three is:
24 feet - 32 revolutions
8 feet - x revolutions
The measures are inverse proportional, hence:
8x = 24 x 32
x = 24 x 32/8
x = 96 revolutions.
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PLEASE HELP ASAP!!!!!!!!
Find the equation of this line.
y
--2
Simplify the fractions.
Enter
k
Answer:
y = - 6/7 x - 10/7
Step-by-step explanation:
Slope = (y2-y1) / (x2-x1)
= 6/-7 = -6/7
y = -6/7 x - a
passes by (-4,2)
2 = 24/7 - a, a = -10/7
y = -6/7 x - 10/7
Which of the Following illustrates how to find the difference of
12a ^2b and —5a^2b?
Answer:
17a^2b
Step-by-step explanation:
Difference = subtracting
12a ^2b - (-5a^2b)
12a ^2b + 5a^2b
17a^2b
succesive approximation
Consider the following equation.
x^2-3x+2= square root √x-2 + 2
Approximate the solution to the equation using three iterations of successive approximation. Use the graph below
25 POINTS PLEASEE :( THIS HAS A TIME LIMIT AND I WILL MARK BRAINLIEST
The Approximate the solution to the equation using three iterations of successive approximation is option b: 27/8.
What is the iterations about?In the equation given:
Note that:
x²-3x+2 = square root √x-2 + 2
Therefore:
x⁴-6x³+9x²= square root x-2
x² = 3.375
Convert 3.35 into fractions and will get 27/8. So, The Approximate the solution to the equation using three iterations of successive approximation is option b: 27/8.
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What is the equation of a circle whose radius is 16 units and center is at (2,-5)?
Answer:
The general equation of the circle is [tex]( {x - a})^{2} + ({y - b})^{2} = {r}^{2} \\ therefore \: we \: \: have \: \\ ( {x - 2})^{2} + (y - ( - 5)) {}^{2} = ({16})^{2} \\ ({x - 2})^{2} + ( {y + 5})^{2} = 256[/tex]HOPE THIS HELPS!Jeff's mother gave him money. he used an equal amount of money each day. at the end of the 7th day, he was left with 1/4 of how much he had at first. at the end of the 9th day, he was left with $10. how much did jeff receive from his mother?
Jeff received 280$ from his mother
Such questions are the simplest as it needs you to just write the conditions accordingly which then simplifies and provides you the answer.
This question can be solved using two tricks which are shown below:-
Trick 1 :
1 – 1/4 = 3/4 (used for the 1st 7 days)
1/4 – 410 (used for 8th and 9th days)
(3/4)/7 ——- (1/4 – 10)/2
(3/4) x (2/7) = 3/14 ——- (1/4 – 10)
1/4 – 3/14 = (7 – 6)/28 = 1/28 ——- 10
28/28 ——- 10 x 28 =$ 280
Trick 2 :
7 days ——- 3/4
1 day ——- 3/28
2 days ——- 6/28
6/28 ——- (1/4 – 10) = 7/28 – 410
1/28 ——- 10
28/28 ——- 10 x 28 = $280
Thus Jeff received 280$ from his mother.
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a doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 99% confident that her estimate is within 3 ounces of the true mean
The sample size that gives 99% confidence level and estimate will be within 3 ounces is 0.7386[tex](standard deviation)^{2}[/tex].
Given confidence level 99% and margin of error is 3 ounces of true mean.
Margin of error is the difference between the actual values and the calculated value of mean.
Sample size is the number of items taken from the population as a sample for research.
We have to find the sample size.
First we have to find the z value for the corresponding p value of 0.99.
z value=2.58
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
3=2.58σ/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]=2.58/3 σ
Squaring both sides
n=[tex]2.58^{2}[/tex]σσ
Hence the sample size needed is 2.58 ([tex](standard deviation)^{2}[/tex].
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HELPPP MEEE PLSSSS meee outttt
Answer: x = 32
Step-by-step explanation:
If m∠ORS = m∠SRQ = 3x - 6 and since the two angles are a linear pair they total 180°. This means half or only one section = 90°
solve for x
3x - 6 = 90
add 6 to both sides
3x = 96
divide each side by 3
x = 32
PLS HELP ITS URGENT I HAVE LIKE A COUPLE QUESTIONS LEFT IM STUCK ON THIS
Answer: 3[tex]i[/tex]
Step-by-step explanation: The reason for this is because [tex]i[/tex] =
[tex]\sqrt{-1}[/tex], and when [tex]\sqrt{-1}[/tex] is multiplied to [tex]\sqrt{9}[/tex], it becomes [tex]\sqrt{-9}[/tex]. Since [tex]\sqrt{9}[/tex] can be simplified to 3, we can just multiply [tex]i[/tex] to 3. This becomes 3[tex]i[/tex].
Hope this helped!
Answer:
3i
Step-by-step explanation:
(1/2) 400t² = 20,000
Answer:
160000
Step-by-step explanation:
if im wrong sorry
Answer:
the answer is 10
Step-by-step explanation:
. Hello !
Because firstly divide 400 by 2
200t²=20,000t²=100....divide both sides by 200t=10....is the value after squaring both sidesA commitee is consist of 6 men and 4 woman ,a sub commitee is made by randomly choosen three commitee members .what is the probability that(a)they are all woman (b) two of them are men
Answer:
a) 1/30
b) 1/6
Step-by-step explanation:
a) There are 10 people total and a group of 3 is being chosen. However, they all need to be women:
For the first person, the probability of it being a woman is 4/10
For the second person, the probability of it being a woman (with the prerequisite that the first was a woman) is 3/9
For the third (with the same requirements) is 2/8
If we multiply all of the fractions together, we get: [tex]\frac{1}{30}[/tex]
b) There are 10 people total and a group of 3 is being chosen. However, two of them need to be men, and 1 needs to be a woman:
For the first person, the probability of it being a man is 6/10
For the second person, the probability of it being a man (with the prerequisite that the first was a man as well) is 5/9
For the third person, the probability of it being a woman (because it can only be two men) is 4/8
If we multiply all the fractions together, we get: [tex]\frac{1}{6}[/tex]
1. Triangle ABC has an angle of ABC = 60°, AB = 3 √3 cm and BC = 4 √3 cm. Determine the length of AC.
Answer:
see below
Step-by-step explanation:
you can use cosine law
(3 sqrt3)^2 + (4 sqrt3)^2 - 2(3 sqrt3)(4sqrt3)cos60 = AC^2
AC = sqrt39
Evaluate if t=2 and x=3: 3(2x² - £)
a.) 102
b.) 30
c.) 48
d.) 12
Evaluate the following
a) 5 ÷ 2 (mod 6)
b) 9 ÷ 7 (mod 7)
c) 3 × 2 ÷ 5 (mod 7)
Neither 2 nor 7 have inverses mod 6 or 7, respectively, so the expressions in (a) and (b) cannot really evaluated... At least we can evaluate (c) :
[tex]5\times3 \equiv 15 \equiv 1 \pmod 7 \\\\ \implies 3\times2\div5 \equiv 3\times2\times3 \equiv18 \equiv \boxed{4 \pmod{7}}[/tex]
Choose the expression that is equivalent to the expression: 2³
a.2x2x2
b.2x3
c.3x3
d.2x2x3
Hello,
2³ = 2 × 2 × 2 → answer A
Petrol costs $1.65 per litre. Calculate how much, correct to the nearest cent, the
petrol will cost Anne for a journey of 120km.
The petrol cost for Anne's journey of 120km is $16.236
How to find the cost for 120 km?Her car has a fuel consumption of 8.2 litres per 100 km .
Therefore,
100 km = 8.2 litres
120 km = ?
cross multiply
volume(litres) = 8.2 × 120 / 100 = 984 / 100 = 9.84 litres
Therefore,
1 litres = 1.65 dollars
9.84 litres = ?
cross multiply
cost of fuel used = 1.65 × 9.84 / 1
cost of fuel used = $16.236
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