Answer:43.289
Step-by-step explana
Write 7.21 as a mixed number in simplest form. 7.21 =
Answer:7 21/100
Step-by-step explanation: We will covert 7.21 into a fraction. .21 = 21/100. Since 21 can only be divided by 3 and 7, the simplest form of 21/100 is 21/100. So, the mixed number is 7 and 21/100
Answer:
7 and 21/100
Step-by-step explanation:
Since .01 is 1/100, 7.21 will be 7 and 21/100. There is no way to further simplify this, therefore, it is our final answer. Hope this helps! :)
Using synthetic division what is (3x² + 7x - 18) = (x - 3)
Answer:
3x + 16 + 30/x - 13
Step-by-step explanation:
Given vectors u = ⟨–3, 2⟩ and v = ⟨2, 1⟩, what is the measure of the angle between the vectors?
The measure of the angle between the vectors
[tex]$\arccos[ (-\sqrt{13 } i )/ (\sqrt{5 }) ]\\\sqrt{5 }[/tex].
What is the measure of the angle between the vectors?
Given:
[tex]$\mathrm{u}=\langle -3,2\rangle$[/tex] and [tex]$v=\langle 2,1\rangle$[/tex]
Computing the angle between the vectors, we get
[tex]$\quad \cos (\theta)=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}| \cdot|\vec{b}|}$[/tex]
To estimate the lengths of the vectors, we get
Computing the Euclidean Length of a vector,
[tex]$\left|\left(x_{1}, \ldots, x_{n}\right)\right|=\sqrt{\sum_{i=1}^{n}\left|x_{i}\right|^{2}}$[/tex]
Let, [tex]$\mathrm{u} &=\langle -3,2\rangle \\[/tex] and [tex]$\mathrm{v} &=\langle 2,1\rangle \\[/tex]
If [tex]$\mathrm{u} &=\langle -3,2\rangle \\[/tex]
[tex]$|u| &=\sqrt{-3^{2}+(2)^{2}} \\[/tex]
[tex]$&=\sqrt{5}i \\[/tex] and
[tex]$\mathrm{v} &=\langle 2,1\rangle \\[/tex]
[tex]$|v| &=\sqrt{2^{2}+(1)^{2}} \\[/tex]
[tex]$&=\sqrt{5}[/tex]
Finally, the angle is given by:
Computing the angle between the vectors, we get
[tex]$ $\cos (\theta)=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}| \cdot|\vec{b}|}$[/tex]
[tex]$&\cos (\Phi)=-\sqrt{13 } i/ \sqrt{5 } \\[/tex]
simplifying the above equation, we get
[tex]$&\Phi=\arccos (\cos (\Phi))[/tex]
[tex]$=\arccos[ (-\sqrt{13 } i )/ (\sqrt{5 }) ]\\\sqrt{5 }[/tex]
Therefore, the measure of the angle between the vectors
[tex]$\arccos[ (-\sqrt{13 } i )/ (\sqrt{5 }) ]\\\sqrt{5 }[/tex].
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Use the laplace transform to solve the given initial-value problem. y'' + y = f(t), y(0) = 0, y'(0) = 1, where f(t) = 0, 0 ≤ t < 1, ≤ t < 2 0, t ≥ 2
In order to solve this IVP using Laplace transforms, we must first write f(t) in terms of the Heaviside function.
f(t)=0*(u(t)-u(t-Pi))+1*(u(t-Pi)-u(t-2Pi))+0*(u(t-2Pi))
f(t)=u(t-π)-u(t-2π)
So, the rewritten IVP is
y'' +y = u(t-π)-u(t-2π)y(0)=0, y'(0)=1
Taking the Laplace transform of both sides of the equation, we get:
s2L{y}-sy(0)-y'(0)+L{y}=(1/s)*e-πs-(1/s)*e-2πs
s2L{y}-1+L{y}=(1/s)*e-πs-(1/s)*e-2πs
(s2+1)L{y}=1+(1/s)*e-πs-(1/s)*e-2πs
L{y}=1/(s2+1)+(1/s(s2+1))e-πs-(1/s(s2+1))*e-2πs
Now, we must take the inverse transform of both sides to solve for y.
The first inverse transform is easy enough. By definition, it is sin(t).
The second two inverse transforms will be a little tougher, we will have to use partial fraction decomposition to break them down into terms that are easier to compute.
A/s+(Bs+C)/(s^2+1)=1/(s(s^2+1))
A(s^2+1)+(Bs+C)(s)=1
As^2+A+Bs^2+Cs=1
Rewriting this system in matrix form, we get:
1 1 0 A 0
0 0 1 * B = 0
1 0 0 C 1
Using row-reduction we find that A=1, B=-1, and C=0. So, our reduced inverse transforms are:
L-1{(e-πs)(1/s-s/(s2+1))}
and
L-1{(e-2πs)(1/s-s/(s2+1))}
Using the first and second shifting properties, these inverse transforms can be computed as.
L-1{(e-πs)(1/s-s/(s2+1))}=u(t-π)-cos(t-π)u(t-π)
L-1{(e-2πs)(1/s-s/(s2+1))}=u(t-2π)-cos(t-2π)u(t-2π)
Combining all of our inverses transforms, we get the solution the IVP as:
y=sin(t)+u(t-π)-cos(t-π)u(t-π)+u(t-2π)-cos(t-2π)u(t-2π)
In mathematics, the Laplace transform, named after its discoverer Pierre Simon Laplace (/ləˈplɑːs/), transforms a function of real variables (usually in the time domain) into a function of complex variables (in the time domain). is the integral transform that Complex frequency domain, also called S-area or S-plane).
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How many cookies did he eat in 3.45
Answer:
20 cookies
Step-by-step explanation:
8 in 1.5 minutes
so we want to find how many in 3.75 minutes since 3 + 45/60 = 3.75
so then its 1.5*2 = 3 so 8*2 = 16 to get that 16 cookies in 3 minutes
then we still have .75 left so then divide 8/2 to get 4 cookies in 0.75 minutes
16+4 = 20
you can also just find how many in 0.25 minutes (15 seconds) you get 6/8
multiply that by 3.75/0.25 = 15 you get 15*(8/6) = 20
P= ().()
Q=(),()
Please help thanks so much
The coordinates for P and Q are as follows,
P = (a, a)
Q = (0, a)
Finding the Missing Coordinates:
Triangle OPQ is an isosceles triangle, hence two of its legs are equal.
Since the coordinates of the end point of the leg OQ lies on the y-axis, and OP is parallel to x-axis, OQ ⊥ QP ............ (1)
Also, it indicates that the x- coordinate of point Q is 0.
⇒ The coordinates of point Q are (0, a)
From (1), we can infer that,
OP = OQ [∵ OP is the hypotenuse]
⇒ The distance of point P from x-axis = a
The distance of point P from y-axis =a
Hence, the coordinates of point P are given as (a, a).
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Today, Stephen is three times as old as Gautham. Ten years ago Stephen turned 2. How old will Gautham be
in 8 years?
I need help im bad at math
Answer: 243
Step-by-step explanation:
If you divide the 18 inch by two to get the r, you will get 9. So you should multiple the 3 and the 9 square. So it should be 3x81=243
FIRST CORRECT ANSWER WILL GET BRAINLIEST
Answer:
(c) f(g(3)) > g(f(3))
Step-by-step explanation:
The relationship between the function values can be found by evaluating the functions.
f(g(3))The order of operations tells us we must first evaluate g(3).
g(x) = -3x +15
g(3) = -3(3) +15 = 6
Then we can evaluate f(x) for x=6:
f(x) = 7x
f(6) = 7(6) = 42
So, the composition is ...
f(g(3)) = 42
g(f(3))As above, we must first evaluate f(3):
f(3) = 7(3) = 21
Then we can evaluate g(x) for x=21:
g(21) = -3(21) +15 = -63 +15 = -48
That means the composition is ...
g(f(3)) = -48
ComparisonThe first is greater than the second.
42 > -48
f(g(3)) > g(f(3))
solve for x
2^x,2^4=2^3x
Answer:
x=2
Step-by-step explanation:
2^x *2^4=2^3x
using law of indices
2^x+4=2^3x
x+4=3x
4=3x-x
4=2x
2=x
Help me pls i very need your answer
[tex]x = \frac{\sqrt{5} + 1}{2} \approx 1.618033989[/tex]
does someone mind helping me with this? Thank you!
5. In one game, the final score was Falcons 3, Hawks 1. What fraction and
of the total goals did the Falcons score? Show your work in the space
percent
below. Remember to check
your
solution.
Step-by-step explanation:
Select the reason that best supports statement 5 in the given proof.
Answer:
B
Step-by-step explanation:
if an angle is congruent, it is the same measurement
Find the most general antiderivative of the function. (check your answer by differentiation. use c for the constant of the antiderivative. ) g(t) = 8 t t2 t
The most general antiderivative of the given function g(t) is (8t + t³/3 + t²/2 + c).
The antiderivative of a function is the inverse function of a derivative.
This inverse function of the derivative is called integration.
Here the given function is: g(t) = 8 + t² + t
Therefore, the antiderivative of the given function is
∫g(t) dt
= ∫(8 + t² + t) dt
= ∫8 dt + ∫t² dt + ∫t dt
= [8t⁽⁰⁺¹⁾/(0+1) + t⁽²⁺¹⁾/(2+1) + t⁽¹⁺¹⁾/(1+1) + c]
= (8t + t³/3 + t²/2 + c)
Here 'c' is the constant.
Again, differentiating the result, we get:
d/dt(8t + t³/3 + t²/2 + c)
= [8 ˣ 1 ˣ t⁽¹⁻¹⁾ + 3 ˣ t⁽³⁻¹⁾/3 + 2 ˣ t⁽²⁻¹⁾/2 + 0]
= 8 + t² + t
= g(t)
The antiderivative of the given function g(t)is (8t + t³/3 + t²/2 + c).
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When constructing a perpendicular line through a point on a line, how can you verify that the lines constructed are perpendicular? (1 point)
Check the angles used in the construction with a straightedge to ensure consistency.
Check the distance along the lines at several places with a compass to ensure they are the same length.
Check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles.
Check the distance between the lines at several places with a compass to ensure they are equidistant
If you know the slope of the lines, you can also use these methods:
- see if the slopes multiplied by each other are -1 (should be if they're perpendicular)
- test if the slopes are opposite reciprocals (if they are, they are perpendicular)
A simple random sample of size 30 is drawn from a population of size 200. if the population mean is 57 and the population standard deviation is 6, what is the standard error of the mean?
Answer:
1.0954.
Step-by-step explanation:
Standard error = std dev / √n
= 6 / √30
= 1.0954.
Rewrite each expression such that the argument x is positive. a. cot(−x)cos(−x) sin(−x)
[tex]\cos(x)[/tex] is an even function, while [tex]\sin(x)[/tex] is odd. This means
[tex]\cos(-x) = \cos(x) \text{ and } \sin(-x) = -\sin(x)[/tex]
[tex]\cot(x)[/tex] is defined by
[tex]\cot(x) = \dfrac{\cos(x)}{\sin(x)}[/tex]
so it is an odd function, since
[tex]\cot(-x) = \dfrac{\cos(-x)}{\sin(-x)} = \dfrac{\cos(x)}{-\sin(x)} = -\cot(x)[/tex]
Putting everything together, it follows that
[tex]\cot(-x) \cos(-x) \sin(-x) = (-\cot(x)) \cos(x) (-\sin(x)) \\\\~~~~~~~~= \cot(x) \cos(x) \sin(x) \\\\ ~~~~~~~~= \cos^2(x)[/tex]
a
a
¹2-5, find £r(:)
=
En
n=l
n=1
b
Given that Σ
[tex]\sum^{\infty}_{n=1} (a/b)^n=5 \\ \\ =\frac{a/b}{1-\frac{a}{b}}=5 \\ \\ \frac{a}{b-a} =5 \\ \\ \frac{a}{b}=\frac{5}{6}[/tex]
So, we need to find
[tex]\sum^{\infty}_{n=1} n(5/6)^n
[/tex]
Let this sum be S.
Then,
[tex]S=(5/6)+2(5/6)^2 +3(5/6)^3+\cdots \\ \\ \frac{5}{6}S=(5/6)^2 + 2(5/6)^3+\cdots \\ \\ \implies \frac{1}{6}S=(5/6)+(5/6)^2+(5/6)^3+\cdots=5 \\ \\ \implies S=\boxed{30}[/tex]
Write a polynomial of least degree with rational coefficients and with the root
–15+10[tex]\sqrt{6\\}[/tex]
Answer:
p(x) = x² +30x -375
Step-by-step explanation:
When a quadratic has real rational coefficients, any irrational or complex roots come in conjugate pairs.
Factored formA root of p means (x -p) is a factor of the polynomial. Here, we have roots of -15+10√6 and -15-10√6, so the factored form can be written ...
p(x) = (x -(-15 +10√6))(x -(-15 -10√6))
Using the factoring of the difference of squares, we can write this as ...
p(x) = (x +15)² -(10√6)²
Standard formExpanding the factored form, we can write the polynomial as ...
p(x) = x² +30x +225 -600
p(x) = x² +30x -375
math help !!!!!!!!!!!!!!!
The values of b, h and k are (c) b = 2, h = -2 and k = -9
How to determine the values of b, h and k?The logarithmic function is given as:
f(x) = log₂(x + 2) - 9
A logarithmic function is represented as:
f(x) = logb(x - h) + k
By comparing both equations, we have
b = 2
h = -2
k = -9
Hence, the values of b, h and k are (c) b = 2, h = -2 and k = -9
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subtract 2/9-2/15. enter your answer below as a fraction in lowest terms, using the slash (/) as the fraction bar.
Answer:
2/9 - 2/15
Solution
LCM = 45
45 ÷9 ×2 = 10
45÷ 15 ×2 = 6
10 - 6 = 4
ANSWER = 4/45
Answer:
l
Step-by-step explanation:
take the lcm of 9 and 15. it will be 45 . than continue
What are the values of a such that the average value of f(x) = 1 2x − x 2 on [0, a] is equal to 1?
The average value of the given function is [tex]f_{avg} = \frac{-2a^{2} + 6a + 6 }{6}[/tex].
According to the statement
we have given that the function f(x) and we have to find the average value of that function.
So, For this purpose, we know that the
The given function f(x) is
[tex]f(x) = -x^{2} + 2x +1[/tex]
And now integrate this function with the limit 0 to a then
[tex]f_{avg} = \frac{1}{b - a} \int\limits^a_0 {f(x)} \, dx = -x^{2} + 2x +1[/tex]
Now integrate this then
[tex]f_{avg} = \frac{1}{a} \int\limits^a_0 {-x^{2} + 2x +1} \, dx[/tex]
Then the value becomes according to the integration rules is:
[tex]f_{avg} = \frac{1}{a} \int\limits^a_0 {-\frac{x^{3} }{3} + \frac{2x^{2} }{2} +x} \,[/tex]
Now put the limits then answer will become as output is:
[tex]f_{avg} = \frac{1}{a} [ {-\frac{a^{3} }{3} + \frac{2a^{2} }{2} +a} \,][/tex]
Now solve this equation then
[tex]f_{avg} = [ {-\frac{a^{2} }{3} + \frac{2a }{2} +1} \,][/tex]
Now
[tex]f_{avg} = \frac{-2a^{2} + 6a + 6 }{6}[/tex]
This is the value which represent the average of the given function in the statement.
So, The average value of the given function is [tex]f_{avg} = \frac{-2a^{2} + 6a + 6 }{6}[/tex].
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A hockey player knows that the two goal posts of a hockey net are 1.83 meters apart. The player tries to score a goal by shooting the puck along the ice from the left side of the net at a point 4.8m from the left post and further from the right post. From the player's position the goal posts are 11 degrees apart. Draw a labeled picture and determine how far away the player is from the right post.
The distance the player is from the right post is = 5.1 meters
Calculation of distance using Pythagorean theoremThe Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
Formula for the Pythagorean theorem =
a²= b²+c²
From the diagram given,
The hypotenuse (a) = x²
b= 1.82²
c = 4.8²
x² = 1.82² + 4.8²
x²= 3.3124 + 23.04
x²= 26.3524
a= √26.3524
a= 5.1 meters.
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State what additional information is required in order to know the
triangles are congruent using the theorem or postulate listed.
Answer: line ZX is congruent to line VX (option 4)
Step-by-step explanation:
We already know <X is congruent to <X, we also know that line YX is congruent to line XW. Now all we need is one more line adjacent to X which is going to be ZX ad VX
which number set(s) does -10 belong to
irrational numbers
whole numbers
rational numbers
integers
real numbers
counting or natural numbers
No number set describes this number.
The number set(s) that - 10 belong to are rational numbers, integers and real numbers. Option C, D and E
Number sets of negative numbersA rational number can be defined as a number expressed as the ratio of two integers, where the denominator is not be equal to zer0
- 10 can be written as = 1/ 10
Integers are whole number that could be positive, negative and even zero
- 10 is a negative whole number
Real numbers are numbers with continuous quantity that can represent distance along a number line
-10 can represent distance along a number line.
Thus, the number set(s) that - 10 belong to are rational numbers, integers and real numbers. Option C, D and E
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identify the TRUE statement relating to a property of the function y = sin x
A. one cycle of the function is 180 degrees
B. The maximum and minimum values of the function are 1 and -1 respectively
C. The amplitude of the function is 2 units
D. The equation of the baseline is y = -1
The true statement relating to a property of the function y =sin x is that the maximum and minimum values of the function are 1 and -1 respectively. Option B
Properties of the function
The following are the properties of the sin trigonometric ratio of the function;
The sine graph rises till +1 and then falls back till -1 from where it rises again.The function y = sin x is an odd functionThe domain of y = sin x is the set of all real numbersThe range of sine function is the closed interval [-1, 1]The amplitude of the function is half its range valueOne cycle of the function is 6. 28From the above listed deductions, we can see that the true statement about the function y = sin x is that the range which is always known as the maximum and minimum values of the function are 1 and - 1 respectively.
Thus, the true statement relating to a property of the function y =sin x is that the maximum and minimum values of the function are 1 and -1 respectively. Option B
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find the area of the shaded region!
please solve this with solutions !ASAP
the area of the shaded part is 30. 89 cm²
How to determine the area
We have the shape to be a rectangle
The area of the shaded part should be;
Area of rectangle - 2 ( area of a semi circle)
The formula for area of a rectangle
Area = length × width
Area = 12 × 12
Area = 144 cm²
Area of a semicircle = 1/2 πr²
Area = 1/ 2 × 3. 142 × 6²
Area = 56. 56 cm²
Area of shaded part = area of rectangle - 2( area of semicircle)
Area of shaded part = 144 - 2(56. 56)
Area of shaded part = 144 - 113. 11
Area of shaded part = 30. 89 cm²
Thus, the area of the shaded part is 30. 89 cm²
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Find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0. ] f(x) = ln x, a = 9
Taylor series is [tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]
To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have
f(x) = ln(x)
[tex]f^{1}(x)= \frac{1}{x} \\f^{2}(x)= -\frac{1}{x^{2} }\\f^{3}(x)= -\frac{2}{x^{3} }\\f^{4}(x)= \frac{-6}{x^{4} }[/tex]
.
.
.
Since we need to have it centered at 9, we must take the value of f(9), and so on.
f(9) = ln(9)
[tex]f^{1}(9)= \frac{1}{9} \\f^{2}(9)= -\frac{1}{9^{2} }\\f^{3}(x)= -\frac{1(2)}{9^{3} }\\f^{4}(x)= \frac{-1(2)(3)}{9^{4} }[/tex]
.
.
.
Following the pattern, we can see that for [tex]f^{n}(x)[/tex],
[tex]f^{n}(x)=(-1)^{n-1}\frac{1.2.3.4.5...........(n-1)}{9^{n} } \\f^{n}(x)=(-1)^{n-1}\frac{(n-1)!}{9^{n}}[/tex]
This applies for n ≥ 1, Expressing f(x) in summation, we have
[tex]\sum_{n=0}^{\infinite} \frac{f^{n}(9) }{n!} (x-9)^{2}[/tex]
Combining ln2 with the rest of series, we have
[tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]
Taylor series is [tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]
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PLEASE HELP IM STUCK
Answer: 45
Step-by-step explanation: Given the way the formula is formatted, the first term is 1. The common difference can be found by subtracting a number from the number that follows (ex. 3-2 or 4-3), therefore it's 1. The desired term is what you're trying to find so 44-1=43. When you put it all together, the formula should be 2+1(44-1) which equals 45 when you follow the rules of PEMDAS.