Answer:
[tex]=\frac{81m^2n^5}{8}[/tex]
Step-by-step explanation:
One is given the following expression:
[tex]\frac{(3m^-^1n^2)^4}{(2m^-^2n)^3}[/tex]
Simplify, distribute the exponent outside of the parenthesis by the terms inside of it. Remember, when a value that already has an exponent is raised to another exponent, the equivalent of these two values is multiplying the exponents together. Use this property here:
[tex]=\frac{(3m^-^1n^2)^4}{(2m^-^2n)^3}[/tex]
[tex]=\frac{3^4m^(^-^1^)^(^4^)n^(^2^)^(^4^)}{2^3m^(^-^2^)^(^3^)n^3}[/tex]
[tex]=\frac{81m^-^4n^8}{8m^-^6n^3}[/tex]
Now simplify this fraction. Keep in mind that a fraction is another way of representing the operation of division. When one wants to divide terms raised to an exponent, one must make sure that these terms have a like base. Then one will subtract the exponents from each other. Do this step with terms that have a variable base:
[tex]=\frac{81m^-^4n^8}{8m^-^6n^3}[/tex]
[tex]=\frac{81m^(^-^4^)^-^(^-^6^)n^(^8^)^-^(^3^)}{8}[/tex]
[tex]=\frac{81m^-^4^+^6n^8^-^3}{8}[/tex]
[tex]=\frac{81m^2n^5}{8}[/tex]
Use the special angles to evaluate: a) cosec 60° cot 30° + cos 45º cosec 45° 2
Answer:
the required answer is 4√2+1/2√2
I need help with this question pls!
Answer:
Answer is D
Step-by-step explanation:
cuh s
13 + {16 + 2 -[25 + 45) x 3] + 9}
Answer: -170
Concept:
When encountering questions that require multiple steps of the calculation, it is suggested to follow the PEMDAS.
ParenthesisExponentsMultiplicationDivisionAdditionSubtractionSolve:
**Disclaimer** I assume that it is supposed to be (25 + 45). If it was, then you may refer to my answer. If the ")" after 45 is just a typo, you may point it out and I will redo it.
Given expression
13 + {16 + 2 - [(25 + 45) × 3] + 9}
Do the parenthesis of the inner most
=13 + {16 + 2 - [70 × 3] + 9}
=13 + {16 + 2 - 210 + 9}
Do addition first, then subtraction
=13 + {18 - 210 + 9}
=13 + {27 - 210}
=13 - 183
=-170
Hope this helps!! :)
Please let me know if you have any questions
I need help asap!!Explain how to do the problem
Answer:
Step-by-step explanation:
the scale factor is 2. one length is 10, and the other is 5. pythagorean therom approved.
6a3-5b2+2c2-3a2bc if a=5 b=2c=-1
Which label on the cone below represents the vertex?
D
B
А.
С
ОА
D
Mark this and stum
Save and Exit
The area of a square piece of land is 784metersquared .What is the perimeter
Answer:
112 m
Step-by-step explanation:
The area (A) of a square is
A = s² ( s is the length of side )
Here A = 784 , then
s² = 784 ( take the square root of both sides )
s = [tex]\sqrt{784}[/tex] = 28
Then
perimeter = 4s = 4 × 28 = 112 m
Answer:
112m
Step-by-step explanation:
the area of the square is 784m^2 so the square root of 784 would give us the length of the sides(since it's a square the length of each sides are equal). √784 would give 28m. 28 m is the length of each sides..so now the perimeter would be the addition of each sides which in case would be 4 times 28 because it's a square. 4 times 28 gives 112m.
A walking trail is 1,580.76 feet long. A lake is located 70.62 feet away from the end of the trail. What is the total distance from the start of the trail to the lake? 1,510.14 feet 1,651.38 feet 2,286.96 feet 8,642.76 feet
Answer:[tex]1651.38\ ft[/tex]
Step-by-step explanation:
Given
A walking trail is [tex]1580.76\ ft[/tex] long and a lake is located [tex]70.62\ ft[/tex] away from end of the trail
The distance from the start of the trail to the lake is the sum of the length of the trail and lake
[tex]\Rightarrow 1580.76+70.62\\\Rightarrow 1651.38\ ft[/tex]
Answer:
B
Step-by-step explanation:
Nuclear Power is a perfect example of exponential relations. Canada produces over half of its electricity using nuclear reactors. One of the major problems associated with nuclear power generation is the radioactive waste. Currently all nuclear waste is stored on site at the power plant and there is no solution for the long term waste.
A) What would you do with the long term waste?
B) How would you take care of Canada’s energy needs for the future?
Nuclear waste is a long term waste and is a major problem the world is facing regarding its disposal.
Answer :
Nuclear fission is exponential. This is known as chain reaction and a number of uranium atoms are fission together to increase exponentially.
Canada, for example produces electricity using the process of fission process in its nuclear reactors.
The nuclear waste includes :
used reactor fuel, uranium mill tailings and other radioactive wastes.These wastes remain radioactive and are dangerous for the human health.
A).
The long term nuclear waste are stored in deep excavations and covered with rocks and mud. They are also stored in some high density and thick cylinders and remained isolated in the dump yard from the people and nature.B).
Most of the energy requirement of Canada can be taken care off by using wind energy. Canada is planning to set up wind energy mills in most of its part and generate electricity from it.Canada has also installed several solar power projects which is clean and can help the people to use this solar energy to produce electricity.Learn More :
https://brainly.com/question/1013815
find the slope of the tangent line of the curve r = cos (3theta) at theta = pi / 3
The slope of the tangent line to the curve at a point (x, y) is dy/dx. By the chain rule, this is equivalent to
dy/dθ × dθ/dx = (dy/dθ) / (dx/dθ)
where y = r(θ) sin(θ) and x = r(θ) cos(θ). Then
dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)
dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)
Given r(θ) = cos(3θ), we have
dr/dθ = -3 sin(3θ)
and so
dy/dx = (-3 sin(3θ) sin(θ) + cos(3θ) cos(θ)) / (-3 sin(3θ) cos(θ) - cos(3θ) sin(θ))
When θ = π/3, we end up with a slope of
dy/dx = (-3 sin(π) sin(π/3) + cos(π) cos(π/3)) / (-3 sin(π) cos(π/3) - cos(π) sin(π/3))
dy/dx = -cos(π/3) / sin(π/3)
dy/dx = -cot(π/3) = -1/√3
A plane took off at a point that is 42 meters from the control tower. The flight path takes the plane over the control tower that is 98 meters high. After traveling 83 meters, which statement is most accurate?
Answer:
D). The plane needs to be about 27 meters higher to clear the tower.
Step-by-step explanation:
Given that,
Height of the tower = 98 m
Distance traveled by plane = 83 m
The distance of the take-off point from the tower = 42m
This shows that it forms a right-angled triangle with
Base(B) = 42m
Hypotenuse(H) = 83m
To find,
The height of this triangle(x) = ?
Using Pythagoras theorem, we know that,
B^2 + x^2 = H^2
⇒ x^2 = H^2 - B^2
⇒ x^2 = (83)^2 - (42)^2
⇒ x^2 = 6889 - 1764
⇒ x = [tex]\sqrt{6889 - 1764}[/tex]
∵ x = 71.58 m
Thus, the height difference from the position of the plane to the tower = 98 - 71.58
= 26.42 m
Thus, option D i.e. 'the plane's height must be 27m above the tower' is the correct answer.
Rita and Tina each make $11 an hour working as cashiers at a supermarket. Last week, Rita worked r hours while Tina worked t hours. Rita also worked overtime hours during the week, for which she was paid an extra $32 flat wage. Which expressions represent the total weekly wages of both Rita and Tina?
Rita and Tina's total weekly wages can be represented as
Answer:
Step-by-step explanation:
11t= tina
Rita= 11r+32
Full working out for this question please.
Answer:
B. 3.2
Step-by-step explanation:
5 companies have 0 computers.
10 companies have 1 computer.
10 companies have 2 computers.
30 companies have 3 computers.
25 companies have 4 computers.
20 companies have 5 computers.
To find mean:
0 x 5 = 0
10 x 1 = 10
10 x 2 = 20
30 x 3 = 90
25 x 4 = 100
20 x 5 = 100
100 + 100 + 90 + 20 + 10 + 0 = 320
20 + 25 + 30 + 10 + 10 + 5 = 100
100 companies were surveyed.
100 companies use 320 computers in total.
320 / 100 = 3.2
Find the area and the circumference of a diameter 8yd Use the value 3.14 for π, and do not round answer
Answer:
circumference = 25.12 yards
area = 50.24 yards squared or yd^2
Step-by-step explanation:
circumference = pi * d
3.14 * 8 =
25.12
area = pi* r^2
r = 1/2 of d = 4
area = pi * 16
3.14 * 16 =
50.24
Answer:
Area: 50.24yds^2 Circumference: 25.12yds
Step-by-step explanation:
Area: The formula for area of a circle is a = πr^2.
The radius (r) of the circle is 4yds because it is half the length of the diameter. The equation would like like this:
A = (3.14)(4)^2
A = (3.14)(16)
A = 50.24yds
Circumference: The formula for circumference is 2πr. We already know all of the variables so we can plug them in.
C = 2(3.14)(4)
C = 25.12yds
Hope this helps
can you help me please.
Answer:
45
Step-by-step explanation:
1st term is 2
2nd term is 3
3rd term is 4
.
.
.
nth term is (n+1)
because common difference is 1, so 1st term = 1 + common difference = 1+1 = 2, for any term, we take n + common difference, so n+1
putting n = 44,
44th term is 44+1 = 45
Answered by GAUTHMATH
HI I NEED HELP WITH THIS QUESTION ASAP!!!!!! ITS URGENT PLEASE HELP
A group of rowdy teenagers near a wind turbine decide to place a pair of
pink shorts on the tip of one blade. They notice that the shorts are at its
maximum height of 16 metres at t = 10 s and its minimum height of 2 metres at
t = 25 s.
a) Determine the equation of the sinusoidal function that describes
the height of the shorts in terms of time.
b) Determine the height of the shorts at exactly t = 10 minutes, to
the nearest tenth of a metre.
a) The sinusoidal function is y = 7·sin(π/15(t - 2.5)) + 9
b) The height of the shorts at t = 10 minute is approximately 6 meters
The above answers were arrived at as follows
a) The general form of a sinusoidal equation is presented as follows;
y = A·sin(B(t - h)) + k
Where;
A = The amplitude of the graph of the function
The period, T = 2·π/B
h = The horizontal shift
k = The vertical shift
The maximum height of the blade = 16 meters
The minimum height of the blade = 2 meters
The time the blade moves from maximum height to minimum height = 25 s - 10 s = 15 s
Therefore, the time it takes the blade to move from maximum height to minimum height, the period, T= 2 × 15 s = 30 s
Therefore;
B = 2·π/30 = π/15
B = π/15
When B·(t - h) = π/2, t = 10
Therefore;
(π/15)·(10 - h) = π/2
10 - h = 15/2
h = 10 - 15/2 = 2.5
The horizontal shift, h = 2.5
The amplitude, A = (Max - Min)/2
∴ A = (16 - 2)/2 = 7
A = 7
The vertical shift, k = Min - (-Amplitude)
∴ k = 2 - (-7) = 9
The vertical shift, k = 9 Up
Therefore, the equation of the sinusoidal equation that describes the height of shorts in terms of time is given by plugging in the values of the variables, A, B, h, and k to get the following equation;
y = 7·sin(π/15·(t - 2.5)) + 9
b) The height of the shorts at exactly, t = 10 minutes = 600 seconds, is given as follows;
y = 7·sin(π/15·(t - 2.5)) + 9
10 minutes = 600 seconds
When t = 10 minutes = 600 seconds
∴ y = 7·sin(π/15(600 - 2.5)) + 9 = 5.5 ≈ 6
The height of the shorts at exactly t = 10 minutes ≈ 6 meters.
Get more information on sinusoidal functions here;
https://brainly.com/question/16820464
Solve the equation. Then check your solution.
x - 4 = 2
a.–6
c.7
b.6
d.–2
Please select the best answer from the choices provided
A
B
C
D
Answer:
b) 6
Step-by-step explanation:
x - 4 = 2
x = 2 + 4
x = 6
help me with the question of O.math
Answer:
By comparing of elements of both matrices, we will get,
[tex]x + y = 5 \: \: \: - - - (1) \\ \sf \: and \\ x - 2 = 3 \\ = > x = 3 + 2 \\ = > \green{ \boxed{x = 5}} \\ \\ so \: \: from \: eqn.(1) \\ 5 + y = 5 \\ = > y = 5 - 5 \\ = > \green{ \boxed{ y = 0}}[/tex]
[tex]\large \green{ \: \: \: \: \boxed{\boxed{\begin{array}{cc} \sf \: mark \: \\ me \: as\\ \bf \: brainliest \: \end{array}}}} \\ [/tex]
carly walks 30 feet in seven seconds. At this rate, how many minutes will it take for carly to walk a mile if there are 5,280 feet in one mile?
Answer:
20.53 minutes
Step-by-step explanation:
Speed = Distance/Time = 30/7
Time = Distance / Speed
= 5280/30/7
= 1232 seconds / 60 = 20.53 minutes
Answered by Gauthmath
Find the number of bit strings that satisfies the given conditions. The bit strings of length 11 having at least four 1s
Answer:
Step-by-step explanation:
Tìm x
(x+1)^2=x+1
Help me!!Pls
what is a fraction between 1/31 and 1/22?
__________
Step-by-step explanation:
Q = { 1/31 < x < 1/22 }
Q = { 1/30, 1/29, 1/28, 1/27, 1/26, 1/25, 1/24, 1/23 }
#mathisfun
Concrete is made by mixing screenings cement and sand in the ratio 3:1:15. How much sand would be needed
to make 125 tonnes of concrete?
Answer:
98.7 tonnes of sand.
Step-by-step explanation:
First find the total :
3 + 1 + 15 = 19
if 19 = 125 tonnes,
what about 15 = ?
(cross multiply)
[tex] \frac{15}{19} \times 125[/tex]
= 1875 ÷ 19
= 98.68
(rounded off to 1 decimal place)
= 98.7 tonnes of sand.
Solve for x.
------------------------------------------------------------
On a coordinate plane, a curved line with a minimum value of (negative 2.5, negative 12) and a maximum value of (0, negative 3) crosses the x-axis at (negative 4, 0) and crosses the y-axis at (0, negative 3).
Which statement is true about the graphed function?
F(x) < 0 over the interval (–∞, –4)
F(x) < 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –4)
Answer:
f(x) > 0 over the interval (–∞, –4)
Step-by-step explanation:
We know that:
Our curve has a minimum at (-2.5, -12)
Our curve has a maximum at (0, - 3) (I assume that is a local maximum).
We know that the curve crosses the x-axes at (-4, 0)
We know that the curve crosses the y-axis at (0, -3)
Notice that when our curve crosses the x-axis at (-4, 0), it goes from above the axis to below the axis.
How we know this?
Remember that "crossing" the x-axis means that the sign of f(x) changes.
At the value x = -2.5 (which is larger than x = -4) the function is negative.
f(-2.5) = -12
and:
f(-4) = 0
So we can see that after f(x) crosses the x-axis at x = -4, the function is negative.
This means that before that point, the function must be positive.
So for values of x smaller than -4, the function should be larger than zero.
f(x) > 0 if x < -4
From this, we can conclude that in the range (-∞, –4), the function is above the x-axis.
Then we would write this as:
f(x) > 0 over the interval (–∞, –4)
The correct option is the last option.
Answer:
Its D
Step-by-step explanation:
100 points please help... i think the answer is 288 pie squared but not sure
What is the surface area of a dome (a half sphere) with a radius of 12 meters?
576 pie meters squared
48 pie meters squared
288 pie meters squared
96 pie meters squared
9514 1404 393
Answer:
(c) 288π m²
Step-by-step explanation:
The area of a sphere is found using the formula ...
A = 4πr²
Then the area of a half-sphere with radius 12 m will be ...
A = (1/2)(4π)(12 m)² = 288π m²
Doubling x and adding 3 is the same as tripling x and adding 1
Answer:
2x + 3 = 3x + 1
x = 2
hope that helps ✌
Answer my question
im being timed
Answer:
the third one
Step-by-step explanation:
→
If u vector= a vector-b vector and v vector= a vector+b vector and magnitude of a = b = 2, then magnitude of u vector multiply v vector =???
Answer:
zero
Step-by-step explanation:
[tex]\overrightarrow{u} = \overrightarrow{a} - \overrightarrow{b}\\\\\overrightarrow{v}= \overrightarrow{a} + \overrightarrow{b}\\\\\overrightarrow{u} . \overrightarrow{v} = a^2 - b^2 \\\\\overrightarrow{u} . \overrightarrow{v} = 2^2 - 2^2 = 0[/tex]
So, vector u and vector v are perpendicular to each other.
Determine the 3 digit chopping and rounding approximately of the number 0.9
Answer:
We want to "chop and round" the periodic number 0.9 at 3 digits.
First, remember that we can write our periodic number as:
0.9 = 0.9999...
Such that the nine repeats infinitely.
Now we want to chop it at the third digit, and then round.
To chop at the third digit we just "cut" the number at the third digit after the decimal point, we will get:
0.9 ≈ 0.999
Now we round.
Remember that to round a number, we need to look at the last digit after the decimal point.
If the last digit is 5 or larger, we round up, adding 1 to the previous decimal.
If the last digit is 4 or smaller, we round down, don't adding anything to the previous decimal.
in our number:
0.999
The last digit is a 9, so we round up.
Then we add "1" to the previous decimal
but the previous decimal is a 9, so when we add 1, it will transform into a 10.
So it also adds one to the previous decimal, which also is a 9, so the process repeats, this time adding 1 to the decimal to its left, in this case, that decimal will be the first decimal at the left of the decimal point.
So after rounding, we will get:
0.999 ≈ 1
Then we can conclude that:
he 3 digit chopping and rounding approximately of the number 0.9 is 1"