Answers
Answer:
[tex]-4r^3-3r^2+2rs-5[/tex]
Step-by-step explanation:
The terms have powers of r that are 2, 0, 1, and 3 (in the order shown here). You want to rearrange those terms so the powers have order 3, 2, 1, 0. The above answer shows that arrangement.
Ordering a polynomial in descending powers of r involves arranging the terms from the highest to the lowest exponent of r. When squaring exponentials, square the digit and double the exponent. For large r compared to d, d can be disregarded.
Explanation:Ordering a polynomial in descending powers of r involves organizing the terms from highest to lowest exponent of the variable r. For example, for a polynomial of r as 6r^4 - 2r + 7r^2 - 3, we would arrange it as 6r^4 + 7r^2 - 2r - 3. Note that the polynomial starts with the term with the highest power of r (r^4), followed by the term with the next highest power (r^2). The process continues down to the term with the lowest power of r (r), and lastly, the constant term (-3). Remember to retain the corresponding coefficients while reordering terms.
When dealing with terms involving the squaring of exponentials, remember to square the digit as usual and double the exponent. For instance, (r^3)^2 would be r^6.
Also, comparisons of terms such as r » d (meaning r is much larger than d), we disregard d as its contribution to the final polynomial will be negligible.
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Related Questions
Simplify the expression –2(p + 4)2 – 3 + 5p. What is the simplified expression in standard form? –2p2 – 11p – 35 2p2 + 21p + 29 –2p2 + 13p + 13 4p2 + 37p – 67
Answers
Answer:
-2p² -11p -35
Step-by-step explanation:
-2(p +4)² -3 +5p = -2(p² +8p +16) -3 +5p
= -2p² -16p -32 -3 +5p
= -2p² -11p -35
Answer:
–2p2 – 11p – 35
Step-by-step explanation:
The result of subtracting two or more numbers
Answers
Answer:
difference
Step-by-step explanation:
When you're subtracting two (or more) numbers, you're looking to see how far apart they are. You're looking for their difference.
The result of a subtraction is the difference between the numbers involved in the operation.
When you're adding two numbers up, you're creating a sum.
When you're multiplying two numbers together, you have a product.
When you're dividing two numbers, you have a quotient.
g(x) 16g(x) = 2 sin(2x - π) + 4.
Using complete sentences, explain how to find the minimum value for the function.
Answers
Explanation:
Use the minimum value of the sine function in place of the sine function in the expression. Evaluate the resulting expression.
min(g(x)) = 2 min(sin( )) +4 = 2(-1) +4 = 2
The minimum value of g(x) is 2.
WILL GIVE BRAINLIEST
which equation has a graph that is parallel to the graph of 4x -2y=1?
a.3x+6y=9
b.6x+3y=9
c.6x-3y=9
d.3x-6y=9
Answers
Answer:
c. 6x -3y = 9
Step-by-step explanation:
The parallel line will have the x- and y-coefficients in the same ratio.
given line: 4 : -2 = -2 : 1
a: 3 : 6 = 1 : 2 . . . not it
b: 6 : 3 = 2 : 1 . . . not it
c: 6 : -3 = -2 : 1 . . . . the one you're looking for
d: 3 : -6 = -1 : 2 . . . not it
Answer:
6x-3y=9
Step-by-step explanation:
I used a graphing app
Arati posted a comment on her blog. Each day the number of responses to her comment was 125% of the number she received on the previous day. If there were 64 responses the first day, how many were there on the fourth day?
Answers
If the next number is 125% of the previous number, that means that the previous number is increasing by 25% each time.
The multiplier for increasing by 25% is:
(100 + 25) ÷ 100 = 1.25
So on day one, there are 64 responses. That means on day two, there will be:
---> 64 x 1.25 = 80 responses
On day 3, there will be:
---> 80 x 1.25 = 100 responses
Finally, on day 4, there will be:
---> 100 x 1.25 = 125 responses
A quicker way of getting this would be to do:
64 x 1.25³ since you are multiplying by 1.25 3 times
--------------------------------------------------
Answer:
125 responses
Answer:
125
Step-by-step explanation:
meh . . .
Kirby places frog and Beth's snail on point 0 in on the number line. As Beth's snail slowly slimed forward in the positive direction, Kirby's frog hopped in the opposite direction. By the time Beth's snail reached the number 2, Kirby's frog me four jumps, each 3 units long. How far apart are the snail and the frog at this point?
Answers
That picture doesn't have anything to do with the problem.
Snail went right, into positive numbers, frog went left, negative numbers. Their distance is the absolute difference.
d = | 2 - 4(-3) | = | 14 | = 14
Answer: 14
Which facts could be applied to simplify this expression? Check all that apply.
5x + 3y + (-x) + 6z
A. To add like terms, add the coefficients, not the variables.
B. Like terms are terms that contain the same variable, raised to the same powers.
C.The simplified expression is 4x + 3y + 6z
D. Only combine terms which contain the same variable.
F. The simplified expression is 5x + 3y + 6z
Answers
The answer is B, C, and D. Like terms are terms with all the same variable, so 5x and -x are like terms.
C is correct. If we add -x to 5x, we get 4x. The other numbers remain unchanged because they have no like terms.
D is correct. Applying the rule of like terms, which is that like terms are numbers with the same variable, only add together numbers with the same variable.
Hope this helps!
Answer:
Options B, C, and D.
Step-by-step explanation:
We have to simplify the given expression given (5x + 3y + (-x) + 6z).
We will use the process as given below.
1) We will identify the like terms, we have to add or subtract.
2) Like terms are those, which have the same variable of the same degree.
3) We get the simplified expression by combining the same terms.
5x + 3y + (-x) + 6z = 4x + 3y + 6z
Therefore, Options B, C and D will be the correct options.
11. What is the altitude of a rhombus if its area is 10 square meters and the length on one side is 2.5 meters?
A. 4 m
B. 10 m
C. 7.5 m
D. 12.5 m
Answers
Answer:
4 m so, A.
Step-by-step explanation:
Area = side x altitude then,
Your altitude = area/side
which =40/12.5= 4 m
Hope my answer has helped you!
Answer: A. 4 m
Step-by-step explanation:
We know that a rhombus is a kind of parallelogram.
Area of parallelogram = (Altitude ) x ( Base)
Thus , Area of rhombus = (Altitude ) x ( Base)
As per given , Base = 2.5 meters
Area of rhombus = 10 square meters
Substitute all values in formula , we get
[tex]10=(\text{Altitude})\times2.5\\\\\Rightarrow\ \text{Altitude}=\dfrac{10}{2.5}=4[/tex]
Hence, the altitude of a rhombus is 4 m.
Thus , the correct answer is A. 4 m ,
HELP ME MATH ILL GIVE YOU BRAINLIEST
Answers
Answer:
zeros: x = -3, -1, +2.end behavior: as x approaches -∞, f(x) approaches -∞.Step-by-step explanation:
I like to use a graphing calculator for finding the zeros of higher order polynomials. The attachment shows them to be at x = -3, -1, +2.
__
The zeros can also be found by trial and error, trying the choices offered by the rational root theorem: ±1, ±2, ±3, ±6. It is easiest to try ±1. Doing so shows that -1 is a root, and the residual quadratic is ...
x² +x -6
which factors as (x -2)(x +3), so telling you the remaining roots are -3 and +2.
___
For any odd-degree polynomial with a positive leading coefficient, the sign of the function will match the sign of x when the magnitude of x gets large. Thus as x approaches negative infinity, so does f(x).
Yolanda is making a banner for a school pep rally. She cuts fabric in the shape of a parallelogram. The angle at the bottom left corner measures 80°. The measure of the angle at the top left corner must measure °.
Answers
Answer:
100°
Step-by-step explanation:
The bottom left and top left angle in a parallelogram are adjacent angles.
From the properties of parallelogram, we know adjacent angles are supplementary, this means they "add up to 180°"
Thus, if one angle is 80, the other angles would be 100 (to make it total 180).
So, top left corner angle measures 100°
Answer:
x=100
Step-by-step explanation:
can someone please help with these 3 I am so confused on what to do thank you!!!!
Answers
Answer:
26. [tex]\frac{3}{4} \leq x <7[/tex]
27. [tex]x\leq 5[/tex]
28. [tex]0\leq b<4[/tex]
Step-by-step explanation:
26. [tex]\sqrt{4x-3} <5[/tex]:
Taking square on both the sides to get:
[tex](\sqrt{4x-3} )^2 < (5)^2[/tex]
[tex]4x-3<25[/tex]
[tex]4x<28[/tex]
[tex]x<\frac{28}{4}[/tex]
[tex]x<7[/tex]
For non-negative values for radical:
[tex]4x-3\geq 0[/tex]
[tex]x\geq \frac{3}{4}[/tex]
So solution for this: [tex]\frac{3}{4} \leq x <7[/tex]
27. [tex]2+\sqrt{4x-4}\leq 6[/tex]
Subtracting 2 from both the sides to get:
[tex]2+\sqrt{4x-4}-2\leq 6-2[/tex]
[tex]\sqrt{4x-4}\leq 4[/tex]
Taking square root on both sides:
[tex](\sqrt{4x-4})^2\leq (4)^2[/tex]
[tex]4x-4\leq 16[/tex]
[tex]x\leq \frac{20}{4}[/tex]
[tex]x\leq 5[/tex]
28. [tex]\sqrt{b+12} -\sqrt{b}>2[/tex]
Adding [tex]\sqrt{b}[/tex] to both the sides to get:
[tex]\sqrt{b+12} -\sqrt{b}+\sqrt{b}>2+\sqrt{b}[/tex]
[tex]\sqrt{b+12} >2+\sqrt{b}[/tex]
Taking square on both sides:
[tex](\sqrt{b+12})^2 >(2+\sqrt{b})^2[/tex]
[tex]b+12>(2+\sqrt{b})^2[/tex]
[tex]b+12>4+4\sqrt{b}+b[/tex]
[tex]4+4\sqrt{b} +b<b+12[/tex]
Subtracting [tex]b[/tex] from both sides to get:
[tex]4+4\sqrt{b} +b-b<b+12-b[/tex]
[tex]4+4\sqrt{b} <12[/tex]
Subtracting 4 from both sides:
[tex]4+4\sqrt{b}-4 <12-4[/tex]
[tex]4\sqrt{b} <8[/tex]
Square both sides again:
[tex](4\sqrt{b})^2 <(8)^2[/tex]
[tex]16b<8^2[/tex]
[tex]b<\frac{64}{16}[/tex]
[tex]b<4[/tex]
and for non-negative radical [tex]b\geq 0[/tex]
therefore, solution is [tex]0\leq b<4[/tex].
Which of the following situations can be modeled by a discrete random variable? Choose ALL that apply.
The time spent on the phone during the day.
The number of text messages sent in a month.
The number of students earing a 100 percent on a test.
The height of a flower in a garden.
Answers
Discrete random variables are countable values obtained by counting. Hence the correct options are 2 and 3.
The situations that can be modeled by a discrete random variable from the options provided are:
The number of text messages sent in a month.
The number of students earning a 100 percent on a test.
what is the solution of log3x-2 4096=4?
Answers
Answer:
4/3
Step-by-step explanation:
The exponential form is (3x+4)^4=4096
Take the fourth of both sides:
3x+4=plus or mins 8
3x+4=8 or 3x+4=-8
So
3x=4 or 3x=-12
x=4/3 or x=-4 (this sound won't work because 3x+4 becomes neg)
So only sol 4/3.
The solution to log3x-2 4096 = 4 is x = 4.493409.
The solution to log3x-2 4096 = 4 is x = 4.493409 after isolating the logarithmic term and converting the equation to exponential form.
To solve the equation log3(x-2) = 4096, we first isolate the logarithmic term by adding 2 to both sides, resulting in log3x = 4098. Next, we rewrite the equation in exponential form as 3^4098 = x, which simplifies to x = 4.493409. Therefore, the solution to the equation log3x-2 4096 = 4 is x = 4.493409.
Cade factored the polynomial y=x^3+5x^2-9x-45 and said that the polynomial crosses the x-axis at -3,3,and 5. What is the factored form of the polynomial? Is case correct?
Answers
Answer:
y = (x +5)(x +3)(x -3)No, Cade is not correctStep-by-step explanation:
The product of roots will be the opposite of the constant in an odd-degree polynomial. The actual zero crossings multiply to give +45, not the -45 that Cade's answer gives.
The numbers Cade lists are the constants in the binomial factors, not the roots of the polynomial. The polynomial's roots are opposite Cade's numbers: 3, -3, -5.
_____
Another way you can tell Cade's answer is wrong is that the sequence of signs of the polynomial coefficients is ++--, so there is one sign change. Descartes' rule of signs tells you that means there is exactly one positive real root. Cade lists two: 3, and 5.
Let's start by using the given roots to write the polynomial in its factored form.
The roots given are x = -3, x = 3, and x = 5. If these are in fact the roots of the polynomial, the polynomial can be written as a product of factors that have these values as solutions. Therefore, the factored form of the polynomial y = x^3 + 5x^2 - 9x - 45 using the roots would be:
y = (x - (-3)) * (x - 3) * (x - 5)
This simplifies to:
y = (x + 3) * (x - 3) * (x - 5)
Now let's expand this factored form to see if we get the original polynomial:
First, let's multiply (x + 3) and (x - 3), which are a difference of squares:
y = (x^2 - 3^2) * (x - 5)
y = (x^2 - 9) * (x - 5)
Now let's distribute (x - 5) into (x^2 - 9):
y = x^3 - 5x^2 - 9x + 45
Comparing this expanded form to the original polynomial y = x^3 + 5x^2 - 9x - 45, we see there's a discrepancy:
The expanded form: y = x^3 - 5x^2 - 9x + 45
The original form: y = x^3 + 5x^2 - 9x - 45
As we can observe, the signs of the x^2 term and the constant term are opposite in the expanded form compared to the original polynomial. Therefore, the roots -3, 3, and 5 do not correspond to the polynomial x^3 + 5x^2 - 9x - 45, and the factored form with these roots is incorrect.
To summarize, the factored form of the polynomial y = x^3 + 5x^2 - 9x - 45 given the roots -3, 3, and 5 would be (x + 3) * (x - 3) * (x - 5), but this factored form is incorrect because it does not expand to the original polynomial. Cade's statement about the polynomial crossing the x-axis at -3, 3, and 5 is incorrect.
What is the equation of a line that contains the points (5, 0) and (5, −2)?
Answers
Answer:
y=mx+b
x=5
Step-by-step explanation:
[tex]x=5[/tex]
Explanation:This is the equation for the line, because both points match this equation. It is a vertical line, since the [tex]x[/tex] is the same for both of them, and it is equal to [tex]5[/tex] both times.
You can then double check your answer by graphing. If you graph [tex]x=5[/tex], then both points, you can see that they both fall on the line, as shown in the attached graph.
I need help asap!!! The person who answers and shows their work on they got the answer first will be marked the brainliest!!!
Answers
Answer:
this is your answer below i used a graphing calculator
Step-by-step explanation:
Assuming there are no prepayment penalties, paying more than your monthly car payment can _____.
Select the best answer from the choices provided.
A.
reduce your maintenance costs
B.
help reduce total interest charges
C.
reduce your auto insurance payment
D.
affect your credit score negatively
Answers
Answer:
B.
help reduce total interest charges
Step-by-step explanation:
Assuming there are no prepayment penalties, paying more than your monthly car payment can help reduce total interest charges
Choose the best description for the real number square root of 35. Irrational, because it is not a terminating or repeating decimal Irrational, because it is a repeating decimal Rational, because it is not a terminating or repeating decimal Rational, because it is a repeating decimal
Answers
Answer:
Irrational because it is not a terminating or repeating decimal.
Step-by-step explanation:
Final answer:
The square root of 35 is an irrational number because it cannot be expressed as a fraction or a terminating/repeating decimal.
Explanation:
The best description for the real number square root of 35 is irrational, because it is not a terminating or repeating decimal. In general, an irrational number cannot be expressed as a quotient of two integers.
For example, let's approximate the square root of 35. We can use a calculator to find that the square root of 35 is approximately 5.91607978309961. This decimal representation goes on indefinitely without repeating or terminating, confirming that it is irrational.
Therefore, the square root of 35 is an irrational number because it cannot be expressed as a fraction or a terminating/repeating decimal.
Write the equation of the line with a slope of 3/2 that contains the point (-4,-2).
Answers
Answer:
y = [tex]\frac{3}{2}[/tex] x + 4
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 )
here m = [tex]\frac{3}{2}[/tex], hence
y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute (- 4, - 2) into the partial equation
- 2 = - 6 + c ⇒ c = - 2 + 6 = 4
y = [tex]\frac{3}{2}[/tex] x + 4
Write an equation to solve the problem.
Three times the quantity eight less than 4 times a number is 60. Find the number.
Answers
Answer:
3 * (4x - 8) = 60
x = 7
Step-by-step explanation:
First you have to find out what is being done first.
Three times the quantity eight less than 4 times a number is 60.
x = a number
3 *
- 8
4 * x
= 60
The first thing to do is 4 times a number.
4 * x = 4x
Then minus 8.
4x - 8
Then multiply by 3.
3 * (4x - 8) = 60
SolvingNow divide both sides by 3
4x - 8 = 20
Add 8 to both sides
4x = 28
Divide both sides by 4
x = 7
Answer:
7
Step-by-step explanation:
let number = x
"4 times a number" = 4x
"eight less than 4 times a number" = eight less than 4x = (4x - 8)
"Three times the quantity eight less than 4 times a number"
= 3 times (4x - 8) = 3(4x-8)
Given that the expression = 60
3(4x-8) = 60
(4x-8) = 20
4x = 20 + 8
x = 28 / 4
x = 7
19. Find the current in a circuit if the power is 500 W (watts) and the resistance is 25 ohms. Round off your answer to two decimal places. Use the formula . A. 4.47 A B. 0.22 A C. 20 A D. 0.05 A
Answers
Answer:
A
Step-by-step explanation:
The formula that relates current, power and resistance is
[tex]I=\sqrt{\frac{P}{R}}[/tex]
Where
I is the current (in amperes)
P is the power (in watts)
R is the resistance (in ohms)
We know P = 500 and R = 25, we plug them into the formula and solve for I:
[tex]I=\sqrt{\frac{P}{R}}\\I=\sqrt{\frac{500}{25}}\\I=\sqrt{20}\\ I=4.47[/tex]
Correct answer is 4.47 Amperes, or choice A.
Find the vertices and foci of the hyperbola with equation quantity x plus one squared divided by sixteen minus the quantity of y plus five squared divided by nine = 1.
A. Vertices: (-5, 3), (-5, -5); Foci: (-5, -6), (-5, 4)
B. Vertices: (2, -5), (-4, -5); Foci: (-4, -5), (2, -5)
C. Vertices: (3, -5), (-5, -5); Foci: (-6, -5), (4, -5)
D. Vertices: (-5, 2), (-5, -4); Foci: (-5, -4), (-5, 2)
Answers
Answer:
C
Step-by-step explanation:
This hyperbola is a horizontal hyperbola of the standard form:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
Since our equation is
[tex]\frac{(x+1)^2}{16}-\frac{(y+5)^2}{9}=1[/tex],
a = 4 and b = 3.
The coordinates for the vertices are (±a, 0) and
the coordinates for the foci are (±c, 0).
We have a, but we need c. To find c, we use Pythagorean's Theorem:
[tex]c^2=4^2+3^2[/tex] or
[tex]c^2=16+9[/tex] giving us that
c = 5.
But these a and c values have to be figured from the center of the hyperbola which is located at (-1, -5).
For the vertices, then, we add the a value of 4 and -4 to the x value of the center, which is -1. The -5 remains, since the vertices and the foci are on the same transcersal axis which is the line y = -5.
For the foci, then, we add the c value of 5 to -1, and again the -5 remains in the y position.
Vertices: (-1+4, -5)-->(3, -5) and (-1-4, -5)-->(-5, -5)
Foci: (-1+5, -5)-->(4, -5) and (-1-5, -5)-->(-6, -5)
Choice C
Which relationship describes angles 1 and 2?
Select each correct answer.
complementary angles
supplementary angles
vertical angles
adjacent angles
A line goes left to right with a ray in the middle creating a right angle and another ray between the right angle with a one labeling the left angle and a two labeling the right angle
Answers
Sounds like your describing complementary angles (a pair of angles that add up to be 90 degrees) but not super sure based on that description you have there.
Tell me does it look like this:
The adjacent angles' relationship describes angles 1 and 2, angle 1 and angle 2 are adjacent angles option fourth is correct.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have a statement about the angle 1 and angle 2:
A line goes left to right with a ray in the middle creating a right angle and another ray between the right angle, with one labeling the left angle and two labelings the right angle.
We can draw as shown in the picture.
As we can see in the figure, angles 1 and angle 2 are adjacent angles because they have a common vertex.
Angle 2 = 90 degree
Angle 1 = 45 degree
Thus, the adjacent angles' relationship describes angles 1 and 2, angle 1 and angle 2 are adjacent angles option fourth is correct.
Learn more about the angle here:
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Consider this expression and the steps to evaluate it.
4^5(−2)^9/4^8(−2)^3
1. Apply the quotient of powers: (−2)^a/4^b
2. Evaluate powers: c/d
Select the value of each variable.
a = _
b = _
c = _
d = _
Answers
Answer:
value of a = 6
value of b = 3
value of c = 64
value of d= 64
Step-by-step explanation:
1. Apply the quotient of powers:
(-2)^a / 4^b
In the given expression:
[tex]4^5(-2)^9/4^8(-2)^3[/tex]
We know if we have the same base then the powers are subtracting if the bases are in numerator and denominator
i.e [tex]a^m/a^n = a^{m-n}[/tex]
Solving:
[tex]=(-2)^{9-3}/4^{-5+8}\\=(-2)^6/4^3[/tex]
So, the value of a = 6
and the value of b = 3
2. Evaluate Powers
c/d
We have
[tex](-2)^6/4^3[/tex]
Solving:
When power is even negative sign changes into plus sign
64/64
So value of c = 64
and value of d= 64
Answer:
a=6
b=3
c=64
d=64
Step-by-step explanation:
I am not sure how to do this problem and need help asap
Answers
Answer:
(2, 4π/15), (2, 14π/15), (2, 24π/15)
Step-by-step explanation:
DeMoivre's theorem tells you the n-th root of a complex number in polar form is ...
(magnitude, angle)^(1/n) = (magnitude^(1/n), (angle +2kπ)/n) for k = 0 to n-1.
__
Your number has a magnitude of 8, so the cube root of that is 2.
Your number has an angle of (4π/5+2kπ), so one third of that is ...
(π/3)(4/5 +2k) . . . for k = 0, 1, 2
Then the cube roots are (magnitude, angle) ...
{(2, 4π/15), (2, 14π/15), (2, 24π/15)}
Of course, you can write (magnitude, angle) in CIS form as ...
magnitude(cos(angle) +i·sin(angle))
as may be required by your grader.
_____
Comment on complex number notation
The notation used in my engineering courses was fairly practical. A complex number could be written as a+bi or as magnitude∠angle. We didn't waste effort writing it as magnitude(cos(angle) +i·sin(angle)) and we avoided the confusion associated with different interpretations of an ordered pair.
A realtor is studying the graph above, which shows the expected value of properties in her area over the next 24 years. If t represents the number of years after 2014, in what year should the increase in property values start to slow down?
Answers
Answer:
2030
Step-by-step explanation:
the graph starts to decline 16 years after 2014 so 2014 + 16 = 2030
What is magma? a. The molten mixture of rock-forming substances, gases, and water from the mantle.. c. Hardened lava on the surface of the Earth. b. Liquid rock that reaches the surface. d. All of the above Please select the best answer from the choices provided A B C D
Answers
Answer:
The answer is c
Step-by-step explanation:
When the lava cools and hardens it becomes igneous rock.
Answer:
The correct answer is A., "The molten mixture of rock-forming substances, gases, and water from the mantle.."
Francesca is looking at an airplane. She measures the angle at which she is looking up and finds it to be 55 degrees. If the airplane is traveling at an altitude of 30000 feet, about how far is the airplane from Francesca?
A. 21,006 feet
B. 36,623 feet
C. 45,043 feet
D. 53,303 feet
Answers
Option: B is the correct answer.
B. 36,623 feet
Step-by-step explanation:The angle of elevation is: 55 degree
We model this problem by taking a right angled triangle such that the side opposite to the 55 degree is of length 30000 feet.
Now let us consider x denote the distance of the plane from Francesa.
i.e. x denote the hypotenuse of the right angled triangle.
Hence, in right angled triangle i.e. ΔABC we have:
[tex]\sin 55=\dfrac{30000}{x}\\\\i.e.\\\\x=\dfrac{30000}{\sin 55}\\\\i.e.\\\\x=\dfrac{30000}{0.81915}\\\\\\i.e.\\\\\\x=36623.2376\ feet[/tex]
Round to the nearest feet we get: x=36,623 feet
Answer:
B is the correct answer Hope it helps!
Joyce painted 4 window frames in 5 hours while earning money for college.
What was her painting rate in window frames per hour?
Answers
Answer:
4/5 frames/h
Step-by-step explanation:
Find the ratio frames per hour by dividing frames by hours:
(4 frames)/(5 hours) = (4/5) frames/hour
The question is about calculating a painting rate. Joyce paints 0.8 window frames per hour. This is calculated by dividing the total number of frames by the total number of hours.
Explanation:The subject of this question is Mathematics as it deals with calculating rates. This can be determined by finding a ratio of the total number of window frames painted, which was four, and the total time taken, which was 5 hours.
We can calculate Joyce's painting rate by dividing the total number of frames she painted by the total number of hours she worked. Which is 4 frames ÷ 5 hours = 0.8 frames/hour. This means that Joyce paints 0.8 window frames per hour.
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Use your calculator to evaluate the limit from x equals 0 to 2 of the sine of x squared, dx. Give your answer to the nearest integer.
Answers
[tex]\int_{0}^{2}sin(x^{2})dx \approx 1units^2[/tex]
Step-by-step explanation:First of all, the graph of the function [tex]f(x)=sin(x^2)[/tex] is shown in the first figure below. We need to calculate the area under the curve which is in fact the definite integral. From calculus, we know that [tex]f(x)=sin(x^2)[/tex] is non integrable, that is, it doesn't have a primitive, so we must use calculator to evaluate [tex]\int_{0}^{2}sin(x^{2})dx[/tex]. To do so, calculator uses the Taylor Series, so:
[tex]sin(x^{2})=\sum_{n=-\infty}^{+\infty}\frac{(-1)^{n}}{(2n+1)!}x^{4n+2}$[/tex]
You an use a calculator or any program online, and the result will be:
[tex]\int_{0}^{2}sin(x^{2})dx=0.804units^2[/tex]
Since the problem asks for rounding the result to the nearest integer, then we have:
[tex]\boxed{\int_{0}^{2}sin(x^{2})dx \approx 1units^2}[/tex]
The area is the one in yellow in the second figure.
The value of the integral is approximately 0.8380, rounded to the nearest integer, is 1.
Evaluating the given integral involves using numerical methods since the antiderivative of sin(x²) doesn't have a simple closed-form expression in terms of elementary functions. One common numerical method is to use numerical integration techniques like Simpson's rule or the trapezoidal rule.
Let's approximate the integral using Simpson's rule with n=4 subintervals.
The interval of integration is [0, 2].
The width of each sub-interval is (2 - 0)/n = (2 - 0) / 4 = 0.5
The endpoints of the sub-intervals are:
x₀ = 0,
x₁ = 0 + 0.5 = 0.5,
x₂ = 0 + 2(0.5) = 1.0
x₃ = 0 + 3(0.5) = 1.5
x₄ = 0 + 4(0.5) = 2.0
Evaluate the function at these points:
f(x₀) = sin(0²) = 0
f(x₁) = sin(0.5²) = 0.2474
f(x₁) = sin(1²) = 0.8415
f(x₃) = sin(1.5²) = 0.7781
f(x₄) = sin(2²) = -0.7568
Apply Simpson's rule:
[tex]\int_{0}^{2} \sin(x^2) \, dx \approx \frac{h}{3} \left( f(x_0) + 4 \sum_{i \text{ odd}} f(x_i) + 2 \sum_{i \text{ even, } i \neq 0, n} f(x_i) + f(x_n) \right)\\ = \frac{0.5}{3} \left( f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + f(x_4) \right)\\ = \frac{0.5}{3} \left( 0 + 4(0.2474) + 2(0.8415) + 4(0.7781) + (-0.7568) \right) \\ = \frac{0.5}{3} \left( 0 + 0.9896 + 1.6830 + 3.1124 - 0.7568 \right) \\ = \frac{0.5}{3} \left( 5.0282 \right)\\ =0.8380[/tex]
Thus, the value of the given integral is approximately 0.8380.
Round the result to the nearest integer, which is 1.
Complete question:
Use your calculator to evaluate [tex]\int_{0}^{2} \sin(x^2) dx[/tex]. Give your answer to the nearest integer.