The velocity at time t is 56 + 6 m/s, the velocity at time t = 3 seconds is 62 m/s, the acceleration at time t is 0 m/s², and the acceleration at time t = 3 seconds is 0 m/s².
Hi, I can help you with your question involving acceleration, time, and a particle.
(a) To find the velocity at time t (v(t)), take the first derivative of the position function f(t) = 56t + 6t + 9.
v(t) = d(56t + 6t + 9)/dt = 56 + 6
(b) To find the velocity at time t = 3 seconds, plug in t = 3 into the velocity function:
v(3) = 56 + 6 = 62 m/s
(c) To find the acceleration at time t (a(t)), take the first derivative of the velocity function v(t) = 56 + 6:
a(t) = d(56 + 6)/dt = 0
(d) To find the acceleration at time t = 3 seconds, since the acceleration is constant (a(t) = 0), it remains the same for all time:
a(3) = 0 m/s²
So, the velocity at time t is 56 + 6 m/s, the velocity at time t = 3 seconds is 62 m/s, the acceleration at time t is 0 m/s², and the acceleration at time t = 3 seconds is 0 m/s².
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What's the solution?
The solution of the graphs of the equations is; )(6, 3 2/3)
What is a system of equation?A system of equation consists of two or more equations that share the same variables.
The solution of a system of equations obtained graphically can be obtained from the point of intersection of the lines of the graph of the equations
Taking the axis as the lowermost and leftmost white lines, we get;
The points on the function f are (0, 1), and (9, 5)
The slope is; (5 - 1)/(9 - 0) = 4/9
The y-intercept is; (0, 1)
The equation is; y = (4/9)·x + 1
The equation of the line g is; x = 6
Therefore, the point of intersection is; y = (4/9)×6 + 1 = 8/3 + 1 = 11/3 = 3 2/3
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The leaning tower of Pisa is approximately 179 ft in ""height"" and is approximately 16. 5 ft out of plumb. Find the angle at which it deviates from the vertical
The angle at which the leaning tower of Pisa deviates from the vertical is approximately 5.31 degrees.
How to find the angle of deviation?In order to calculate the angle at which the leaning tower of Pisa deviates from the vertical, we can use the concept of tangent function.
First, we need to calculate the distance that the top of the tower is displaced from the vertical axis. This can be done using the Pythagorean theorem, which states that the displacement (d) is equal to the square root of the height of the tower (h) squared plus the amount the tower is out of plumb (p) squared:
d = √(h² + p²)
d = √(179² + 16.5²)
d = 180.14 ft
Next, we can use the tangent function to find the angle of deviation (θ):
tan(θ) = p/h
tan(θ) = 16.5/179
θ = tan⁻¹(16.5/179)
θ ≈ 5.31 degrees
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Consider the construction of a pen to enclose an area. you have 400 ft of fencing to make a pen for hogs. if you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area? shorter side ft longer side ft
The dimensions of the rectangular pen that maximize the area are a shorter side of 100 ft and a longer side of 200 ft along the river.
To maximize the area of the rectangular pen using 400 ft of fencing, with a river on one side of the property, we need to determine the optimal dimensions. Let's denote the length of the pen along the river as 'x' and the width perpendicular to the river as 'y'.
Since the river is on one side, we only need to use the fencing for the other three sides. The total fencing length is 400 ft, so the equation representing the fencing is:
x + 2y = 400
We need to find the maximum area of the pen, which is given by the product of its length and width, i.e., A = xy.
First, we need to express 'x' in terms of 'y' using the fencing equation. From the equation, we get:
x = 400 - 2y
Now, substitute this expression for 'x' in the area equation:
A(y) = (400 - 2y)y = 400y - 2y²
To find the maximum area, we need to find the critical points of this equation by taking the derivative with respect to 'y' and setting it to zero:
dA/dy = 400 - 4y = 0
Solve for 'y':
4y = 400
y = 100 ft
Now, find 'x' using the expression we derived earlier:
x = 400 - 2y
x = 400 - 2(100)
x = 400 - 200
x = 200 ft
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Russ placed $8000 into his credit union account paying 6% compounded semiannually (twice a year). How much will be in Russ’s account in 4 years
Answer:
Step-by-step explanation:
QUESTION IN PHOTO I MARK BRAINLIEST
The value of x for the circle is,
⇒ x = 13.2
We have to given that;
In circle Y,
m arc WX = 142°
m ∠WZX = (8x - 35)°
Since, angle WZX is half the measure of arc WX,
Hence, We get;
⇒ (8x - 35)° = 142 / 2
⇒ 8x - 35 = 71
⇒ 8x = 35 + 71
⇒ 8x = 106
⇒ x = 13.2
Thus, The value of x for the circle is,
⇒ x = 13.2
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Determine the product of 23.5 and 2.3
Answer:
Therefore, the product of 23.5 and 2.3 is 54.05.
Step-by-step explanation:
To determine the product of 23.5 and 2.3, we can use the following steps:
Align the numbers vertically with the ones digit of the second factor (2.3) under the tenths digit of the first factor (3 in 23.5).
23.5
x 2.3
-----
Multiply the ones digit of the second factor by the first factor and write the result below, shifted one place to the right.
23.5
x 2.3
-----
71
Multiply the tenths digit of the second factor by the first factor and write the result below, shifted two places to the right.
23.5
x 2.3
-----
71
470
Add the two partial products together.
23.5
x 2.3
-----
71
470
-----
54.05
Therefore, the product of 23.5 and 2.3 is 54.05.
On the average the time spent by college students every week on computer gaming is 15 hours with a standard deviation 3. a random sample of 350 students were taken. find the best point estimated of the population mean and 95% confidence interval for the population mean
The best point estimate is 15 hours. The 95% confidence interval for the population mean is (14.71, 15.29).
The best point estimate of the population mean is the sample mean, which is 15 hours since it was stated in the problem that the average time spent by college students on computer gaming is 15 hours.
To calculate the 95% confidence interval for the population mean, we use the formula:
CI = [tex]\bar{X}[/tex] ± z*(σ/√n)
where [tex]\bar{X}[/tex] is the sample mean, z is the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96), σ is the population standard deviation (given as 3), and n is the sample size (given as 350).
Plugging in the values, we get:
CI = 15 ± 1.96*(3/√350)
Simplifying, we get:
CI = 15 ± 0.29
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A freezer chest is in the shape of a rectangular prism. Measured on the inside, the chest is 4 feet wide, 2. 5 feet tall, and 2 feet long. How much space is inside to hold frozen foods?
The freezer chest has 20 cubic feet of space inside to hold frozen foods.
To find the amount of space inside the freezer chest, we need to calculate its volume. The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.
Using the measurements given, we can plug them into the formula and calculate:
V = 4 ft x 2.5 ft x 2 ft
V = 20 cubic feet
Therefore, there is 20 cubic feet of space inside the freezer chest to hold frozen foods.
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Assuming that the daily wages for
workers in a particular industry
averages Birr 11. 90 per day and the
standard deviation is Birr 0. 40. If the
wages are assumed to be normally
distributed, determine what percentage
of workers receive wages
A. Between Birr 10. 90 and Birr 11. 90
B. Between Birr 10. 80 and Birr 12. 40
C. Between Birr 12. 20 and Birr 13. 10
D. Less than Birr 11. 00
E. More than Birr 12. 95
Using statistics, we can calculate the following percentages:
A. The percentage of workers who receive wages between Birr 10.90 and Birr 11.90 is approximately 49.38%.
B. The percentage of workers who receive wages between Birr 10.80 and Birr 12.40 is approximately 89.15%.
C. The percentage of workers who receive wages between Birr 12.20 and Birr 13.10 is approximately 22.53%.
D. The percentage of workers who receive wages less than Birr 11.00 is approximately 1.22%.
E. The percentage of workers who receive wages more than Birr 12.95 is approximately 0.47%.
These percentages are obtained by calculating the areas under the normal distribution curve using z-scores and the standard normal distribution table.
We are given that the daily wages in a particular industry are normally distributed with a mean of Birr 11.90 and a standard deviation of Birr 0.40.
A. To find the percentage of workers who receive wages between Birr 10.90 and Birr 11.90, we need to calculate the z-scores for both values and use the standard normal distribution table.
z1 = (10.90 - 11.90) / 0.40 = -2.50
z2 = (11.90 - 11.90) / 0.40 = 0
From the standard normal distribution table, the area to the left of z = -2.50 is 0.0062, and the area to the left of z = 0 is 0.5000. Therefore, the percentage of workers who receive wages between Birr 10.90 and Birr 11.90 is:
0.5000 - 0.0062 = 0.4938, or approximately 49.38%.
B. To find the percentage of workers who receive wages between Birr 10.80 and Birr 12.40, we need to calculate the z-scores for both values.
z1 = (10.80 - 11.90) / 0.40 = -2.75
z2 = (12.40 - 11.90) / 0.40 = 1.25
From the standard normal distribution table, the area to the left of z = -2.75 is 0.0029, and the area to the left of z = 1.25 is 0.8944.
Therefore, the percentage of workers who receive wages between Birr 10.80 and Birr 12.40 is:
0.8944 - 0.0029 = 0.8915, or approximately 89.15%.
C. To find the percentage of workers who receive wages between Birr 12.20 and Birr 13.10, we need to calculate the z-scores for both values.
z1 = (12.20 - 11.90) / 0.40 = 0.75
z2 = (13.10 - 11.90) / 0.40 = 3.00
From the standard normal distribution table, the area to the left of z = 0.75 is 0.7734, and the area to the left of z = 3.00 is 0.9987. Therefore, the percentage of workers who receive wages between Birr 12.20 and Birr 13.10 is:
0.9987 - 0.7734 = 0.2253, or approximately 22.53%.
D. To find the percentage of workers who receive wages less than Birr 11.00, we need to calculate the z-score for this value.
z = (11.00 - 11.90) / 0.40 = -2.25
From the standard normal distribution table, the area to the left of z = -2.25 is 0.0122. Therefore, the percentage of workers who receive wages less than Birr 11.00 is approximately:
0.0122, or approximately 1.22%.
E. To find the percentage of workers who receive wages more than Birr 12.95, we need to calculate the z-score for this value.
z = (12.95 - 11.90) / 0.40 = 2.63
From the standard normal distribution table, the area to the left of z = 2.
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A box of tissues is shaped like a rectangular prism and has a volume of 288 cubic inches.
We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.
How to find the volume?To find the dimensions of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is:
V = l x w x h
where V is the volume, l is the length, w is the width, and h is the height.
We know that the volume of the box of tissues is 288 cubic inches. We want to find the length, width, and height.
We can start by listing all the factors of 288:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
We can see that some of these factors are repeated, so we can pair them up to find the dimensions of the rectangular prism.
For example, we can pair 2 and 144, since 2 x 144 = 288. This means that the length of the rectangular prism could be 144 inches and the width could be 2 inches.
We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.
We can continue pairing the factors until we find all the possible combinations. Once we have all the possible combinations, we can choose the one that makes the most sense based on the context of the problem (in this case, the dimensions of a box of tissues).
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Pleasee help
f(x) = 3x² - 7x + 4
f(2)= [?]
Answer:
f(2) = 2
Step-by-step explanation:
We are given
f(x) = x² - 7x + 4
To find f(2), just plug in 2 wherever you see an x and simplify
f(2) = 3 · 2² - 7 · 2 + 4
= 3 · 4 - 7 · 2 + 4
= 12 - 14 + 4
= 2
Each deck of cards in a a box has a weight of 3.4 oz.the box contains 64 decks of cards.what is the total weight of the cards inside the box?teh oz are rounded to the nearest oz
The total weight of the cards inside the box is approximately 217.6 oz.
Each deck of cards weighs 3.4 oz, and there are 64 decks of cards in the box. Therefore, the total weight of the cards inside the box is 3.4 oz/deck x 64 decks = 217.6 oz. As the answer needs to be rounded to the nearest ounce, we round 217.6 to the nearest ounce, which gives us 218 oz.
However, the question asks for the weight of the cards, which is only accurate to one decimal place. Therefore, we round 217.6 to one decimal place, which gives us 217.6 oz. Hence, the total weight of the cards inside the box is approximately 217.6 oz.
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A particle is moving along the x-axis on the interval 0 ≤ t ≤ 10, and its position is given by x of t equals one third times x cubed minus five halves times x squared plus 6 times x minus 10. at what time(s), t, is the particle at rest?
answers:
t = 0
t = 2 and 3
t = 1 and 5
t = 6
The particle is at rest at t = 3. Therefore, the particle is at rest at t = 2 and t = 3.
To find when the particle is at rest, we need to find the values of t where the velocity of the particle is zero.
The velocity function is obtained by taking the derivative of the position function: v(t) = x'(t) = x²(t) - 5x(t) + 6
Setting v(t) = 0, we get a quadratic equation in x(t): x²(t) - 5x(t) + 6 = 0. Factoring the quadratic, we get: (x(t) - 2)(x(t) - 3) = 0
Therefore, x(t) = 2 or x(t) = 3. We now need to check which values of t correspond to these values of x(t).
At x(t) = 2, we get: v(t) = x²(t) - 5x(t) + 6 = 4 - 10 + 6 = 0. Thus, the particle is at rest at t = 2. At x(t) = 3, we get: v(t) = x²(t) - 5x(t) + 6 = 9 - 15 + 6 = 0
Thus, the particle is at rest at t = 3. Therefore, the particle is at rest at t = 2 and t = 3.
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what is 2X (2² + sin 3) = ?
2X (2² + sin 3) can be simplified as 8X + 2X sin 3
How to simplify the functionTo solve the expression, we will first have to compute the values inside the parentheses and then apply the given operations. so we Calculate the values inside the parentheses by multiplying across the bracket:
2² is equal to 4, and sin 3 is a trigonometric function that returns the sine of the angle 3
Therefore, the expression 2X (2² + sin 3) simplifies to:
2X (4 + sin 3)
or
8X + 2X sin 3
where X is an unknown variable and sin 3 is a trigonometric function
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Answer:
Solution
verified
Verified by Toppr
I=∫e
2x
sin3xdx
I=sin3x∫e
2x
dx−∫(
dx
d
sin3x∫e
2x
dx)dx
I=sin3x
2
e
2x
−∫
2
3
cos3xe
2x
dx
I=sin3x
2
e
2x
−
2
3
∫cos3x∫e
2x
dx−∫(
dx
d
cos3x∫e
2x
dx)dx
I=sin3x
2
e
2x
−
2
3
[
2
cos3xe
2x
−∫(−sin3x
2
e
2x
)dx]
I=
2
sin3xe
2x
−
4
3
cos3xe
2x
−
4
3
∫sin3xe
2x
dx
I=
2
sin3xe
2x
−
4
3
cos3xe
2x
−
4
3
I
I+
4
3
I=
2
sin3xe
2x
−
4
3
cos3xe
2x
4
7I
=
4
2e
2x
sin3x−3cos3xe
2x
I=
7
e
2x
(2sin3x−3cos3x)
∴∫e
2x
sin3dx=
7
e
2x
(2sin3x−3cos3x)
Solve any question of Integrals with:-
Patterns of problems
Patterns of problems
>
Solve :∫e xe e xe e e x
dx
Medium
View solution>Solve:-∫ a 2b 2(a 2 −b 2) 2
Step-by-step explanation:
pls brain
If my refrigerator uses 300 watts when the motor is running, and the motor runs for 30 minutes of every hour, then how much energy does it use per day? How many BTU of energy would that be equal to?
The amount of energy the refrigerator uses per day is 3.6 kilowatt-hour (kWh)
The refrigerator energy usage per day in BTU is 12283.704 BTU
What is the BTU?The BTU is an acronym for the British Thermal Unit, which is a measure of heat, which is specified in energy units.
The duration the refrigerator fan runs per hour = 30 minutes
The amount of energy the refrigerator uses every hour = 300 watts × 0.5 hour/hour = 150 watts
The amount of energy the refrigerator uses per hour = 150 watt-hour
The amount of energy the refrigerator uses per day = 24 × 150 watt-hour = 3600 watt-hour = 3.6 kilowatt-hour (kWh)1 kWh = 3412.14 BTU
Therefore;
3.6 kWh = 3.6 × 3412.14 BTU = 12283.704 BTUThe amount of energy in BTU the refrigerator uses per day = 12283.704 BTU
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Find the surface area of the square pyramid (above) using its net (below).
The surface area of the square pyramid is approximately 41.83 cm².
To start with, let's define a square pyramid.
The slant height of the pyramid can be found using the formula:
l = √(h² + (s/2)²)
where h is the height of the pyramid and s is the length of one side of the base.
Plugging in the given values, we get:
l = √(7² + (4/2)²) = √(57)
Now that we know the slant height, we can find the area of each triangular face using the formula:
A = (1/2)bh
where b is the base of the triangle, and h is the height of the triangle.
Plugging in the given values, we get:
A = (1/2)(4)(√(57)) = 2√(57)
Since there are four triangular faces, the total area of all the triangular faces is:
4A = 8√(57)
Finally, we can find the total surface area of the pyramid by adding the area of the square base to the area of all the triangular faces:
surface area = 16 + 8√(57) = approximately 41.83 cm²
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Complete Question:
Find the surface area of the square pyramid where the base is 4cm and the height is 7cm.
help pls. my mom is mad bc i don’t have this done.
_______________________________
A = L × B = 7.3cm × 9cm= 65.7cm= 65.7cm × 90m= 5,913m²_______________________________
HELPPP SOMEBODY PLEASEEE WITH THIS MATHHHH
The correct statement is given as follows:
The function g(t) reveals the market value of the house increases by 3.6% each year.
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter b for this problem is given as follows:
b = 1.036.
As the parameter b has an absolute value greater than 1, the function is increasing, with a rate given as follows:
1.036 - 1 = 0.036 = 3.6% a year.
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Explain the role of the brackets, and how they effects the sum. Provide the answer for both sums. Sum 1 Sum 2 10 + 7 – 5 + 3 = 10 + 7 – (5 + 3) =
The role of the brackets, and how they effects the sum is given as the inside signs get changed after the opening of the bracket.
The associative property of addition is a mathematical statement that asserts that the arrangement of three or more integers does not affect their total. This indicates that no matter how the numbers are organised, the total of three or more integers remains the same.
The associative property of addition is a mathematical principle that asserts that when adding three or more integers, the amount obtained is constant regardless of how the numbers are grouped. Grouping here refers to where the brackets are positioned.
The sum for the 1st term is 10 + 7 – 5 + 3 = 15
The sum of the 2nd term is 10 + 7 – (5 + 3) = 17 - 8 = 9
Here, the bracket used made all the difference so after opening of the bracket the sign inside changed which impacted the summation of the terms above.
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(2x−3)(2x−3)=left parenthesis, 2, x, minus, 3, right parenthesis, left parenthesis, 2, x, minus, 3, right parenthesis, equals
The expression (2x-3)(2x-3) is equal to (2x-3)^2.
To expand the expression (2x-3)(2x-3), we can use the FOIL method (which stands for First, Outer, Inner, Last).
Multiplying the first terms of each binomial, we get 2x times 2x, which is 4x^2.
Multiplying the outer terms, we get -3 times 2x, which is -6x.
Multiplying the inner terms, we get -3 times 2x again, which is also -6x.
Multiplying the last terms of each binomial, we get -3 times -3, which is 9.
Combining like terms, we get 4x^2 - 12x + 9.
Therefore, (2x-3)(2x-3) is equal to (2x-3)^2, which is equivalent to 4x^2 - 12x + 9.
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Question
What is the scale factor for the similar figures below?
The value of the scale factor for the similar figures is 1/2
What is the scale factor for the similar figures?From the question, we have the following parameters that can be used in our computation:
The similar figures
The corresponsing sides of the similar figures are
Original = 8
New = 4
Using the above as a guide, we have the following:
Scale factor = New /Original
substitute the known values in the above equation, so, we have the following representation
Scale factor = 4/8
Evaluate
Scale factor = 1/2
Hence, the scale factor for the similar figures is 1/2
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A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likel voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0. 014, 0. 064). What was the difference (pre- debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate?
The difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.
The range of the 95% confidence interval for the actual difference between the proportions of probable voters who would support this candidate before and after the debate was (-0.014, 0.064). To find the difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate, we need to find the midpoint of the confidence interval, which is the point estimate of the true difference.
In the given question, the interval is (-0.014, 0.064), then the expression for the likely difference is
(0.064 + (-0.014))/2 = 0.050/2
= 0.025
Hence, the difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.
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Set up triple integrals in cylindrical coordinates that compute the volumes of the following regions (do not evaluate the integrals): a) the region A bounded by the sphere x2 + y2 + z2 12 and the paraboloid x2 + y2 + z = 0, b) the region B in the first octant bounded by the surfaces z = x2 and x2 + y2 + z = 1, and c) the region C inside both spheres x2 + y2 +(z – 2)2 = 16 and x2 + y2 + 2 = 16
a) To find the volume of the region A bounded by the sphere x^2 + y^2 + z^2 = 12 and the paraboloid z = x^2 + y^2, we can use cylindrical coordinates.
In cylindrical coordinates, the equations of the surfaces become:Sphere: ρ^2 + z^2 = 12Paraboloid: z = ρ^2The region A is bounded by the sphere and the paraboloid, so we need to integrate over the range of ρ, φ, and z that satisfies both equations. The limits for ρ are 0 to √(12 - z^2), the limits for φ are 0 to 2π, and the limits for z are 0 to 4. So the triple integral for the volume of region A in cylindrical coordinates is:∫∫∫ ρ dρ dφ dz, where the limits of integration are ρ: 0 to √(12 - z^2), φ: 0 to 2π, and z: 0 to 4.b) To find the volume of the region B in the first octant bounded by the surfaces z = x^2 and x^2 + y^2 + z = 1, we can again use cylindrical coordinates. In cylindrical coordinates, the equations of the surfaces become:z = ρ^2 (since we are in the first octant where x and y are non-negative)z = 1 - ρ^2The limits for ρ are 0 to 1, and the limits for φ are 0 to π/2. So the triple integral for the volume of region B in cylindrical coordinates is:∫∫∫ ρ dρ dφ dz, where the limits of integration are ρ: 0 to 1, φ: 0 to π/2, and z: ρ^2 to 1 - ρ^2.c) To find the volume of the region C inside both spheres x^2 + y^2 + (z - 2)^2 = 16 and x^2 + y^2 + 2 = 16, we can once again use cylindrical coordinates. In cylindrical coordinates, the equations of the surfaces become:Sphere 1: ρ^2 + (z - 2)^2 = 16Sphere 2: ρ^2 = 12The region C is bounded by both spheres, so we need to integrate over the range of ρ, φ, and z that satisfies both equations. The limits for ρ are 0 to 2√3, the limits for φ are 0 to 2π, and the limits for z are 2 - √(16 - ρ^2) to 2 + √(16 - ρ^2). So the triple integral for the volume of region C in cylindrical coordinates is:∫∫∫ ρ dρ dφ dz, where the limits of integration are ρ: 0 to 2√3, φ: 0 to 2π, and z: 2 - √(16 - ρ^2) to 2 + √(16 - ρ^2).
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find scale factor of the dilation
Answer:
Step-by-step explanation:
The original image is the the black one. The dilated image is blue. It got bigger. So it is an enlargment.
Each side got bigger by times 2
So the dilation is 2
what percentage is equivalent to 96/160
Answer:
60%
Step-by-step explanation:
Take 96 and divide it by 160.
(easier if done on a calculator.)
For example: Find A/B as a percentage: take "A" and divide it by "B"
Binary operations
if a * b = a - 2b, evaluate
5 * 2
can someone help ?
In the given binary operation, a and b are two numbers, and the operation is defined as a * b = a - 2b.
How to perform binary operation?
Binary operations are mathematical operations that take two operands and produce a single result. In this problem, we are given a binary operation "*". The operation is defined such that for any two numbers a and b, a * b = a - 2b.
We are then asked to evaluate 5 * 2 using this operation. To do so, we substitute a = 5 and b = 2 into the expression a * b = a - 2b:
5 * 2 = 5 - 2(2)
Simplifying the right-hand side of the equation, we get:
5 * 2 = 5 - 4
5 * 2 = 1
Therefore, 5 * 2 equals 1 when the binary operation is defined as a * b = a - 2b.
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HELP PLS!! I AM LACKING BRAIN CELLS RN!! :(
Answer:
17.5 feet
Step-by-step explanation:
The picnic are shortest side is 5 units long on the scale drawing
Since each unit on the scale drawing is 1 inch, the shortest side length on the drawing is 5 inches
Each inch on the drawing corresponds to an actual size of 3.5 feet
Therefore 5 inches corresponds to 5 x 3.5ft = 17.5 feet
Therefore the actual length of the shortest side of the picnic area is 17.5 feet
I need to know how to solve this equation
Answer:
3/y
Step-by-step explanation:
15x÷5xy
15x/5xy....you will cancel x by x and simplify by 5(GCF)
3/y ...... it is the simplify form of the given equetion.
A paper pulp company has discovered their cost and revenue functions for each day: C(x) = 2x2 - 250x + 525 and R(x) = -3x2 + 750x + 125, where x is the amount of pulp in tons. If they want to make a profit, what is the range of pulp in tons per day that they should produce? Round to the nearest tenth of a ton which would generate profit
Based on the cost and revenue function, if they want to make a profit, the range of pulp in tons per day that they should produce is between 152.6 and 152.8 tons per day.
To find the range of pulp in tons per day that will generate profit, we need to set the profit function equal to zero and solve for x. The profit function P(x) is given by:
P(x) = R(x) - C(x)
Substituting the given revenue and cost functions, we get:
P(x) = -3x^2 + 1000x - 400
Setting P(x) = 0, we can solve for x using the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
Plugging in the values from our profit function, we get:
x = [-(1000) ± sqrt((1000)^2 - 4(-3)(-400))] / 2(-3)
Simplifying, we get:
x = [1000 ± sqrt(1000000 + 4800)] / 6
x = [1000 ± sqrt(1004800)] / 6
x ≈ 152.7 or x ≈ 55.6
Since we're looking for the range of pulp in tons per day that will generate profit, we only want the positive solution, which is approximately 152.7 tons per day. Therefore, the company should produce between 152.6 and 152.8 tons per day to generate profit, rounded to the nearest tenth of a ton.
Note: The question is incomplete. The complete question probably is: A paper pulp company has discovered their cost and revenue functions for each day: C(x) = 2x^2 - 250x + 525 and R(x) = -3x^2 + 750x + 125, where x is the amount of pulp in tons. If they want to make a profit, what is the range of pulp in tons per day that they should produce? Round to the nearest tenth of a ton which would generate profit.
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TASK CARD 1
-2x³
a) Write the polynomial in standard form
b) Determine the degree
c) Determine the lead coefficient
Answer: The given polynomial is -2x³.
a) To write the polynomial in standard form, we arrange the terms in descending order of degrees:
-2x³
b) The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the degree of the polynomial is 3.
c) The lead coefficient is the coefficient of the term with the highest degree. In this case, the lead coefficient is -2.
Step-by-step explanation:
