The approximation of 1 = integral (x – 3)e** dx by composite Trapezoidal rule with n=4 is: -25.8387 4.7846 -5.1941 15.4505
Answers
The approximation of the integral I is -5.1941 using the composite Trapezoidal rule with n = 4.
We need to divide the interval [0, 2] into subintervals and apply the Trapezoidal rule to each subinterval.
The formula for the composite Trapezoidal rule is given by:
I = (h/2) × [f(x₀) + 2f(x₁) + 2f(x₂) + ... + 2f(xₙ₋₁) + f(xₙ)]
Where:
h = (b - a) / n is the subinterval width
f(xi) is the value of the function at each subinterval point
In this case, n = 4, a = 0, and b = 2. So, h = (2 - 0) / 4 = 0.5.
Now, let's calculate the approximation:
\(f\left(x_0\right)\:=\:f\left(0\right)\:=\:\left(0\:-\:3\right)e^{\left(0^2\right)}\:=\:-3\)
\(f\left(x_1\right)\:=\:f\left(0.5\right)\:=\:\left(0.5\:-\:3\right)e^{\left(0.5^2\right)}\:=-2.535\)
\(f\left(x_2\right)\:=\:f\left(1\right)\:=\:\left(1\:-\:3\right)e^{\left(1^2\right)}\:=\:-1.716\)
\(f\left(x_3\right)\:=\:f\left(1.5\right)\:=\:\left(1.5\:-\:3\right)e^{\left(1.5^2\right)}\:=\:-1.051\)
\(f\left(x_4\right)\:=\:f\left(2\right)\:=\:\left(2\:-\:3\right)e^{\left(2^2\right)}\:=\:-0.065\)
Now we can plug these values into the composite Trapezoidal rule formula:
I = (0.5/2) × [-3 + 2(-2.535) + 2(-1.716) + 2(-1.051) + (-0.065)]
= (0.25)× [-3 - 5.07 - 3.432 - 2.102 - 0.065]
= -5.1941
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Related Questions
\(\sqrt{7} (2\sqrt{7}+4)\)
Answers
Answer:
\( \sqrt{7 \times 2} \sqrt{7 + 4 \sqrt{7} } \\ 14 + 4 \sqrt{7} \)
at a certain university, 60% of the professors are women, and 70% of the professors are tenured. if90% of the professors are women, tenured, or both, then what percent of the men are tenured?
Answers
75% of the men professors are tenured.
Let's assume there are 100 professors at the university for easier calculations. Given that 60% of the professors are women, we have 60 women professors.
Given that 70% of the professors are tenured, we have 70 tenured professors.
Since 90% of the professors are women, tenured, or both, we can calculate the total number of professors who are women or tenured or both:
90% of 100 professors = 0.9 * 100 = 90 professors
Since we know that 60 of them are women, we can subtract that from the total to find the number of tenured professors who are not women:
90 professors - 60 women professors = 30 tenured professors who are not women
Now, let's calculate the number of men professors:
Total professors - Women professors = Men professors
100 professors - 60 women professors = 40 men professors
Out of the 40 men professors, 30 of them are tenured. Therefore, the percentage of men who are tenured is:
(30 tenured men / 40 men professors) * 100% = 75%
Therefore, 75% of the men professors are tenured.
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The area of a triangular sail is given by the expression 1/2 bh, where b is the length of the base and h is the height. What is the area of a triangular sail in a model sailboat when b = 12 inches and h = 7 inches?
Answers
42 square inches.
Step-by-step explanation:
A = 1/2 b × h
A = 1/2 x 12 x 7
A = 6 × 7
A = 42
1.1 1.2 Completely simplify the expressions below: 1.1.1 -3(2x - 4y)² 1.1.2 x+2 3 5 x+1 Completely factorise the expressions below: 1.2.1 ny + 4z + 4y + nz 1.2.2 3x² - 27x+60
Answers
The factorized expressions is 3(x-4)(x-5).
We are given that;
The expression 3x² - 27x+60
Now,
1.1.1 After simplification
-3(2x - 4y)² = -12(x-y)²
1.1.2 x+2/3*5x+1
= (3x+5)/(3x+3)
1.2.1 ny + 4z + 4y + nz
= (n+4)(y+z)
1.2.2 3x² - 27x+60
= 3(x-4)(x-5)
Therefore, by the expression the answer will be 3(x-4)(x-5).
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Convert milligrams per liter to micrograms per (fluid ounce)
Answers
To convert milligrams per liter (mg/L) to micrograms per fluid ounce (µg/fl oz), we can use the conversion factor of 29.5735.
This conversion factor takes into account the difference in volume between a liter and a fluid ounce.
1 fl oz = 29.5735 mL
1 L = 1000 mL
So, to convert from milligrams per liter to micrograms per fluid ounce, we divide by 29.5735 and multiply by 1000:
(mg/L) * 1000 / 29.5735 = (µg/fl oz)
Therefore, to convert a value x from milligrams per liter to micrograms per fluid ounce:
x (µg/fl oz) = x (mg/L) * 1000 / 29.5735
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Find the slope of the line tangent to the following polar curve at the given point. At the point where the curve intersects the origin (if this occurs), find the equationn of the tangent line in polar coordinates. r = 9 + 7 cos theta; (16,0) and (2, pi) Find the slope of the line tangent to r = 9 + 7 cos theta at (16,0). Select the correct choice below and fill in any answer boxes within your choice. Find the slope of the line tangent to r = 9 + 7 cos theta at (2, pi). Select the correct choice below and fill in any answer boxes within your choice. At the point where the curve intersects the origin (if this occurs), find the equationn of the tangent line in polar coordinates. Select the correct choice below and fill in any answer boxes within your choice. The equationn of the tangent line when the curve intersects the origin is The curve does not intersect the origin.
Answers
To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0), we can use the formula:
dy/dx = (dy/dtheta) / (dx/dtheta) = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))
where r' = dr/dtheta.
First, we need to find r' by taking the derivative of r with respect to theta:
r' = dr/dtheta = -7 sin(theta)
Then, we can plug in the given values to find the slope at (16, 0):
dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]
= [(-7 sin(0) sin(0) + (9 + 7 cos(0)) cos(0))] / [(-7 sin(0) cos(0)) - (9 + 7 cos(0)) sin(0))]
= (9 + 7) / (-9) = -2
Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0) is -2.
To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi), we can use the same formula as above:
dy/dx = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))
First, we need to find r' by taking the derivative of r with respect to theta:
r' = dr/dtheta = -7 sin(theta)
Then, we can plug in the given values to find the slope at (2, pi):
dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]
= [(-7 sin(pi) sin(2) + (9 + 7 cos(pi)) cos(2))] / [(-7 sin(pi) cos(2)) - (9 + 7 cos(pi)) sin(2))]
= (-2) / (7)
Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi) is -2/7.
The polar curve r = 9 + 7 cos(theta) intersects the origin when r = 0, which occurs when cos(theta) = -9/7, which is not possible since the range of cosine function is [-1, 1]. Therefore, the curve does not intersect the origin.
Since the curve does not intersect the origin, the answer is "The curve does not intersect the origin" for the equation of the tangent line in polar coordinates.
What is the slope of the graph?
Answers
Answer:
The slope of the graph is 10.
(2x-1) (2x+2) as a trinomial????
Answers
Answer:
4x^2 + 2x -2
Step-by-step explanation:
4x^2 + 4x - 2x - 2
4x^2 + 2x -2
what is the cosine form of the function 10sin(wt 40)
Answers
The cosine form of the function 10sin(wt - 40) is 10cos(wt - 50).
The cosine form of the function 10sin(wt - 40) can be found using the identity sin(x - y) = sin(x)cos(y) - cos(x)sin(y).
By applying this identity to the given function, we can rewrite it in terms of cosine.
10sin(wt - 40) = 10(sin(wt)cos(40) - cos(wt)sin(40))
Now, we can use the fact that cos(90 - x) = sin(x) and sin(90 - x) = cos(x) to further simplify the expression.
10(sin(wt)cos(40) - cos(wt)sin(40)) = 10(sin(wt)sin(50) + cos(wt)cos(50))
Finally, we can use the identity cos(x + y) = cos(x)cos(y) - sin(x)sin(y) to rewrite the expression in terms of cosine.
10(sin(wt)sin(50) + cos(wt)cos(50)) = 10cos(wt - 50)
Therefore, the cosine form of the function 10sin(wt - 40) is 10cos(wt - 50).
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I have a calculus math problem I need help with
Answers
The area of the field is:
A = (x + 20)y
The length of fence needed is:
x + y + x + 20
(remember that 20 ft are not needed because the building, and y ft are not needed because the river)
We have 1000 ft of fencing, then:
1000 = x + y + x + 20
1000 - 20 = 2x + y
980 = 2x + y
Isolating y from the preceding equation:
y = 980 - 2x
Substituting this into the area equation:
A = (x + 20)(980 - 2x)
Distributing:
\(\begin{gathered} A=980x-2x^2+20\cdot980-40x \\ A=-2x^2+940x+19600 \end{gathered}\)At the maximum, the derivative of A with respect to x is zero, then:
\(\begin{gathered} \frac{dA}{dx}=\frac{d}{dx}(-2x^2+940x+19600) \\ \frac{dA}{dx}=-2\frac{d}{dx}(x^2)+940\cdot\frac{dx}{dx}+\frac{d}{dx}(19600) \\ \frac{dA}{dx}=-4x+940 \\ 0=-4x+940 \\ 4x=940 \\ x=\frac{940}{4} \\ x=235 \end{gathered}\)Recalling the equation of y and substituting this result:
y = 980 - 2x
y = 980 - 2*235
y = 510
The dimensions are:
length: 255 ft (on the side without the building)
width: 510 ft
Answer:
See below
Step-by-step explanation:
Long side = x
Other long side = x - 20
short side = y
Area enclosed = xy
x + x -20 + y = 1000 or y = 1020 -2x <=====sub into first equation
area = x * ( 1020-2x) = -2x^2 + 1020x
this is a dome shaped parabola
max will occur at x = -b/2a = - 1020/ (2 * -2) = 255 ft
then y = 1020 -2x = 510 ft
(area = xy = 130 050 ft^2 )
Other than itself, which angle is congruent to CBE?
Answers
Answer:
<GBF
Step-by-step explanation:
<GBF is congruent to <CBE because they are vertical angles.
The vertical angle theorem states this is true.
Vertical angles are formed by a pair of intersecting lines and are the angles directly across from each other.
Since <GBF and <CBE are vertical angles, they are hence congruent.
2) The representative agent lives for infinite periods (0,1,2,…) and receives exogenous incomes of y0,y1,y2,…, respectively. The lifetime present discounted value of utility is given by: ∑t=0[infinity]βtln(ct) with β(<1) being the discount factor and ct is consumption at time t. The agent is allowed to save or borrow at the real interest rate r, but she cannot die with debt or wealth. Assume also that the initial wealth is zero. a. Solve the optimization problem of the agent using the period-by-period budget constraints. In particular, show the Euler equation. b. Using the given functional form, write the Euler equation between time 1 and time 3 . In other words, show how c1 and c3 are related. c. Write the present discounted value of optimal lifetime consumption as a function of c0 (and, potentially, other parameters or exogenous variables). d. Write the present discounted value of optimal lifetime utility as a function of c0 (and, potentially, other parameters or exogenous variables). e. Find the present discounted value of lifetime income as a function of y0 (and, potentially, other parameters or exogenous variables) when income is growing each period at the rate of γ, where 0<γ0 ? Explain!
Answers
a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.
b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.
c. C0 = ∑t=0[infinity](β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.
d. U0 = ∑t=0[infinity](β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.
Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.
a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:
At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.
b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.
Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin
d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.
c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity](β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.
d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity](β(1 + r))^tln(ct).
This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.
e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.
This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.
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When a square with area $4$ is dilated by a scale factor of $k,$ we obtain a square with area $9.$ Find the sum of all possible values of $k.$
Answers
Answer:
Yes I do because I'm good.Yes I do because I'm good.
Step-by-step explanation:
Answer: 0
Step-by-step explanation:
So basically, \(k^{2}\) = 9/4. So \(k\) = 3/2. But you can also have negative scale factors, so it would be -3/2.
3/2 + (-3/2) = 0.
Hope this helps.
Select the correct answer. What is the probability that the manufacturing unit has carbon emission beyond the permissible emission level and the test predicts this? A. 0. 2975 B. 0. 0525 C. 0. 0975 D. 0. 5525 E. 0. 6325.
Answers
Answer:
0.2975
Step-by-step explanation:
simplify this problem\( \frac{9x}{4x - 4} + \frac{ {x}^{2} + 6x }{ {x}^{2} + 5x - 6} \)
Answers
1. Factor the denominators as follow:
\(\begin{gathered} 4x-4=4(x-1) \\ \\ \\ x^2+5x-6 \\ =x^2+6x-x-6 \\ =x(x+6)-(x+6) \\ =(x-1)(x+6) \\ \\ \\ \\ \\ \frac{9x}{4(x-1)}+\frac{x^2-6x}{(x-1)(x+6)} \end{gathered}\)2. Write the expresion with the less common denominator:
Multiply the first fraction by (x+6) (both parts, numerator and denominator):
\(\frac{9x}{4(x-1)}\cdot\frac{x+6}{x+6}=\frac{9x(x+6)}{4(x-1)(x+6)}\)Multiply the second fraction by 4 (both parts, numerator and denominator):
\(\frac{x^2-6x}{(x-1)(x+6)}\cdot\frac{4}{4}=\frac{4(x^2-6x)}{4(x-1)(x+6)}\)Rewrite the expression with the less common denominator:
\(\begin{gathered} \frac{9x(x+6)}{4(x-1)(x+6)}+\frac{4(x^2-6x)}{4(x-1)(x+6)} \\ \\ =\frac{9x(x+6)+4(x^2-6x)}{4(x-1)(x+6)} \end{gathered}\)3. Remove parentheses and simplify:
\(\begin{gathered} \frac{9x^2^{}+54x+4x^2-24x}{(4x-4)(x+6)} \\ \\ =\frac{13x^2+30x}{4x^2+24x-4x-24} \\ \\ =\frac{13x^2+30x}{4x^2+20x-24} \end{gathered}\)Then, the given expression simplified is:\(\frac{9x}{4x-4}+\frac{x^2-6x}{x^2+5x-6}=\frac{13x^2+30x}{4x^2+20x-24}\)![simplify this problem[tex] \frac{9x}{4x - 4} + \frac{ {x}^{2} + 6x }{ {x}^{2} + 5x - 6} [/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/3FEf63pRqLXeuugCPzvxJcejYts4in3X.png)
On a farm there was a cow. And on the farm there were 2 sheep. There were also 3 chickens. What is the total mass of the 1 cow, the 2 sheep, the 3 chickens, and the 1 farmer on the farm?
Make a conjecture about how many ants might be on the farm. If you added all these ants into the previous question, how would that affect your answer for the total mass of all the animals?
What is the total mass of a human, a blue whale, and 6 ants all together?
Which is greater, the number of bacteria, or the number of all the other animals in the table put together?
Answers
The total mass of the living things on the farm is 588 kg.
Mass calculationSince on a farm there was a cow, 2 sheep and 3 chickens, to determine what is the total mass of the 1 cow, the 2 sheep, the 3 chickens, and the 1 farmer on the farm, the following calculation must be performed :
(6.2 x 10) + (4 x 10 x 10) + (2 x 6 x 10) + (3 x 2 x 1) = X62 + 400 + 120 + 6 = X588 = XTherefore, the total mass of the living things on the farm is 588 kg.
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What is half of a 3/4 cup?
Answers
Answer:0.375
Step-by-step explanation:
3/4=0.75
0.75/2=0.375
(3/4)/2=0.375
What is the solution to the equation 6x + 2 = 9x-1
Answers
Answer:
1
Step-by-step explanation:
Step 1:
6x + 2 = 9x - 1
Step 2:
2 = 3x - 1
Step 3:
3 = 3x
Answer:
1 = x
Hope This Helps :)
Answer:
Answer:
1
Step-by-step explanation:
Step 1:
6x + 2 = 9x - 1
Step 2:
2 = 3x - 1
Step 3:
3 = 3x
Answer:
1 = x
A management dilemma defines the research question.True or False
Answers
A management conundrum is an issue or difficulty that a manager faces that necessitates a choice. This difficulty or challenge frequently defines the study question and motivates researchers to conduct research to discover a solution that is the given statement is true.
What is research?Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Student research also has the following characteristics: Students create questions, tactics, and outcomes that are, at least for them, unique. Students employ the same broad techniques as research mathematicians. They go through data collection, visualization, abstraction, conjecture, and proof cycles.
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What is the value of the sin each of the following 5607 506 702 803 562
Answers
Answer:
sin(5607) = 0.67641680533
sin(506) = -0.202179403335
sin(702) = -0.989367016834
sin(803) = -0.948263002181
sin(562) = 0.33827666045
Step-by-step explanation:
put sin into a calculator and then put in the number
hope this helps! :)
1. Determine the value of x for
which r | s.
(2x + 6)
42°
Answers
Answer:
The answer for x would be x=19
Step-by-step explanation:
19×2= 38
38+6= 42
Mr. Wells has 8 chicken pot pies to share among 6 people. If each person gets the same size serving, how much chicken pot pie will each person get?
Answers
Answer:
\(1\frac{1}{3}\)
Step-by-step explanation:
we divide 8 by 6
8/6
1 2/6
1 1/3
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a cross-country course is in the shape of a parallelogram with a base of length 7 mi and a side of length 6 mi. what is the total length of the cross-country course?
Answers
The total length of the parallelogram-shaped cross-country course is equal to 26 miles.
We can calculate the total length of the cross-country course using the formula for the perimeter of a parallelogram, which is twice the sum of the lengths of its adjacent sides. In this case, the adjacent sides are the base of length 7 mi and the side of length 6 mi.
So, we can find the total length by first finding the sum of these two sides:
7 mi + 6 mi = 13 mi
Then, we can multiply this sum by 2 to get the total length:
2 x 13 mi = 26 mi
Therefore, the total length of the cross-country course is 26 miles.
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An employee at an organic food store is assembling gift baskets for a display. Using wicker baskets, the employee assembled 2 small baskets and 4 large baskets, using a total of 60 pieces of fruit. Using wire baskets, the employee assembled 2 small baskets and 10 large baskets, using a total of 132 pieces of fruit. Assuming that each small basket includes the same amount of fruit, as does every large basket, how many pieces are in each?
The small baskets each include______pieces and the large ones each include_____pieces.
Answers
Answer:12 and 15
Step-by-step explanation:
Find the surface area of the hexagonal pyramid.
The base area is 166.3 cm2.
Answers
Answer:
The surface area of the hexagonal pyramid is 291.93 cm2
Step-by-step explanation:
The complete question is
Given -
Base area of pyramid = 166.3 cm2
Height of the pyramid = 12 cm
Surface area of hexagonal pyramid is
\(A=\frac{1}{3} * 3^{\frac{3}{4}}*\sqrt{A_B*(6h^2+\sqrt{3} A_B)+A_B}\)
Here AB is the base area and h is the height
Substituting the given values we get
\(A=\frac{1}{3} * 3^{\frac{3}{4}}*\sqrt{166.3*(6*12^2+\sqrt{3} * 166.3)+166.3}\\A = \frac{1}{3} * 2 * \sqrt{(166.3 *1152.04)+166.3)}\\A = \frac{2}{3} * 437.893\\A = 291.93 }\)
The surface area of the hexagonal pyramid is 291.93 cm2
Halla el volumen del siguiente prisma triangular...
Answers
Answer:
El volumen del prisma triangular es 110 centímetros cúbicos.
Step-by-step explanation:
El volumen del prisma (\(V\)), en centímetros cúbicos, es igual al producto del área superficial del triángulo (\(A\)), en centímetros cuadrados, y la profundidad del prisma (\(z\)), en centímetros:
\(V = A\cdot z\)
\(V = \frac{1}{2}\cdot b\cdot h\cdot z\) (1)
Donde:
\(b\) - Base del triángulo, en centímetros.
\(h\) - Altura del triángulo, en centímetros.
Si sabemos que \(b = 4\,cm\), \(h = 5.5\,cm\) y \(z = 10\,cm\), entonces el volumen del prisma triangular es:
\(V = \frac{1}{2}\cdot (4\,cm)\cdot (5.5\,cm)\cdot (10\,cm)\)
\(V = 110\,cm^{3}\)
El volumen del prisma triangular es 110 centímetros cúbicos.
4/5 divided by 7/15 pls help
Answers
Answer:
12/7
Step-by-step explanation:
4/5 ÷ 7/15
Keep Change Flip
4/5 × 15/7
Simplify
4/1 × 3/7
Multiply
12/7
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Drag each expression to the correct location on the table.
Determine which expressions represent real numbers and which expressions represent complex numbers.
Answers
Answer:
Step-by-step explanation:
This is about understanding real and complex numbers.
Complex Numbers; 7 - 5i, √-6, 0 + 9i, , -i² + i³
Real Numbers; i⁶, 2 - 7i², -12, √(-5)²
Let's first define real and complex numbers.
A real number is any number that can be represented on a number line. That means it can be a rational or an irrational number. Meanwhile, Complex numbers are numbers that cannot be represented on a number line but instead take the form of x + yi, where x and y represent real numbers while the letter i next to y represents an imaginary part.The. expressions we are given are;
i⁶, 2 - 7i², 7 - 5i, √-6, 0 + 9i, -12, √(-5)², -i² + i³
i⁶ can be expressed as; i² × i² × i² . Now the square of an imaginary number is -1. Thus; i² × i² × i² = -1 × -1 × -1 = -1 which is a real number.2 - 7i²; we know that the square of an imaginary number is -1, Thus;
2 - 7i² = 2 - 7(-1) = 9 which is a real number.
7 - 5i; This is a complex number because it is of the form x + yi.√-6; This is a complex number because negative roots are only imaginary and not possible.0 + 9i; This is a complex number because it is of the form x + yi.-12 is a real number as it can be represented on the number line.√(-5)² = √25 = 5 which is a real number-i² + i³ can be expressed as; -i² + i(i²). Square of imaginary number = -1. Thus; -i² + i(i²) = 1 - 1i. This is a complex number.Read more at; https://brainly.com/question/16930811
help me pleasee, my brain won't work
Answers
The given fractions have equal value, so Liam is correct.
How to find the equivalent fractions?Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.
Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.
Thus, we can say that:
The fraction -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.
The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient
The fractions have equal value, so Liam is correct
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what would be the leading coefficient of f(x)=6-x+7x^2
Answers
Answer:
7
Step-by-step explanation:
The leading coefficient of the given expression is 7.
What is coefficient?A coefficient is a factor that is multiplied by a variable or a term in an expression. It can be a number or a symbol representing a constant value. For example, in 7x - 3y + 5, the coefficients are 7, -3, and 5.
Given that a quadratic function f(x) = 6-x+7x², we need to find the leading coefficient,
So, rearranging the terms in the function in standard form,
f(x) = 7x²+x-6
The leading coefficient is the coefficient of the term with the highest power or degree in a polynomial,
Here, the highest power coefficient is 7.
Hence, the Leading coefficient of the given expression is 7.
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