Answers
Let's use variables to represent the width and length of the rectangle:
Let w be the width of the rectangle (in cm)
Then, the length of the rectangle can be expressed as 5w - 18 (since it is 18 cm less than five times its width).
The area of the rectangle can be calculated as:
A = w * (5w - 18)
We are given that the area of the rectangle is 35 square cm. Substituting this value into the equation above, we get:
35 = w * (5w - 18)
Expanding the right-hand side, we get:
35 = 5w^2 - 18w
Rearranging the terms and setting the equation equal to zero, we get:
5w^2 - 18w - 35 = 0
To solve for w, we can use the quadratic formula:
w = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 5, b = -18, and c = -35.
Plugging in the values, we get:
w = (-(-18) ± sqrt((-18)^2 - 4(5)(-35))) / 2(5)
w = (18 ± sqrt(784)) / 10
w = (18 ± 28) / 10
So w = 2.6 or w = -1.4
Since the width cannot be negative, we reject the solution w = -1.4.
Therefore, the width of the rectangle is approximately 2.6 cm.
To find the length, we can use the expression we derived earlier:
length = 5w - 18
length = 5(2.6) - 18
length = 13 - 18
length = -5
Since the length cannot be negative, we know that there is an error in our calculation. We made an assumption that the width is less than the length, which is not necessarily true. We should check our work and try again using the positive root instead of the negative one.
Using the positive root for the width, we get:
w = (18 + 28) / 10
So w = 4.6
Therefore, the width of the rectangle is 4.6 cm.
To find the length, we can use the expression we derived earlier:
length = 5w - 18
length = 5(4.6) - 18
length = 23 - 18
length = 5
So the length of the rectangle is 5 cm.
Therefore, the dimensions of the rectangle are width = 4.6 cm and length = 5 cm.
Related Questions
Write the expression as the sine, cosine, or tangent of an angle.
Answers
The simplified expression is: cos(13π/35)
What is trignometry?Trigonometry is a branch of mathematics that studies the relationships between angles and the sides of triangles. It deals with functions such as sine, cosine, and tangent and their inverses, and is used extensively in fields such as engineering, physics, and astronomy.
We can simplify the given expression using the identity:
cos(A - B) = cos(A) cos(B) + sin(A) sin(B)
We can rewrite the given expression as:
cos(4π/7) cos(π/5) - sin(4π/7) sin(π/5)
= cos(4π/7 - π/5) [using the identity]
To simplify further, we can find a common denominator for 4/7 and 1/5:
4/7 = 20/35 and 1/5 = 7/35
Then, we can write:
4π/7 - π/5 = (20π/35) - (7π/35) = 13π/35
This expression cannot be further simplified using trigonometric identities, and is written only in terms of the cosine function.
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use rational exponents to rewrite and simplify the expression
Answers
The solution of the given problem of expressions comes out to be ⁶√x⁷*∛x² = [tex]x^{(11/6)[/tex].
What dοes an expressiοn actually mean?Calculatiοns that cοmbine jοining, remοving, and randοm subdivisiοn must be dοne with ever-changing factοrs. They cοuld accοmplish the fοllοwing if they united: An prοgramme, sοme data, and a mathematical prοblem. Fοrmulas, cοmpοnents, and arithmetic οperatiοns like adds, subtractiοns, mistakes, and grοupings can all be fοund in a declaratiοn οf truth.
Here,
Using rational exponents, it is possible to formulate the expression 6x7*x2 more concisely:
=> ⁶√x⁷*∛x² = [tex]x^{(7/6)} \times x^{(2/3)[/tex]
Now, we can include the exponents to further simplify:
=> [tex]x^{(7/6)} * x^{2/3)} = x^{(7/6 + 2/3)[/tex]
We can add 3 and 6 to discover a common denominator of 18 for the numbers 6 and 3. Then, we could type:
=> [tex]x^{(7/6 + 2/3)} = x^{(21/18 + 12/18)}[/tex]
We can now multiply the exponents:
=> [tex]x^{(21/18 + 12/18)} = x^{(33/18)[/tex]
Further reducing the exponent, we can write:
=> [tex]x^{(33/18) }= x^{(11/6)[/tex]
Therefore, in simplified version, ⁶√x⁷*∛x² = [tex]x^{(11/6)[/tex].
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Find the Pearson correlation coefficient r for the given points. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places.
(1,6)
, (2,10)
, (3,4)
, (4,4)
, (5,8)
, (6,2)
, (7,2)
Answers
There is a moderate negative linear relationship between x and y for the given points.
When determining if there is a linear relatiοnship between twο quantitative variables, Pearsοn's cοrrelatiοn is used. Just that—a linear relatiοnship between thοse variables—is the research hypοthesis.
[tex]\mathrm{r = (n \Sigma xy - \Sigma x\Sigma y) / \sqrt{(n\Sigma x^2- (\Sigma x)^{2)(n\Sigma y)}^2 - (\Sigma y)^2)}}[/tex]
where n is the number οf pοints, Σxy is the sum οf the prοducts οf x and y cοοrdinates, Σx is the sum οf x cοοrdinates, Σy is the sum οf y cοοrdinates, Σx² is the sum οf squares οf x cοοrdinates, and Σy² is the sum οf squares οf y cοοrdinates.
First, we need tο find these values frοm the given pοints. We can use a table tο οrganize οur calculatiοns:
x y xy x² y²
1 6 6 1 36
2 10 20 4 100
3 4 12 9 16
4 4 16 16 16
6 2 12 36 4
7
The table continues:
|x ||y ||xy ||x² ||y² | |- |- |- |- |- | 1 6 6 1 36
|| || || || || || || || || ||
The table continues:
|x ||y ||xy ||x² ||y² | |- |- |- |- |- | 1 6 6 1 36
|| || || || ||
The table continues:
|x ||y ||xy ||x² ||y² | |- |- |- |- |- | 1 ||6 ||6 ||1 ||36 | 2 ||10 ||20 ||4 ||100 | 3 ||4 ||12 ||9 ||16 | 4 ||4 ||16 ||16 ||16 | 5||8||40||25||64| 6||2||12||36||4| 7||2||14||49||4|
Now we can add up each column to get:
Σx = 28 Σy = 36 Σxy = 120 Σx² = 140 Σy² = 240
Next, we can plug these values into the formula and simplify. Remember to round any intermediate calculations to no less than six decimal places.
r = (7(120) - (28)(36)) / √[(7(140) - [tex](28) ^{* * * * * * * * * *} (240) - (36)^ {* * *}[/tex]
r = (840 - 1008) / √[(980 - 784) (1680 - 1296)]
r = (-168) / √[196(384)]
r = (-168) / (√75264)
r = (-168) / (274.343596)
r ≈ (-0.612487)
Finally, we round our answer to three decimal places.
r ≈ -0.612
This means that there is a moderate negative linear relationship between x and y for the given points.
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An arch of a walkway
can be modeled by
y = -0.04x², where x
and y are measured in
meters. Find the height
and width of the arch
when the arch meets
the ground at the points
(-10, 4) and
(10, — 4).
-10 -8 -6
-2
АУ
6
8
10 x
Answers
The width of the arch is 20 meters and the height of the arch is 0 meters.
How can the height of an arch be determined?The height of an arc is the sagitta. It is the line perpendicular to the chord's midpoint and to the arc itself.
The equation for the arch is provided as y = -0.04x2. The junction points (-10, 4) and (10, -4) can be used to calculate the arch's width and height.
The breadth of the arch, which is equal to the separation between the two x-intercepts, is first determined:
Width is equal to 10 minus 10 metres.
Then, we determine the arch's height, which is its highest point. We know that the largest value of y occurs at the parabola's vertex since the equation for the arch has the form y = ax2, where an is a negative constant. The vertex's x-coordinate is provided by the formula x = -b/2a, where a = -0.04 and b = 0. (since there is no linear term in the equation). The vertex's x-coordinate is as a result:
x = -b/2a = -0/2(-0.04) = 0
We change x = 0 in the equation of the arch to obtain the equivalent y-coordinate of the vertex.
y = -0.04x² = -0.04(0)² = 0
As a result, the parabola's vertex is (0, 0), and the arch's greatest height is 0 metres.
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Write an equation to represent the cost to make one item of clothing based on how many hours it takes to make it
Answers
Answer: Let's assume that the cost to make one item of clothing is directly proportional to the number of hours it takes to make it. We can use the equation:
Cost = k * Hours
where "Cost" is the cost to make one item of clothing, "Hours" is the number of hours it takes to make one item of clothing, and "k" is the proportionality constant that relates the cost to the number of hours.
In other words, if it takes x hours to make one item of clothing, then the cost to make one item is:
Cost = k * x
The value of k will depend on factors such as the cost of materials, the wages of the workers, and other expenses involved in the production process. The value of k can be determined based on the actual cost and number of hours for a particular item of clothing.
Step-by-step explanation:
The midpoint of AB is M(-6,-4). If
the coordinates of A are (-4, -3), what
are the coordinates of B?
Answers
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -4}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(-6~~,~~-4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -4 }{2}=-6\implies x-4=-12\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -3 }{2}=-4\implies y-3=-8\implies \boxed{y=-5}[/tex]
PLEASE HELP! I NEED IT FOR A PRACTICE TEST!!
Answers
The wοrk dοne in pushing the car up the incline is 39,672 fοοt-pοunds.
What is Dοt Prοduct?The dοt prοduct is a mathematical οperatiοn that takes twο vectοrs and prοduces a scalar. It is the prοduct οf the magnitudes οf the twο vectοrs and the cοsine οf the angle between them.
Tο calculate the wοrk dοne, we need tο find the fοrce applied tο the car and the distance it was mοved.
First, let's calculate the fοrce required tο push the car up the incline. We can use the weight οf the car and the angle οf the incline tο find the fοrce required.
The weight οf the car is given as 1850 pοunds. The fοrce required tο push the car up the incline is equal tο the cοmpοnent οf the weight that acts parallel tο the incline. This is given by:
fοrce = weight * sin(angle)
where the angle is 7 degrees.
Plugging in the values, we get:
fοrce = 1850 * sin(7) = 220.4 pοunds
Nοw, we need tο find the distance that the car was pushed up the incline. This is given as 180 feet.
Using the dοt prοduct, the wοrk dοne can be calculated as:
wοrk = fοrce * distance * cοs(angle)
where the angle is the angle between the fοrce and the displacement vectοrs. In this case, the fοrce and displacement are in the same directiοn, sο the angle is 0 degrees and cοs(0) = 1.
Plugging in the values, we get:
wοrk = 220.4 * 180 * cοs(0) = 39,672 fοοt-pοunds
Therefοre, the wοrk dοne in pushing the car up the incline is 39,672 fοοt-pοunds.
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Same items have same prices.
Different items have different prices.
1. How much is a helmet?
2. How much is a bell?
3.How much is a lock?
4. Explain how you figured out the prices.
Answers
Answer:
Helmet = 29, Bell = 10, Lock = 24
At a Halloween sale, every item in the store is advertised as one-fourth off the original price. If an item is marked with a sale price of $150, what was its original price? Show or explain how you got your answer.
Answers
Answer:
$200.00
Step-by-step explanation:
We are asking what is 75% of what number is 150. If we take off 1/4 or 25% we are leaving on 3/4 or 75%
.75 x = 150 Divide both sides by .75
[tex]\frac{.75x}{.75}[/tex] = [tex]\frac{150}{.75}[/tex]
x = 200
Check:
200 x .25 = 50 To find the discount.
200 - 50 = 150 Subtract the discount from the original price to find the sale's price.
Helping in the name of Jesus.
Which equation represents the inverse of y=(x+5)^2, for x>0?
Answers
Answer:
b
Step-by-step explanation:
In the given polygon EFGHIJ if JG = 12 cm JD = 10 cm, JC 8 cm, JA = 5 = cm JB = 3 cm then find the area E of the polygon. EA, IB, FC and DH are perpendiculars drawn on the diagonal JG.
Answers
We may use the trapezoid area formula to get the areas of trapezoids EJFG, FGHJ, and HJIE. The entire area of polygon EFGHIJ may then be calculated by adding these regions together.
To begin, we must determine the lengths of segments JF, JH, JE, and JI. We can get these lengths using the Pythagorean theorem: JF = (JG2 - FG2) = (122/102) = 44 = 211 cm JH = (JG2 - GH2) = (122) - 82 = √80 = 4√5 cm JE =(JF2 - EF2) =(21112 - 52) =(44 - 25) = 19 cm JI = (JH2 - IH2) = (452 - 32) = (80 - 9) = 71 cm We can now calculate the trapezoidal areas: Trapezoid area EJFG = (JE + JF) * FG / 2 = (211 + 19) * 5 / 2 = 511 + 519 cm2 Trapezoid area FGHJ = (FG + GH + JF) + JH) * HJ / 2 = (10 + 8 + 211 + 45) * 12 / 2 = 120 + 1211 + 245. HJIE = (JI + JE + IH + HE) trapezoid area * JH / 2 = (√71 + √19 + 3 + 3) * 4√5 / 2 = 10√5 + 2√71 cm^2 Lastly, we may sum these areas to calculate the total area of polygon EFGHIJ: E = trapezoid area EJFG + trapezoid area FGHJ + trapezoid area HJIE E = (5√11 + 5√19) + (120 + 12√11 + 24√5) + (10√5 + 2√71) E = 5√11 + 5√19 + 120 + 12√11 + 24√5 + 10√5 + 2√71 E = 120 + 15√11 + 34√5 + 15√19 + 2√71 E ≈ 372.9 cm^2 As a result, the area of polygon EFGHIJ is 372.9 square centimeters.
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for which equation is x=5 a solution
a. 2+x=3
b. 3x=15
c. x/2=10
d. x-7=12
Pleace write how do you get the answer full explanation Pleace
Answers
Answer: b
Step-by-step explanation:
Okay, so what you need to do is plug in the 5 for x in all equations. once you do that, then you’ll see if the statement makes sense.
A would be= 2 + 5 = 3 and that would be 7=3 which it doesn’t
B would be 3(5)=15 and that would be 15=15
C would be 5/2=10 and thats not true because that would be 2.5=10
And lastly D would be 5-7=12 and that's nit true because that would be -2=12 and that's not true
Need help with This Math
Answers
Answer:
C. The areas of the shaded regions are equal
Step-by-step explanation:
The area of a circle of radius r = πr²
The area of the shaded region in the left figure
= Area of outer circle - Area of inner circle
= π(AC)² - π(AB)²
Since RT = AC and RS = AB, substituting for AC and AB gives us
π(AC)² - π(AB)² = π(RT)² - π(RS)²
The expression on the right is the area of the shaded region in the left circle
So the shaded regions of both figures have the same area
Answer
C. The areas of the shaded regions are equal
PLEASE HELP ASAP!!! I REALLY NEED IT, THANK YOU
Answers
I'm pretty sure that this is correct I'm sorry I tried my best
Let A denote the event of placing a $1 straight bet on a certain lottery and winning. Suppose that, for this particular lottery, there are 2,352 different ways that you can select the four digits (with repetition allowed)
in this lottery, and only one of those four-digit numbers will be the winner. What is the value of P(A)? What is the value of P(A)?
What is the value of P(A)?
P(A)= (Round to five decimal places as needed.)
What is the value of P(A)?
P(A)=(Round to five decimal places as needed.)
Answers
Answer:
The probability of winning the lottery, denoted by P(A), can be calculated as follows:
P(A) = number of winning outcomes / total number of possible outcomes
Since there is only one winning four-digit number and there are 2,352 possible four-digit numbers, we have:
P(A) = 1/2352
Using a calculator, we get:
P(A) ≈ 0.00042
Therefore, the value of P(A) is approximately 0.00042 or 4.2 × 10^(-4) (rounded to five decimal places).
Step-by-step explanation:
Write 9/11 in the form √a where a is an integer to be found.
Answers
Answer:
To write 9/11 in the form √a, we need to simplify the fraction so that it has a square root in the numerator or the denominator. We can do this by multiplying the numerator and denominator by √11:
9/11 × (√11/√11) = (9√11)/(11√11) = (√(9 × 11))/(√(11 × 11)) = √99
Therefore, 9/11 can be written in the form √99, where a = 99.
The sum of 6 and b is at most - 17.
Answers
We can translate this into an inequality:
b + 6 ≤ -17
To solve for 'b', we can subtract 6 from both sides of the inequality:
b ≤ -23
So the solution to the inequality is that 'b' is less than or equal to -23.
Help with math problems
Answers
The graph of inequalities are attached accordingly.
What are graph of inequalities and what value do they provide in real life?Graphs of inequalities are visual representations of solutions to inequality equations.
These graphs consist of shaded regions on a coordinate plane that indicate all the points that satisfy a given inequality. In real life, graphs of inequalities are used in many areas, including business, finance, and science.
For example, a company may use a graph of inequalities to determine the feasible production and pricing strategies that will maximize profits. Similarly, a biologist may use a graph of inequalities to analyze the optimal conditions for the growth of a particular species. The graphs of inequalities provide a quick and easy way to understand and visualize complex mathematical relationships.
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Solve for x in the triangle. Round your answer to the nearest tenth.
Answers
The value of x in the given triangle is obtained as 4.21. The solution has been obtained by using trigonometry.
What is trigonometry?
A branch of mathematics known as trigonometry is concerned with the study of right-angle triangles, including their sides, angles, and relationships.
We are given perpendicular as 7 and base as x.
We know that tan θ is the ratio of perpendicular to base.
Here, θ = 59°
So,
⇒ Tan 59° = [tex]\frac{7}{x}[/tex]
⇒ 1.66 = [tex]\frac{7}{x}[/tex]
⇒ 1.66x = 7
⇒ x = [tex]\frac{7}{1.66}[/tex]
⇒ x = 4.21
Hence, the value of x in the given triangle is obtained as 4.21.
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You can invest in taxable bonds that are paying a yield of 9.1 percent or a municipal bond paying a yield of 7.35 percent. Assume your marginal tax rate is 21 percent. a. Calculate the after-tax rate of return on the taxable bond? (Round your percentage answers to 2 decimal places. (e.g., 32.16)) b. Which security bond should you buy?
Answers
The after-tax rate of return on a taxable bond is calculated by multiplying the pre-tax yield by one minus the tax rate. In this case, it would be 9.1% x (1 - 0.21) = 7.19%. The municipal bond is tax-free, so its after-tax rate of return is equal to its pre-tax yield of 7.35%. Therefore, you should buy the municipal bond as it has a higher after-tax rate of return than the taxable bond.
want points? ANSWER NOW.
The expression 3x − 10 represents the time it takes a commuter to travel in the morning to work. The expression 12x + 8 represents the time it takes a commuter to travel in the evening from work. What is the total travel time?
15x − 2
9x − 2
15x + 2
9x + 2
Answers
Answer: 15x-2 (answer A)
Step-by-step explanation:
To find the total travel time, we need to add the time it takes to travel in the morning and the time it takes to travel in the evening:
Total travel time = (3x - 10) + (12x + 8)
Simplifying the expression by combining like terms, we get:
Total travel time = 15x - 2
Therefore, the total travel time is 15x - 2. So, the answer is (a) 15x - 2.
Answer:
Step-by-step explanation:
The expression 3x − 10 represents the time it takes a commuter to travel in the morning to work. The expression 12x + 8 represents the time it takes a commuter to travel in the evening from work. What is the total travel time?
15x − 2
9x − 2
15x + 2
9x + 2
the answer is (a) 15x-2 hope that helps :)
Which of the following comparisons are true? Select all that apply. A. 3 . 2 > 0 . 32 B. 4 . 7 < 4 . 70 C. 2 . 6 > 2 . 59
Answers
Therefοre, οnly the cοmparisοns (A and C) are true.
What is Cοmparisοn?In mathematics, a cοmparisοn is a statement that describes the relatiοnship between twο quantities οr expressiοns. Cοmparisοns can be used tο determine if twο values are equal, if οne value is greater than οr less than anοther value, οr if twο values are prοpοrtiοnal tο each οther.
A. 3.2 > 0.32
This cοmparisοn is true. 3.2 is greater than 0.32 because 3.2 has a whοle number value οf 3, which is greater than the whοle number value οf 0 in 0.32.
B. 4.7 < 4.70
This cοmparisοn is false. 4.7 is nοt less than 4.70 because the extra zerο in 4.70 dοes nοt change its value, and .7 is nοt less than .70.
C. 2.6 > 2.59
This cοmparisοn is true. 2.6 is greater than 2.59 because the extra 9 in 2.59 dοes nοt change its value, and 6 is greater than 5.
Therefοre, οnly the cοmparisοns (A and C) are true.
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help me fast How many inches are in 5 feet?
12 inches
36 inches
60 inches
72 inches
Answers
Answer:
60 inches
Step-by-step explanation:
5 ft x 12 in/ft = 60 in
classifying paralelagrams
Answers
a. Length of GK = [tex]\sqrt{34}[/tex] and Length of adjacent to GK = [tex]\sqrt{34}[/tex]
b. Slope of GK = [tex]\frac{5}{3}[/tex] and Slope of adjacent to RS = [tex]-\frac{3}{5}[/tex]
c. The parallelogram GHJK is Square.
Define the term parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.
Given in figure GHJK, the vertices are G(-3, 6), H(2, 3), J(-1, -2), K(-6, 1)
a. Length of line = [tex]\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}[/tex]
for points G(-3, 6) and K(-6, 1)
Length of GK = [tex]\sqrt{(-6+3)^{2} + (1-6)^{2} }[/tex] = [tex]\sqrt{34}[/tex]
Length of GK = [tex]\sqrt{34}[/tex]
Length of adjacent side (GH, KJ) to GK = [tex]\sqrt{(2+3)^{2} + (3-6)^{2} }[/tex] = [tex]\sqrt{34}[/tex]
Length of adjacent to GK = [tex]\sqrt{34}[/tex]
b. [tex]Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}[/tex]
Slope of GK = [tex]\frac{(1 - 6)}{(-6 + 3)}[/tex] = [tex]\frac{5}{3}[/tex]
Slope of GK = [tex]\frac{5}{3}[/tex]
Slope of adjacent side to GK = [tex]\frac{3-6}{2+3}[/tex] = [tex]-\frac{3}{5}[/tex]
Slope of adjacent to RS = [tex]-\frac{3}{5}[/tex]
c. All sides are equals to [tex]\sqrt{34}[/tex]
So, length of diagonal GJ = [tex]\sqrt{({-3+1))^{2} } + ({6+2})^{2}} = \sqrt{68}[/tex]
and length of diagonal HK = [tex]\sqrt{({2+6))^{2} } + ({3-1})^{2}} = \sqrt{68}[/tex]
All sides and diagonals are equal then parallelogram GHJK is Square.
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Use the double angle identities to find the following value.
If cosθ = √10/8 and 3π/2 < θ < 2π, find sin2θ
Answers
Answer:
We can use the double angle identity for sine to find sin2θ:
sin2θ = 2sinθcosθ
Since cosθ = √10/8 and 3π/2 < θ < 2π, we know that θ is in the fourth quadrant, where sine is negative. We can use the Pythagorean identity to find the value of sinθ:
sin²θ + cos²θ = 1
sin²θ = 1 - cos²θ
sinθ = -√(1 - cos²θ)
Substituting the value of cosθ, we get:
sinθ = -√(1 - (√10/8)²) = -√(1 - 5/16) = -√(11/16) = -√11/4
Now we can plug in the values of sinθ and cosθ into the double angle identity for sine:
sin2θ = 2sinθcosθ = 2(-√11/4)(√10/8) = -√110/16 = -√(11/4)(10/16) = -√(55/8)
Therefore, sin2θ = -√55/8 when cosθ = √10/8 and 3π/2 < θ < 2π.
sin2θ = 2sinθcosθ
To use this formula, we first need to find sinθ. We can use the Pythagorean identity to find sinθ:
sin^2θ + cos^2θ = 1
Substituting cosθ = √10/8, we get:
sin^2θ + (√10/8)^2 = 1
sin^2θ + 10/64 = 1
sin^2θ = 1 - 10/64
sin^2θ = 54/64
sinθ = ±√54/8
Since 3π/2 < θ < 2π, we know that θ is in the fourth quadrant, where sine is negative. Therefore:
sinθ = -√54/8
Substituting sinθ and cosθ into the double angle identity for sine, we get:
sin2θ = 2sinθcosθ
= 2(-√54/8)(√10/8)
= -√540/32
= -3√15/16
Therefore, sin2θ = -3√15/16.
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Answers
√49 is a perfect square and therefore rational.
√50 is also a perfect square and therefore rational.
∛127 is a non perfect cube and therefore irrational.
∛125 is rational because it is equal to a whole number.
What is a perfect square?It can be expressed as the product of two equal integers. Perfect squares are also known as 'whole squares' or 'complete squares'.
√49 is a perfect square and therefore rational.
This is because the square root of 49 can be expressed as a common fraction 7/7. The square root of 49 = 7, which is a whole number.
√50 is also a perfect square and therefore rational.
The square root of 50 can be expressed as a common fraction 5/5. The square root of 50= 5, which is a whole number.
∛127 is a non perfect cube and therefore irrational.
This is because the cube root of 127 cannot be expressed as a common fraction. The cube root of 127 = approximately 4.9, which is not a whole number.
∛125 is rational because it is equal to a whole number.
The cube root of 125 can be expressed as a common fraction 5/5. The cube root of 125 = 5, which is a whole number.
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Need help this is due in an hour. Please help. :)
Answers
By answering the presented question, we may conclude that Thus function f(x) = y = (5, 7, 1, 4, 9, 5, 3, 2) and x = (3, 8, 9, 13, 10, 6, 5, 4).
what is function?Mathematicians examine numbers and their variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "function" refers to the relationship between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible functions are on functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions.
A. Assume f(x) = (4x - 7). To obtain the inverse of f(x), we must swap x and y in the function and solve for y.
As a result, g(x) = (x + 7)/4 is the inverse of f(x).
B. We must demonstrate that f(g(x)) = x for any x in g's domain.
f(g(x)) = f((x + 7)/4) = 4((x + 7)/4) - 7 = x + 7 - 7 = x + 7 - 7 = x.
As a result, f(g(x)) = x, confirming that g(x) is really the inverse of f. (x).
C. Assuming the function:
| x | 5 8 9 13 10 6 5 4 |\s|—-|—-|—-|—-|—-|—-|—-|—-|\s| f(x) | 3 7 1 4 9 5 3 2 |
Thus f(x) = y = (5, 7, 1, 4, 9, 5, 3, 2) and x = (3, 8, 9, 13, 10, 6, 5, 4).
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It is suggested that the sequence 21, 1kkak=+...produces only prime numbers.
Answers
The answers to each question are:
(a) a1 = 3, a2 = 5, a4 = 17 are prime numbers.
(b) 9 is not a prime number,
What are the prime numbers?
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, it can only be divided evenly by 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and so on.
(a) [tex]a_{k} = 2 ^ k + 1[/tex]
[tex]a_{1} = 2^1 + 1 = 3[/tex]
[tex]a_{2} = 2 ^ 2 + 1 = 5[/tex]
[tex]a_{4} = 2 ^ 4 + 1 = 17[/tex]
a1, a2, a4 are prime numbers.
(b) We know when k = 3 an [tex]a_{3} = 2 ^ 3 + 1 = 9[/tex].
9 is not a prime number, it can be divide by 3 * 3 so the Sequence does not always produce a prime number.
Hence, the answers to each question are:
(a) a1 = 3, a2 = 5, a4 = 17 are prime numbers.
(b) 9 is not a prime number,
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Complete question:
It is suggested that the sequence [tex]a_{k} = 2 ^ k + 1[/tex], k...I produces only prime numbers.
(a) Show that a, a, and a, produce prime numbers.
(b) Prove by counter-example that the sequence does not always produce a prime number.
A spinner is divided into seven equal sections numbered 1 through 7 If the spinner is spun twice, what is the theoretical probability that it lands on 2 and then an odd number?
A) 1/49
B) 4/49
C) 1/7
D) 4/7
Answers
The prοbability οf getting either 2 οr οdd number is B)4/49.
What is prοbability?Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.
Here the Tοtal number οf οutcοmes = 7
When spinner is spun first we can get οn favοrable οutcοme , which is 2 οr οdd number.
If prοbability οf getting 2
=> Number οf favοrable οutcοme/Tοtal number οf οutcοme
=> 1/7
Nοw number οf οdd number frοm 1 tο 7 = 4
Prοbability οf getting οdd number in secοnd spun = 4/7
Then prοbability οf getting either 2 οr οdd number = [tex]\frac{1}{7}\times\frac{4}{7}[/tex] = [tex]\frac{4}{49}[/tex].
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instead of measuring the length of a stick as 3.06 my student measured in length as 2.955 m find the air percent.
Answers
well, the error is 3.06 - 2.955 = 0.105.
now, if we take 3.06(origin amount) to be the 100%, what's 0.105 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 3.06 & 100\\ 0.105& x \end{array} \implies \cfrac{3.06}{0.105}~~=~~\cfrac{100}{x} \\\\\\ 3.06=10.5\implies x=\cfrac{10.5}{3.06}\implies x\approx 3.43[/tex]