A rope is fixed between two trees that are 10 metres apart. When a child hangs on to the centre of the rope, it sags so that the centre is 2 metres below the level of the ends. Find the lenth of the rope.
Answers
The length of the rope is 2√29 meters.
What is an isosceles triangle?
An isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.
Given that the distance between two trees is 2 meters. A boy hangs on a rope tied to the trees in the middle of the rope.
it sags so that the center is 2 meters below the level of the ends.
Thus it forms an isosceles triangle. △ACD and △BCD are two right triangles.
Since △ABD is isosceles triangle and AD = BD.
In △ACD, Hypotenouse = AD, Base = AC = 10/2 = 5 cm, Height = CD = 2 meters
Apply Pythagorean theorem on △ACD:
AD² = AC² + CD²
AD² = 5² + 2²
AD² = 29
AD = √29
Therefore, BD = √29
The length of the rope is AD + BD = 2√29 meters.
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Related Questions
this is my quation kfwn vehfwqkn uewfhkjn uewfhskj uefwshjl efwuhskcj fwqeukjscngefww
Answers
Answer:
1/6
Step-by-step explanation:
There are 6 letters and the spinner lands on one at a time
Please help
The graph shows the reciprocal parent function
Which statement best describes the function
Answers
The statement that best represents the function must be identified by reading the graph.
Let's check which of the following statements best characterizes the function:A) When x < 0, the function is negative.
This is accurate; as you can see, the function is negative for x < 0 because it is below the horizontal axis.
We shall see that choice A is the proper one. "When x < 0, the function is negative."
The function tends to infinity on the positive side at an x close to zero.
The function tends to negative infinity at x close to zero on the negative side.
The function tends to zero as x's absolute value grows.
So we can conclude that this is an inverse function similar to:
y = f(x) = 1/x
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Can u please help me with this question.
Answers
Answer:
you can use compass to make straight line
The table shows the amount of certain school supplies left over in the school bookstore at the end of the year.
Item Total
Pens 36
Markers 48
Erasers 24
The bookstore manager will make packages of the remaining school supplies and sell them for $5 per package. Each package will be identical and contain the same number of items, and there will be none left over. The manager wants to create the greatest number of packages possible. How much will the bookstore earn if all of the packages of supplies are sold?
Multiple choice question.
Answers
The amount earned by the bookstore if all of the packages of supplies are sold is given as follows:
$60.
How to obtain the amount earned?Before obtaining the amount earned, we must obtain the number of packages, with is given by the greatest common factor of the amounts of each item.
The amounts of each item are given as follows:
36, 48 and 24.
Their greatest common factor is obtained factoring them simultaneously by the same prime factors as follows:
36 - 48 - 24|2
18 - 24 - 12|2
9 - 12 - 6|3
3 - 4 - 2
Hence:
gcf(36, 48, 24) = 2² x 3 = 12.
Which is the number of packages. As each package sells for $5, the amount earned is given as follows:
12 x 5 = $60.
Each package is composed by:
36/12 = 3 pens.48/12 = 4 markers.24/12 = 2 erasers.More can be learned about the greatest common factor at https://brainly.com/question/219464
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Simplifying algebraic expression
Answers
Answer:
-33
Step-by-step explanation:
Plug 9 in for c, then simplify the resulting expression.
5c - 9c + 3
5(9) - 9(9) + 3
↓ execute multiplication
45 - 81 + 3
↓ simplify by adding 81 and 3
45 - 84
↓ execute subtraction
-33
Answer:
[tex] \sf \: - 33 \: (if \: c = 9)[/tex]
Step-by-step explanation:
Given expression,
→ 5c - 9c + 3
Now we have to use,
→ c = 9
Simplifying the given expression,
→ 5c - 9c + 3
→ 5(9) - 9(9) + 3
→ 45 - 81 + 3
→ -36 + 3
→ -33 => (answer)
Hence, required answer is -33.
decide whether the function is a polynomial function. If so right it in standard form and state it’s degree type in leading coefficient if so write it in standard form and state its degree type in leading coefficient P(x)=-3x^2+10-4x
Answers
For the polynomial p(x) = -3x² - 4x + 10, the degree is 2 and the leading coefficient is -3
What is an polynomial?Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction.
Polynomial is an expression composed of variables, constants and exponents combined using mathematical operations such as addition, subtraction, multiplication
Given the polynomial:
p(x) = -3x² + 10 - 4x
Rewriting the polynomial in standard form is done by rearranging based on exponents. Hence:
p(x) = -3x² - 4x + 10
The degree is 2 (x²) and the leading coefficient is -3(-3x²)
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vivian and her dad drive from Boston to niagara falls it takes them 9 hours to drive 495 miles what is their driving rate in miles per hour.
Answers
Answer:
55 miles per hour
Step-by-step explanation:
The equation is:
R = d / s
We know
d = 495 miles
s = 9 hours
Let's solve
R = 495 / 9
R = 55 miles per hour
So, their driving rate is 55 miles per hour
Consider your construction of pentagon ABCED.
What segments, if any, are parallel? Explain how you made your
determination.
Answers
Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.
Define pentagonal.Pentagons are two-dimensional polygons having five sides and fifth angles. When we mix the Greek terms "penta" and "gon," which mean "five" and "angles," respectively, we have the word "pentagon."
Here,
we know that a pentagonal prism has five rectangular sides in addition to two pentagonal bases at the top and bottom.
Pentagonal prisms are pentagon-shaped if we look at them from the bottom.
When viewed from the side, a pentagonal prism would have a rectangular shape.
If we were to look at the pentagonal prism from the front, it would appear rectangular.
Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.
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What is the ratio of sin t?
Answers
Sine of an angle is defined as the ratio of the side opposite (perpendicular side) to that angle divided by hypotenuse of the triangle.
sin is a trigonometric ratio.
If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse.
sin Q = perpendicular / hypotenuse.
sin Q is the base of the trigonometry ratios and it is one of the ratio.
sine is an acute angle.
some formula of sine angle are ,
1- sine Q = 1/ cosec Q .
2- sin ^2 Q = 1- cos^2 Q .
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A group consisting of 14 aggressive zombies quadruples in size every hour. Which equation matches the number of zombies after 6 hours?
Answers
The exponential equation that matches the number of zombies after 6 hours is the possible option;
Z = 14 × 4⁶
What is an exponential equation?An exponential equation is one in which the argument is an index or power of a constant.
The initial number in the group of zombies = 14
The amount by which the group increases every hour = The group quadruples every hour
The required equation; The equation that matches the number of zombies after 6 hours
The information in the question indicates that the sequence is a exponential, which can be presented using the following equation;
Z = a·rⁿ
Where;
Z = The number of zombies after n hours
a = The first term = The initial number of zombies in the group = 14
r = The common ratio = The amount that multiplies members of the group every hour = 4
n = The number of hours after which the number in the group is evaluated
Therefore, after 6 hours, n = 6, and we get;
a₆ = 14 × 4⁶ = 14 × 4⁵ = 14336
The equation from the possible options, obtained from a similar question posted online, that matches the number of zombies after 6 hours is therefore;
Z = 14 × 4⁶
The possible options are;
Z = 4·(14)⁶
Z = 4·(1 + 14)⁶
Z = 14·(1 + 4)⁶
Z = 14·(4)⁶
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It takes 126 cubes that have edge lengths of 1/3 ft to completely fill a plastic bin. What is the area of the base of the bin?
Answers
The area of the base of the bin is 9 ft^2.
The given information states that the bin is filled with 126 cubes that have edge lengths of 1/3 ft. To determine the area of the base of the bin, we must first determine the total volume of the bin.
Since each cube has a volume of 1/27 ft^3, the total volume of the bin is 126/27 ft^3. Since the volume of a rectangular prism is equal to the length times the width times the height, we can solve for the area of the base of the bin by rearranging the formula to A = V/h, where A is the area, V is the volume, and h is the height.
We can substitute the values given to obtain A = 126/27 ft^3/h. Since the height of the bin is equal to the edge length of the cubes, which is 1/3 ft, we can substitute that value into the equation to get A = 126/27 ft^3/1/3 ft = 9 ft^2. Therefore, the area of the base of the bin is 9 ft^2.
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Find the length of the third side. If necessary, round to the nearest tenth
Answers
On solving the provided question, we can say that it is right angle triangle provided, so cos 60 = 3/H => 1/2 = 3/H => H = 6
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
it is right angle triangle provided,
so
cos 60 = 3/H
1/2 = 3/H
H = 6
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need to find domain
O 2. 20 18 16 14 12 10 8 6 4 2 2 4 6 8 10 12 14 16 18 20 3. -5-4 D:
Answers
The collection of values that can be plugged into a function's domain are called its parameters.
How do you find domain?A specific area of thinking, action, or interest is referred to as a domain, particularly one over which someone has authority. [formal]...the great artists who experimented with several mediums. Alternative words: region, globe, field, department [informal] More Domain synonyms.
The domain is used to facilitate user navigation and increase accessibility. Slugs are links that consist of the domain plus the text "/text."
Let y = f(x) be a function where x and y are the independent and dependent variables. The chosen x-value is said to fall within the domain of f if a function f offers a means of effectively producing a single value y while using a value for x to that end.
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Write the expression. Then, check all that apply. twice the difference of a number and six A 2-column table with 4 rows. Column 1 is labeled Key Words with entries twice, the difference of, a number, six. Column 2 is labeled Replace with entries 2 times, (minus), n, 6. Replace “a number” with the variable, n. The two operations are multiplication and addition. The two operations are multiplication and subtraction. The constants are 2 and 6. The expression is written as 2(n – 6). The expression is written as 2 × 6 – n.
PLS HELP ME!
Answers
The expression for the sentence that is twice the difference of a number and six is given as follows:
2(n - 6).
How to write the expression?The sentence for this problem is defined as follows:
"Twice the difference of a number and six."
The number is unknown, hence the variable that represents the number is given as follows:
n.
The difference between the number and six is given by the subtraction of n by 6, as follows:
n - 6.
(the - symbol represents the subtraction).
The expression twice is equivalent to a multiplication of the expression n - 6 by 2, as follows:
2(n - 6).
(the multiplication symbol is implicit before the parenthesis, meaning that the distributive property is applied).
Which is the expression that represents the sentence given at the beginning of the answer.
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Find m angle Bm∠Bm, angle, B.
Note that m angle Bm∠Bm, angle, B is acute. Round to the nearest degree
Answers
The measure of angle B where angle B is an acute angle by using the Law Of Sines is 61° .
What is an Acute Angle ?
The Acute Angle can be defined as an angles that measure less than 90° , the acute angle is smaller than Right Angle and also smaller than the Linear Angle ( measuring 180° ).
From the figure ,
we can see that the measure of the sides are given as a = 9 , b = 8 and
the measure of angle A is 79° .
By Applying the Law Of Sines ;
we get ,
[tex]\frac{SinA}{a} =\frac{SinB}{b}[/tex]
Substituting the values in the above equation ,
we get ;
[tex]\frac{Sin79\textdegree}{9} =\frac{SinB}{8}[/tex]
Simplifying further ,
we get ;
[tex]SinB = \frac{Sin79\textdegree}{9} \times 8[/tex]
substituting the value of Sin79° as 0.9816 ;
we get ;
[tex]SinB = \frac{0.9816}{9} \times 8[/tex]
[tex]SinB=0.8725[/tex]
So , B ≈ 61° .
Therefore , the measure of angle B is 61° .
The given question is incomplete , the complete question is
Find the measure of Angle B in the given figure .
Note that the angle B is acute . Round to the nearest degree .
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How many 0's are located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of 1/2^5.5^8 ?
Answers
There are seven zeroes located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of 1/(2^5.5^8).
Terminating decimal is a decimal number which have a finite number of digits after the decimal point. Decimals like 3.45, 6.78, 1.987 are terminating decimals. Decimals which have 0 as the non terminating digit like 3.7800000.. are also called as terminating decimals.
Let P=1/(2^5.5^8)
Multiplying and dividing the numerator by 2^3
P= 2^3/(2^5.5^8.2^3)
P=8/(2^8.5^8)
P=8/10^8
P=0.00000008
The number of zeroes located to the right of the decimal point and before the first non-zero digit are seven.
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A sine function has the following key features:
Period = 4
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
Answers
The sine function becomes, [tex]y = 4sin(\frac{\pi }{2}x) + 1[/tex].
What is sine function?
The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others.
The general sine function is
[tex]y = Asin(b(x+c)+D[/tex]
Where
Amplitude = A
Period = [tex]\frac{2\pi }{B}[/tex]
Phase shift = c
Vertical shift = D
Given:
A = 4 (amplitude)
[tex]\frac{2\pi }{B} = 4[/tex] (period)
[tex]B = \frac{\pi }{2}[/tex]
Since midline: y = 1
And we know that graph of [tex]4sin(\frac{\pi }{2}x)[/tex], midline to be y = 1.
It must have vertical shift D = 1.
Since, y - intercept (0, 1)
⇒ x = 0, y = 1
⇒ It has no phase shift ⇒ c = 0
Since it satisfy [tex]y = 4sin(\frac{\pi }{2}(x+c))+D[/tex]
The graph of the sine function is attached below.
Hence, the sine function becomes, [tex]y = 4sin(\frac{\pi }{2}x) + 1[/tex].
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Please help I have no idea
Answers
Answer:
The surface area of this cuboid is 420 square inches.
Step-by-step explanation:
All we have to do is calculate each rectangle. For the width, we have 10 x 5 which is 50. Then we multiply it by 2 because we have two of those sides. Then we get 100. Then we have 11 x 5 which is 55. We multiply that by 2 and we get 110. Then we do that to the final two sides and we get 220. So the final answer if we add them all up is 420 square inches.
PLEASEEE HELPPP !!
picture attached
If m ∠ P = (12x + 7), m ∠ Q = (6x - 7), and ∠ P and ∠ Q are complementary angles, find m ∠ Q.
Answers
The value of m ∠ Q is 23°.
What are complementary angles?
Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right-angled triangle are complementary. We say two angles "Complement" one other when their sums equal 90 degrees.
Here, we have
Given: m ∠ P = (12x + 7), m ∠ Q = (6x - 7), and ∠ P and ∠ Q are complementary angles.
The sum of the measures of two complementary angles is 90°.
So, m∠P + m∠Q = 90°
Substitute 12x+7 for m∠P and 6x−7 for m∠Q.
12x+7 + 6x−7 = 90°
18x = 90°
x = 5°
To find m∠Q, substitute 5 for x in 6x−7.
6×5 - 7 = 23°
m ∠ Q = 23°
Hence, the value of m ∠ Q is 23°.
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HELP THIS IS URGENT!!!! During a sale, a store offered a 35% discount on a camera that originally sold for $750. After the sale, the discounted price of the camera was marked up by 35%. To the nearest whole number, what percent of the original price was the price after markup?
Answers
Answer:
the percentage is 62%
Step-by-step explanation:
Cos theta = -1/6 what is tan theta
Answers
Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .
What is trigonometry?Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.
Here.
Given : Cosθ = -1/6
To find : Tanθ
Since cosθ is in second quadrant
Thus,
Cosθ = B/H
According to pythagoras theorem,
H²= B²+ P²
=> 6² = 1² + P²
=> 36-1 =P²
=>P= √35
So ,
value of Tanθ comes out to be
=> tanθ = - √35 /1
=>tanθ = - √35
Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .
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EMERGENCY i need thissss helpp. tysmm <33
Answers
a. 7x4x6 = 168
b. 7x4 = 28
c. 28 x 6 = 168
Step-by-step explanation:
a. You find the volume of a prism by multiplying the base and its height. So, you would multiply 7x4 by 6, which would give you 168 cubic units.
b. Find the base by multiplying the length by the width. Therefore, you multiply 7 x 4, which gives you 28 square units. Now, multiply the base (28) by the height (6) to get the volume (168 cubic units).
7. Mai and Tyler are selling items to earn money for their elementary school. The school
earns w dollars for every wreath sold and p dollars for every potted plant sold. Mai
sells 14 wreaths and 3 potted plants and the school earns $70.50. Tyler sells 10
wreaths and 7 potted plants and the school earns $62.50.
This situation is represented by this system of equations:
[ 14w + 3p = 70.50
10w+7p = 62.50
Explain why it makes sense in this situation that the solution of this system is also a
solution to 4w + (-4p) = 8.00.
Answers
On solving the provided question we can say that - her in the equation 14w + 3p = 70.50 and 10w+7p = 62.50 , w = 12; p = 18
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
[tex]14w + 3p = 70.50 \\[/tex]
10w+7p = 62.50 ,
[tex]w = 12\\[/tex]
p = 18
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what is 1 half of 2 thirds
Answers
Explanation: first you multiply 1/2 and 2/3 which is 1.2/2.3 which =2/6 =1.2/3.2=1/3
Find an equation for the line that passes through the points (-5, 2) and (3, 4)
Answers
Step-by-step explanation:
1. Find the slope first using y2 - y1/ x2 - x1. This should look like 4 -2/ 3 - (-5), which can also be written as 4 - 2/ 3 + 5.
2. Simplify the fraction. This should look like 2/8, which can also be written as 1/4 once you divide it by 2.
3. Use the point-slope formula to find the y-intercept of the equation now. The formula is y2 - y1 = m (x2 - x1). Input either (-5, 2) or (3,4) into the equation. I'll use (3,4) as an example. After inputting that point, the equation would be y - 4 = 1/4 (x - 3).
4. Simplify this equation by distributing the 1/4 into the parentheses first. Once done, the equation will be y - 4 = 1/4x - 0.75.
5. Add 4 on both sides of the equation to get y by itself. After that the equation will be y = 1/4x + 3.25.
Please help me with my HW
Answers
Answer:
Step-by-step explanation:
(9a⁴b⁷) x (6a³b⁸)
(9 x 6) x (a⁴ x a³) x (b⁷ x b⁸)
54 x a⁷ x b¹⁵ = 54a⁷b¹⁵
Answer:
(9a⁴b⁷).(6a³b⁸)
=54a⁷b¹⁵
find the total surface area of this triangular prism
Answers
The surface area of the triangular prism is 156cm² when the triangle sides are 8cm and 15 cm rectangle sides are 17cm and 2 cm.
Given that,
We have to find the total surface area of the triangular prism in the given picture.
We know that,
First, we need to calculate the area of the triangle
a = area of triangle
a = 1/2 ×15 cm × 8 cm
a = 60 cm²
Now,
We must determine the three rectangles' areas.
a₁ = 2cm × 17cm
a₁ = 34cm²
a₂ = 2cm × 15cm
a₂ = 30cm²
a₃ = 2cm ×8cm
a₃ = 16cm²
Now, we must multiply the triangle by two and sum all the estimated areas.
a₁ + a₂ + a₃ + 2a =60cm² + 34cm² + 30cm² + 2 × 16cm² = 156cm²
Therefore, The surface area of the triangular prism is 156cm² when the triangle sides are 8cm and 15 cm rectangle sides are 17cm and 2 cm.
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halfway between -5/6 and 1/3 on a number line
Answers
The halfway between the number is -1/4 on the number line.We can find halfway by using midpoint formula.
How do we show number on number line?If the given number is positive mark it on the right side of the origin. If it is a negative number mark it on the left side of zero.Then divide each unit into the values equal to the fraction's denominator.
What is a Number Line in Math?A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides horizontally or vertically.
Now
Using midpoint formula
[tex]x_{1}[/tex]+[tex]x_{2}[/tex]/2 =-5/6 +1/3 divide 2
Find common denominator and write the numerators above common denominator
-5+2/12 =-3/12
=-1/4
Hence we find midpoint between numbers.
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What is the difference between a difference of two squares and a perfect square trinomial?
Answers
Depending on whether a and b are real numbers, they can factor as (a + b) (a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.
what is perfect square ?When you square an integer, you get perfect squares. The number 81, for example, is a perfect square since it can be derived by squaring 9: 99=81. Because 12 can be squared to make 144, 144 is a perfect square. 13 may be squared to make 169, which is a perfect square. Mathematics-related language. Informally: When an integer (a "whole") number is multiplied by itself, whether the result is positive, negative, or zero, the result is referred to as a square number, a perfect square, or simply "a square." All square numbers are therefore 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
Perfect square trinomials, also referred to as trinomial squares, are the squares of binomial expressions.
Depending on whether a and b are real numbers, they can factor as (a + b)(a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.
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What is the y-intercept of the quadratic function f/x )=( x 8 )( x 3?
Answers
The y-intercept of the quadratic function f(x) = (x - 8)(x + 3) is (0, -24).
The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.
This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).
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