If the function is; F(x) = ∫[tex]e^{-5t^{4} } }[/tex] dt, then the MacLaurin polynomial of degree 5 for F(x) is x - x⁵.
A Maclaurin polynomial, also known as a Taylor polynomial centered at zero, is a polynomial approximation of a given function. It is obtained by taking the sum of the function's values and its derivatives at zero, multiplied by powers of x, up to a specified degree.
The function is : F(x) = [tex]\int\limits^x_0 {e^{-5t^{4} } } \, dt[/tex];
We know that : eˣ = 1 + x +x²/2! + x³/3! + x⁴/4! + ...
Substituting x = -5t⁴;
We get;
[tex]e^{-5t^{4} } }[/tex] = 1 - 5t⁴ + 25t³/2! + ...
Substituting the value of [tex]e^{-5t^{4} } }[/tex] in the F(x),
We get;
F(x) = ∫₀ˣ(1 - 5t⁴ + ...)dt;
= [t - t⁵]₀ˣ
= x - x⁵;
Therefore, the required polynomial of degree 5 for F(x) is x - x⁵.
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The given question is incomplete, the complete question is
Let F(x) = ∫[tex]e^{-5t^{4} } }[/tex] dt. Find the MacLaurin polynomial of degree 5 for F(x).
The principal claims he only loses about 30 students a year. Do the values in the table support his claim? explain.
Indeed, the values in the table back up his assertion.
What is unitary method?
This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.
We typically utilize this technique for math calculations.
This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
According to our question-
2% of 250 = 5, 4% of 200 = 8, and 8% of 150 = 12.
5 + 8 + 12 = 25
Hence, Indeed, the values in the table back up his assertion.
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Go step by step to reduce the radical sqrt 162
The final solution after reducing the given number radical is; 9√2
How to simply a number radical?
The radical of a number is defined in the same way we define the root of a number. The root can be a square root, fourth root or even cube root, up to the nth root.
Now, we are given the number radical as; √162
Now, 162 can be broken down into its' factors as √(81 * 2)
We know from properties of surds that;
√(a * b) = √a * √b
Thus, we now have;
√162 = √81 * √2
This can be simplified further to get;
9√2
Thus, that is the final solution to the number radical simplification.
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maryam reduced 6.25% if her present weight is 45kg what ws her previous one
Answer:47.8125kg
Step-by-step explanation:
x: previous weight
x = 45+45x6.25% = 47.8125
Would the following compound inequality be classified as an “and” inequality or an “or” inequality? Inequality: 6 > x + 1 > 3 dont guess
The inequality 6 > x + 1 > 3 is 'And' type Inequality.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
An 'Or' inequality is also referred to as a disjunction.
In other words, there is no connection on the number line between the range of values that meet either component of the inequality. Finding a truthful statement that satisfies either one of the inequality conditions or both inequality conditions is the aim whenever 'Or' compound inequalities are solved.
For example, x > 7 OR x < 3
Another name for a compound inequality with a 'And' is a conjunction. Compound inequality of this kind is stated as a long inequality, such as
3 > x > 9. Similar to 3>x and x > 9, this is.
The solutions to this and other compound inequalities fall within a range of potential values between 3 and 9. The range of values used to solve "And" inequalities must meet both requirements. These inequalities display a range of overlapping values.
So, the inequality is 'And' type of Inequality.
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Determine the power and the rms value for each of the following signals:
a) 5 + 10cos(10t + π/3)
b) 10cos(100t + π/3) + 16 sin(150t + π/5)
c) (10 + 2 sin (3t)) cos 10t
d) 10 cos(5t)cos(10t)
e) 10 sin(5t)cos(10t)
f) e^(jαt) cos(w0t)
The power and the r m s value for each of the following signals are a)p=50w and r m s =7.07 b)p=178w, r m s =√178 c)p=51w, r m s =√51
d)p=25w, r m s =√25 e)p=25w, r m s =√25 and f)p=1/2, r m s =√1/2.
(a) 5+10cos(100t+π/3)
=A cos(w0t+θ)
power of the signal
P=10^ 2/2=100/2=50w
p=50w
r m s value of the signal
=√50
=7.07
b) 10cos(100t+π/3)+16sin(150t+π/5)
power of the signal.
p=10^ 2/2+16^ 2/2
p=178w
r m s value of the signal=√178
c) (10+2sin(3t)cos10t
=10cos10t+2sin3tcos210t
=2sin3tcos10t
=1/2(sin(3+10)+sin(3-10))
(sin a cos b=1/2(sin(a + b)+sin(a-b))
=2x1/2(sin13t-sin7t)
=sin13t-sin7t
=10cos10t+sin13t-sin7t
power of the signal is
p=10^ 2/2+1^ 2/2+1^ 2/2
p=51w
r m s value of the signal=√51
d) 10 cos(5t)cos(10t)
=10(cos(5+10)T+ cos (5-10)t/2
(cos a cos b=1/2(cos a+ cos b)+cos(a-b))
=10(cos(15)t+ cos (-5)t/2
=5cos15t-5cost
power value of the signal
p=5^ 2/2+5^ 2/2
p=25w
r m s value of the signal=√25
e) 10 sin(5t)cos(10t)
=10(sin(5+10)t+ sin(5-10)t/2
=10/2(sin15t-sin5t)
=5sin15t-5sin5t
power of the signal
p=5^ 2/2+5^ 2/2
p=25w
r m s value of the =√25
F) f) e^(jαt) cos(w0t)
=e jαt cos wot
=(cosαt+ cos wot+jsin2tcoswot
=(cos(α+wo)t+ cos(α-wo)t/2+j(sin(2+wo)t+ sin cos-wot/2
=1/2cos(α+wo)T+1/2cos(α-wo)T
power of the signal
p=(1/2)^ 2/2+(1/2)^ 2/2+(1/2)^ 2/2+(1/2)^ 2/2
p=1/2
r m s value=√1/2
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[tex]\pi[/tex]
Please help for geometry here the photo
Answer:f = 57 g = 33
Step-by-step explanation:
Add f and g together and make them equal 90 and then solve for x and plug x back in to both angles 57 and 33
Answer:
m<F + m<G + m<H=180°[Sum of angles of traingle is Supplementary]
or,90°+(4x +13)°+(2x +11)°=180°
or,6x + 24°=180°-90°
or,6x=90°-24°
or,X=66°/6
:.X=11°
Now,
m<F=(4x+13)°=(4×11+13)°=57°
m<G=(2x+11)=(2×11+11)°=33°
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Which rule describes the translation?
(x, y) → (x-8, y-3)
(x, y) → (x-3, y + 8)
(x, y) → (x+8, y - 3)
(x,y) → (x+3, y + 8)
Rose purchased a total of 17 books and toys for the Rupert play school. earn book cost $11 and each toy cost $6.How many books and toys did she buy for $157?
Answer: 11 Books, 6 Toys
Step-by-step explanation:
Let the number of books be B, and the number of toys be T
B+T=17
11B+6T=157
Let's use the elimination method:
11B+6T=157
6B+6T=102
And finally you get
5B=55
B=11
Use the value of B to get T
11+T=17
T=6
Therefore, the answer is
B=11,T=6
PLEASE HELP (picture provided)
Answer:
Step-by-step explanation:
its the next one down
HELP ASAP ( 15 POINTS)
The constant of proportionality, given that this is a proportional relationship, is 11. 7
How to find the constant of proportionality?To find the constant of proportionality, the following formula is used :
= Y value / Corresponding x value
The constant of proportionality can only be found for proportional relationships.
In this instance, we have x and y of ( 7, 81. 9 ).
The constant of proportionality is:
= 81 .9 / 7
= 11. 7
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(dy/dx) = e^(3x+2y)
solve the differential equation by separation of variables
What is the following simplified product? Assume x ≥ 0.
(√6x² +4√8x³)(√x-x√√5x5
O3x√6x+x4√30x
+24x² √2x+8x5 √/10x
3x√6x+x4√30x +24x² √√2+8x5/10
3x6x-x√30x+24x²
√2-8x5 10
3x√6x-x√30x +24x² √√2x-8x5 /10x
Answer:
(c) 3x√(6x) -x⁴√(30x) +24x²√2 -8x⁵√10
Step-by-step explanation:
You want to simplify the product ...
[tex](\sqrt{6x^2}+4\sqrt{8x^3})(\sqrt{9x}-x\sqrt{5x^5})[/tex]
ChoicesAs with a lot of problems of this type, the correct answer choice can be selected by examining a term or two.
Multiplying the last two terms of the binomials, we get ...
[tex]4\sqrt{8x^3}\cdot (-x\sqrt{5x^5})=-4x\sqrt{40x^8}=-4x\sqrt{10(2x^4)^2}=\boxed{-8x^5\sqrt{10}}[/tex]
This term is only found in choice C.
__
Additional comment
The expression is simplified by making use of the radical relations ...
(√a)(√b) = √(ab)
√(a²b) = a√b
The given expression can be rewritten with squares taken out of the radicals as ...
(x√6 +8x√(2x))·(3√x -x³√(5x))
Then, using FOIL or the distributive property, we have ...
= 3x√(6x) +24x²√2 -x⁴√(30x) -8x⁵√10 . . . . . matches C
Complete the conversion 2.5 T Lb
Answer:
2.5 Tons to lb
1 ton = 2,000 lb
2.5 tons x 2000 lb = 5,000 lb
Is (3,4, -2) a solution of the following system? 5x1 X2 + 2x3 = 7 -2x1 + 6x2 + 9x3 = 0 – 7x1 + 5x2 – 3x3 = -7
Yes, (3,4, -2) is a solution of the system. You can find the solution by substituting the values.
To check if (3,4,-2) is a solution of the system, we can substitute those values into each of the equations and see if they are true.
5x1 + 2x3 = 7
becomes
5(3) + 2(-2) = 7
which simplifies to
15 - 4 = 7
-2x1 + 6x2 + 9x3 = 0
becomes
-2(3) + 6(4) + 9(-2) = 0
which simplifies to
-6 + 24 - 18 = 0
-7x1 + 5x2 - 3x3 = -7
becomes
-7(3) + 5(4) - 3(-2) = -7
which simplifies to
-21 + 20 + 6 = -7
As we can see all the equation are true, (3,4,-2) is a solution of the system.
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What is 2D coordinate system?
A two-dimensional (2D) coordinate system is a system used to define the position of points in a two-dimensional plane.
What is 2D coordinates system?A 2D coordinate system can also be used to represent other kinds of data, such as temperature, elevation, or pressure. In this case, the two coordinates are usually called the x-axis and y-axis, and they are both used to measure the same physical quantity.
It is most commonly used in mathematics and engineering to plot graphical data such as graphs, charts, and diagrams. In a 2D coordinate system, each point is represented by two numbers, called coordinates, which indicate the position of the point in relation to a fixed reference point, called the origin. These coordinates usually describe the horizontal (x) and vertical (y) distances between the point and the origin. The set of all points in the 2D coordinate system is called the coordinate plane.
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find the perimeter of equivaul triangle whose each sides is 7cm
Answer:
21 cm
Step-by-step explanation:
An equilateral triangle has all 3 sides equal.
So the perimeter of the equilateral triangle
= 3 x side
= 3 x 7
= 21 cm
Hence,
The perimeter of the equilateral triangle is 21 cm.
Circle all perfect squares:
49
32
2
9
42
16
How do you learn 4x tables?
When you multiply 4 with any number, you can use the doubling-up trick (that's the one you used for the two times table) twice. Here is an example: 2 x 4 is the same as 2 + 2 = 4 and then 4 + 4 = 8. So, 2 x 4 = 8.
Here is next double, double example are: 5 x 4 is the same as 5 + 5 = 10, so then 10 + 10 = 20. So, the answer is 5 x 4 = 20.
Here, is the table of four.
4×1=4
4×2=8
4×3=12
4×4=16
4×5=20
4×6=24
4×7=28
4×8=32
4×9=36
4×10=40
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What are the properties of midline theorem?
The midline theorem in Geometry claims that cutting along the midline of a triangle creates a segment that is parallel to the base and half as long.
It is a theorem used in coordinate geometry and calculus. If P1(x1, y1) and P2(x2, y2) are the coordinates of a line, then the midpoint formula is given as Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
Property of the midpoint theorem are:
If we join the midpoints of the three sides of the triangle we get 4 smaller and congruent triangles.A line drawn through the midpoint of one side of a triangle that is parallel to another side will bisect the third sideThe two triangles must have the same size and shape, so all three sides have the same length, and all three angles have the same measure.The theorem applies SAS congruencyTo know more about midline theorem visit:
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Jee from Boton goe to hi grandpa Iaac in New York by bu at an average peed of 35 mph and it take him 6 hour. In a while, Jee and Iaac go back from New York to Boton in Iaac' car at an average peed of 42 mph. How long doe Jee' trip from New York to Boton take?
Jee's trip from New York to Boston would take approximately time 4.5 hours.
To calculate the time it would take Jee to travel from New York to Boston, we need to divide the total distance (approximately 280 miles) by the average speed (42 mph). This gives us a total time of 6.67 hours. We then need to subtract the time it took Jee to travel from Boston to New York (6 hours) to get the total time for the return trip. 6.67 hours - 6 hours = 4.5 hours. Therefore, Jee's trip from New York to Boston takes approximately time 4.5 hours. Jee's trip from New York to Boston would take approximately 4.5 hours.
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5 11 12+2 1 6= plese help me figuer this out
Answer:
51,328
Step-by-step explanation:
5 11 12+2 1 6=51328
one number exceeds (is more than) another number by 6, and the sum of the two numbers is 26. find the two numbers
Answer:
10 and 16
Step-by-step explanation:
let on number be x then the other number is x + 6
sum the 2 numbers and equate to 26
x + x + 6 = 26
2x + 6 = 26 ( subtract 6 from both sides )
2x = 20 ( divide both sides by 2 )
x = 10
x + 6 = 10 + 6 = 16
the 2 numbers are 10 and 16
What is the equation of the line that passes through the point (-6, 5) and has a slope of 1/2
The equation of a line passes through the point (-6, 5) and
has a slope of 1/2 is y = (1/2)x + 8.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, A line passes through the point (-6, 5) and has a slope of 1/2.
First, we need to determine the y-intercept 'b'.
5 = (1/2)(-6) + b.
5 = - 3 + b.
b = 8.
y = (1/2)x + 8 is the required equation of the line.
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What is the domain of the graph?
The domain of the graphed function in this problem is given as follows:
2 <= x <= 5.
How to obtain the domain of the function?The domain of a function is the set composed by all the input values that the function accepts.
On the graph, the domain of the function is given by the values of x.
For this problem, the values of x are a closed interval between x = 2 and x = 5, hence the domain of the function is defined by the interval presented as follows:
2 <= x <= 5.
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A jet travels 490 miles in 5 hours. At this rate, how far could the jet fly in 12 hours? What is the rate of speed of the jet?
Answer: 1,176 miles
Step-by-step explanation:
490 / 5 = 98 miles
98 mph X 12 hours is 1,176
Tyrone has $95 to spend. He already bought pants for $22. How many $5 t-shirts can he buy if he wants to have at least $15 left over?
a. Write an inequality that demonstrates this situation
b. solve your inequality
c. Explain what your answer means to Tyrone
Answer:
a. Write an inequality that demonstrates this situation
Let x be the number of $5 t-shirts Tyrone can buy
The inequality that demonstrates this situation is:
x*5 + 22 <= 95 - 15
b. solve your inequality
x5 + 22 <= 80
x5 <= 58
x <= 11.6
x <= 11
c. Explain what your answer means to Tyrone
Tyrone has $95 to spend, he already bought pants for $22, so he has $95-22 = $73 left to spend. He wants to have at least $15 left over after buying t-shirts, so he can buy up to $73-15 = $58 worth of t-shirts. Each t-shirt costs $5, so he can buy a maximum of 11 t-shirts (58/5=11.6) with no remainder. So Tyrone can buy 11 t-shirts and he will have $73-11*5 = $18 left. This means that Tyrone can buy 11 t-shirts and still have $18 left over.
Step-by-step explanation:
How do you find the 1st and 2nd element of a pair?
An ordered pair is a set of two values, (x,y), where x and y are the coordinates. In an ordered pair, the first element is typically referred to as the x-coordinate, or the "first component" and it represents the horizontal position of the point on a coordinate plane. The second element is typically referred to as the y-coordinate, or the "second component" and it represents the vertical position of the point on a coordinate plane.
So, to find the first and second element of a pair, you can refer to the first element as the x-coordinate or the first component and the second element as the y-coordinate or the second component.
For example, in the ordered pair (4,3), the first element is 4, which represents the x-coordinate, and the second element is 3, which represents the y-coordinate.
What is the answer for this I need help pls
Answer: the total spent on the meal is $88.25875.
Step-by-step explanation:
The total spent on the meal can be calculated by adding the cost of the meal, the tax, and the tip.
First, we need to calculate the cost of the tax: 72.5 x 0.0675 = 4.88375
Then we need to calculate the cost of the tip: 72.5 x 0.15 = 10.875
Finally, we add the cost of the meal (72.5), the tax (4.88375) and the tip (10.875) to find the total cost of the meal: 72.5 + 4.88375 + 10.875 = 88.25875
Therefore, the total spent on the meal is $88.25875.
Solve the inequality for x.
-8+2x>4
By solving the given inequality in question, i.e -8+2x>4 , the solution obtained is x>6, which means the inequality satisfies for all the values of x that are greater than 6.
What is inequality?An inequality is a statement that compares two values and asserts that one value is greater than, less than, or not equal to the other value. Inequalities are used to describe a range of values that a variable can take on. The most common symbols used to express inequalities are ">", "<", "≥" and "≤", which represent "greater than", "less than", "greater than or equal to" and "less than or equal to" respectively.
Give an example of inequality?An example for inequality can be , the inequality x > 2 , which states that x is greater than 2, which means that any value of x that is greater than 2 satisfies the inequality.
Inequality can be solved either graphically or algebraically. The solution of an inequality is the set of all values that make the inequality true.
To solve the inequality -8 + 2x > 4, you can follow these steps:
Add 8 to both sides of the inequality: -8 + 2x > 4 becomes 2x > 12Divide both sides of the inequality by 2 : 2x > 12 becomes x > 6So the solution of the inequality is x > 6.
This means that x is greater than 6. So any value of x that is greater than 6 satisfies the inequality.
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evaluate using order of operations: A = L=50 W= 15 give your answer in simplest form
The value of the equation A = LW is A = 750
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The value of L = 50
The value of W = 15
A = LW be equation (1)
Substituting the values of L and W in the equation , we get
A = 50 x 15
On simplifying the equation , we get
A = 750
Therefore , the value of A is 750
Hence , the equation is A = 750
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