Answer:
Step-by-step explanation:
a. To find out how much floor space each box will cover, we need to multiply the volume of the box by the height of the stack of items. The volume of the box is x3 + 10x2 + 29x + 20 cubic units and the height of the stack of items is x + 5 units. So the floor space covered by each box is (x3 + 10x2 + 29x + 20) * (x + 5) square units.b. To find the maximum number of boxes Darren can place on the floor of the storage unit, we need to divide the total floor area of the storage unit by the floor space covered by each box. The total floor area of the storage unit is x* + 5x° + x7 _ 20x - 14 square units and the floor space covered by each box is (x3 + 10x2 + 29x + 20) * (x + 5) square units, then we can divide the total floor area by the floor space covered by each boxx* + 5x° + x7 _ 20x - 14 / (x3 + 10x2 + 29x + 20) * (x + 5) = maximum number of boxesc. To find out how much of the floor space is not covered by a box, we can subtract the floor space covered by the maximum number of boxes from the total floor area of the storage unit.Total floor area - floor space covered by the maximum number of boxes = remaining floor space.Please note that this is a polynomial equation and the solution will be different depending on the value of x.
a) Floor space of each box = ([tex]x^3 + 10x^2 - 29x + 20[/tex]) / (x + 5)
b) Maximum number of boxes = ([tex]x^4 + 5x^3 + x^2 - 20x - 14[/tex]) / (([tex]x^3 + 10x^2 - 29x + 20[/tex]) / (x + 5))
c) Uncovered floor space = [tex]x^4 + 5x^3 + x^2 - 20x - 14 - ((x^3 + 10x^2 - 29x + 20) / (x + 5) * Maximum number of boxes)[/tex]
We have a storage unit with a given floor area and boxes with specified volumes and heights.
We'll determine the floor space each box covers, the maximum number of boxes Darren can place on the floor, and how much floor space is left uncovered when he places the maximum number of boxes without overlap.
a) Floor space covered by each box:
To find the floor space covered by each box, we divide the volume of the box by its height. This gives us the area each box covers on the floor.
The floor space of each box can be calculated by dividing its volume by its height.
The volume of each box is given by the expression [tex]x^3 + 10x^2 - 29x + 20[/tex], and its height is x + 5. Therefore, the floor space covered by each box can be represented as:
Floor space of each box = Volume of the box / Height of the box
Floor space of each box = [tex](x^3 + 10x^2 - 29x + 20) / (x + 5)[/tex]
b) Maximum number of boxes Darren can place:
To find the maximum number of boxes Darren can place on the floor, we need to divide the total floor area by the floor space covered by each box.
The maximum number of boxes Darren can place is determined by dividing the total floor area, given by [tex]x^4 + 5x^3 + x^2 - 20x - 14[/tex], by the floor space covered by each box. We already calculated the floor space of each box as [tex](x^3 + 10x^2 - 29x + 20) / (x + 5)[/tex]. Now, we'll perform the division:
Maximum number of boxes = Total floor area / Floor space of each box
Maximum number of boxes = [tex](x^4 + 5x^3 + x^2 - 20x - 14) / ((x^3 + 10x^2 - 29x + 20) / (x + 5))[/tex]
c) Uncovered floor space with maximum number of boxes:
To find the uncovered floor space when Darren places the maximum number of boxes without overlap, we subtract the total floor area covered by the boxes from the total floor area of the storage unit.
The floor space not covered by boxes can be determined by subtracting the total floor area covered by the boxes from the total floor area of the storage unit.
We already know the total floor area of the storage unit is [tex]x^4 + 5x^3 + x^2 - 20x - 14[/tex], and we calculated the floor space covered by each box in part (a). The maximum number of boxes Darren can place was determined in part (b). Now, we'll perform the subtraction:
Uncovered floor space = Total floor area of storage unit - (Floor space of each box × Maximum number of boxes)
Uncovered floor space =[tex]x^4 + 5x^3 + x^2 - 20x - 14 - ((x^3 + 10x^2 - 29x + 20) / (x + 5) * Maximum number of boxes)[/tex]
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Complete Question
Darren is placing shipping boxes in a storage unit with a floor area of
[tex]x^4+5x^3+x^2-20x-14[/tex] square units. Each box has a volume of [tex]x^3+10x^2-29x+20[/tex].
cubic units and can hold a stack of items with a height of x + 5 units.
a) How much floor space will each box cover?
b) What is the maximum number of boxes Darren can place on the floor of the storage unit?
c) Assume Darren places the maximum number of boxes on the floor of the storage unit, with no overlap. How much of the floor space is not covered by a box?
What is the quotient of 154,504 divided by 28 with long division?
Brandon invested $11,000 in an account paying an interest rate of 1% compounded
quarterly. Robert invested $11,000 in an account paying an interest rate of 13/%
compounded monthly. After 20 years, how much more money would Robert have in
his account than Brandon, to the nearest dollar?
Answer: $4,914
Step-by-step explanation:
To calculate the final balance in Brandon's account, we need to use the formula for compound interest: A = P(1 + r/n)^(nt)
where A is the final balance, P is the initial investment, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we have:
P = $11,000
r = 1% = 0.01
n = 4 (because the interest is compounded quarterly)
t = 20
so, A = $11,000(1 + 0.01/4)^(4*20) = $11,000(1.0025)^80 = $22,817.20
To calculate the final balance in Robert's account, we need to use the same formula, but with different values for r, n, and t.
In this case, we have:
P = $11,000
r = 13/100 = 0.13
n = 12 (because the interest is compounded monthly)
t = 20
so, A = $11,000(1 + 0.13/12)^(12*20) = $11,000(1.01083333)^240 = $27,731.34
To find the difference in the final balances, we subtract the final balance in Brandon's account from the final balance in Robert's account:
$27,731.34 - $22,817.20 = $4,914.14
To the nearest dollar, the difference is $4,914.
Answer:391
Step-by-step explanation:
Help please!
select all the equations with the same slope
Answer: the second, third and fifth options.
Step-by-step explanation:
When an equation is set up in a y=mx+b format, the slope is always equal to the value m.
11. Angel made 1 1/3pounds of trail mix for a
hike. Is there a way Angel can break up
the trail mix into four bags? Explain.
let's firstly convert the mixed fraction to an improper fraction.
[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{trail mix}}{\cfrac{4}{3}}\div \stackrel{bags}{4}\implies \cfrac{4}{3}\div \cfrac{4}{1}\implies \cfrac{4}{3}\cdot \cfrac{1}{4}\implies \cfrac{4}{4}\cdot \cfrac{1}{3}\implies \stackrel{per~bag}{\cfrac{1}{3}}[/tex]
an insured has chosen joint and 2/3 survivor as the settlement option. what does this mean to the beneficiaries?
Joint and 2/3 survivor means that if the insured passes away, two of the beneficiaries will receive two-thirds of the insurance benefits, and the remaining third will be divided among all three beneficiaries.
Understanding Joint and 2/3 Survivor Settlement OptionJoint and 2/3 survivor is a settlement option for life insurance policies which means that when the insured passes away, two of the beneficiaries will receive two-thirds of the death benefits, while the remaining third will be divided equally among all three beneficiaries. This is beneficial because it ensures that two of the beneficiaries will receive the majority of the death benefits, while the remaining third will be split equally among all three. This provides a more secure financial future for the two beneficiaries receiving the most money as well as allowing the remaining third to be split equally, providing more financial security for all beneficiaries.
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a truck is moving at the rate of 50 miles per hour, and the diameter of each wheel is 3 feet. what is the angualr speed of the wheels in raidans per minute
The angular speed of the wheels is approximately 1480 / π radians per minute.
We can start by converting the velocity of the truck from miles per hour to feet per minute, since the diameter of the wheels is given in feet.
50 miles/hour = 50 x 5280 feet/hour = 264,000 feet/hour
264,000 feet/hour / 60 minutes/hour = 4,400 feet/minute
Next, we can find the circumference of the wheel and then divide it by the velocity of the truck to find the angular velocity in radians per minute:
Circumference = 2 * π * r = 2 * π * (diameter/2) = 2 * π * (3 feet / 2) = 3π feet
Angular velocity (ω) = velocity / circumference = 4,400 feet/minute / (3π feet) = 1480 / π radians/minute
So the angular speed of the wheels is approximately 1480 / π radians per minute.
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the last 2 are so difficult help?
The two mathematical expressions can be written as:-
2) . [ 23 + ( 14 ÷ 2 ) - 20 ] = 5
3) . [ 9² - ( 8 x 4 ) + 26 ] = 75
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The two expressions will be solved as:-
For the first problem, the numbers are 23,2,14, and 20. The expression will be written as:-
[ 23 + ( 14 ÷ 2 ) - 20 ] = 5
[ 23 + 2- 20 ] = 5
[ 25 - 20 ] = 5
5 = 5
The numbers for the second expression are 8,26,9 and 4. The expression can be written as:-
[ 9² - ( 8 x 4 ) + 26 ] = 75
[ 81 - 32 + 26 ] = 75
[ 49 + 26 ] = 75
75 = 75
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12
Enter the statement, with the values in the same order, but with parentheses so that the statement is true.
7x5-4x5+16÷4=26 when
(select) (select)
-
(select) (select)+(select) (select)=26
The expression using brackets is (3x)(x⁴) + (2)(2) = 26
How to determine the equivalent expressionFrom the question, we have the following parametes that can be used in our computation:
7x5-4x5+16÷4=26
Express the superscripts in the expression properly
So, we have the following representation
7x⁵ - 4x⁵ + 16 ÷ 4 = 26
Evaluate the like terms
3x⁵ + 16 ÷ 4 = 26
Divide 16 by 4
3x⁵ + 4 = 26
Factorize and use brackets
(3x)(x⁴) + (2)(2) = 26
Hence, the expression is (3x)(x⁴) + (2)(2) = 26
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Choose the items that complete the sentence about the key features of f(x) = 8x. The y-intercept is , the asymptote is y = , and the range is y >
According to the following graph, the y intercept is 0, the asymptote is ∞ and the range is (-∞, ∞)
In math the term called graph is defined as a pictorial representation or a diagram that represents data or values in an organized manner and the points on the graph often represent the relationship between two or more things.
Here we know that the function is f(x) = 8x.
When we plot the function then we get the graph like the following.
While we looking into plotted graph, then we have identified that the y-intercept is 0.
And the horizontal asymptote is the limit as x goes to ∞.
And the range is the set of values above the horizontal asymptote (-∞, ∞).
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(a) Draw the graph of y=x²+x-5 for values of x ranging from -4 to +3. Use a scale of 1cm to 1 unit on both axes. (b) On the same graph draw the line y = 2(x-1). From your graph: (c) find the roots of the equation x²+x-5=0 (d) deduce the roots of the equation x²+x-7=0 (e) deduce the roots of the equation x²+x-5=2(x-1) (f) state the minimum value of x2+x-5.
We must first plot the given linear equation before we can draw the graph for it. Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.
How do you deduce roots?link the points that lie on it to form a straight line.
Y = 2x - 1 is the first equation.
Calculate the corresponding values of y by substituting various values of x into the equation.
X Y = 2x-1 point (x, y)
0 -1 (0, -1)
2 3 (2, 3)
4 7 (4, 7)
-1 -3 (-1, -3)
-3 -7 (-3, -7)
On the graph paper, place these points and draw a straight line connecting them.
Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.
In order to determine the critical point, we will set the first derivative of the function to zero and solve for x. We may determine whether this point will be a maximum or minimum by taking the second derivative, or f"(x). It will be a minimal value if the second derivative is positive.
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Lance and 7 other friends go to an activity center together. They each pay $5. 95 for dinner, 84 for laser tag, $3. 60 for bowling
shoes, and $2. 25 for video games. The total amount they spent is 8 (5. 95) +8 (4) +8 (3. 60) +8 (2. 25).
Part A
Rewrite the expression so that it only has one multiplication operation
Enter the correct answer in the box
The correct expression that will form with one multiplication operation is 8 × (5.95 + 84 + 3.60 + 2.25).
Firstly rewriting the correct expression according to the amount spent by each person on different entities. The expression will be -
Total amount spent by 8 people = number of people × (amount spent on dinner + laser tag + bowling shoes + video games)
Now keeping the values in formula to find the total amount spent by eight people in desired format.
Total amount spent by eight people = 8 × (5.95 + 84 + 3.60 + 2.25)
Performing addition to simplify the expression is -
Total amount spent by eight people = 8 × 95.8
Thus, the correct simplified expression will be 8×95.8.
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The first three terms of a sequence are given. Round to the nearest thousandth
[tex]2~~,~~\stackrel{2\cdot \frac{5}{2}}{5}~~\stackrel{5\cdot \frac{5}{2}}{\cfrac{25}{2}}~~,~~...\hspace{5em}\stackrel{\textit{common ratio}}{r=\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ a_1=2\\ n=9\\ r=\frac{5}{2} \end{cases}[/tex]
[tex]a_9=2\left( \frac{5}{2} \right)^{9-1}\implies a_9=2\left( \frac{5}{2} \right)^8\implies a_9=2\left( \cfrac{390625}{256} \right) \\\\\\ a_9=\cfrac{390625}{128}\implies {\Large \begin{array}{llll} a_9=3051\frac{97}{128} \end{array}}[/tex]
*
The endpoints of AB are A(-7, 0) and B(7, 7).Find the coordinates of the midpoint M.
Step-by-step explanation:
( x1 + x2 /2 , y1 + y2 / 2 )
= ( -7 + 7 / 2 , 0 + 7 / 2 )
= ( 0, 3.5 )
What are the answers they are due next period
Helppp
Answer:A.½ B.-½ C.2⁷/20
Step-by-step explanation:A. 5¾+(-¼) =23/4 - ¼ =22/
=5½
B. -⅔+⅙ = (-4+1)/6=-½
C. -8/5-¾= (-32-15)/20 =47/20 =2⁷/
the sum of the relative frequencies for all classes will always equal group of answer choices the sample size. the number of classes. one. any value l
The sum of the relative frequencies for all classes will always equal option (C) 1 i.e. when all relative frequencies on a set of values are added it is always equal to one.
A relative frequency tells us the number of times a particular value for a data item has been perceived to occur in relation as compared to the total number of values for that set of data items.
It is calculated by dividing the absolute frequency by the total number of values for the set of data items. It is used to express proportions, ratios, percentages, etc.
Absolute frequency is a mathematical term used in statistics to calculate the number of times a value occurs in a trial set of values. It is used to calculate relative frequency, and display a graph to give a visual representation.
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what is the solution to the inequality?
The solution to the inequality |2x + 3| < 7 is x < 2 or x > -5.
What is inequality?
An inequality is a statement that compares two expressions and asserts that one is greater or less than the other. It can be represented using mathematical symbols such as <, >, ≤, ≥, ≠.
|2x + 3| < 7 is a type of absolute value inequality. The absolute value of a number is its distance from zero on the number line, and is always positive. So, |2x + 3| is the absolute value of 2x + 3, which is always greater than or equal to zero.
To solve this inequality, we need to consider two cases:
If 2x + 3 is greater than or equal to zero, we can drop the absolute value bars and solve the inequality as is:
2x + 3 < 7
2x < 4
x < 2
If 2x + 3 is less than zero, we need to reverse the inequality sign:
-2x - 3 < 7
-2x < 10
x > -5
Hence, the solution to the inequality |2x + 3| < 7 is x < 2 or x > -5.
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Debts, or other outstanding bills or loans that must be repaid are called:
A) Assets
B) Liabilities
C) Net Worth
I add this to math but it's actully personal finance sorry i couldnt find it on pick a subject my bad
Debts, or other outstanding bills or loans that must be repaid are called option B: Liabilities.
What is Debt?
Debt can be defined as the sum that the borrower owes the lender. A debt is an amount of money that has been borrowed for a set period of time and must be repaid, plus interest.
A liability is a debt that a person or business has, typically in the form of money. Through the transmission of economic benefits like money, products, or services, liabilities are eventually satisfied.
Liabilities are items that are listed on the balance sheet's right side and consist of debts including loans, accounts payable, mortgages, deferred income, bonds, warranties, and accumulated expenses.
Therefore, debts are a form of liability.
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In a multicellular organism such as a dog or cat which structures listed would present the greatest in number?
In a multicellular organism such as a dog or cat have tens of trillions of cells and 60 to 80 million cells respectively. So we can say that dog have greatest number of cells
Organisms with many cell types and specialized cells that are gathered together to perform specific duties are known as multicellular organisms. An example of a multicellular organism with organization is a tree or a cat, which have tissues, organs, and organ systems.
Although we are unsure of the actual number of cells in a typical dog, we can estimate it roughly. We may apply this number to dogs, which have in the tens of trillions of cells, as some sources give a ballpark estimate of about fifty trillion cells within a human body. 60 to 80 million cells make up a cat.
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2 of 4
Workers in an office of 40 staff were asked their favourite type of take-away.
The results are summarised in the table.
Take-away
Pizza
Curry
Fish & chips
Kebab
Other
Work out the size of each angle to draw a pie chart.
Od
a=
b 0
C=
Frequency
5
4
10
12
9
e=
Angle
a
b
C
d
el
The size of each angle to draw the pie chart is given as follows:
Angle a: 45º.Angle b: 36º.Angle c: 90º.Angle d: 108º.Angle e: 81º.How to obtain the size of each angle?The size of each angle in this problem is found applying the proportions.
First we obtain the relative frequency of each item, dividing the absolute frequency by 40.
Then we obtain the angle size, multiplying the relative frequency by 360º, which is the angle measure of the entire circumference of the pie chart.
Then the angle measures are obtained as follows:
Angle a: 5/40 x 360 = 45º.Angle b: 4/40 x 360 = 36º.Angle c: 10/40 x 360 = 90º.Angle d: 12/40 x 360 = 108º.Angle e: 9/40 x 360 = 81º.More can be learned about proportions at https://brainly.com/question/24372153
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please help!!
Examine the two news headlines from real observational studies and determine at least one plausible lurking variable that could explain the cause and effect. Remember, do not argue about the link expressed in the headline, but rather accept the association as true. Your task is to determine the other variable(s) that could be the actual cause(s). b. “Is Gluten the Culprit in Our Fight Against Obesity?”
A plausible lurking variable that could explain the cause and effect in the headline "Is Gluten the Culprit in Our Fight Against Obesity?" is overall diet.
It's possible that individuals who consume a diet high in gluten also consume a diet high in overall calories and processed foods, leading to weight gain and obesity. This would mean that it is not specifically gluten causing the obesity, but rather a combination of factors in the individual's diet.
What is a lurking variable?A lurking variable is a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable.
Although it is not taken into account in the study, it might affect how the variables are related.
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2x+8=-3.5x+19 decide wether each question is true for all one, or no values of x
Answer:
x = 2
Step-by-step explanation:
2x + 8 = -3.5x+19
2x = -3.5x + 11
5.5x = 11
x = 2
Let's check
2(2) + 8 = -3.5(2) + 19
4 + 8 = -7 + 19
12 = 12
So, x = 2 is the only correct answer.
Can someone help with problem 1 and 2
To find the sum of interior angles of a polygon, multiply the number of triangles formed inside the polygon to 180 degrees.
How to find the sum of interior angles ?
The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.Each interior angle of a regular hexagon has a measure of 120°. Because the sum of these angles will always be 360°, then each exterior angle would be 60° (360° ÷ 6 = 60°). If each exterior angle is 60°, then each interior angle is 120° (180° − 60° = 120°).The angles that lie inside a shape, are said to be interior angles, or the angles that lie in the area bounded between two parallel lines that are intersected by a transversal are also called interior angles.
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PLEASE HURRY, TEST QUESTION, LIMITED TIME!
Question- Write the standard form equation of the circle given the center of (-3, -8) and the circumference of 14π. Show all work using the equation editor to calculate the missing pieces of the equation.
Answer: (x + 3)^2 + (y + 8)^2 = 14pi^2
(x-h)^2 + (y-k)^2 = r^2
What is the length of every median in an equilateral triangle whose side length is 5?
Answer:
√18.75 ≈ 4.33
Step-by-step explanation:
The median joins a vertex and the opposite side's midpoint.
side = 5
half side = 2.5
a² + b² = c²
2.5² + b² = 5²
b² = 18.75
b = √18.75
b = 4.33
The length of every median in an equilateral triangle whose side length is 5 is 4.330127018922193.
An equilateral triangle is one in which the angles and all three sides are equal. An equilateral triangle is also known as an equiangular triangle since each of its angles has a value of 60 degrees. Due to its equal sides and angles, the equilateral triangle is regarded as a regular polygon or triangle.
In an equilateral triangle, all three medians have the same length.
The length of a median in an equilateral triangle can be found using the formula:
median length = (side length * sqrt(3))/2.
Therefore, in an equilateral triangle with a side length of 5, the length of each median would be,
[tex]=5*\sqrt{3}/2 \\=2.5*\sqrt{3}\\= 4.330127018922193[/tex].
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log₂ 3+ log₂ (x-4)= 4
Answer:
In Explanation
Step-by-step explanation:
To solve for x in the equation log₂ 3+ log₂ (x-4)= 4, we can first use the logarithm identity: log₂ a + log₂ b = log₂ (ab)
So, we can rewrite the equation as:
log₂ (3(x-4)) = 4
Then we can use the definition of logarithm to find the value of x:
2^4 = (3(x-4)) = 3x-12
16 = 3x - 12
28 = 3x
x = 9 + 4 = 9
Therefore, x = 9 is the solution of the equation log₂ 3+ log₂ (x-4)= 4
(Please give brainlist)
Which i a better cheme a ingle dicount of 45%or ucceive dicount of 30%and20%on the ame article
The single discount of 45% is better than the successive discount of 30% and 20%.
Let us assume that the Maximum retail price = 100x
As in case 1,
The percentage discount is given as 45%
So, the value of the selling price of the item will be = (100-45)% of 100x
=55% of 100x = 55x ------(i)
Now in case 2,
The successive discount of 30% and 20% is given.
So, let us assume that the Maximum retail price = 100x
So, after giving the discount of 30%
The value of the selling price will be = (100-30)% of 100x
=70% of 100x = 70x
Now again giving the discount of 20%
Then the value of new selling price will be = (100-20)% of 70x
=80% of 70x = 56x ------(2)
In case (1) the selling price is 55x while in case 2 the selling price is 56x.
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It depends on the price of the article. A 45% single discount will always result in a larger price reduction than a 30% discount followed by a 20% discount on the same price.
However, the overall savings from the two different discount schemes may be the same if the price of the article is high enough. To determine which discount scheme is better, it is necessary to know the price of the article and calculate the total savings under both schemes.
For instance: For example, if we are considering the price of an article is Rs 100, then the successive percentage would be 30% and 20% for the discount, the price falls to Rs 56, whereas with a single 45%discount, the amount comes to Rs55.
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I need help im begging yall to help the question is which graph represents the solution to the given system y=-3x-4 and y+4-3x? A. infinit many solutions B no solutions C.(0.-4) D.(0,4) im in the last test of the semester
Answer:
D is the one trust me man I do this all the time and good luck on your exam
Given point M and plane α such that M ∉ α. MO is perpendicular to plane α. MP and MQ are inclined to α which make 30° and 60° with plane α, respectively. Find the length of PQ in terms of
MO if ∠POQ = 120°
The length of PQ in terms of MO if ∠POQ = 120° is PQ = -x * √3/3.
Let MO = x.
Since MO is perpendicular to plane α, MP and MQ form right angles with MO.
Using the Pythagorean Theorem, we have:
MP = x * tan(30°) = x * √3/3
MQ = x * tan(60°) = x * √3
Since ∠POQ = 120°, we have:
PQ = MP * 2 * cos(120°)
= 2 * x * √3/3 * -1/2
= -x * √3/3
Therefore, the length of PQ in terms of MO is PQ = -x * √3/3.
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Suppose 0 is an angle in the standard position whose terminal side is in quadrant IV and cot 0 = -9/18. Find values of five remaining trigonometric functions of 0.
The values of five remaining trigonometric functions of θ.
sinθ = 1/√5, cosθ = 2/√5, tanθ = 2, secθ = √5/2, cosecθ = √5
We have to determine values of five remaining trigonometric functions of θ. Suppose θ is an angle in the standard position whose terminal side is in quadrant IV and cot θ = -9/18.
The ratio of trigonometry is:
sinθ = Perpendicular/Hypotenuse
cosθ = Adjacent Side/Hypotenuse
tanθ = Perpendicular/Adjacent Side
cotθ = Adjacent Side/Perpendicular
sec = Hypotenuse/Adjacent Side
cosec = Hypotenuse/Perpendicular
We know that;
Adjacent Side = 9, Perpendicular = 18
Now finding the value of Hypotenuse using the Pythagorean Theorem
(Hypotenuse)^2 = (Adjacent Side)^2 + (Perpendicular)^2
(Hypotenuse)^2 = (9)^2 + (18)^2
(Hypotenuse)^2 = 81 + 324
(Hypotenuse)^2 = 405
Taking square root on both side, we get
Hypotenuse = 9√5
Now finding the other trigonometry ratio:
sinθ = Perpendicular/Hypotenuse
sinθ = 9/9√5
sinθ = 1/√5
cosθ = Adjacent Side/Hypotenuse
cosθ = 18/9√5
cosθ = 2/√5
tanθ = Perpendicular/Adjacent Side
tanθ = 18/9
tanθ = 2
secθ = Hypotenuse/Adjacent Side
secθ = 9√5/18
secθ = √5/2
cosecθ = Hypotenuse/Perpendicular
cosecθ = 9√5/9
cosecθ = √5
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Steve is constructing a
triangle from scrap wood.
He has one piece that is
20 inches and a second
piece that is 15 inches
When he is looking for
a third piece, what range
of sizes should he try
to find?
Answer:
Step-by-step explanation:
the new one will tell you be