You are sailing from your lakeshore cabin to a marina 60º north of east and 0.5 miles across the lake.
Which of the following expressions uses the complementary angle of 60° to determine how far you would travel on your trip west?
a.
0.5cos30°
b.
0.5cos60°
c.
0.5sin30°
d.
0.5sin60°
Answers
Answer:- c. 0.5sin30°
Explanation:-
Let AB= 0.5 miles be the distance across the lake to 60º north of east.
AC= distance travel to the east
Now, in right ΔABC
[tex]sin60^{\circ}=\frac{AC}{AB}\\\\\Rightarrow\ AB=ACsin60^{\circ}\\\Rightarrow\ AB=0.5\ sin60^{\circ}[/tex]
Now Distance towards west [tex]AD=|\ -0.5\ sin60^{\circ}|[/tex] [distance is a positive quantity]
[tex]AD=0.5\ sin60^{\circ}[/tex]
[tex]AD=0.5\ cos(90^{\circ}-60^{\circ})[/tex] [Taking complementary angle of 60° ]
[tex]AD=0.5\ cos(30^{\circ})[/tex]
Thus C. is the right option.
Answer:
the answer is C.
Step-by-step explanation:
Related Questions
In the regression equation, what does the letter "x" represent?
Answers
the graph of g(x) is the graph of f (x)=x+9 reflected across the y axis.
which equation describes the function g?
1. g(x)=x-9
2. g(x)=-x-9
3. g(x)=-9x+9
4. g(x)=-x+9
Answers
Answer:
4. g(x)=-x+9
Step-by-step explanation:
The correct answer is actually g(x)=-x+9. Just took the text. XD
Answer-
[tex]g(x)=-x+9[/tex]
Solution-
The given function is,
[tex]f(x)=x+9[/tex]
Given that g(x) is the reflection of f(x) over y-axis.
The reflection of the point (x, y) across the y-axis is the point (-x,y).
So, in case of reflection over y-axis the sign of only x-coordinate is changed and y-coordinate remains same.
So changing the sign of x in f(x) will yield its reflection over y-axis i.e g(x)
Therefore, g(x) is,
[tex]g(x)=-x+9[/tex]
Use the chain rule to find ∂z/∂s and ∂z/∂t. z = sin(θ) cos(ϕ), θ = st5, ϕ = s7t
Answers
[tex]\theta=st^5[/tex]
[tex]\phi=s^7t[/tex]
[tex]\dfrac{\partial z}{\partial s}=\dfrac{\partial z}{\partial\theta}\dfrac{\partial\theta}{\partial s}+\dfrac{\partial z}{\partial\phi}\dfrac{\partial\phi}{\partial s}[/tex]
[tex]\dfrac{\partial z}{\partial s}=\cos\theta\cos\phi t^5-\sin\theta\sin\phi (7s^6t)[/tex]
[tex]\dfrac{\partial z}{\partial s}=t^5\cos(st^5)\cos(s^7t)-7s^6t\sin(st^5)\sin(s^7t)[/tex]
[tex]\dfrac{\partial z}{\partial t}=\dfrac{\partial z}{\partial\theta}\dfrac{\partial\theta}{\partial t}+\dfrac{\partial z}{\partial\phi}\dfrac{\partial\phi}{\partial t}[/tex]
[tex]\dfrac{\partial z}{\partial t}=\cos\theta\cos\phi(s5t^4)-\sin\theta\sin\phi s^7[/tex]
[tex]\dfrac{\partial z}{\partial t}=5st^4\cos(st^5)\cos(s^7t)-s^7\sin(st^5)\sin(s^7t)[/tex]
We use the chain rule to find the partial derivatives ∂z/∂s and ∂z/∂t, considering z as a function of θ and ϕ, treating θ and ϕ as intermediate variables. We then differentiate θ with respect to s and t, and similarly for ϕ.
Explanation:To find the partial derivatives ∂z/∂s and ∂z/∂t, we first need to make use of the chain rule in calculus. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. Here, z is a function of θ and ϕ, which are themselves functions of s and t - θ = st^5 and ϕ = s^7t.
First, find the partial derivative ∂z/∂s. We differentiate z = sin(θ)cos(ϕ) with respect to s, treating θ and ϕ as intermediates, and then differentiate θ and ϕ with respect to s.
Similarly, to find the partial derivative ∂z/∂t, we differentiate z = sin(θ)cos(ϕ) with respect to t treating θ and ϕ as intermediates, and then differentiate θ and ϕ with respect to t.
Please note that further calculation will require the exact differentiation of trigonometric functions and power functions.
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If you were to spin the spinner below, what would be the probability of landing on green or purple?
you have 1/4 one is purple another orange and the other two green
Answers
Final answer:
The probability of landing on green or purple on the spinner is 3/4, or 75%.
Explanation:
To determine the probability of landing on green or purple when spinning a spinner that has 1/4 of its sections as purple, another 1/4 as orange, and the remaining two quarters green, you would simply add the probability of landing on each of those colors since they are mutually exclusive events. The probability of landing on purple is 1/4 and the probability of landing on green is 2/4 since there are two quarters of the spinner that are green.
We calculate the probability as follows:
Probability of landing on purple = 1/4Probability of landing on green = 2/4 or 1/2To find the combined probability of landing on green or purple, you add the two probabilities together:
Probability of landing on green or purple = Probability of purple + Probability of green
Probability of landing on green or purple = 1/4 + 1/2
Probability of landing on green or purple = 1/4 + 2/4
Probability of landing on green or purple = 3/4
Thus, the probability of landing on green or purple is 3/4, which means there is a 75% chance of the spinner landing on either of these colors.
Examine the function for relative extrema and saddle points. (if an answer does not exist, enter dne.) h(x, y) = x2 − 9xy − y2
Answers
h(x,y) = x² - 9xy - y²
Calculate partial derivatives.
[tex]h_{x} = 2x \\ h_{xx} = 2 \\ h_{y} = -2y \\ h_{yy} = -2 \\ h_{xy} = 0 [/tex]
For the critical points,
[tex]h_{x} = 2x=0 \, \Rightarrow \, x=0 \\h_{y}=-2y=0 \,, \Rightarrow \, y=0[/tex]
To perform a test for a saddle point, calculate
[tex]D = h_{xx}(0,0) h_{yy} (0,0) -[ h_{xy}(0,0)]^{2} = (2)(-2) - (2)^{2} = -8[/tex]
Because D < 0, a saddle point exists at (0,0).
Ordering numbers from greatest to least is called putting them in _____ order.
Answers
Ordering numbers from greatest to least is known as putting them in descending order. This organization method is a form of emphatic order, which could also be the answer if the context relates to emphasizing the importance of the items being ordered rather than their numerical value.
Ordering numbers from greatest to least is called putting them in descending order. When we arrange objects based on the level of importance or magnitude, this is often referred to as emphatic order, which prioritizes items from least to most important or vice versa. In mathematics, specifically, when numbers are organized from the largest to the smallest, they are said to be in descending order, which is the opposite of ascending order, where numbers are arranged from smallest to greatest.
There are various ways in which ideas, objects, or numbers can be ordered. For example, chronological order refers to presenting events in the sequence they happened in time, whereas sequential order is similar but can apply to any sequence of actions or items, not just those related to time. Conversely, spatial order involves the arrangement of items as they are placed in space.
In the context of your question, when asked to rank objects by their distance from the origin, a descending order would start with the object that is farthest away (largest distance) and end with the object that is closest to the origin (smallest distance).
Charlotte embroidered a piece of cloth with a length of 4 meters and a width of 2 meters in 412 hours.
What is the approximate speed, in square meters per hour, at which Charlotte can embroider? Round your answer to the nearest whole number.
Answers
If you fly from Los Angeles California to Miami Florida. the plane travels a distance of 3772 km in the air. the flight takes 6 hours and 15 minutes. what is the playing the average speed?
Answers
Ralph sold brownies for $0.66 a piece in order to earn money to buy baseball cards. If the cards cost $0..90 per pack, and if Ralph had no money left over after buying them, what is the least number of brownies he must have sold?
Show method for answer if possible?
Answers
If he only sold one he wouldn't have enough money, he also can't sell part of a brownie
Ralph must have sold at least 9 brownies at $0.66 each to be able to buy a pack of baseball cards for $0.90 with no money left.
Ralph sold brownies for $0.66 each to earn money to buy baseball cards that cost $0.90 per pack. To find the least number of brownies Ralph must have sold, we need to determine how many brownies he needs to sell to make at least $0.90, with no money left over after the purchase.
Since Ralph has no money left over, the total amount he earned from selling brownies should be a multiple of $0.90.
To find the least number of brownies, we perform the following calculation:
Find the smallest multiple of $0.90 that is also a multiple of $0.66.
Divide that amount by the price of each brownie, which is $0.66.
By performing this calculation, we find that the least number of brownies sold would have to be a number that, when multiplied by $0.66, is both a multiple of itself and $0.90. The least common multiple (LCM) of 66 and 90 cents is $5.94, which corresponds to selling 9 brownies (because $5.94 divided by $0.66 per brownie equals 9).
Therefore, Ralph must have sold at least 9 brownies to buy a pack of baseball cards with no money left over.
25 pints of apple juice are poured into 1/2 pint bottles. how many bottles can be filled with apple juice
Answers
The number of bottles to fill 25 pints of apple juice will be equal to 50.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The Number of the bottles = 25 / ( 1 / 2 )
= 25 x 2
= 50
Therefore, the number of bottles to fill 25 pints of apple juice will be equal to 50.
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find the sale price of the item.round to two decimal places if necessary.
Original price $89.00
Markdown:33%
The sale price is $___
Answers
The original price of the item is $89.
$89 is 100% of the original price.
You want to take off 32%.
100% - 32% = 67%
That means you want to find out how much 68% of $89 is.
68% of $89 =
= 0.68 * 89
= 60.52
Answer: $60.52
You asked for a 33% markdown, but the pic shows 32%, so I did 32%.
Maya is showing her work in simplifying (5.2 − 4.5) − 5.5 + 4.8. Identify any error in her work or reasoning.
Answers
change the mixed number to percentage
7 7/8
Answers
so, let's convert 7 and 7/8 from mixed to improper first.
[tex]\bf 7\frac{7}{8}\implies \cfrac{7\cdot 8+7}{8}\implies \cfrac{63}{8}\implies 7.875\\\\ -------------------------------\\\\ \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&100\\ 7.875&p \end{array}\implies \cfrac{1}{7.875}=\cfrac{100}{p}\implies p=\cfrac{7.875\cdot 100}{1}[/tex]
Write the steps for how to use a number line to multiply a 2 digit number by 20. Give an example
Answers
To multiply a two-digit number by 20 using a number line, first choose a two-digit number. Each step on your number line will represent this number. Then count 20 steps on your number line from 0. The number you land on is the product. Alternatively, you can multiply the number by 2 and then move the decimal point one place to the right.
Explanation:To use a number line to multiply a two-digit number by 20, follow these steps with an example:
Choose a two-digit number. Let's use 15 as an example.On your number line, make a mark at zero and at your two-digit number (in this case, 15).Each step on your number line will represent an increment of 15. This means the step after 15 will be 30, then 45, and so on.Count 20 steps on your number line from 0. The number you land on will be the product of your two-digit number (15) and 20.Alternatively, as per the shortcuts mentioned, multiplying by 10 involves moving the decimal point one place to the right. Multiplying a number by 20 is thus equivalent to multiplying the number by 2 and then by 10. As an example, 15 x 20 can also be calculated as (15 x 2) x 10 = 30 x 10 = 300.
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What is 800+60+4 in standard form
Answers
Just add the numbers.
ABC is reflected across x = 1 and y = -3. What are the coordinates of the reflection image of B after both reflections?
A. (-7, -1)
B. (-7, 1)
C. (7, 1)
D. (7, -1)
Answers
Answer:
The correct option is C
Step-by-step explanation:
From the given figure it is noticed that the coordinates of point B are (-5,-7).
If a figure is reflected across x = 1, then
[tex](x,y)\rightarrow (1-(x-1),y)[/tex]
[tex](x,y)\rightarrow (2-x,y)[/tex]
So the coordinates of B after reflection across x = 1 are
[tex](-5,-7)\rightarrow (2-(-5),-7)[/tex]
[tex](-5,-7)\rightarrow (7,-7)[/tex]
If a figure is reflected across y = -3, then
[tex](x,y)\rightarrow (x,-3-(y+3))[/tex]
[tex](x,y)\rightarrow (x,-6-y)[/tex]
So the coordinates of B after reflection across x = 1 followed by reflection across y= -3 are
[tex](7,-7)\rightarrow (7,-6-(-7))[/tex]
[tex](7,-7)\rightarrow (7,1)[/tex]
Therefore the coordinates of the reflection image of B after both reflectionsthe are (7,1) and option C is correct.
What are the steps for using a compass and straightedge to construct a square? Drag and drop the steps in order from start to finish.
1.Construct a line perpendicular to line m through point F. Label a point on this line as point G.
2.Use a straightedge to draw line m and label a point on the line as point F.
3.Without changing the compass width, place the compass point on point H and draw an arc in the interior of ∠HFK .
4.Use the straightedge to draw JH¯¯¯¯¯ and JK¯¯¯¯¯.
5.With the compass open to the desired side length of the square, place the compass point on point F and draw an arc on line m and an arc on FG←→ . Label the points of intersection as points H and K.
6.Keeping the same compass width, place the compass on point K and draw an arc in the interior of ∠HFK to intersect the previously drawn arc. Label the point of intersection as point J.
Answers
1. Use a straightedge to draw line m and label a point on the line as point F
2. Construct a line perpendicular to line m through point F. Label a point on this line as point G.
3. With the compass open to the desired side length of the square, place the compass point on point F and draw an arc on line m and an arc on FG←→ . Label the points of intersection as points H and K.
4. Without changing the compass width, place the compass point on point H and draw an arc in the interior of ∠HFK.
5. Keeping the same compass width, place the compass on point K and draw an arc in the interior of ∠HFK to intersect the previously drawn arc. Label the point of intersection as point J.
6. Use the straightedge to draw JH¯¯¯¯¯ and JK¯¯¯¯¯.
These are the right answers
Use multiplication and distributive property to find the quotient of 75 divided by 3
Answers
Ellen Saver went to her bank. She had a balance of $2,447.67 in her savings account. She withdrew $231.49 and the teller credited her account with $36.61. What is her new balance?
$2,179.57
$2,252.79
$2,642.77
$2,715.77
Answers
suppose Marcus delivers papers at a rate of 9 papers in 18 minutes. How much longer would it take him to deliver 100 papers and 72 papers? justify your response.
Answers
Amount of time to deliver:
72 papers: 144 minutes (2 hours 24 minutes)
100 papers: 200 minutes (3 hours 29 minutes)
12x−3y=, when x=−1/4 and y=3
Answers
(answer)
12(-1/4)-3(3)
-3-9
-12
What is the gcf of a^2b^5 and a^2b^6
Answers
Then you have b^5 and b^6, so they both have b^5 in common.
The GCF is a^2b^5
If sales tax is 5%, what is the sales tax on an item costing $65?
Answers
What is the product of 5 + 2i and 7 + 3i?
(1) 41 + 29i
(2)29 + 29i
(3)41 + i
(4)35 + 6i
(5)29 + 41i
Answers
Answer is (4)
this is my home work of 8th ducking grade butch so see if you could answer it
Answers
That means that something = 32 / (4/5) = 40.
To turn this multiplication around, it helps to think about 2 * 3 = 6, how would you write 3 = ?. You quickly :"see" that it should be 3=6/2.
If $2300 is spent on vacations or travel each year, estimate how much should be set aside each month for those expenses?
a.
Approximately $200 per month should be set aside for vacation or travel expenses.
b.
Approximately $2300 per month should be set aside for vacation or travel expenses.
c.
Approximately $1250 per month should be set aside for vacation or travel expenses.
d.
Approximately $230 per month should be set aside for vacation or travel expenses.
Answers
The estimate should be set Approximately $200 per month aside for vacation or travel expenses.
What is estimation?It is a rough calculation of the value, number, quantity, etc. It doesn't use real calculation but estimation by some method like prediction, using approximation etc.
Given that $2300 is spent on vacations or travel each year.
It is known that 12 months in a year
= 2300/12
we can round 2300 to 2400 because it is an estimatation value and divide by 12
= 2400/12
= 200
Thus, an approximation of $200 each month.
The estimate should be set Approximately $200 per month aside for vacation or travel expenses.
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Jake is comparing the prices of two mattress cleaning companies. Company A charges $30 per mattress and an additional $13 as service charges. Company B charges $28 per mattress and an additional $15 as service charges.
Part A: Write an equation to represent each company's total charges for cleaning a certain number of mattresses. For both equations (one for Company A and one for Company B), define the variable used. (4 points)
Part B: Which company would charge less for cleaning 4 mattresses? Justify your answer. (3 points)
Part C: How much money is saved by using the services of Company B instead of Company A to clean 7 mattresses? (3 points)
Answers
y= total charges
x=number of mattresses
Company A: y=$30x+13 Company B: y=$28x+15
B)
plug x=4 into both equations to get
A: y=30(4)+13=$133
B: y=28(4)+15=$127
Company B charges less because 127<133
C)
Plug in 7 for x
A: y=30(7)+13=$223
B: y=28(7)+15=$211
A-B=223-211
=$12 Saved
Explain what it means to have a correlation in a scatterplot.
Answers
Correlation is used to show trends in a scatter plot
The following are the possible correlation types in a scatter plot
Positive correlationNegative correlationWhen the x value and the y values increase at the same time, then the correlation is positive.
However, when the x value and the y values increase at the same time, then the correlation is negative.
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Answer:
Sample Response/Explanation: A correlation exists in a scatterplot if there is a general trend in the outputs as inputs increase. If the outputs generally increase in value, then there is a positive correlation. If the outputs generally decrease in value, then there is a negative correlation.
Step-by-step explanation:
i did it
At time t = 0 a car moves into the passing lane to pass a slow-moving truck. The average velocity of the car from t =1tot =1+his
v = 3(h+1)2.5 +580h−3 ave 10h
Estimate the instantaneous velocity of the car at t = 1, where time is in seconds and distance is in feet.
Answers
The correct given equation is:
v = [3 (h + 1)^2.5 + 580 h – 3] / 10 h
So to solve for the instantaneous velocity at t = 1, we must set h = 0. However we cannot do that since h is in denominator and a number divided by a denominator is infinite. Therefore we must set h to something almost zero. In this case, h = 0.0000001, so that:
at t = 1
v = [3 (0.0000001 + 1)^2.5 + 580 (0.0000001) – 3] / 10 * 0.0000001
v = 58.75 ft/s
The question is asking for the instantaneous velocity of a car at t = 1 second, which would normally be found by differentiating the position function. However, due to potential typos in the provided equation, the instantaneous velocity cannot be calculated directly.
Explanation:The problem asks for the instantaneous velocity of the car at time t = 1 second. To find the instantaneous velocity, we would typically take the derivative of the position function with respect to time. However, the given equation v = 3(h+1)2.5 + 580h - 3 ave 10h appears to have some issues, possibly due to typos, and cannot be processed as is. In general, if the average velocity function over time h was given correctly, we would evaluate the derivative of that function at h = 0 to find the instantaneous velocity at t = 1 second.
Find the particular solution of the differential equation \frac{dy}{dx} + y\cos(x) = 5\cos(x)
Answers
[tex]e^{\sin x}\dfrac{\mathrm dy}{\mathrm dx}+y\cos xe^{\sin x}=5\cos xe^{\sin x}[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[e^{\sin x}y\right]=5\cos xe^{\sin x}[/tex]
[tex]e^{\sin x}y=5\displaystyle\int\cos xe^{\sin x}\,\mathrm dx[/tex]
[tex]e^{\sin x}y=5e^{\sin x}+C[/tex]
[tex]y=5+Ce^{-\sin x}[/tex]