The total distance from Charles' starting point at the marina to his destination is calculated by adding the vectors representing each leg of his journey and using the Pythagorean theorem to find the length of the resultant vector. This comes out to be approximately 40 km.
Explanation:This problem can be solved using vector addition and the Pythagorean theorem. Charles’ first leg of the journey is 10° west of north, therefore we could consider it as a vector directed north-west. Charles travels 1.5h at 18 km/h, therefore the lenght of this vector is 27km. Charles’ second leg of the voyage heads 60° east of north, that could be considered as a vector heading north-east. He sails for 1.5h at 20 km/h resulting in a vector of 30 km.
Now, if we place these two vector head to tail keeping their direction intact, we form a right triangle. Using Pythagorean theorem, the hypotenuse of the triangle will give us the distance from initial to final point. Therefore, the formula becomes √(27² + 30²) = √(729 + 900) = √1629 ≈ 40.36 km which is approximately 40 km to the nearest kilometer.
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the temperature at 6:00AM was 0.8F. BY. 3:00pm the temperature had increased to 2.4 F find the differnce between the two temperatures. Draw models to find the difference
A trough is 12 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 13 ft3/min, how fast is the water level rising when the water is 8 inches deep?
I have been getting 13/30, but apparently, that is wrong?
V=.5 * h * l * b
Because of similar triangles:
b = 5h (b/h = 5/1)
l = 12
V = .5 * h * 5h * 12
V = 30h^2
(dV/dt) = 60 h (dh/dt)
dV/dt = 13
h = .5 (because this is in feet)
13 = 60*.5(dh/dt)
13/30 = dh/dt
The rate at which the water level is rising when the water is 8 inches deep in the trough is 13/30 ft/min.
Explanation:To find how fast the water level rises when the water is 8 inches deep, we need to use the equation V = 30h^2, which represents the volume of the trough as a function of its height h. We are given that the trough is being filled at a rate of 13 ft^3/min, so we can set dV/dt (the rate of change of volume) equal to 13.
Substituting the given values into the equation dV/dt = 60h * dh/dt, we get 13 = 60 * h * dh/dt. Since h = 0.5 (in feet), we can solve for dh/dt which turns out to be 13/30 ft/min.
Therefore, the water level is rising at a rate of 13/30 ft/min when the water is 8 inches deep.
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Bruno's hourly salary is 6.75. Last Week he worked a 20 hour week. How Much did he earn
Simplify:
4p + 12 – 3q – 4p – 18 + 6q
A. 8p + 3q – 6
B. 8p – 3q + 6
C. 3q + 6
D. 3q – 6
The simplifying value of the expression is,
⇒ 3q - 6
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 4p + 12 - 3q - 4p - 18 + 6q
Now,
Simplify the expression as;
⇒ 4p + 12 - 3q - 4p - 18 + 6q
⇒ 4p - 4p - 3q + 6q + 12 - 18
⇒ 0 + 3q - 6
⇒ 3q - 6
Thus, The simplifying value of the expression is,
⇒ 3q - 6
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Mr. Welch bought 24 ft of fencing.
How many yards of fencing did he buy? (1 yd = 3 ft)
1 yard = 3 feet
divide 24 feet by 3 feet to get yards
24 / 3 = 8 yards
The Hamptons family has a fish tank holding 10,450 ml of water.The water is leaking at a rate of 270 ml per minute.
Part A: Define the input and output in the given scenario.
Part B: Write a function to model this situation.
Part C: How many liters of water will be left in the tank after 10 minutes.?
1. What events led to the attack at Pearl Harbor?
I know that this isn't math but I just need help please. :(
-4.2 (-2.8+4.5) what is the value of the expression
What is the best way to 7x7 in expanded form?
Answer: Add 7 7 times
Step-by-step explanation: if you add 7 7 times like this 7+7+7+7+7+7+7 then that is your answer easy way too.
Julia plays volleyball and finished the regular season with 25 digs. The graph relates her total number of digs for the season to the number of games played in the post-season tournament. Graph in the coordinate plane with title Julia’s volleyball digs. Vertical axis goes from 0 to 60 in increments of 5 and is labeled number of digs. Horizontal axis goes from 0 to 10 in increments of 1 and is labeled games played. A ray on the graph starts at point begin ordered pair 0 comma 25 end ordered pair and goes through points begin ordered pair 4 comma 37 end ordered pair and begin ordered pair 8 comma 49 end ordered pair. What is the equation in standard form that represents the relationship shown in the graph? y=3x+25 y−37=3(x−4) 3x+y=25 −3x+y=25 y=−3x+25
Answer:
As given : Graph in the coordinate plane with title Julia’s volleyball digs. Vertical axis goes from 0 to 60 in increments of 5 and is labeled number of digs. Horizontal axis goes from 0 to 10 in increments of 1 and is labeled games played. A ray on the graph starts at point begin ordered pair 0 comma 25 end ordered pair and goes through points begin ordered pair 4 comma 37 end ordered pair and begin ordered pair 8 comma 49 end ordered pair.
As the ray passes through (0,25) and (4,37) and (8,49).
Equation of line passing through (a, b) and (p,q) is given by:
→ [tex]\frac{y-b}{x-a}=\frac{q-b}{p-a}[/tex]
→Equation of line passing through (0,25) and (4,37) is :
[tex]\frac{y-25}{x-0}=\frac{37-25}{4-0}=3\\\\y -25=3x\\y =3x + 25[/tex]
As , y= 3 x + 25, also passes through (8,49) also.
Equation of line is : y = 3 x + 25 or in Standard form : - 3 x + y = 25
Option (D) is the standard form of line which is : - 3 x + y = 25
What is 24 divided by 1272
does it matter whether you remove x tiles or 1 tiles first
If there are 1000 grams in a kilogram and 454 grams in a pound, how many pounds are there per kilogram?
Answer:2.2 pounds per kilogram
Step-by-step explanation:
454gram = 1 pound
since; 1000g = 1kg
454g = x
x= 454/1000
x=0.454kg
there is 0.454kg in 1 pound
but the question says how many pound is in 1kg
0.454kg = 1 pound
1 kg = x
cross multiply
0.454x = 1
Divide bothside by 0.454
x = 1/0.454
x = 2.2 pound
Therefore; there are 2.2pounds in 1 kilogram.
There are 2.20 pounds are there per kilogram
Given that,
1 kg = 1000 gm
1 pound = 454 gm
Since we know that,
A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Since,
1 pound = 454 gm
Therefore,
⇒ 454 gm = 1 pound
⇒ 1 gm = 1/454 pound
And since,
1 kg = 1000 gm
= 1000x(1/454) pound
= 2.20 pounds
Hence,
1 kg = 2.20 pounds
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Use the sequence below to answer parts a and b (8,17,26,35,44,53,...) Create an explicit formula to determine the 12th term of the sequence Create a recursive formula to prove the 7th term is 62.
The explicit formula for the sequence (8, 17, 26, 35, 44, 53, ...) is 8 + (n-1) * 9, and the 12th term can be found by substituting n = 12. The recursive formula for the sequence is a1 = 8 and an = an-1 + 9. Using this recursive formula, we can verify that the 7th term is indeed 62.
Explanation:To create an explicit formula for the sequence (8, 17, 26, 35, 44, 53, ...), we notice that the difference between each term is 9. So, the explicit formula for the sequence is 8 + (n-1) * 9, where n represents the position of the term in the sequence. Using this formula, we can find the 12th term by substituting n = 12: 8 + (12-1) * 9 = 89.
To create a recursive formula to prove that the 7th term is 62, we observe that each term is the previous term plus 9. So, the recursive formula for the sequence is:
a1 = 8an = an-1 + 9Using this recursive formula and starting with a1 = 8, we can find the 7th term as follows:
a1 = 8a2 = a1 + 9 = 8 + 9 = 17a3 = a2 + 9 = 17 + 9 = 26a4 = a3 + 9 = 26 + 9 = 35a5 = a4 + 9 = 35 + 9 = 44a6 = a5 + 9 = 44 + 9 = 53a7 = a6 + 9 = 53 + 9 = 62Therefore, the 7th term in the sequence is indeed 62.
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find the rate of change for 2x+4y=10
rate of change for 2x+4y=10
here rate of change can be found by finding slope
the general form for slope is y=mx+b
isolating y on the left side:
2x+4y=10
4y=[tex] y=\frac{-2x+10}{4}
[/tex]-2x+10
from here slope is -1/2
Rate of change =-1/2
what is -5x + 2 equals negative 48
The amount of money Kelly earns is proportional to the number of hours she works. Kelly earns $32.40 working 4 hours. Create an equation that models the relationship between the amount of money Kelly earns, in dollars, and h, the number of hours she works.
Rewrite the expression with parentheses to equal the given value 12+6÷2+4 value 13
Thomas earns $2100 per month and then got a 15 raise .how much will Thomas make per month after his raise
Final answer:
Thomas will earn $2415 per month after a 15% raise on his current salary of $2100, which results in a raise amount of $315.
Explanation:
Thomas currently earns $2100, and with a 15% raise, we need to calculate the increase in his monthly pay. To find the amount of the raise, we calculate 15% of his current earnings. That is, we multiply his earnings by the raise percentage expressed in decimal form: $2100 × 0.15 = $315.
After finding the raise amount, we add it to his current salary to find his new monthly earnings. $2100 + $315 = $2415 per month. Therefore, after a 15% raise, Thomas will make $2415 per month.
the exact radius of a circle with circumference 36 meters
(20 points)
What is the perimeter of the figure?
229-4/9 ft
229-2/3 ft
230-2/3 ft
231 ft
60 5/6 + 56 1/6 = 117
59 1/3 + 54 1/3 = 113 2/3
117 + 113 2/3 = 230 2/3 feet
If the equatorial diameter of the sun is 1.39 million km how many kilometers is the sun's radius
PLEASE HELP ME.
Show Work.
Use two unit multipliers to convert 70 meters to inches.
To convert 70 meters to inches, use the unit multiplier method. 70 meters is equal to 2755.91 inches.
Explanation:To convert meters to inches, we can use the unit multiplier method. There are two unit multipliers we can use:
1 meter = 39.37 inches and 1 inch = 0.0254 meters.
Start with the given quantity of 70 meters.Multiply by the unit multiplier 39.37 inches / 1 meter. This will cancel out the meters and leave us with the equivalent value in inches.Multiply the result by the unit multiplier 1 meter / 0.0254 inches. This will cancel out the inches and convert the value back to meters.Simplify the expression to find the final answer.Therefore, 70 meters is equal to 2755.91 inches.
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The difference between three-fifths of a number and 7 is -36
The value of a number such that The difference between three-fifths of that number and 7 is -36 is -145/3.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
Subtraction = Minus of any two or more numbers with each other called subtraction.
Let's say that number is x.
Three-fifth of x ⇒ (3/5)x
The difference of (3/5)x and 7 will be,
(3/5)x - 7 = -36
Add 7 on both sides
(3/5)x = -29
Multiply 5/3 on both sides
x = -29(5/3)
x = -145/3
Hence "The value of a number such that The difference between three-fifths of that number and 7 is -36 is -145/3".
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Working together , 5 friends collected 40 5/8 bags of food for the homeless . On a average how many bags of food did each friend collect ?
Answer This Problem,Please! :D
Type the integer that makes the following subtraction sentence true:
*blank*– 5 = -6
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 7 liters of natural oil for every 5 liters of synthetic oil. If 355 liters of synthetic oil are used, how many liters of petrolyn oil will be made?
every day, mike gets paid from his job. on monday, he gets 19 cents; on tuesday, he gets 14 cents; on wednesday, he gets 20 cents; on thursday, he gets 15 cents; and so on. how much money will he have by the 4th day?
PLEASE HELP 30 points!!!!
what is the slope of this line in the picture?
5 different mixed numbers that add up to 10 with only 3rds and 4ths