Answer: 3.5
Step-by-step explanation:
To find the length of the missing leg, we need to use the Pythagorean Theorem (a^2 + b^2 = c^2 where c is the hypotenuse)
1) Plug in numbers
2^2 + b^2 = 4^2
2) Square
4 + b^2 = 16
3) Flip Equation and Subtract
16 - 4 = b^2
16 - 4 = 12
4) Square Root of 12
The square root of 12 is ~3.46, so you need to round to the nearest tenth, which is 3.5
f(x) = cube root 2x
g(x) = 2x + 1
Find (f/g) (X) Include any restrictions on the domain
Answer:
B.
Step-by-step explanation:
any arithmetic operation with functions just means to do this operation with the functional expressions.
f/g is really just the expression of f divided by the expression of g.
so, this results in a fraction with the denominator (bottom part) = 2x + 1
as you know, a division by 0 is not a valid operation, and therefore we have to forbid any value for x that would create a 0 in the denominator.
so, for what x do we get
2x + 1 = 0
2x = -1
x = -1/2
therefore, we have to exclude x = -1/2.
[tex] \rm \int_{ \infty }^{ - \infty } \frac{ { {e}^{ { - x}^{2} } }(5 {x}^{2} + 2 {x}^{4} )}{ {x}^{2}( {x}^{2} + 1)} dx \\ [/tex]
Consider the integral
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx[/tex]
which is the negative of yours. Bit strange to integrate over [tex](\infty,-\infty)[/tex], but if that's what you actually intended, just multiply the final result by -1. Of course, I've already canceled the superfluous factors of [tex]x^2[/tex].
Expand the integrand into partial fractions.
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = \int_{-\infty}^\infty \left(2 + \frac3{1+x^2}\right) e^{-x^2} \, dx[/tex]
Recall that for [tex]\alpha>0[/tex],
[tex]\displaystyle \int_{-\infty}^\infty e^{-\alpha x^2} \, dx = \sqrt{\frac\pi\alpha}[/tex]
Now let
[tex]\displaystyle I(a) = \int_{-\infty}^\infty \frac{e^{-ax^2}}{1+x^2} \, dx[/tex]
Together, these give
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = 2\sqrt\pi + 3I(1)[/tex]
Differentiate [tex]I(a)[/tex] under the integral sign with respect to [tex]a[/tex] to obtain a simple linear differential equation.
[tex]\displaystyle \frac{dI}{da} = -\int_{-\infty}^\infty \frac{x^2 e^{-ax^2}}{1+x^2} \, dx \\\\ ~~~~~~~~ = - \int_{-\infty}^\infty \left(1 - \frac1{1+x^2}\right) e^{-ax^2} \, dx \\\\ ~~~~~~~~ = -\sqrt{\frac\pi a} + I(a)[/tex]
Solve for [tex]I(a)[/tex] with the initial value [tex]I(1) = \sqrt\pi[/tex]. Using an integrating factor,
[tex]\displaystyle \frac{dI}{da} - I(a) = -\sqrt{\frac\pi a} \\\\ e^{-a} \frac{dI}{da} - e^{-a} I(a) = -\sqrt{\frac\pi a}\,e^{-a} \\\\ \frac{d}{da}\left[e^{-a} I(a)\right] = -\sqrt{\frac\pi a}\,e^{-a}[/tex]
By the fundamental theorem of calculus,
[tex]\displaystyle e^{-a} I(a) = e^{-a}I(a)\bigg|_{a=0} - \sqrt\pi \int_0^a \frac{e^{-\xi}}{\sqrt\xi} \, d\xi \\\\ I(a) = \pi e^a - \sqrt\pi \, e^a \int_0^a \frac{e^{-\xi}}{\sqrt\xi} \, d\xi[/tex]
so that
[tex]\displaystyle I(1) = \pi e - \sqrt\pi\,e \int_0^1 \frac{e^{-\xi}}{\sqrt\xi} \, d\xi[/tex]
Substitute [tex]t=\sqrt\xi[/tex].
[tex]\displaystyle I(1) = \pi e - 2\sqrt\pi\,e \int_0^1 e^{-t^2} \, dt[/tex]
Recall the error function,
[tex]\mathrm{erf}(x) = \displaystyle \frac2{\sqrt\pi} \int_0^x e^{-t^2} \, dt[/tex]
which we can use to write
[tex]I(1) = \pi e - 2\sqrt\pi e \cdot \dfrac{\sqrt\pi}2\,\mathrm{erf}(1) = \pi e - \pi e \,\mathrm{erf}(1)[/tex]
Finally, we arrive at
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = \boxed{2\sqrt\pi + 3\pi e - 3\pi e \, \mathrm{erf}(1)}[/tex]
Which expression simplifies to 2√/15? A. V17 OB. √19 OC √30 OD. √60
please help just have 3 minutes left
Answer:
Step-by-step explanation:
Suppose the odds are 38 to 1 that someone will lie to you at least once in the next seven days. State this as a probability.
Answer:
38/39
Step-by-step explanation:
P=s/(s+f)
P=38/(38+1)
P=38/39
At the beginning of each of her four years in college, Miranda took out a new Stafford loan. Each loan had a principal of $5,500, an interest rate of 7.5% compounded monthly, and a duration of ten years. Miranda paid off each loan by making constant monthly payments, starting with when she graduated. All of the loans were subsidized. What is the total lifetime cost for Miranda to pay off her 4 loans? Round each loan's calculation to the nearest cent.
a.
$23,650.00
b.
$29,481.08
c.
$7,834.32
d.
$31,337.27
The total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27.
What is interest?Interest is the sum of money paid for using someone else's funds. You must pay interest when you borrow money from lenders. You receive interest when you lend money to borrowers. It could be stated in terms of money or the rate of payment. You will learn more about interest in this article, including the different sorts of interest, what they are, and how to determine how much interest will be charged on a loan or a loan amount.
Given that,
At the beginning of each of her four years in college
Miranda took out a new Stafford loan.
Each loan had a principal of $5,500,
An interest rate of 7.5% compounded monthly
A duration of ten years.
Miranda paid off each loan by making constant monthly payments, starting with when she graduated.
All of the loans were subsidized.
The total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27
Therefore, the total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27
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Answer: D 31,337.27
Step-by-step explanation:
The length of a rectangle is twice its width.
If the perimeter of the rectangle is 36 m, find its area
Answer:
length= 12 width=6
Step-by-step explanation:
when adding perimeter you add the length and width twice each so divide 36 by two and get 18
if the length is twice the width then you could make the equation w+2w=18
by adding like terms you get 3w=18
to get n by itself you divide 18 by 3 and get w=6
if the width is 6 and the length is twice that then the length is 12
Answer:
A=72
Step-by-step explanation:
The length of a rectangle is TWICE it's width meaning 2 times. (Note that L= length, W=width, and A=Area)
L=2w
4w+2w=36
6w=36 <- ( 6 is width)
then
2x6=12
Then
12x6=72
So the area of the rectangle is 72.
Hope that makes sense!
if 2/5 kilogram of soil fills 1/3 of a container,can1 a kilogram of soil fit in the container? Explain or show your reasoning
Answer:
Yes
Step-by-step explanation:
1 kilogram of soil will fill:
1/3 ÷ 2/5 = 5/6 (of a container)
Because 5/6 < 1
=> 1 kilogram of soil will fit in the container
Question 7 of 20:
Select the best answer for the question.
7. Percent means "per
O A. 100
OB. 1000
O C. 1
O D. 10
11
K
OMark for review (Will be highlighted on the review p
A dressmaker needs to cut 18-inch pieces of ribbon from rolls of ribbon that are 3 feet in length. How many 18-inch pieces can the dressmaker cut from 15 of these rolls of ribbon?
3y^3+20y^2=7y
Solve the polynomial by factoring. The answer is y(3y-1)(y+7)
I can't seem to figure out how they got the answer. I need an explanation before my test tomorrow.
Answer:
Hello,
Step-by-step explanation:
[tex]3y^3+20y^2-7y=y(3y^2+20y-7)\\\\=y(3y^2+21y-y-7)\\\\=y(3y(y+7)-(y+7))\\\\=y(y+7)(3y-1)\\[/tex]
Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original price of $10.50 each, but later decreased the price of each by $2.00. If they sold all 98 pieces and took in $893.00
find how many they sold at the original price and how many they sold at the reduced price.
Answer:
See work below.
30 sold for full price and 68 sold for a discount.
Step-by-step explanation:
Find the unit tangent vector for the following parameterized curves.
r(t)=cos(t)i+sin(t)j+sin(t)k, 0≤t<2π.
The unit tangent vector for the parametrized curve is [tex]\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}[/tex].
How to determine the unit tangent vector of a parametrized curveIn this question we know a three-dimension parametrized curve, of which we must derive its unit tangent vector in accordance with the following formula:
[tex]\vec T(t) = \frac{\vec R'(t)}{\|\vec R'(t)\|}[/tex]
Where:
[tex]\vec T(t)[/tex] - Tangent vector.[tex]\|\vec R'(t)\|[/tex] - Magnitude of the first derivative of the parametrized curve.First, determine the first derivative of the parametrized curve:
[tex]\vec R'(t) = -\sin t \,\hat{i} + \cos t \,\hat{j} + \cos t \,\hat{k}[/tex]
Second, derive the magnitude of the parametrized curve:
[tex]\|\vec R'(t)\|[/tex] = √[(- sin t)² + (cos t)² + (cos t)²]
[tex]\|\vec R'(t)\|[/tex] = √(1 + cos² t)
Third, substitute every term in the unit tangent curve formula:
[tex]\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}[/tex]
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Whats the constant term for y=3x + 5
1. 3
2. 5
i answered this one already on your other post for it
3 is the constant/slope
5 is the y intercept
In the last year school board election Mrs Jackson received 60.1% of the votes write three equivalent fractions for 60.1% with denominator of 1000 and 100and 10
QUESTION 94
Percentages
In January 2021, a study by the Bureau of Transportation statistics found that 12 out of 35 flights arrived
on time. What percent of the flights were on time?
Choose one 4 points
O 72%
O 34.3%
O 34%
O 27%
Answer: 34.3%
Step-by-step explanation:
[tex]Given:\ 12/35\ flights\ on\ time[/tex]
To find the percent, divide then multiply by 100:
[tex]\frac{12}{35} = 0.343\times100=\large\boxed{34.3}[/tex]
Need help with D pls will give brainly
The length of the pen is 2√3 feet
Area of a triangleThe formula for calculating the area of a rectangle is expressed according to the formula below:
Area of a right triangle = 1/2 * base * height
A = 1/2 bh
Given the following parameters
Area = 20 square feet
If the height is five times the length, then;
h = 5b
Substitute
A = 1/2 bh
A = 1/2(b)5b
30 = 1/2(5b²)
60 =5b²
b² = 12
b = 2√3
Hence the length of the pen is 2√3 feet
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Find the values of x and y. Write all radicals in simplest form.
Answer:
For the 60-30-90 degree triangle:
x=12
y=[tex]12\sqrt{3}[/tex]
For the 30-60-90 degree triangle:
x=16
y=[tex]8\sqrt{3}[/tex]
For the 45-45-90 degree triangle:
x=7
y=[tex]7\sqrt{2}[/tex]
Step-by-step explanation:
For 30-60-90 triangles, the side opposite the 30 degree angle is x, while the side opposite the hypotenuse is 2x, while the side opposite the 60 degree angle is [tex]x\sqrt{3}[/tex].
For 45-45-90 triangles, the sides opposite the 45 degree angles are x, while the hypotenuse is [tex]x\sqrt{2}[/tex].
f(x) = 5x-7, then what is the solution to f(x) = 4?
(1) 13
(3) -87
(2)-7
(4) 2}
I need some work or explanation please ASAP
The solution to function f(x) = 4 is 2 1/5.
Given that, f(x) = 5x - 7
Now, function f(x) = 4 implies that
i.e. 5x - 7 = 4
i.e. 5x = 4 + 7
i.e. 5x = 11
i.e. x = 11/5
x =2 1/5
So, option (4) is correct.
The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
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The function is f(x)= 5x-7. The solution to f(x)=4 is when x is 11/5.
Given that,
The function is f(x)= 5x-7
A function is nothing but in mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain),where there is exactly one output for every input, and the output can be connected to its input.
f(x), where x is the input, is a common way to refer to a function. A function represented as y = f(x).
We have to find the solution to f(x)=4
Take 5x-7 in the place of f(x) because they are equal.
5x-7=4
5x=4+7
5x=11
x=11/5
Therefore, the solution x value is 11/5.
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Please answer this screenshot please 10 points good idea yes.
Answer:
Yes it is a function
Step-by-step explanation:
There is a relationship between x and y. It is not linear but quadratic
Answer:
yes it is a function
Step-by-step explanation:
that is the answer bc I said I was
Tom and Louise share £40 in the ratio 1 : 3 work out how much money Tom gets
Answer:
5
Step-by-step explanation:
because I give him and the answer is incorrect I know but I gave him believe me
Urgent (I added 50 points)
The diagram below is drawn on a one-centimetre square grid
Work out the area of the shaded triangle:
The area of the shaded triangle will be 11.5 square centimeters.
What is the area of the shaded region?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The area of the square will be given as,
A₁ = 5 x 5
A₁ = 25
The area of the triangles will be given as,
A₂ = 1/2 (1 x 5 + 4 x 3 + 2 x 5)
A₂ = 1/2 (27)
A₂ = 27/2
Then the area of the shaded triangle will be given as,
A = A₁ - A₂
A = 25 - 27/2
A = (50 - 27) / 2
A = 23/2
A = 11.5 square cm
The area of the shaded triangle will be 11.5 square centimeters.
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Answer:
In the graph, excluding the shaded triangle, there are three right angled triangles surrounding the shaded triangle in a square
Area of shaded triangle = area of square - area of three triangles
[tex]{ \sf{area = (5 \times 5) - ( \frac{1}{2} \times 4 \times 3) - ( \frac{1}{2 } \times 5 \times 2) - ( \frac{1}{2} \times 5 \times 1)}} \\ \\ { \sf{area = 25 - 6 - 5 - 2.5}} \\ \\ { \sf{area = 11.5 \: {cm}^{2} }}[/tex]solve the equation for x (3x/4)+2=4x-1
Answer:
Step-by-step explanation:
Approximate √10 to the nearest tenth
Scientific notation question HW
Answer:
the scientific notation of 83300 is 8.33*10^4
i really need help! please
solve the equation by performing two operations on both sides. State the operation in order of use
Answer:
C. Multiply by 5, then subtract 7.
Step-by-step explanation:
You want to know the two steps required to solve this 2-step linear equation.
SolutionThe variable x has 7 added to it, and the sum is divided by 5. To find the value of x, we must undo these operations in reverse order.
To undo division by 5, we must multiply by 5.
Then, to undo the addition of 7, we must subtract 7.
Here is the "work":
[tex]\dfrac{x+7}{5}=10\qquad\text{given}\\\\x+7 = 50\qquad\text{multiply both sides by 5}\\\\x=43\qquad\text{subtract 7 from both sides}[/tex]
The operations in order of use are ...
Multiply both sides by 5 first, then subtract 7 from both sides.
__
Additional comment
The properties of equality tell you that you must do the same operation to both sides of the equation.
The system of equations graphed below has how many solutions?
y = 2x + 2
y= 2x
The given system has zero solutions.
Lines that never cross one other are said to be parallel. Hence, a pair of parallel lines must have the same slope but distinct intercepts. (On the other hand, identical lines have same intercept).
In the general equation of a line, y = mx + b, m represents the slope of the line.
The general equations of parallel lines would be of the form:
(1) y = mx + b
(2) y = mx + c
where b and c are any constants.
Now, we observe that the given equations are of the above form with m=2, b=2 and c=0, therefore, they are parallel lines. Since, parallel lines never intersect each other, they have no solution.
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What is an equation of the line that passes through the points (3, 6) and (-1, -6)?
Find the rate of change of f(x) = x² - 2x + 3 on [-1,2].
Answer:
-1.
Step-by-step explanation:
Rate of change = [ f(2) - f(-1)] / [2 - (-1)]
= [(2)^2 - 2(2) + 3) - ((-1)^2 - 2(-1) + 3] / 3
= ( 3 - 6)/3
= -1.
television and DVD player cost a total of $1242. The cost of the television is two times the cost of the DVD player. Find the cost of each item.
Answer: TV costs $828 and DVD player costs $414.
Step-by-step explanation: let x represent the cost of tv while y represents the cost of the player. x+y = 1242. since the tv costs twice as much as the dvd player, we can say that 2y=x. now replace x with 2y in our equation and we get 2y+y= 1242, 3y = 1242. now divide both sides by 3 and y = 414. Now that we now the value of y, just sub it into our original equation, x+y = 1242. x + 414 = 1242. x = 828.