Answer:
m = -1
Step-by-step explanation:
Slope = rise/run = [tex]\frac{-5-1}{7-1} = \frac{-6}{6} = -1[/tex]
What is 4/10 X 3/4 in a fraction form
Answer:0.3
Step-by-step explanation:
answer my question next please its about zara sells apples one
Answer:3/10
Step-by-step explanation: 4x3 is 12 and 4x10 is 40, so 12/40, the GCF of these numbers are 4 so 12/4=3 and 40/4= 10
So 3/10
If a and b are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is
9 8 7 6
A 3 2
B 1 (A). 4 (B). 5 (C). 6
(D). 9
(E). Depends on the values of A and B
If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B that is option E.
What is digit?In mathematics, digits are single numbers that are used to represent values. In math, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used in various combinations and repetitions to represent all of the values. A digit is a symbol that can represent any of the ten numbers from 0 to 9. If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B. A digit can be any of the following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A number is a measurement of something. It can be written with one, two, three, or more digits.
Here,
If a and b are nonzero digits, the number of digits (which does not have to be the same) in the sum of the three whole numbers is determined by the values of A and B that is option E.
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Three times a number minus 6 is equal to two times the sum of a number and 8.
Write as a equation
Please help (Geometry)
PICTURE INCLUDED
Answer: ASA postulate
Step-by-step explanation:
There is a congruent side included between two pairs of congruent angles.
U and V are similar figures. The scale factor of V to U is 5 : 1. What would be the area of figure U, if the area of figure V is 75 square yards?answer choices75 square yards9 square yards3 square yards15 square yards
The area of the figure/geometric shape U will be 15 yard^2.
What are geometric shapes in mathematics?
In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.
Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.
In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc. In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.
Now
As the scale factor for similar shapes V and U is 5:1.
Then their area should also be in same ratio.
Given Area of V=75 square yard
Therefore,
Area of U=75/5
Area of U =15 square yard
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One of the cases for the known measures of an oblique triangle is given. State whether the Law of Cosines can be used to solve the triangle.
In the given oblique triangle , the required value of c using cosine rule is given by c = 34.4.
As given in the question,
In the given oblique triangle ABC,
a = 12 feet
b = 30 feet
∠A = 20°
Let us consider in triangle side opposite to angle A, B, and C are a, b, and c respectively.
Using cosine rule we have,
a² = c² + b² - 2cbcos A
Substitute the values we get,
⇒ 12² = c² + 30² - 2(c )(30) cos 20°
⇒ 144 = c² + 900 - 60c ( 0.9396)
⇒ c² -56.376c + 900 - 144 = 0
⇒ c² -56.376c +756 = 0
using quadratic formula :
c = [ ( 56.376) ± √56.376² -4(1)(756) ]/ 2
= [ 56.376 ± 12.42 ] / 2
= (56.38 + 12.42) / 2 or (56.38 - 12.42) / 2
= 34.4 or 21.98
Correct value is c = 34.4
Therefore, using the cosine rule the required values c of the triangle is equal to 34.4 .
The above question is incomplete, the complete question is :
One of the cases for the known measures of an oblique triangle is given. In triangle ABC, where a = 12 feet, b = 30 feet, and A = 20°. State whether the Law of Cosines can be used to solve the third side of the triangle .
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The smallest amount of rotation about the vertex from one ray to the other, measured in degrees.
The smallest amount of rotation about a vertex from one ray to the other can be calculated by subtracting the sum of the two ray measures from 180°.
The smallest amount of rotation about a vertex from one ray to the other can be calculated using the formula θ = 180° - (α + β), where θ is the measure of the angle of rotation, α and β are the measures of the two rays that are connected by the vertex. The amount of rotation between two rays is measured in degrees, which is equal to the angle between the two rays. The formula used to calculate the amount of rotation is the arctangent of the ratio of the difference in the y-coordinates to the difference in the x-coordinates. For example, if the two rays have measures of 90° and 30°, the smallest amount of rotation from one ray to the other would be 60°. This can be calculated by taking 180° - (90° + 30°) = 180° - 120° = 60°. In conclusion, the smallest amount of rotation about a vertex from one ray to the other can be calculated by subtracting the sum of the two ray measures from 180°.
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In two or more complete sentences, prove how to find the third term of the expansion of
(x+2y)^4
Answer:
-2
Step-by-step explanation:
y = −2− x 2 y = - 2 - x 2
Answer:
[tex]24x^{2}y^2[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5cm} \underline{Binomial Theorem}\\\\$\displaystyle (a+b)^n=\sum^{n}_{k=0}\binom{n}{k} a^{n-k}b^{k}$\\\\\\where \displaystyle \binom{n}{k} = \frac{n!}{k!(n-k)!}\\\end{minipage}}[/tex]
We can use the Binomial Theorem to find any term of a binomial expansion.
The first term is when k = 0, so the third term is when k = 2.
Compare the given expression (x + 2y)⁴ with the formula to find the values of a, b and n.
Therefore:
a = xb = 2yn = 4k = 2Substitute the values into the formula to find the third term:
[tex]\implies \displaystyle\binom{4}{2}x^{4-2}(2y)^2[/tex]
[tex]\implies \dfrac{4!}{2!(4-2)!}x^{2}2^2y^2[/tex]
[tex]\implies \dfrac{4 \times 3\times \diagup\!\!\!\!2\times \diagup\!\!\!\!1}{2\times 1\times \diagup\!\!\!\!2\times \diagup\!\!\!\!1}\;x^{2}4y^2[/tex]
[tex]\implies \dfrac{12}{2}\:x^24y^2[/tex]
[tex]\implies 6x^{2}4y^2[/tex]
[tex]\implies 24x^{2}y^2[/tex]
I need help with this question please
Without evaluating each expression, determine which value is the greatest. Explain how you know.
1.7 % -9
2. (-7)+(-93)
3. (-72).9 3/
4. (-75) ÷ (-9)
The value of 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex] is the greatest. The solution is obtained by using the arithmetic operations.
What are arithmetic operations?
In mathematics, mainly there are four basic operations upon which all the calculations are done. The operations are:
1. Addition(‘+’) wherein the sum of the numbers is obtained.
2. Subtraction(‘-’) wherein the difference of the numbers is obtained.
3. Multiplication(‘×’) wherein the product of the numbers is obtained.
4. Division(‘÷’) wherein the quotient of the numbers is obtained.
We are given first expression as 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex]
The answer for this expression can be a positive or a negative number depending on the fact which of the terms is greater.
The second expression is (-7[tex]\frac{5}{6}[/tex] ) + (- 9[tex]\frac{3}{4}[/tex])
The answer for this expression will be a negative number because addition of two negative numbers is always negative.
The third expression is (-7[tex]\frac{5}{6}[/tex] ) . 9[tex]\frac{3}{4}[/tex]
The answer for this expression will be a negative number because multiplication of one negative number and one positive number is always negative.
The fourth expression is (-7[tex]\frac{5}{6}[/tex] ) ÷ (- 9[tex]\frac{3}{4}[/tex])
The answer for this expression will be a positive number because division of two negative numbers is always positive. But, dividing two numbers will give us value close to 1 because the numbers 7 and 9 are very close to each other.
Hence, the value of 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex] is the greatest.
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Triangle XYZ has sides that are 18 mm and 25mm.The third side is represented by the inequality < × < 43
The third side is represented by the inequality 7 < x < 43, where x is the third side.
When you know two sides of a triangle, you can calculate the range for the third side.
Let x would be the third side.
First, since 25 - 18 = 7, the third leg must be greater than 13. Otherwise, the two smaller legs would not be able to connect to form the third leg.
Second, if we combine 18 with 25 and get 63, the third leg must be smaller than 69. Otherwise, the third leg would be able to reach further than the previous two legs.
This means 7 < x < 43.
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What is the answer to 3 divided by 6870
Answer:
2290
ignore this--> (I need 20 words to answer the question lol)
Answer:
2290
Step-by-step explanation:
2290*3 gives 6870
Directions: Using the digits 1 to 9 at most one time each, find the dimensions of three rectangular prisms so that their volumes are as close as possible. Note: diagram may not be drawn to scale. All the volumes are under 100 cubic units.Can you find 3 volumes that are within the range of 50 and 90?Can you find 3 volumes that are within the range of 60 and 80?The difference between all 3 volumes is less than 10.
The dimensions of the rectangular prism would be (1,8,9), (2,5,7), and (3,4,6).
What is a rectangular prism?
A rectangular prism is a solid geometric shape that has three mutually perpendicular rectangular faces, and is also known as a rectangular parallelepiped or a box. It has six faces, eight vertices, and twelve edges.
The shape is defined by three dimensions: length, width and height, and is specified by the three sets of parallel and mutually perpendicular edges that form its six faces. The opposite faces of a rectangular prism are equal in area and parallel to each other. The opposite edges are also parallel and equal in length.
You can’t get a perfect match, but you can get pretty close, with dimensions of (1,8,9), (2,5,7), (3,4,6)
Hence, the dimensions of the rectangular prism would be (1,8,9), (2,5,7), and (3,4,6).
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have you seen or read about an example where data were presented on an issue, but the sample was not representative of the population from which it was drawn? if you can't recall a specific example, locate one using an internet search.
A specific example of a non-representative sample can be seen in the 2016 US presidential election.
The national polls indicated that Hilary Clinton had a lead in the polls, but Donald Trump went on to win the election. This is because the sample used in the polls was not representative of the population. The sample was disproportionately composed of college-educated individuals, when the actual electorate was more evenly balanced between college-educated and non-college-educated individuals. This caused the samples to be biased and not representative of the population.
For example, if we assume that the population is composed of 50% college-educated individuals and 50% non-college-educated individuals, then the sample should also be composed of 50% college-educated individuals and 50% non-college-educated individuals to be representative. If the sample is not composed of 50% college-educated individuals and 50% non-college-educated individuals, then the sample is not representative of the population.
This can be calculated by using the formula: (Number of College Educated Individuals in Sample/Total Sample Size) X 100.
For example, if the sample size is 100 and there are 75 college-educated individuals in the sample, then the sample is not representative of the population because (75/100) X 100 = 75%, which is not equal to the 50% of the population that is college-educated.
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High school students from grades 9–10 and 11–12 were asked to choose the kind of band to have play at a school dance: rap, rock, or country.
Their choices were as follows:
Grades 9–10: Rap 40; Rock: 25; Country: 60
Grades 11–12: Rap: 55; Rock: 30; Country: 40
Which of the following is a correct two-way relative frequency table for the data?
Rap Rock Country Total
Grades 9–10 16% 10% 24% 50%
Grades 11–12 22% 12% 16% 50%
Total 38% 22% 40% 100%
Rap Rock Country Total
Grades 9–10 22% 12% 16% 50%
Grades 11–12 16% 10% 24% 50%
Total 38% 22% 40% 100%
Rap Rock Country Total
Grades 9–10 40 25 60 125
Grades 11–12 55 30 40 125
Total 95 55 100 250
Rap Rock Country Total
Grades 9–10 55 30 40 125
Grades 11–12 40 25 60 125
Total 95 55 100 250
Points earned on this question: 0
The correct option is C for the frequency table.
What is a frequency table?A table that depicts the frequency of occurrence of a given characteristic according to a specified set of class intervals.
The correct two-way frequency table for the date will look like this:
RAP ROCK COUNTRY TOTAL
Grades 9-10 40 30 55 125
Grades 11-12 60 25 35 120
TOTAL 100 55 90 245
The sum of the row total is equal to the sum of the column total
125 + 120 = 100 + 55 + 90
245 = 245
The correct option for the frequency table is C.
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which of the following time-series plots is the most appropriate? hint: pay close attention to the title, axes labels, and scale.
The most appropriate time-series plot will depend on the data being visualized. The title, axes labels, and scale should all be chosen to accurately describe the data and provide the clearest understanding of the data.
The most appropriate time-series plot for a particular dataset will depend on the data being visualized. The title, axes labels, and scale should all be chosen carefully to accurately describe the data and provide the clearest understanding of the data. For example, for a time series of stock prices, the title could be "Stock Price Over Time", the axes could be labeled "Time" and "Price", and the scale could range from the lowest to the highest stock price. Additionally, the time intervals should be appropriately labeled, such as monthly, quarterly, or annually. It is important to choose the right type of plot to ensure that the data is accurately and clearly represented.
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The complete question is
which of the following time-series plots is the most appropriate? hint: pay close attention to the title, axes labels, and scale should all be chosen to accurately.
1.The angles of a quadrilateral are m,3m, 2m and 3m in that order. a Write an equation in m. Find m. C Find the angles of the quadrilateral. d Make a sketch of the quadrilateral. e What kind of quadrilateral is it? 2.Calculate the size of each angle of a e regular octagon.3. In Figure 6.25: Find the value of x. a b Find the unknown angles in the hexagon. 117⁰ 1319 2x 3x 142⁰
Answer:
=> A/Q,
m + 3m + 2m+ 3m 360° =
9m = 360°
m = 360/9
m = 40°
Angle A = m = 40°
Angle B = 3m = 120°
Angle C 2m = 80° =
Angle D = 3m = 120°
The average mass of apple of 2 bags A and B is 6.4kg. Given that bag A contains 0.9kg of apple than bag B, find the mass of apple in bag B
Using the formula for the average value between two numbers, we will see that bag B weighs 11.9 kg
How to find the weight of bag B?If we have two values x and y, the average value between these two is given by the formula below.
average = (x + y)/2
Here we know that the average between the wheights of bags A and B is 6.4 kg, and A = 0.9kg
Then we can write the equation:
6.4kg = (B + 0.9kg)/2
We can solve that equation for B to get:
2*6.4kg = B + 0.9kg
12.8kg - 0.9kg = B
11.9kg = B
Bag B weighs 11.9 kilograms.
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Darius biked for 2 hours and traveled 21 miles. Kala biked 42 miles in 5 hours. Determine how many miles each person biked in one hour. Who biked more quickly?
Step-by-step explanation:
that's so easy just learn it times
math homework help me
Answer:
D
Step-by-step explanation:
because
( 5 + 2 + 1 ) is (x + y + z)
Find the set of all z such that neither 2+z nor 2-3z is in the interval (-1,2]. Express your answer as an interval or as a union of intervals.
the set of all z ∈ (-3,1) such that neither 2+z nor 2-3z is in the interval (-1,2].
Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities.
the set of all z such that neither 2+z nor 2-3z is in the interval (-1,2].
here, we shall assume two cases,
case first.
z > -1,
2+z > -1
z > -1 -2
z > -3
and,
2-3z > -1
-3z > -3
z > 1
z belongs to ( -3 , 1)
case 2nd,
z<=2
2+z < = 2
z <= 2-2
z ≤ 0
and 2-3z ≤ 2
-3z ≤ 0
z ≤ 0
z is less than equal to 0
So, by above conditions
z belongs to (-3,1).
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A particle is moving along the x-axis. The position of the particle at time t is given by x(t) = t³ - 6t + 9t - 2, 0 ≤ t ≤ 5. Find the total distance the particle travels in 5 units of time.
The total distance traveled by the particle over 5 units of time is 140 units.
What is the total distance?
To find the total distance a particle travels over a certain time interval, we need to find the definite integral of its velocity function over that interval. The velocity function is the derivative of the position function.
In this case, the position function of the particle is x(t) = t³ - 6t + 9t - 2 and we need to find the total distance traveled by the particle over 5 units of time.
The velocity function is x'(t) = 3t² - 6 + 9 = 3t² + 3
The total distance traveled over 5 units of time is the definite integral of the velocity function evaluated between 0 and 5.
∫(3t²+3) dt from 0 to 5
= [t³ + 3t] from 0 to 5
= (5³ + 3*5) - (0 + 0) = 125 + 15 = 140
The total distance traveled by the particle over 5 units of time is 140 units.
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The following exercises reveal structural properties of the set of solutions to a system of linear equations. The problems are set in R3, but the results extend to any R" (a) (i) Suppose p = (1,3,4) and q = (5,8, 12) are two points in R3. Show that the line joining p and q consists of all points of the form lq+ (1 - p as varies over all real numbers. (Hint: Think of the line as anchored p and going in directions (q-p) and -(q-p.) General Statement: The line joining two points p and q in Rn consists of all points of the form lq + (1 - \p as varies over all real numbers. (ii) Suppose p = (1,3,4) and q=(5,8, 12) are solutions to the linear system of equations: 01111 + 212.22 + 213.43 = 21 02111 + 022.2 2 + 23.13 = 2 03121 + 232.22 + 233.3 = 3 04141 +242.12 +243.13 = 24 Check that all points on the line joining p and q are also solutions to the above system of equations. General Statement: If a system of linear equations in n variables has two solutions, then all points on the line joining the two solutions are also solutions to the system. Therefore, if a system of linear equations has at least two solutions, it has infinitely many solutions. (b) Suppose p = (1, 3, 4) is a solution to the system of homogeneous equations: 01111 + 212.22 + 213.23 = 0 021.11 + 02222 +223.23 = 0 03121 + 232.22 + 233.13 = 0 04141 +242.22 +243.23 = 0 Check that any multiple of p, i.e., a vector of the form (1,3,4) where is any real number, is also a solution of the system. Is this an application of the previous question? General Statement: If a homogeneous system of equations has a non-zero solution then it has infinitely many solutions.
The general statement for the previous question is that if a homogeneous system of equations has at least one non-zero solution, then it has infinitely many solutions, which can be found by taking multiples of the non-zero solution.
(a) (i)
Let p = (1,3,4) and q = (5,8,12) be two points in R3. The line joining p and q can be written as lq + (1-\p) where l is a real number. By substituting in the coordinates of p and q, we get l(5,8,12) + (1-\1,3,4) = (l + 1-\, l+3-\, l+4-\). This is the equation for the line joining p and q, where l can be any real number.
(ii)
To check that all points on the line joining p and q are also solutions to the system of linear equations, we substitute the equation of the line into the system of equations.
01111 + 212.22 + 213.43 = 21
(l + 1-\) + 2(l+3-\) + 3(l+4-\) = 21
Simplifying, this gives: l + 6 - \ = 21. Therefore, all points on the line joining p and q are solutions to the system.
(b)
To check that any multiple of p, i.e., a vector of the form (1,3,4) where is any real number, is also a solution of the system, we substitute the equation of the multiple of p into the system.
01111 + 212.22 + 213.23 = 0
(l + 1-\) + 2(l+3-\) + 3(l+4-\) = 0
Simplifying, this gives: l + 6 - \ = 0. Therefore, all multiples of p are solutions to the system.
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5. For adults, the maximum safe water temperature in a spa is 104 F. The water temperature in Bill’s Spa is 102 F.
The temperature is increased by t F.
Write, solve, and graph an inequality to show the value of t for which the water temperature is still safe.
Graph needed*
An inequality which represents the value of t for which the water temperature is still safe is t ≤ 2 and it has been plotted in the graph attached below.
How to write, solve, and graph the required inequality?In order to write, solve, and graph an inequality that represents the value of t for which the water temperature is still safe, we would take note of the following important information;
The maximum safe water temperature in a spa is equal to 104°F.The water temperature in Bill’s Spa is equal to 102°F.The temperature was increased by t°F.The safe water temperature in a spa is at most 104°F.Let the variable t represent the safe water temperature.Now, we can write an inequality that represents the value of t for which the water temperature is still safe as follows;
102 + t ≤ 104
By subtracting 102 from both sides of the inequality, we have the following:
102 - 102 + t ≤ 104 - 102
t ≤ 2
Next, we would use an online graphing calculator to graph the above inequality as shown in the image attached below.
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using the properties of combinations of continuous functions, determine the interval(s) over which the function f (x )equals fraction numerator x squared minus 5 x minus 6 over denominator x minus 3 end fraction is continuous.
The interval over which the function is continuous equation is (-∞, 3) U (3, +∞).
The function f(x) = (x2 - 5x - 6)/(x - 3) is continuous over all real numbers except x = 3, since the denominator is equal to 0 at x = 3.
We can use the properties of combinations of continuous functions to determine the interval(s) over which the function f(x) is continuous equation.
First, we need to consider the function f(x) in two parts. The first part is f(x) when x ≠ 3, and the second part is when x = 3.
For the first part, when x ≠ 3, the function f(x) is continuous over all real numbers, since both the numerator and denominator are continuous over all real numbers.
For the second part, when x = 3, the function f(x) is discontinuous, since the denominator is equal to 0.
Therefore, the interval over which the function f(x) is continuous is (-∞, 3) U (3, +∞).
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Halla la solución de la expresión: 32 - 14 +26 - (81/9)2
Answer:
26
Step-by-step explanation:
32 - 14 + 26 - (81/9)2
Dividing
32 - 14 + 26 - (9)2
Multiplying
32 - 14 + 26 - 18
Adding & Subtracting from left to right
18 + 26 - 18
44 - 18
26
The sum of the base and the height of a triangle is 10 cm. Find the dimensions for which the area is a maximum.
The maximum area of a triangle with a base and height of 10 cm is 50 cm^2. The dimensions for this would be a base of 5 cm and a height of 5 cm.
1. The area of a triangle is calculated by taking the base multiplied by the height, then dividing by 2.
2. Since the sum of the base and the height of the triangle is 10 cm, the base and the height must be equal.
3. Therefore, the base and the height are both 5 cm, and the area of the triangle is (5 cm * 5 cm) / 2, which equals to 50 cm^2.
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The yield of corn on Mr. Geller's farm since 2001 can be modeled by the function N(t) = 10t + 88.5 (measured in kilograms) and the price per kilogram of corn can be modeled by P(t) = 81? - 10t + 1.1, where t is the number of years since 2001. According to this model, what is Mr. Geller's total amount of income generated by planting corn in 2008? Round your answer to the nearest cent.
The required total income generated by planting corn in 2008 is the amount of $1917.85.
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The yield of corn on Mr. Geller's farm since 2001 can be modeled by the function N(t) = 10t + 88.5
Let's find the amount of corn produced in 2008:
N(7) = 10 x 7 + 88.5 = 158.5 (kilograms)
Next, let's find the price of corn in 2008:
P(7) = 81 - 10 x 7 + 1.1 = 12.1 ($/kilogram)
Finally, we can multiply the amount of corn by the price per kilogram to find the total income:
158.5 x 12.1 = 1917.85
Rounding to the nearest cent, the total income generated by planting corn in 2008 is $1917.85.
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In 2003, the price of a certain automobile was approximately with a depreciation of 1,750 per year. After how many years will the cars value be $11,250? A) write an equation to model the problem. Let the represent the number of years after 2003. For example, the year 2005 would be represented by t=2. B)Solve the equation to find the answer to the question above.
The number of years after 2003 that the car's value will be $11,250 is t = 7.5 years.
In 2003, the price of a certain automobile was approximately with a depreciation of 1,750 per year. After how many years will the cars value be $11,250 A) write an equation to model the problem. Let the represent the number of years after 2003.
A) The equation to model the problem is:
Price in year t = 2003 Price - (t - 1)(1,750)
B) To solve the equation for t, we can rearrange it to isolate t:
t = (2003 Price - 11,250) / 1,750
Therefore, the number of years after 2003 that the car's value will be $11,250 is t = 7.5 years. This means that the car's value will be $11,250 in the year 2010.5.
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A building's shadow On a morning of a day when the sun will pass directly overhead, the shadow of an 80-ft building on level ground is 60 ft long. At the moment in question, the angle & the sun makes with the ground is increasing at the rate of 0.27°/min. At what rate is the shadow decreasing? (Remember to use radi- ans. Express your answer in inches per minute, to the nearest tenth.) 80'
The rate at which shadow is decreasing On a morning of a day when the sun will pass directly overhead, the shadow of an 80-ft building on level ground is 60 ft long and is 10.4 inches per minute.
Given,
Height of the building, [tex]h[/tex] = 80 ft = 960 inches
Length of shadow, [tex]x[/tex] = 60 ft = 720 inches
The angle that the sun makes with the ground is increasing,
[tex]\frac{d\theta}{dt} = 0.27[/tex] degree [tex]= \frac{3\pi }{2000} rad/min[/tex]
[tex]tan\theta = \frac{960}{x} \\\frac{d }{dy} tan\theta = \frac{d}{dy} \frac{960}{x} \\sec^{2}\theta \frac{d\theta }{dt} = -\frac{960}{x^{2} } \\\\\frac{dx}{dt} = \frac{(60^{2})(\frac{5}{3})^{2} }{960} \\\\\\\frac{dx}{dt} = 10.4 inches /min[/tex]
Hence, the shadow is decreasing at a rate of 10.4 inches per minute.
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