Using the fundamental theorem of calculas the derivative of function g(x)=[tex]xt^{3}+t^{5}[/tex] at x=0 is [tex]t^{3}[/tex].
Given a function g(x)=[tex]xt^{3}+t^{5}[/tex].
We are required to find the derivative of the function g(x) at x=0.
Function is relationship between two or more variables expressed in equal to form. The values entered in a function are part of domain and the values which we get from the function after entering of values are part of codomain of function. Differentiation is the sensitivity to change of the function value with respect to a change in its variables.
g(x)=[tex]xt^{3}+t^{5}[/tex]
Differentiating with respect to x.
d g(x)/dx=[tex]t^{3}[/tex]+0 [Differentiation of x is 1 and differentiation of constant is 0]
=[tex]t^{3}[/tex]
Hence using the fundamental theorem of calculas the derivative of function g(x)= [tex]xt^{3}+t^{5}[/tex] at x=0 is [tex]t^{3}[/tex].
The function given in the question is incomplete. The right function will be g(x)=[tex]xt^{3}+t^{5}[/tex].
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.
Solve question
6= x/4 + 2
Answer:
x=16
Step-by-step explanation:
6= x/4 + 2
Subtract 2 from both sides.
4= x/4
Multiply 4 to both sides.
x=16
Hope this helps!
A number, h, rounded to 1 d.p. is 47.2
Another number, k, rounded to 1 d.p. is 4.8
What are the lower and upper bounds of
h - k?
The lower and upper bounds of h - k are 42.31 and 42.49 respectively.
Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.
The upper and lower bounds can be written using error intervals
The lowest value of h is 47.15
The greatest value of h is 47.24
The greatest value of k is 4.84
The lowest value of k is 4.75
Thus upper bound of h -k = 47.24 - 4.75 = 42.49
Thus lower bound of h -k = 47.15 - 4.84 = 42.31
Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively.
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You are wearing a pair of cargo pants with six pockets. you put $10 on one of those pockets, but you cannot remember which one after checking two pockets without success, what is the possibility that the money will be in the next park view check?
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
According to the given information ,there still 4 pockets to check .
Then
the possibility that the money will be in the next pocket :
[tex]=\frac{1}{4}[/tex]
Answer: Answer above me is correct
The function f(x) = x2 is graphed above. which of the graphs below represents the function g(x) = (x 1)2?
The graph (C) Y represents the function g(x) = (x 1`)2.
What is a graph of a function?The graph of a function f is the set of ordered pairings where display style f(x) = y in mathematics. When x and f(x) are both real values, these pairings represent Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane.To find which of the graphs below represents the function g(x) = (x 1)2:
Parabola: It's a conic section formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements.
The equation of parabola: [tex]y =x^{2}[/tex]The graph of [tex]y=x^{2}[/tex] is given.To draw the graph of [tex]y=(x+1)^{2}[/tex], shift the graph of [tex]y=x^{2}[/tex] one unit left.The graph of [tex]y=(x+1)^{2}[/tex] is attached below.Therefore, the graph (C) Y represents the function g(x) = (x 1)2.
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What is the probability of selecting a male from a group of 4 male and 8 female
Answer:0.333
Step-by-step explanation:4+8=12 so there is only 4 chances it can be male so 4/12=0.333
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
probability (P) is calculated as
P = (desired result ) ÷ ( number of possible results )
here desired result is choosing a male from 4 males
number of possible results = 4 + 8 = 12 , then
P( male) = [tex]\frac{4}{12}[/tex] = [tex]\frac{1}{3}[/tex]
how does math connect to animation?
Answer:
Math allows the animator to find the unknowns from a set of equations and to work out the aspects of the geometric figures when dealing with the objects that move and change.
Step-by-step explanation:
To learn more:
weusemath.org/?career=animator
Hope this helps!
An engineer is designing an arch-shaped gate for the entrance to an amusement park. the gate must be 80 feet wide and 25 feet tall. what will be the equation of the parabolic shape of the gate? a. x2 = -16(y − 25) b. (x − 16)2 = -4(y − 25) c. x2 = -64(y − 25) d. (x − 25)2 = -16(y − 16) e. x2 = -40(y − 25)
The equation of the parabolic shape of the gate is:
(x - 40)² = -64(y - 25)
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
The vertex is at the middle of the parabola, that is, a width of 80/2 = 40 meters and a height of 25 meters, hence h = 40, k = 25, and the equation is:
y = a(x - h)² + k
y = a(x - 40)² + 25
When x = 0, y = 0(start of the arc), hence the leading coefficient is found as follows:
0 = 1600a + 25
a = -25/1600
a = -1/64.
Hence the equation is:
y = -1/64(x - 40)² + 25
(x - 40)² = -64(y - 25)
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What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 5x2 x 3
The solutions to the system of equations involving quadratic function f(x) and linear function g(x) are (-1,5) and (4/3,29/3), respectively.
What is a polynomial function?A polynomial function is a relationship in which a dependent variable equals a polynomial expression. A polynomial expression is one that has numbers and variables that are raised to non-negative powers.To find the solution to the given system of equations:
A polynomial expression has the following generic form:a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ.The degree of the polynomial expression has the greatest power on a variable.When degree = 2, the function is quadratic.When degree = one, the function is linear.Given quadratic equation: f(x) = 3x^2 + x + 3
We must solve the linear equation g(x). Because it is a linear equation, we utilize the two-point approach to solve it.The two point formula is: y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)
We take the points g(2) = 11, g(1) = 9
g(x) - g(1) = ((g(2)-g(1))/(2-1))*(x-1)
or, g(x) - 9 = ((11-9)/(2-1))*(x-1)
or, g(x) - 9 = 2(x-1)
or, g(x) = 2x - 2 + 9 = 2x + 7
g(x) = 2x +7, is the linear function g(x)
We are asked to solve the system of equations f(x) and g(x).
To get the solution, we must first determine what is the common solution to both f(x) and g(x).
For that, we equate f(x) and g(x).
3x² + x + 3 = 2x + 7
or, 3x² - x - 4 = 0
or, 3x² + 3x - 4x - 4 = 0
or, 3x(x+1) -4(x+1) = 0
or, (3x-4)(x+1) = 0
∴ Either 3x-4=0 ⇒ x = 4/3
or, x+1=0 ⇒ x = -1.
g(-1) = 5 (from the table)
f(-1) = 3(-1)² + (-1) + 3 = 3 - 1 + 3 = 5
g(4/3) = 2(4/3) + 7 = 8/3 + 21/3 = 29/3
f(4/3) = 3*(4/3)² + (4/3) + 3 = 16/3 + 4/3 + 9/3 = 29/3
∴ f(-1) = g(-1) and f(4/3) = g(4/3).
Therefore, the solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (-1,5) and (4/3,29/3).
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The correct question is given below:
What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?
f(x) = 3x^2 + x + 3
Alina measured a distance to be 2.18 miles. what is the margin of error? 2.1 miles to 2.2 miles 2.175 miles to 2.185 miles 2.185 miles to 2.195 miles 2.2 miles to 2.3 cm
Answer:
(b) 2.175 miles to 2.185 miles
Step-by-step explanation:
When a value is rounded, the original "exact" value is presumed to be within 1/2 of the value of one least-significant unit of the rounded number.
ApplicationA rounded value of 2.18 has a least-significant digit with a place value of 0.01 units. Half that value is the "margin of error". That is, the range of numbers that would be rounded to 2.18 is ...
2.18-0.005 ≤ x < 2.18+0.005
2.175 ≤ x < 2.185 . . . . miles
PLEASE HELP IM SO STUCK
Answer:
(-4,0) , (0,9)
Step-by-step explanation:
x-intercept is the point where the line touches the x-axis, which means, y = 0.
So when y = 0,
-9x + 4(0) = 36
-9x = 36
x = [tex]\frac{36}{-9}[/tex]
x = -4
Therefore, the coordinates of the x - intercept is (-4,0)
y-intercept is the point where the line touches the y-axis, which means , x = 0.
so when x = 0,
-9(0) + 4y = 36
4y = 36
y = [tex]\frac{36}{4}[/tex]
y = 9
Therefore, the coordinates of the y - intercept is (0,9)
Answer:
x - intercept (-4,0)
y -intercept (0,9)
Step-by-step explanation:
Put in 0 for x.
-9(0) + 4y = 36
4y = 36 Divide both sides by 4
y = 9
(0,9) This is where the line will cross the y axis.
Put in 0 for y
-9y + 4(0) = 36
-9y = 36 Divide both sides by -9
Y = -4
Which describes the combined variation shown in the equation F = kxy/z?
1) F varies directly with x, and inversely with y
and z.
2)F varies directly with z, and inversely with x
and y.
3)F varies directly with y, and inversely with x and z.
4) F varies directly with x and y, and inversely
with z.
Answer:
option 4
Step-by-step explanation:
F = [tex]\frac{kxy}{z}[/tex]
k is the constant of variation
• if the variables are on the numerator they vary directly
• if the variables are on the denominator they vary inversely
In this case F varies directly with x and y ( variables on numerator ) and inversely with z ( variable on denominator )
Helpppppppppp show your steps to the answer
Answer:
9
Step-by-step explanation:
you have to plug in the numbers and solve it, so it would go as follows:
-(-3^2)- 2(-5)(2) - /2/
-9 + 20 - 2 =
9
i hope this helps
PLS HELP ITS MATH PLS
[tex] \: \: \: \: \: \: \: y = \frac{ - 7x}{8} + 4 \\ \: \: \: \: \: \: multiply \: all \: by \: 8 \\ \: \: \: \: \: \: \: \: 8y = - 7x + 32 \\ \: \: \: \: \: \: \: \: \: 7x + 8y = 32[/tex]
( 7 , 8 , 32 )A man is 32 years older than his son. Ten years ago he was three times as old as his son was then. Find the present age of each
Answer:
Son: 26 yrs. Dad: 58 yrs.
Step-by-step explanation:
Let s equal to the present age of the son and let d equal to the present age of the dad. We can make two equations based on the information given to us. The first is about the fact that the dad is 32 yrs. older than the son:
d = s+32
the second is about the fact that 10 yrs. ago, he was triple his son's age.
d-10 = 3(s-10)
We can use the distributive property and we have:
d-10 = 3s-30
Then, let's add 10 to each side:
d = 3s-20
We can substitute the first equation into the second, resulting in:
s+32 = 3s-20
Adding 20 to both sides:
s+52 = 3s
2s = 52
s = 26
Now that we have the son's age, the dad's age is 26+32 = 58.
Son's age: 26
Dad's age: 58
An architectural drawing lists the scale as 1/4" = 1'. if a bedroom measures 312" by 514" on the drawing, how large is the bedroom?
The length of the bedroom exists at x = 9 and y = 6.
How to estimate the length of the bedroom?From the given information, we get
Then [tex]$\frac{(1/4)}{(9/4)} = \frac{1}{x}[/tex]
Solve this for x.
simplifying the value of x we get
Equate (1/9) to 1/x.
x = 9 (feet).
Convert 1.5 inches to feet using a proportion:
[tex]$\frac{(1/4)}{(1.5)} = \frac{1}{y}[/tex]
Solve this for y.
simplifying the value of y we get
(1/4)y = 3/2
Multiply both sides of the equation by 4.
y = 6
Therefore, the length of the bedroom exists at x = 9 and y = 6.
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A bag contains blue, orange and red jelly beans only there are 6x blue jelly beans, 2x-3 orange jelly beans and 15-x red jelly beans there are a total of 54 jelly beans in the bag.
a) how many orange jelly beans are there in the bag?
b) how many blue jelly beans are there in the bag?
Answer:
a.9
b.36
Step-by-step explanation:
Blue beans + orange beans + red beans = 54
6x + 2x-3 + 15-x = 54
6x+2x-x=54+3-15
7x=42
divide both sides by 7
x=6
a. orange beans = 2x-3
but x=6
2(6)-3
12-3
=9
b.blue beans =6x
6(6)
=36
the length of the sides of a triangle are in the ratio 3:4:5. find the lengths of the sides of the triangle if its perimeter is 96cm
Answer:
let the angles be 3x,4x&5x
Now,
perimeter (p)=sum of all sides
or, 96=3x+4x+5x
or, 96=12x
or,96/12=x
or,8=x
or,x=8
Then,
3x=3*8
=24
4x=4*8
=32
5x=5*8
=45
select the graph that correctly represents the following equation. 4x-3y=-1
The graph of the given equation is shown below
Graph of a straight lineFrom the question, we are to determine the graph that represents the given equation
The given equation is
4x - 3y = -1
The graph of the equation is shown below
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What is a fitted value for a multiple regression model and the data that is used to create it?
Fitted value is a prediction of the mean response value.
According to the statement
we have to explain the fitted value for the regression model and the data which uses to collect the value.
So, For this purpose, we know that the
A Fitted value is a statistical model's prediction of the mean response value when you input the values of the predictors, factor levels, or components into the model.
An the fitted value used in this model is called the predicted values of response variable in the case of multiple regression model.
And data which is used to create the fitted value is the simple data by which we create the fitted value by the predict the value of given data.
So, Fitted value is a prediction of the mean response value.
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x6 = 64 solve for X please
Answer:
x = 2
Step-by-step explanation:
note that 64 = [tex]2^{6}[/tex]
then
[tex]x^{6}[/tex] = [tex]2^{6}[/tex] , so x = 2
Find the equation of the line using exact numbers
Answer:
y = - [tex]\frac{1}{3}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2-y_{1} } }{x_{2-x_{1} } }[/tex]
with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (3, 4) ← 2 points on the line
m = [tex]\frac{4-5}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex] = - [tex]\frac{1}{3}[/tex]
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = - [tex]\frac{1}{3}[/tex] x + 5 ← equation of line
Solve the problems involving (HCF) highest common factor for each of the the following
B) A restaurant donated 540 pieces of fried chicken and 360 cups of drink for a gathering event. The restaurant has set the condition the every visitor will receive the portion of food equally. Find :
(1) Find the maximum number of visitors that can be invited to the event.
(2) Find the numbers of pieces of chicken to be received by the visitors who attended the event.
Step-by-step explanation:
the highest or greatest or largest common factor is the product of the prime factors the numbers have in common :
540 ÷ 2 = 270
270 ÷ 2 = 135
135 ÷ 2 no
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 3 no
5 ÷ 5 = 1
540 = 2² × 3³ × 5¹
360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 2 no
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 3 no
5 ÷ 5 = 1
360 = 2³ × 3² × 5¹
so, the HCF = 2² × 3² × 5¹ = 4×9×5 = 180
(1)
to satisfy the condition max. 180 visitors can be invited.
(2)
540 / 180 = 3
so, every visitor can receive 3 pieces of chicken.
and 360 / 180 = 2 cups of drink.
How many diagonals does a regular n-gon have? ( An n-gon is a regular polygon with n sides)
Answer:
Use this equation to find out!
Step-by-step explanation:
Since you didn't specify the n-gon, you have to use this equation to find out!
Number of Diagonals = n(n-3)/2
Hope this helps! :)
Solve this:
NO INCORRECT or report
Answer:
D
Step-by-step explanation:
Let x be the first batch
let y be the second batch
y=2x
His brothers each received 9 rolls from the second batch i.e. 9×4=36
So
2x= 36+ (10÷6)x
2x - (10÷6)x = 36
12x-10x = 216
x=108
and y= 2 × 108= 216
Hey guys please help? Trigonometry
So, the task is: find cos a, if:
1) sin a = (3√11)/10, a ∈ (0; π/2)
2) sin a = (3√11)/10, a ∈ (π/2; π)
Could someone please explain how to solve it? I can't figure out what difference a ∈ (0; π/2) and a ∈ (π/2; π) make in the way I have to solve it mmh... I'll pin my attempt to do the first one (failed for some reason)
Step-by-step explanation:
a ∈ (0; π/2) here means that our angle, a must lie between 0 and pi/2, exclusive.
So this mean our angle must be in between 0 and pi/2, but can not be neither 0 and pi/2.
Here we have
[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]
We must find cos.
Using the Pythagorean theorem
[tex]( \sin( \alpha ) ) {}^{2} + ( \cos( \alpha ) ) {}^{2} = 1[/tex]
It is mostly notated as this,
[tex] \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1[/tex]
But they mean the same thing, we know
[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]
So we plug that in for sin a.
[tex]( \frac{3 \sqrt{11} }{10} ) {}^{2} + \cos {}^{2} ( \alpha ) = 1[/tex]
[tex] \frac{99}{100} + \cos {}^{2} ( \alpha ) = 1[/tex]
[tex] \cos {}^{2} ( \alpha ) = \frac{100}{100} - \frac{99}{100} [/tex]
[tex] \cos {}^{2} ( \alpha ) = \frac{1}{100} [/tex]
Since cos is Positve over the interval (0; π/2), we take the positive or principal square root.
[tex] \cos( \alpha ) = \frac{1}{10} [/tex]
2. We would get the same work for the second part, the only difference is that cosine is negative over the interval
(π/2, π)
So the answer for 2 is
[tex] \cos( \alpha ) = - \frac{1}{10} [/tex]
Disclaimer: Your work you did was correct, just remember for fractions like
[tex]1 - \frac{99}{100} [/tex]
Convert 1 into a fraction that has a denominator of 100.
[tex] \frac{100}{100} - \frac{99}{100} = \frac{1}{100} [/tex]
Write the event as set of outcomes. when we roll two dice, the total showing is eight.
Find an equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0)
The equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16
Equation of a straight lineFrom the question, we are to determine the equation of the line parallel to the given equation and that passes through the given point
Lines that are parallel to each other will have the same slope.
First, we will determine the slope of the line in the given equation.
The given equation of the line is
8x − 3y = 1
Express the equation in the slope-intercept form of a line, y = mx + b
Where m is the slope and
b is the y-intercept
That is,
8x − 3y = 1
8x -1 = 3y
3y = 8x - 1
y = 8/3(x) - 1/3
By comparing,
∴ The slope of the line is 8/3
Since we are to find the equation of a line parallel to this, the slope of the line will also be 8/3
Now, find the equation of a line containing the point (-2, 0) and that has a slope of 8/3
Using the point-slope form of a line
y - y₁ = m(x - x₁)
x₁ = -2
and y₁ = 0
∴ y - 0 = 8/3(x - -2)
y = 8/3(x +2)
3y = 8(x +2)
3y = 8x + 16
8x -3y = -16
Hence, the equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16
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Help!!
why might you choose to write a recursive formula rather than an explicit formula to define a sequence
a. you need to know the 54th term in the sequence
b. the sequence is neither arithmetic or geometric
c. you need to know the value of three non-sequential terms in the sequence
d. the sequence is strictly geometric
We might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.
What is a sequence?A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the series is defined as the number of items (which could be infinite). Unlike a set, the same components can appear numerous times in a sequence at different points, and the order does important. Formally, a sequence can be defined as a function from natural numbers (the sequence's places) to the elements at each point. The concept of a sequence can be expanded to include an indexed family, which is defined as a function from an index set that may or may not contain integers to another set of elements.Recursive formulas are commonly used to compute the nth term of a sequence, where a(n) is the sum of all the preceding values.
Using its position, explicit formulas can compute a(n).
Therefore, we might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.
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Answer: (D)
Step-by-step explanation:
took quiz
The rectangles below have the same perimeter.
Rectangle:A Base=3 height=9
Rectangle B:base=4
Answer:
32 mm²
Step-by-step explanation:
perimeter of left rectangle = 2(9 mm + 3 mm) = 24 mm
length of right rectangle = L
perimeter of right rectangle = 2(L + 4 mm) = 2L + 8
perimeter of right rectangle = 24 mm
The perimeter of the right triangle is 2L + 8 and also 24, so 2L + 8 must equal 24. We can solve for L and find the length of the right rectangle.
2L + 8 = 24
2L = 16
L = 8
area of right triangle = length × width
area = 8 mm × 4 mm
area = 32 mm²
**Disclaimer** Hi there! I assumed the purple triangle to be the one on the right. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.
Answer: [tex]\Large\boxed{Area=32~mm^2}[/tex]
Step-by-step explanation:
Given information
Rectangle A:
Base (b) = 3 mmHeight (h) = 9 mmRectangle B:
Base (b) = 4 mmHeight (h) = ?Both rectangles have the same perimeter
Given formula
1) P = 2 (b + h)
P = Perimeterb = baseh = height2) A = b × h
A = Perimeterb = baseh = heightFind the height of rectangle BSubstitute values into 1) formula to find the perimeter of rectangle A
P = 2 (b + h)
P = 2 (3 + 9)
Simplify by addition
P = 2 × 12
Simplify by multiplication
P = 24 mm
Substitute values into 1) formula to find the perimeter of rectangle B
P = 2 (b + h)
24 = 2 (4 + h)
Divide 2 on both sides
24 / 2 = 2 (4 + h) / 2
12 = 4 + h
Subtract 4 on both sides
12 - 4 = 4 + h - 4
h = 8 mm
Find the area of rectangle B (Purple)Substitute values into 2) formula
A = b × h
A = 4 × 8
Simplify by multiplication
[tex]\Large\boxed{Area=32~mm^2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Find the distance in nm between two slits that produces the first minimum for 405-nm violet light at an angle of 57. 5°
The distance between two slits is d =2.89*10^-7 m
Distance between slits, d=2.89*10^-7 m
It is given that,
Wavelength, λ = 410nm= 410*10^-9 m
Angle, θ =45
We need to find the distance between two slits that produces first minimum. The equation for the destructive interference is given by :
dsinθ =(n+1/2) λ
For first minimum, n = 0
dsinθ =(1/2) λ
So, d is the distance between slits
d ={1/2 λ}sinθ
=2.89*10^-7 m
So, the distance between two slits is d =2.89*10^-7 m. Hence, this is the required solution.
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