To calculate the height of a tree with a 60-meter long shadow when the Sun is 30 degrees above the horizon, use the tangent trigonometric function. The tree's height is calculated to be around 34.62 meters tall.
Explanation:The student is asking how to calculate the height of a tree given the length of its shadow when the Sun is 30 degrees above the horizon. This is a trigonometry problem involving a right-angled triangle, where the tree represents the opposite side, the shadow represents the adjacent side, and the angle given is the angle of elevation of the Sun. Since we have the angle and the length of the adjacent side, we can use the tangent trigonometric ratio to find the height of the tree. The tangent of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side (tangent = opposite/adjacent).
Therefore, the tree is approximately 34.62 meters tall.
Sammy has a 10-foot ladder, which he needs to climb to reach the roof of his house. the roof is 12 feet above the ground. the base of the ladder must be at least 1.5 feet from the base of the house. how far is it from the top of the ladder to the edge of the roof? draw a sketch.
Determine the interval on which f(x) = the square root of the quantity of x plus 2 is integrable.
(−∞, 2)
[−2, ∞)
(−∞,−2) U (−2, ∞)
All reals
The interval on which f(x) is integrable is:
[-2, ∞)
Step-by-step explanation:We are given a function f(x) as:
[tex]f(x)=\sqrt{x+2}[/tex]
We know that a function is integrable over a given interval if it is continuous over a given interval.
Now, we know that the square root function is well defined if the function under the square root sign is positive.
This means here the function is well defined if:
[tex]x+2\geq 0[/tex]
i.e.
[tex]x\geq -2[/tex]
Also, the square root function is continuous over it's domain.
and hence it is integrable over it's domain.
This means that the function is integrable over:
[-2,∞)
What is the limit ? And how do I get the answer?
HELP! SIMPLIFY!
simplify:
1) (m³ n⁵) (mn⁴)
------------------
m⁻³ n²
2) 6a² b³
-----------
4a
3) 5⁶ a⁶ b³
-----------
5² ab³
Margo borrows $1000, agreeing to pay it back with 5% annual interest after 15 months. How much interest will she pay?
2(v-h)/k=r
Solve equation for v in terms of all other variables involved
For the given expression, the equation for v in terms of all other variables involved will be v=(r·k)/2+h.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the given expression is 2(v-h)/k=r
We have to solve the expression in the term v as,
2(v-h)/k=r
Open the brackets and multiply 2 in the bracket as
(2v-2h)/k=r
Apply the cross-multiplication operation as
2v-2h=r·k
Rearrange the equation as
2v=r·k+2h
The equation for v in terms of all other variables involved is obtained as,
v=(r·k)/2+h
Thus, for the given expression, the equation for v in terms of all other variables involved will be v=(r·k)/2+h.
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Algebra 1A unit 4 lesson 2 Answers please help ?!!
34.) If a quadrilateral is a parallelogram and the diagonals are perpendicular, then it must be a rectangle.
A. True
B. False
Answer:
The correct answer is: False
You are going to bake an over-sized sheet cake. The recipe calls for 2 cups of sugar for every 3 cups of flour. How many cups of flour are needed if you use 18 cups of sugar?
Answer:27
Step-by-step explanation:
How to find the sum of the squares of the roots of an equation?
Final answer:
To calculate the sum of the squares of the roots of a quadratic equation, apply Vieta's formulas to find the sum and product of the roots and use them in the identity (α + β)² - 2αβ to avoid directly solving for the roots.
Explanation:
To find the sum of the squares of the roots of an equation, especially for a quadratic equation of the form ax²+bx+c=0, we use the relationship between the coefficients and the roots provided by Vieta's formulas.
The sum of the roots, denoted as α and β, is given by -b/a, and the product of the roots is c/a. To find the sum of the squares of the roots (α² + β²), you can use the identity (α + β)² = α² + 2αβ + β², or α² + β² = (α + β)² - 2αβ.
By substituting the sum and product of the roots from Vieta's formulas, you can calculate the sum of the squares without actually solving for the roots. This approach is especially useful in equilibrium problems or other situations where you might encounter square roots or higher powers and wish to simplify calculations.
Explain how you can tell without calculating whether the sum of a postitive number and a negative number will be positive, negative or zero.
You and your friend get the same magazine. You spend $15 for twelve issues. Your friend pays $1.50 per issue but gets the first two issues free. How many issues will your friend get if he also spends $15?
In the diagram shown below, ∠K=18º and ∠H=18º.
Prove KJ=13.75. Justify your steps in a paragraph proof.
Sara has 16 red flowers and 24 yellow flowers. She wants to make a bouquet with the same number of each color flowers in each bouquet. How many red flowers will be in each bouquet.
Which statement about the triangle is true
Answer:
the other answer is wrong number 2 is correct
Step-by-step explanation:
The average (A) of two number,M and N, is given by the formula A=m+n/2. Find the average of the two numbers 36 and 72.
Answer: 54
Step-by-step explanation:
Average = Total/ total number
Average= 36 +72/2
= 108/2
= 54
54 is the average of the two numbers 36 and 72.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We need to find the average of the two numbers 36 and 72.
The average (A) of two number, M and N, is given by the formula A=m+n/2
Let m = 36
n=72
Now to find the average of two numbers we have to plug in these values in the formula
A=36+72/2
=108/2
=54
Hence, 54 is the average of the two numbers 36 and 72.
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Which distance is longer? 1 mile 1000 meters 10000 centimeters?
(X-3)(x+2) = 0 what is the answer to this ?
On traditional maps, Earth is represented in a flat plane, or by Euclidean geometry. However, a globe is a more accurate model that comes from elliptical geometry. How does a globe represent the fact that there are no parallel lines in elliptical geometry? The equator is not parallel to any other latitudinal lines. The North and South Poles are never connected by a geodesic. The geodesics connecting the North and South Poles never intersect. The geodesics connecting the North and South Poles intersect at both of the Poles.
Answer:
D. The geodesics connecting the North and South Poles intersect at both of the Poles
Step-by-step explanation:
Answer:
D) The geodesics connecting the North and South Poles intersect at both of the Poles.
Step-by-step explanation:
got it right on edge 2021 :)
How to find the circular permutation for 5 things taken 5 at a time
Irst. write an expression for the probability that both socks are bl
HELP ASAP!
1. Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s. Which statement best describes the meaning of f(250)?
The house sold for $250,000.
The house stayed on the market for an average of 250 days before being sold.
This is the average number of days the house stayed on the market before being sold for $250,000.
The house sold on the market for $250,000 and stayed on the market for an average of 250 days before being sold.
2. Laura rents a movie for a flat fee of $2.00 plus an additional $0.50 for each night she keeps the movie. Choose the cost function that represents this scenario if x equals the number of nights Laura has the movie.
c(x) = 2.00x + 0.50
c(x) = 2.00 + 0.50x
c(x) = 2.50x
c(x) = (2.00 + 0.50)x
Answer:c(x)=2.00 +0.05x
Step-by-step explanation:
use prime factorization to find gcf of 57 and 27
Given: B = {(4, 2), (4, -2), (16, 4), . . .} Is B a function and why?
Set B = {(4, 2), (4, -2), (16, 4), . . .} is not a function because it has an 'x' value (4) that corresponds to more than one 'y' value (2,-2), which contradicts the definition of a function.
Explanation:The given set B = {(4, 2), (4, -2), (16, 4), . . .} is not a function. In mathematical terms, for a set of ordered pairs to be considered a function, each input (or 'x' value) must have exactly one output (or 'y' value). However, in B, the input 4 corresponds to two different outputs: 2 and -2. This violates the definition of a function, proving that B is not a function.
It's useful to remember this as a rule: in functions, a particular x-value can only be paired with a single y-value. In contrast, in non-functions, a single x-value can be linked to multiple y-values, as demonstrated by set B.
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A sixth-grade class has 12 boys and 24 girls.
Write two more statements comparing the number of boys in the class to the number of girls
Which of the following is true for the relation f(x) = 5x + 1?
Only the inverse is a function.
Only the equation is a function.
Neither the equation nor its inverse is a function.
Both the equation and its inverse are functions.
Answer:
Both the equation and its inverse are functions.
Step-by-step explanation:
A function is relation in which one input gives one and only one output.
Here, the given function,
[tex]f(x)=5x+1[/tex]
Which is a polynomial,
A polynomial is a function because for each input value it gives only one output value.
⇒ f(x) is a function.
Now, For finding the inverse of f(x),
Replace f(x) by y,
y = 5x + 1
Switch x and y,
x = 5y + 1
Isolate y on the left side,
-5y = 1 - x
[tex]y = \frac{1-x}{-5}=\frac{x-1}{5}[/tex]
Replace y by [tex]f^{-1}(x)[/tex],
[tex]f^{-1}(x)=\frac{x-1}{5}[/tex]
Which is also a polynomial,
Hence, the inverse of f(x) is also a function,
Last option is correct.
If a radical is multiplied by a number or variable, you should put the number or variable _____ the radical sign.
Final answer:
Numbers or variables are placed outside of the radical sign when multiplied by a radical. This representation indicates that the entire radical, not just the number inside, is to be multiplied by that number or variable.
Explanation:
If a radical is multiplied by a number or variable, you should put the number or variable outside the radical sign. In mathematics, multiplication or division by the same number on both sides of an equation does not change the equality. When you multiply a radical by a number or variable, you are essentially multiplying the contents inside the square root by that number or variable, but outside of the radical sign to maintain proper order of operations.
When writing an expression involving radicals mathematically, numbers or variables outside the radical do not directly interact with the values inside until simplification or further operations are performed. For example, if you're multiplying 3 by √2, you would write it as 3√2, not √(3×2). The multiplication of the coefficient (the number in front of the radical) applies to the entire radical, not just the number inside it.
Consider the two conditional statements. Draw a conclusion from the given conditional statements, and write the contrapositive of each conditional statement. Then, draw a conclusion from the two contrapositives. How does the first conclusion relate to the second conclusion?
If you are eating a banana, then you are eating fruit.
If you are eating fruit, then you are eating food.
a.If you are eating a banana, then you are eating food.
If you are not eating a banana, then you are not eating fruit. If you are not eating fruit, then you are not eating food.
If you are not eating a banana, then you are not eating food.
The second conclusion is the contrapositive of the first conclusion.
b.
If you are eating a banana, then you are eating food.
If you are eating fruit, then you are eating a banana. If you are eating food, then you are eating fruit.
If you are eating food, then you are eating a banana.
The second conclusion is the contrapositive of the first conclusion.
c.If you are eating a banana, then you are eating food.
If you are not eating fruit, then you are not eating a banana. If you are not eating food, then you are not eating fruit.
If you are not eating food, then you are not eating a banana.
The second conclusion is the contrapositive of the first conclusion.
d.If you are eating food, then you are eating a banana.
If you are not eating fruit, then you are not eating a banana. If you are not eating food, then you are not eating fruit.
If you are not eating food, then you are not eating a banana.
The second conclusion is the contrapositive of the first conclusion.
Answer:
c is the answer
Step-by-step explan ation:
Simplify the fraction
what is 16 over 38
Solve for c:
= 7 + 8 + 9 −10