Answer:
g(x) = x+5
Step-by-step explanation:
Given that,
[tex]f(x)=x^4+5x^3-3x-15[/tex]
[tex]q(x) = (x^3-3)[/tex]
We need to find the polynomial. We know that, Euclid division lemma states that
[tex]f(x)=q(x)\times g(x)+r(x)[/tex]
Where
f(x) is dividend
g(x) is the poynomial
q(x) is quotient
r(x) is remainder
So,
[tex]x^4+5x^3-3x-15=(x^3-3)\times g(x) +0\\\\g(x)=\dfrac{x^4+5x^3-3x-15}{(x^3-3)}\\\\g(x)=x+5[/tex]
So, the polynomial is (x+5).
Answer: its C
Step-by-step explanation: i just took the test
The cellphone Luke wants to buy is on sale for 15% off the original price. It was originally priced at $150. What is the amount of the discount?
Find the length of the missing side of the triangle to the nearest tenth.
Answer:
a = 18.8
Step-by-step explanation:
With it being a right angle, you can use the pythagorean theorem equation.
[tex]a^{2} + b^{2} =c^{2} \\a^{2} + 18^{2} =26^{2} \\a^{2} +324 = 676\\a^{2} = 676 - 324 \\a^{2} = 352\\a = \sqrt{352} \\a = 18.76 = 18.8[/tex]
Consider the initial value problem y" + 16 = 48t, y(0) = 5, y'(0) = 2. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(S). Do not move any terms from one side of the equation to the other (until you get to part (b) below). 48/s^2 help (formulas) b. Solve your equation for Y(s). Y(s) = L{y(t)} = (58^3+2s^2+48)/(s^2(s^2+16)) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t).
a. To solve the initial value problem using Laplace transforms, we start by taking the Laplace transform of both sides of the given differential equation. The Laplace transform of y(t) is denoted as Y(s). The Laplace transform of the second derivative y"(t) can be expressed as s²Y(s) - sy(0) - y'(0), where y(0) and y'(0) are the initial conditions. The Laplace transform of 48t is simply 48/s².
Applying the Laplace transform to the given differential equation, we get:
s²Y(s) - sy(0) - y'(0) + 16Y(s) = 48/s²
Substituting the initial conditions y(0) = 5 and y'(0) = 2, we have:
s²Y(s) - s(5) - 2 + 16Y(s) = 48/s²
Simplifying this equation gives the corresponding algebraic equation in terms of Y(s).
b. Now, we solve the equation obtained in part (a) for Y(s). Rearranging the terms, we have:
(s² + 16)Y(s) = 48/s² + s(5) + 2
Combining like terms, we get:
(s² + 16)Y(s) = (48 + 5s² + 2s) / s²
Dividing both sides by (s² + 16), we obtain:
Y(s) = (48 + 5s² + 2s) / (s²(s² + 16))
So, Y(s) is equal to the Laplace transform of y(t).
c. To find y(t), we take the inverse Laplace transform of Y(s) obtained in part (b). We can use partial fraction decomposition and the properties of Laplace transforms to simplify the expression and find the inverse Laplace transform.
Taking the inverse Laplace transform of Y(s), we find:
y(t) = L^(-1){Y(s)} = L^(-1){(48 + 5s² + 2s) / (s²(s² + 16))}
The inverse Laplace transform can be calculated using tables or software, and it yields the solution y(t) to the initial value problem.
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Question 1
Find mZN
620
K
N
Need help with this question?
Answer:
∠ N = 31°
Step-by-step explanation:
The inscribed angle KLN is half the measure of its intercepted arc KL, so
∠ N = [tex]\frac{1}{2}[/tex] × 62° = 31°
Calculate the total surface area of the pyramid. Show your work!
Answer: 22.44
Step-by-step explanation:
Base × Height /2 → (3 × 2.24)/2
3.36 · 4 = 13.44
13.44 + 3²
22.44
A square stained-glass window has an area of 4 feet2 what is the perimeter of the window
What angle of rotation maps p onto P'?
1. Determine the value of y for y = x -2
x 9 -1 5 -7 3
y ? ? ? ? ?
Please help! (It's called functional relationships by the way) Will mark brainliest (If you send any cutt or tyink links that are scams, I WILL REPORT YOU SO DON'T ANSWER IF U DON'T KNOW!!!!!!!)
Answer: The answer is 3
Step-by-step explanation:
Hope this helps you! Have a good day! :)
please help please!!!
I think the anwser is c -2 and 9
let θ be an angle in quadrant iii such that = cos θ − 4 5 . find the exact values of csc θ and tan θ
Let θ be an angle in quadrant iii such that = cosθ − 45, the exact values of csc θ and tan θ are 5/3 and -3/4 respectively.
As an angle θ is in quadrant III, and cosθ = -4/5
To identify the exact value of cscθ and tanθ, we will first calculate the value of sinθ by using the Pythagorean identity
sin²θ + cos²θ = 1
⇒ sin²θ + (-4/5)² = 1
⇒ sin²θ = 1 - (-4/5)² = 1 - 16/25 = 9/25
⇒ sinθ = √(9/25) = 3/5
Now, we can calculate the value of cscθ as
cscθ = 1/sinθ = 1/(3/5) = 5/3
Next, we can estimate the value of tanθ by using the identity
tanθ = sinθ/cosθ= (3/5) / (-4/5) = -3/4
Therefore, the exact values of cscθ and tanθ are
cscθ = 5/3 and tanθ = -3/4.
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Assume that f(0) = 1 and f(0) = 0, then 2 {0}} is dt2 A. s-F(s) – s. B. (s – 1)2F(s – 1) - (s – 1). C. (s2 – 1)F(s) – s +1. D. sF(s – 1) - 5-1. E. (s – 1)F(s – 1) – s. (IX) The Existence and Uniqueness Theorem, guarantees that one of the differential equations has a unique solution passing through the point (2, 4) A. (y – 2x)y = =r+y. B. y' = (y – 4)2/3 C. y' = (y – 4)1/3 D. cos(y - 4)y' = x. E. y'= Vy - 4.
The (s - 1)2F(s - 1) - (s - 1) option matches the given function (option B).
Let's go through the options one by one to determine the correct answer.
Option A: s-F(s) - s
This option doesn't match the given function.
Option B: (s - 1)2F(s - 1) - (s - 1)
This option matches the given function.
Option C: (s2 - 1)F(s) - s + 1
This option doesn't match the given function.
Option D: sF(s - 1) - 5 - 1
This option doesn't match the given function.
Option E: (s - 1)F(s - 1) - s
This option doesn't match the given function.
Based on the given function, the correct answer is Option B: (s - 1)2F(s - 1) - (s - 1).
Regarding the second question, the Existence and Uniqueness Theorem guarantees the existence and uniqueness of a solution passing through a given point (x0, y0) only if the function is continuous and satisfies certain conditions. None of the provided options mention the function's continuity or satisfy the conditions for the Existence and Uniqueness Theorem. Therefore, none of the options can be determined as having a unique solution passing through the point (2, 4).
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A piece of blue yarn is 8 3/10 yards long. A piece of pink yarn is 4 times as long as the blue yarn. What is the total length of the blue and pink yarn
Answer:
41.5 Yards
Step-by-step explanation:8 3/10 * 4 = 33.2,
33.2+8 3/10 = 41.5
Rosie bought a ring in the USA she paid 345 US dollars work out in pounds the amount rosie paid for the ring
Answer:
Step-by-step explanation:
You arder eighteen borritos to go from a Mexican restaurant, nine with hot peppers and nine without. However, the restaurant forget to be them. If you ve buite stranicom, find the probability of the given event
Answer : The probability of the given event occurring would be 0.75 or 75%.
Explanation :The given problem states that you ordered eighteen burritos, with nine having hot peppers and nine not having hot peppers. However, the restaurant forgot your order. We are supposed to find the probability of the event happening.
Let the probability of getting a burrito with hot peppers be P(h) and the probability of getting a burrito without hot peppers be P(n).
The total number of burritos ordered is 18.
Thus, P(h) + P(n) = 18. We can assume that all burritos are the same.
Thus, P(h) = 9/18 = 0.5 and P(n) = 9/18 = 0.5.
Therefore, the probability of getting an order that is incorrect would be: 1 - (0.5 * 0.5) = 1 - 0.25 = 0.75 or 75%. Therefore, the probability of the given event occurring would be 0.75 or 75%.
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Why didn't some materials Sink in water and some others didn't?
Answer: Materials sink in water depending on how heavy they are. It is about how heavy something is compared to the same amount (volume) of water. This ratio of an object’s mass to its volume is known as density. Density is what really determines whether something will sink or float.
Find the area of the shape shown below. Please help :(
Answer:
the area is 42 square units
Step-by-step explanation:
lets break it down
12 x 1 = 12
12 x 5 = 60
60 / 2 = 30
12 + 30 = 42
can I get a solution
[tex] \sqrt{x - 1} - 3 = 0[/tex]
is this solution correct or not can you please give me the following steps for this solution by solving for x if possible
Answer:
I don't think it is correct.
Step-by-step explanation:
Square root just means half of a number. If you square this number, it just goes back to it's original form, just without the square root sign. But however, You must square the 10 at the end of the equation as well. This solution is not correct.
What is the length of AC
A)72
B)8
C)None of these
D)136
E)132
F)96
-PLEASE SOLVE-
I think the answer is 4 but I’m not sure!! PLEASE HELPP!
Answer:
4) -3
Step-by-step explanation:
The minimum y value of this absolute value function is -3
Find the radius of the circle.
6(x – 3)2 + 6(y + 7)2 = 216
Answer:
radius=6
Step-by-step explanation:
Which expression is equivalent to
[tex](3 {u}^{3} {v}^{4}) ^{2} [/tex]
A.
[tex]3 {u}^{5} {v}^{6} [/tex]
B.
[tex]3 {u}^{6} {v}^{8} [/tex]
C.
[tex]9 {u}^{6} {v}^{8} [/tex]
D.
[tex]9 {u}^{5} {v}^{6} [/tex]
Answer:
C
Step-by-step explanation:
When 3 is squared, it becomes 9. That means that both A and B are incorrect.
The powers on u and v are doubled not added to become u^6 and v^8 so that makes C the only possible answer.
Luba walked 5 miles in 1 1/2 hours. How fast did she walk in miles per hour?
A. 2/15 miles per hour
B. 9/10 miles per hour
C. 2 3/4 miles per hour
D. 3 1/3 miles per hour
Answer:
c or d sorry if I'm wrong
Step-by-step explanation:
I think it's your d because of the shortest answers and they're the only two that makes sense
Suppose a conic section passes through the point (2, - 7). If the conic section has focus ( - 1, -3), directrix 2 = 3, then it is a ellipse parabola hyperbola cannot be determined.
The conic section has focus ( - 1, -3), directrix 2 = 3, then it is a parabola.
How to find if the conic section is a ellipse parabola hyperbola?For a parabola, the focus and directrix play important roles in determining its shape. The distance between a point on the parabola and the focus is equal to the perpendicular distance between that point and the directrix.
Let's calculate the distances and verify if they are equal:
Distance between the point (2, -7) and the focus (-1, -3):
d₁ = √[(2 - (-1))² + (-7 - (-3))²] = √[9 + 16] = √25 = 5
Distance between the point (2, -7) and the directrix 2 = 3:
d₂ = |y - directrix| = |(-7) - 3| = |-10| = 10
Since d₁ ≠ d₂, we can conclude that the conic section cannot be an ellipse.
In an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant. However, in this case, the distances are not equal.
Similarly, for a hyperbola, the difference between the distances from any point on the hyperbola to the two foci is constant. Since the distances are not equal in this case, we can also rule out a hyperbola.
Therefore, based on the given information, the conic section is a parabola.
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the same
2. When graphing a system of equations with no solution, the y-intercept of the lines would be?
Answer:
not telling u, imbecil
Step-by-step explanation:
hahhahahahah
Find x. This is not drawn to scale.
H
150°
GX 54°
J
E
Are
F
Answer:
48°
Step-by-step explanation:
We solve the above question using circle theorem.
Finding x
The formula is given as
x = 1/2 (150° - 54°)
x = 1/2 (96)°
x = 48°
If a car travels at 60 MPH, how many seconds does it go per mile?
Answer:
60 seconds
Step-by-step explanation:
The table below represents a linear function.
Х y
-1 5
1 9
3 13
5 17
Which function has a greater slope and a greater y-intercept than the linear functon represented
in the table?
UWA
A. y = 2x + 8.5
B. y = 3x + 7.5
C. y = 5x + 6.5
y = 10x + 5.5
58, 72, 74, 92, 84, 40, 74, 81, 76, 83 What was the mean score on Mr. Shenton’s final exam?
Answer: 73.4
Step-by-step explanation:
To find the mean, you add up all your data value then divide the sum by the # of values in the set.
58 + 72 + 74 + 92 + 84 + 40 + 74 + 81 + 76 + 83
= 734
There are 10 numbers in the set.
734 ÷ 10 = 73.4
The mean score on Mr. Shenton's final exam is 73.4
The slope of AB of problem 7 is
Answer:
Slope of line is 0 and intercept is 7 Step-by-step explanation:
At a certain time of day, the angle of elevation is 40°. To the nearest foot, find the height of a tree whose shadow is 31 feet long.
Answer: Height of tree = 26 ft
Make a triangle ABC with 40 degrees angle. The shadow is the base of the triangle equals 31 feet.
Base = AC = 31
Perpendicular = CB = ?
Hypotenuse = AB
Using trigonometric equation
tan 40 (deg) = CB / AC
CB = Tan 40 x AC
CB = 0.83909 x 31
CB = 26.011
Thus the height of the tree = 26 ft