Answers
Answer:
62.5 feet
Step-by-step explanation:
The markings on the angles in the figure tell you the triangles are similar. Similar triangles have proportional corresponding sides. This is used to write and solve an equation for x.
SimilarityThe angles in each triangle are marked with the following symbols:
square corner - signifying a right angleone arctwo arcsThe purpose of the marks is to signify that angles with the same mark are congruent. When the angles of one triangle are congruent to the angles of another triangle, the two triangles are similar.
Similar triangles have another feature: corresponding sides are proportional. That is, their ratios are identical.
This can be taken a couple of different ways:
sides of one triangle have the same ratio to each other as the corresponding sides of the other trianglecorresponding sides of the two triangles have the same ratioApplicationIn the given triangles, we can identify the corresponding sides as ...
smaller triangle : larger triangle
between right angle and double arc angle — 36 ft : 50 ft
hypotenuse — 45 ft : x ft
Our description of similarity tells us we can write the statements of proportionality as either of ...
36 : 50 = 45 : x . . . . . side ratios in the same triangle are the same36 : 45 = 50 : x . . . . . side ratios between triangles are the sameSolving the proportionFor proportions written in this way, the "outer" and "inner" products are the same. This is sometimes expressed by saying "the product of the means is equal to the product of the extremes."
a : b = c : d ⇒ ad = bc
When the ratios are written as fractions, this result is what you get from "cross multiplication":
a/b = c/d ⇒ ad = bc . . . . . the result of multiplying both sides by bd
Once the proportion is written in this product form, the value of any of the variables can be found by dividing both sides of the equation by the coefficient of that variable.
Desired distanceUsing either of the proportions we wrote above, the product form is ...
36x = 45·50
x = (45·50)/36 . . . . . . divide by the coefficient of x
x ≈ 62.5 . . . . feet
The distance from the playground to the swimming pool is 62.5 feet.
Related Questions
Could someone explain how to get the correct answer when trying to find the f(X) and g(X) on a graph like this? Thanks!
Answers
Answer:
f(3) = g (3)
Step-by-step explanation:
graphically, we notice that the graphs of f and g intersect
at the point of coordinates (3 , 0)
Then
f(3) = 6 = g(3)
Then
f(3) = g (3)
Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).
4x − y = −6
x + 4y = 7
x − 4y = −9
4x + y = 2
Answers
Answer:
x + 4y = 7
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 ) = (- 1, 2 ) and (x₂, y₂ ) = (3, 1 )
m = [tex]\frac{1-2}{3-(-1)}[/tex] = [tex]\frac{-1}{3+1}[/tex] = - [tex]\frac{1}{4}[/tex] , then
y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 1, 2 )
2 = [tex]\frac{1}{4}[/tex] + c ⇒ c = 2 - [tex]\frac{1}{4}[/tex] = 1 [tex]\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex]x + [tex]\frac{7}{4}[/tex] ← in slope- intercept form
multiply through by 4 to clear the fractions
4y = - x + 7 ( add x to both sides )
x + 4y = 7 ← equation in standard form
equation of line in two point form is needed here.
(y - y1) = [ (y2 - y1)/(x2-x1) ] (x - x1)y - (2) = [ (1 - 2)/(3 - (-1)) ] (x - (-1))y - 2 = [ -1/4 ] (x + 1)y = -(x/4) -1/4 + 2y = -x/4 + 7/44y = -x + 7x + 4y = 7PLEASE ANSWER QUICKLY
Answers
Answer:
3
Step-by-step explanation:
f(x) = 3x² - 2x + 1
f(x) = ax² + bx + c
a = 3
Which number is equivalent to (1/3)^-4
A 81
B −1/81
C −1/12
D 12
Answers
The fraction (1/3)⁻⁴ is equal to 81.
Given that:
Fraction: (1/3)⁻⁴
Rewrite the expression by applying the rule that states a negative exponent is equal to the reciprocal of the positive exponent:
(1/3)⁻⁴= 1 / (1/3)⁴
Now, let's simplify (1/3)⁴:
(1/3)⁴ = (1/3) × (1/3) × (1/3) × (1/3)
(1/3)⁴ = 1/81
So, the expression becomes:
1 /(1/3)⁴ = 1 / (1/81)
Now, dividing by a fraction is equivalent to multiplying by its reciprocal:
1 / (1/81) = 1 × 81 = 81
Therefore, the fraction (1/3)⁻⁴ is equal to 81.
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for f(x) = x+1 and g(x)= 2x+3, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d.(gof)(2)
Answers
Answer:
a) 2x + 4
b) 2x + 5
c) 8
d) 9
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=x+1\\g(x)=2x+3 \end{cases}[/tex]
Function composition is an operation that takes two or more functions and combines them into a single function.
(f o g)(x) means find g(x) first and then substitute the result into f(x).
(g o f)(x) means find f(x) first and then substitute the result into g(x).
Part (a)
[tex]\begin{aligned}(f \circ g)(x) & = f[g(x)]\\& = g(x)+1\\ & = (2x+3)+1\\& = 2x+4\end{aligned}[/tex]
Part (b)
[tex]\begin{aligned}(g \circ f)(x) & = g[f(x)]\\& = 2[f(x)]+3\\& = 2(x+1)+3\\ & = 2x+2+3\\& = 2x+5\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}(f \circ g)(2) & = f[g(2)]\\& = g(2)+1\\ & = (2(2)+3)+1\\ & = (4+3)+1\\& = 8\end{aligned}[/tex]
Part (d)
[tex]\begin{aligned}(g \circ f)(2) & = g[f(2)]\\& = 2[f(2)]+3\\& = 2(2+1)+3\\ & = 2(3)+3\\ & = 6+3\\& = 9\end{aligned}[/tex]
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(fog)(x)
f(g(x))f(2x+3)2x+3+12x+4(gof)(x)
g(f(x))g(x+1)2x+2+32x+5(fog)(2))
2(2)+48(gof)(2)
2(2)+59A small pizza has an area of 730 square centimeters.
Write an inequality that describes p, the area of a
pizza that is larger than a small pizza.
Answers
The inequality that describes p, the area of a pizza that is larger than a small pizza 730 < p
How to determine the inequality
From the information given, we have that;
Area of the small pizza = 730 square centimeters
p = area of the larger pizza
In writing inequality, we have to use the signs
< less than
> greater than
Since p has greater area, we have
730 < p
Thus, the inequality that describes p, the area of a pizza that is larger than a small pizza 730 < p
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Answer:
the answer is actually p > 730
Step-by-step explanation:
i juts checked on Kahn academy and i got it right..
Every person has blood type O, A, B, or AB. A random group of people are blood-typed, and the results are shown in the table. A 2-column table with 4 rows is shown. The first column is labeled Blood Type with entries O, A, B, AB. The second column is labeled Number of People with entries 22, 20, 6, 2. Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .
Answers
Has type B= 6/50= 3/25 = 12%
Has type AB= 2/50 = 1/25 = 4%
Has type B or type AB = 8/50 = 4/25 = 16%
The length of a rectangular field is 9m longer than its width, if the perimeter of the field is 270m find its width.
Answers
==================================================
Work Shown:
width = w
length = w+9
perimeter = 2*(length + width)
P = 2(w+9+w)
P = 2(2w+9)
P = 4w+18
4w+18 = P
4w+18 = 270
4w = 270 - 18
4w = 252
w = 252/4
w = 63 meters is the width
w+9 = 63+9 = 72 meters is the length
Check:
perimeter = 2*(length + width)
perimeter = 2*(72 + 63)
perimeter = 2*(135)
perimeter = 270
The answer is confirmed.
Una estrategia de cálculo mental con
números decimales consiste en buscar
parejas de números cuya suma sea un
número entero. Aplica esta estrategia para
calcular mentalmente:
a. 15,75 + 1,2 + 0,25
b. (–1,8) + 2,45 + (–0,20)
c. 3,5 + 11,8 + 12,5
d. 7,38 – 1,5 + 2,62
Answers
Esta estrategia se puede aplicar sumando 15,75 + 0,25, –1,8 + –0,20, 3,5 + 12,5 y 2,62 + 7,38 antes de sumar el tercer número dado en cada caso.
¿En qué consiste está estrategia?La estrategia propuesta consiste en sumar dos números decimales que den como resultado un número entero antes de sumar el tercer número decima. Por ejemplo si teneos 1,4 + 0,6 + 1,2, se debe sumar primero 1,4 + 0,6 lo que es igual a 2 antes de sumar el 1,2.
¿Por qué utilizar esta estrategia?Este estrategia es beneficiosa porque facilita sumar números decimales.
¿Cómo aplicar está estrategia?15,75 + 1,2 + 0,25 = 16 (0,25+15,75) + 1,2 = 17,2 (–1,8) + 2,45 + (–0,20) = -2 (-1,8-0,20) + 2,45 = 0,453,5 + 11,8 + 12,5 = 16 (12,5+3,5) +11,8 = 27.87,38 – 1,5 + 2,62 = 10 (7,38+2,62) + 2,62 = 12,62Aprenda más sobre números decimales en: https://brainly.com/question/24620232
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An isosceles triangle has a perimeter (9y-15)cm. what is the length of the remaining equal sides of it's third side is (3y-7) cm.
Answers
The length of each of the equal sides is become x = (3y-4) cm
According to the statement
we have given that the perimeter of the isosceles triangle and length of third side. and we have to find the length of same side of triangle.
So,
An isosceles triangle is a triangle that has two sides of equal length.
Let the equal sides of isosceles triangle be x cm each.
We know that the
Sum of sides of a triangle = perimeter
x+x+(3y-7) = 9y-15
2x = 9y-3y-15+7
After solving the equation it become
2x= 6y-8
x=(6y-8)/2
Now the length of equal sides is x=3y-4
So, The length of each of the equal sides is become x = (3y-4) cm
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The water usage at a car wash is modeled by the equation w(x) = 4x3 6x2 − 11x 7, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day. c(x) = 4x3 4x2 − 11x 8 c(x) = 3x3 4x2 − 11x − 8 c(x) = 3x3 4x2 − 11x 8 c(x) = 4x3 4x2 − 11x − 8
Answers
A function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.
What is an equation?A relationship between two variables is defined as an equation; if we plot the graph of the linear equation, we will get a straight line.To find a function, C(x), to model the water used by the car wash on a shorter day:
Given information -
The water usage at a car wash is modeled by the equation W(x) = 4x³ + 6x² − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open.The amount of decrease in water used is modeled by D(x) = x³+ 2x² + 15, where D is the amount of water in cubic feet and x is time in hours.Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.
We are trying to find:
C(x) = W(x) - D(x)C(x) = (4x³ + 6x²− 11x + 7) - (x³ + 2x² + 15)C(x) = 4x³ - x² + 6x² - 2x³ - 11x + 7 - 15C(x) = 3x³ + 4x² - 11x - 8Therefore, a function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.
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The correct question is given below:
The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day
Select the correct answer. a number is selected at random from the set {2, 3, 4, ... 10}. which event, by definition, covers the entire sample space of this experiment?
Answers
[tex]( \: 2 \: 3 \: 4 \: 5 \:6 \: 7 \:8 \: 9 \: 10 \: )[/tex]
[tex]Event \: P \\P:"choosing \: a \: natural \: number \: from \: 2 \: to \: 10 \: inclusive"[/tex]
________ is the number of defects in a sample divided by the number of opportunities while ________ is the number of defects divided by the number of units tested within a sample.
Answers
DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B
What is DPU?Defects per unit (DPU) can be defined as the number of defects divided by the number of opportunities
It is also seen as the universal measure of quality.
For example, if there are 100 defects in 1,000 units produced, then the defects per unit will be 0.01.
Defects per million opportunities can be defined as a mathematical calculation of the estimated quality of a process
From this information, we can conclude that DPU and DPMO are measure of defects in a sample.
Thus, DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B
Complete question is;
________ is the number of defects in a sample divided by the number of opportunities while ________ is the number of defects divided by the number of units tested within a sample.
a. DPMO, DPU
b. DPU, DPMO
c. RTY, FTY
d. FTY, RTY
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13. The average of 15, 19, 23, 41, and x is 20. What is the value of x? (A) 2 (B) 20 (C) 23.6 (D) 31
Answers
Answer:
A
Step-by-step explanation:
(x + 15 + 19 + 23 + 41) / 5 = 20
x + 15 + 19 + 23 + 41 = 100
x + 98 = 100
x = 2
Answer: it’s 2 (A)
Step-by-step explanation:
20 * 5 = 100
15 + 19 + 23 + 41 = 98
100-98=2
Consider this equation.
Use the graph to find the approximate solutions to this equations
Answers
The equation be 2(x-2)-5=√x+3-1 then the graphical solution of the equations exists approximately x = 3 and x = 6.
What is the solution of the equation?The solution of an equation creates that equation true.
The equation of can be simplified, therefore:
2(x-2)-5=√x+3-1
simplifying the above equation, we get
2x -9 =√x+2
4 x²-37x + 79 = 0
The graphical solution of the equations exists at approximately x = 3 and
x = 6
In ending, the solution of an equation makes the equation true.
Therefore, the graphical solution of the equations exists approximately x = 3 and x = 6
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Expand 10a(2a-7) pls its very urgent
Answers
Answer:
[tex]20a^2-70a[/tex]
Step-by-step explanation:
1) Expand by distributing terms.
[tex]10\times2a+10a\times-7[/tex]
2) Take out the constants.
[tex](10\times2)aa+10a\times-7[/tex]
3) Simplify [tex]10\times2[/tex] to [tex]20.[/tex]
[tex]20aa+10a\times7[/tex]
4) Use Product Rule:[tex]x^ax^b=x^{a+b}[/tex].
[tex]20a^2+10a\times-7[/tex]
5) Simplify [tex]10a\times-7[/tex] to [tex]-70a.[/tex]
[tex]20a^2-70a[/tex]
Thank you,
Eddie
Answer:
20a² - 70a
Step-by-step explanation:
(10a)(2a-7)
= 10a*2a + 10a*-7
= 20a² - 70a
The graph of the step function g(x) = –⌊x⌋ + 3 is shown.
On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 2, 5) to (negative 1, 5). Each segment is 1 unit lower and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, negative 1) to (5, negative 1).
What is the domain of g(x)?
{x| x is a real number}
{x| x is an integer}
{x| –2 ≤ x < 5}
{x| –1 ≤ x ≤ 5
Answers
Using it's concept, the domain of the function is given as follows:
{x| –2 ≤ x <= 5}
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function, that is, the values for which the function is defined.
The function described in this problem is defined from x = -2 until x = 5 hence the domain of the function is given as follows, by the interval:
{x| –2 ≤ x <= 5}
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Answer:
So I got 64 on my test, but it doesn't let you see what was right and what was wrong, so I guess we will never know☹️☹️☹️☹️.
BTW in was on edge
Which graph represents the equation y2 = –4x?
On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 1, 0), and a directrix at x = 1.
On a coordinate plane, a parabola opens down. It has a vertex at (0, 0), a focus at (0, negative 1), and a directrix at y = 1.
On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 4, 0), and a directrix at x = 4.
On a coordinate plane, a parabola opens down. It has a vertex at (0, 0), a focus at (0, negative 4), and a directrix at y = 4.
Answers
Answer:
its A
Step-by-step explanation:
Answer: The first one (A)
Step-by-step explanation:
Suppose A and B are points on the number line. If AB = 8 and B lies at −7, where could A be located?
Answers
The value of A is A(1,-15) and the distance between AB is 8 so these are the correct answers.
According to the statement
We have given that the
AB = 8 and B lies at −7, and we have to find the position of the A on the number line.
Let a be a point on number line and b be the second point on number line.
And The distance between two numbers on number line is calculate by subtracting the smaller number from larger number.
Here
AB = 8
B = -7
We have to look at the options one by one.
For A = -1
As A>B
AB = -1-(7) = -1+7 = 6
For A = 1
As A>B so
AB = 1-(-7) = 8
So with A = 1 , AB = 8
This is one of the right answers.
For A=15
As A>B
AB = 15-(-7) = 22
For A=-15
As B>A
AB = -7 -(-15) = 8
As with A=1 and A=-15, the distance between AB is 8 so these are the correct answers.
So, The value of A is A(1,-15) and the distance between AB is 8 so these are the correct answers.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Suppose A and B are points on the number line. If AB = 8 and B lies at −7, where could A be located?
Select ALL that apply.
A −1
B 1
C 15
D −15
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The minor arc measures of circle Z are shown in the figure.
Circle Z is shown. Radii Z Y, Z X, Z W, Z V, Z U, and Z T are shown. The arc measure of Y X is 71 degrees, the arc measure of X W is 32 degrees, the arc measure of W V is 71 degrees, the arc measure of V U is 78 degrees, the arc measure of U T is 54 degrees, and the arc measure of T Y is 54 degrees.
Use the drop-down menus to complete each statement.
Angle UZT is congruent to angle
.
Angle VZW is congruent to angle
.
Answers
The completed statement are:
Angle UZT is congruent to angle TZY.Angle VZW is congruent to angle YZX.What is the angle about?Part A:
Angle UZT is congruent to angle TZY.
Using the image attached figure, we can see that:
∠UZT = 54°
∠TZY = 54°
Hence one can say that ∠TZY = ∠UZT are both congruent angles.
Part B:
Angle VZW is congruent to angle YZX.
Using the image attached attached, we can see that:
∠VZW = 71°
∠YZX = 71°
Hence, ∠YZX = ∠VZW are both regarded as congruent angles .
Therefore, The completed statement are:
Angle UZT is congruent to angle TZY.Angle VZW is congruent to angle YZX.Learn more about Angles from
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Answer: a, c
Step-by-step explanation:
Does anyone know this? Evalute the power type your answer in the open box. Look at picture.
Answers
I hope that this helps! :)
Pls help
Write the equation for a parabola with a focus at (-4,3) and a directrix at y=5
Answers
Answer:
y=(1/-4)(x+4)^2 +4
Step-by-step explanation:
Don't ask
If a polynomial function, f(x), with rational coefficients has roots 0, 4, and 3 startroot 11 endroot, what must also be a root of f(x)? 3 i startroot 11 endroot negative 3 i startroot 11 endroot 3 minus startroot 11 endroot negative 3 minus startroot 11 endroot
Answers
Answer:
C
Step-by-step explanation:
C
Answer:
Step-by-step explanation:
its c
If a1=6 and a5=12, what does a3=?
Answers
a3=9
assuming the pattern is constant, a3 is right in the middle of a1 and a5 so the answer would be right in the middle of 6 and 12. the average of 6 and 12 is 9, so a3=9.
hope this helps!
give me some questions of grade 7
Answers
Q1: For 30 minutes, a person jogged 10 times along the perimeter of a rectangular field at 12 kilometers per hour. Find the square meters of the field if its length is twice its width.
Q2: A car is traveling at a speed of 75 kilometers per hour. In one minute, how many meters does the car travel?
Q3: What is the length of 2000 millimeters in inches? Round your answer to the nearest hundredth.
Hope this helps =)
A fruit basket contains only apples and bananas. If there are 8 apples and 13 bananas, what is the ratio of bananas to fruit? Select all that apply.
13:8
13:21
StartFraction 8 Over 13 EndFraction
21 to 13
StartFraction 13 Over 21 EndFraction
Answers
The ratio of bananas to fruit is 13 : 21
How to determine the ratio of bananas to fruit?The given parameters are
Banana = 13
Apple = 8
The total number of fruits is
Fruit = Banana + Apple
Substitute the known values in the above equation
Fruit = 13 + 8
Evaluate the sum
Fruit = 21
The ratio of bananas to fruit is then represented as:
Ratio = Banana : Fruit
Substitute the known values in the above equation
Ratio = 13 : 21
Hence, the ratio of bananas to fruit is 13 : 21
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An airplane covers 3500 km in three hours. What would be the distance covered by the plane in 4.5 hours if it flies at the same constant speed. ( I need the proportion equation please help ASAP.)
Answers
Answer:
5,250 km
Step-by-step explanation:
[tex]\frac{hours}{miles}[/tex] = [tex]\frac{hours}{miles}[/tex]
[tex]\frac{3}{3500}[/tex] = [tex]\frac{4.5}{x}[/tex] Cross Multiply
3x = (4.5)(3500)
3x = 15750 Divide both sides of the equation by 3
x = 5,250
Let startfraction cosine (2 x) over cosine (x) sine (x) endfraction = 0 where 0° ≤ x ≤ 180°. what are the possible values for x?
Answers
45° only the possible values for x.
What is the meaning of trigonometric ratio?
Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.The given equation can be presented as follows;
[tex]\frac{cos (2 . x )}{cosine(x) + sin(x)} = 0[/tex]
We have that cos(2·x) = cos²(x) - sin²(x)
Also, we have, by the difference of two squares, the following relation;
cos²(x) - sin²(x) = (cos(x) - sin(x))(cos(x) + sin(x))
Therefore, the given equation can be written as follows;
[tex]\frac{cos (2 . x )}{cosine (x) + sin(x) } = \frac{(cos(x) - sin(x) * (cos(x) + sin(x)}{(cos(x) + sin(x))} = 0[/tex]
Crossing the common term, (cos(x) + sin(x)), in the numerator and the denominator, we have-
[tex]\frac{(cos(x) - sin (x) * (cos(x) + sin(x)}{(cos(x) + sin(x))} = cos (x) - sin(x) = 0[/tex]
From cos(x) - sin(x) = 0, we have;
Adding sin(x) to both sides of the equation
cos(x) - sin(x) + sin(x) = 0 + sin(x)
cos(x) = sin(x)
Therefore, the opposite leg and the adjacent leg of the right triangle formed with reference to the angle x are equal
∴ x = 90/2 = 45° only for 0° ≤ x ≤ 180°
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A package is oscillating on a spring scale with a period of 5.00 s. at time t = 0.00 s the package has zero speed and is at x = 8.50 cm. at what time after t = 0.00 s will the package first be at x = 4.50 cm?
Answers
Under the assumption of simple harmonic motion, the package will be at x = 4.50 centimeters at a time of 0.805 seconds.
How to analyze an object on simple harmonic motion
Simple harmonic motion is a kind of periodic motion represented by sinusoidal functions. Physically speaking, it is a good approximation for periodic motion due to small perturbations and with absence of frictions and viscous forces on the system.
The position of an object under simple harmonic motion is described by the following equation:
x (t) = A · cos (2π · t / T + Ф) (1)
Where:
A - Amplitude, in centimetersT - Period, in secondsФ - Angular phase, in radiansx(t) - Position, in centimetersIf we know that T = 5 s, A = 8.50 cm, Ф = 0 rad and x = 4.50 cm, then the time when the package will reach x = 4.50 cm is:
4.50 = 8.50 · cos (2π · t / 5)
9 / 17 = cos (2π · t / 5)
0.322π = 2π · t / 5
t = 0.805 s
Under the assumption of simple harmonic motion, the package will be at x = 4.50 centimeters at a time of 0.805 seconds.
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Solve for x: 12x2 – 6 (a2 + b2)x + 3a2b2 = 0
Answers
Answer:
x:12×2−6(a2+b2)x+3a2b2=0
Step-by-step explanation:
equation
