Two boats are travelling at 30 miles/hr, the first going north and the second going east. The second crosses the path of the first 10 minutes after the first one was there. At what rate is their distance increasing when the second has gone 10 miles beyond the crossing point
Answers
Answer:
their distance is increasing at the rate of 41.6 miles/hr
Step-by-step explanation:
Given the data in the question;
first we determine the distance travelled by the first boat in 10 min when the second boat was crossing its path;
⇒ ( 30/60 ) × 10 = 5 miles
so as illustrated in the diagram below;
y² = x² + ( x + 5 )²
2y[tex]\frac{dy}{dt}[/tex] = 2x[tex]\frac{dx}{dt}[/tex] + 2(x+5)[tex]\frac{dx}{dt}[/tex]
y[tex]\frac{dy}{dt}[/tex] = ( 2x + 5 ) ][tex]\frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt}[/tex] = [( 2x + 5 )/y ][tex]\frac{dx}{dt}[/tex] ------ let this be equation 1
Now, given that, [tex]\frac{dx}{dt}[/tex] = 30 miles/hr, when x = 10
so
y = √( 10² + 15² ) = √325
so from equation 1
[tex]\frac{dy}{dt}[/tex] = [( 2x + 5 )/y ][tex]\frac{dx}{dt}[/tex]
we substitute
[tex]\frac{dy}{dt}[/tex] = [( 2(10) + 5 ) / √325 ]30
[tex]\frac{dy}{dt}[/tex] = [ 25 / √325 ] × 30
[tex]\frac{dy}{dt}[/tex] = 41.6 miles/hr
Therefore, their distance is increasing at the rate of 41.6 miles/hr
Related Questions
Kevin will be taking six classes next semester (Algebra, World History, Psychology, Political Science, Chemistry, and Art Theory) and would like to know how many different ways he can order his class schedule given that his university offers six time slots for classes each day. Assuming there are no constraints and each class can be taken in any time slot, how many different ways can Kevin order his classes?
Answers
=========================================================
Explanation:
We have 6 slots to fill A,B,C,D,E,F
There are 6 choices for choice A, then 5 choices for slot B, 4 for C, and so on until we reach one choice for slot F. Count down by 1 each time a slot is filled.
Multiply out those values to get: 6*5*4*3*2*1 = 720
For more information, check out the concept of factorials.
---------
Another approach is to use the nPr permutation formula which is
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
where in this case n = 6 and r = 6.
If the gross domestic product is currently 12,443.9 billion dollars and grows by 5 percent, how much will it be next year?
Answers
Answer:
12,448.9
Step-by-step explanation:
i'm sorry if this is wrong
3. A recipe for banana cakes calls for 6 cups of mashed banana to 9 cups of flour. How many cups of
flour per cup of mashed banana does the recipe require?
Answers
3:1
What is 15/4 as a decimal?
Answers
Answer:
3.75
Step-by-step explanation:
Answer: 3.34
REEEEEEEEEEEEEEEEEEEEEEEEE
The persons income increased from 27,000 to 40,000 over the last year. What is the percent change
Answers
Answer:
32.5
Step-by-step explanation:
Multiply the two fractions. Simplify your answer. 1/2 x 4/7
Answers
Answer:
2/7
Step-by-step explanation:
The solution of fractions after multiplying the two fractions would be [tex]\dfrac{2}{7}[/tex].
Given that,
Multiply the two fractions,
[tex]\dfrac{1}{2} \times \dfrac{4}{7}[/tex]
Used the concept of multiplication which states that,
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Now, simplify the fractions by multiplying,
[tex]\dfrac{1}{2} \times \dfrac{4}{7}[/tex]
[tex]\dfrac{4}{14}[/tex]
Simplify for the simplest form,
[tex]\dfrac{2}{7}[/tex]
So, the solution is [tex]\dfrac{2}{7}[/tex].
To learn more about multiplication visit:
https://brainly.com/question/10873737
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the students in Jake's class , 6 have visited a zoo and 6 have visited a factory 3 students have visited both a zoo and a factory . How many students have visited a zoo but not a factory ?
Answers
Answer:
3
Step-by-step explanation:
6 have visited a zoo.
6 have visited a factory.
3 visited both.
Of the 6 who visited a zoo, 3 also visited a factory.
Of the 6 who visited a factory, 3 also visited a zoo.
Here is the list of students:
3 visited a zoo but not a factory.
3 visited a factory but not a zoo.
3 visited both.
Answer: 3
Which graph represents y = –2x?
Answers
Answer:
B, the second one down on the first page
Step-by-step explanation:
hope this helps! :D
brainliest is immensely appreciated!! <3
Plz help me NOW and I will mark you brainliest
Answers
Answer:
Translate from words to mathematical equation.
"n is m% of what?"
m% = m/100
what = a variable ... "x". for example.
"is" means "="
"of" means multiply
n = (m/100)•x
If G&M Foods issues a $1,000 bond with an interest rate of 3.5 percent and a maturity date of January 1, 2025, G&M is agreeing to pay the bondholder __________ interest each year until January 1, 2025, when it must repay the full $1,000.
Answers
G&M is agreeing to pay the bondholder the interest amount of $35 each year until January 1, 2025.
Using this formula
Interest=Bond amount× Interest rate
Where:
Bond amount=$1,000
Interest rate=3.5% or 0.035
Let plug in the formula
Interest=$1,000×0.035
Interest=$35 each year
Inconclusion G&M is agreeing to pay the bondholder the interest amount of $35 each year until January 1, 2025.
Learn more about interest rate here:https://brainly.com/question/25545513
Which represents the RANGE of the following relation? {(-6, 5), (-4, 3), (-1, 0), (4, 3)}
Answers
Answer:
5, 3, 0, 3 are all the ranges! Hope this helps
Step-by-step explanation:
Ranges are on the right, domains are on the left
Maybe Audrey waited 6 pounds 14 in ounces at birth convert her weight to ounces
Answers
Answer:
110 ounces :))
Step-by-step explanation:
A right triangle has side lengths of 5 inches, 12 inches, and 13 inches. The triangle will be rotated 180° about a point.
What is the length of the longest side of the triangle after the rotation? Enter the answer in the box?
Answers
13in will be the longest like before .
Refer to the attachment for more observation.
The length of the longest side of the triangle after the rotation is 13 inches.
What is Right Angle?It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.
Ancient geometry defined a right angle as the intersection of two straight, or right, lines in relation to dimensional axes.
Given:
A right triangle has side lengths of 5 inches, 12 inches, and 13 inches.
As, we know that the longest side is the Hypotenuse which is 13 inches and the base is 12 inches and perpendicular is 5 inches.
After 180° rotation only the base and perpendicular change the longest side still remain the same.
Learn more about Right Angle here:
https://brainly.com/question/7116550
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2 1/12 divided 2 5/8 fractions
Answers
Answer: 50/63 or 0.793650
Step-by-step explanation:
When rolling a die what is probability of rolling a one
Answers
Answer:
1/6
Step-by-step explanation:
6 sides. 1 face with number 1. 1/6
6/7 divided by 12/14 please show the work
Answers
Answer:
1
Step-by-step explanation:
When dividing one fraction by another, the best way to solve it is to multiply by the reciprocal. The reciprocal just flipping the fraction over. So you would leave the 6/7 and the multiply by 14/12( because you are multiplying by the reciprocal). When you do that, you then can just multiply the top and the bottom to form one fraction. The numerator is 6*14 = 84, and the denominator is 7*14 = 84. So you are left with 84/84 which anything over itself is equal to one.
Hope this helps!
When two numbers are multiplied to get product, each number is called a(n)?
1.factor
2.substitute
Answers
Answer:
Each number is called a factor
Step-by-step explanation:
The multiplication of two numbers is equivalent to adding as many copies of one of them
You buy a serving spoon for $4.05 and a bread knife for $3.99. What is the total cost of your purchase?
A. $8.94
B. $7.04
C. $7.94
D. $8.04
Correct answer on gradpoint is D: $8.04
Answers
Answer: d. $8.04
Step-by-step explanation:
$4.05 + $3.99 = $8.04
Answer:
d. 8.04
Step-by-step explanation:
4.05+3.99=8.04
Compound interest compounded quarterly is given every ______ months. *
1 point
1
3
6
Answers
Answer:
3 months
a quarter is a period of three months
Step-by-step explanation:
A container 2/3 gallon of apple juice. If four people from the cross-country Tracy team share the juice equally how much juice will each team member get?
Answers
Answer:
1/6 gallon
Step-by-step explanation:
Total juice = 2/3 of container
Total people = 4
Juice for 1 people = 2/3/(4)
=> 2/3 × 1/4
=> 1/3 × 1/2
=> 1/6
Marco wants to buy a new smartphone that costs $495, with some additional accessories. He has already saved $75. Write and solve an inequality to find the least amount of money, m, that Marco still needs to save before he can buy the smartphone and accessories. Enter your answer in the box.
Answers
Answer:
495-75=m m=420
Step-by-step explanation:
He needs to save 495 dollars, and hes already saved 75
and needs to find out how much more he needs to save to have 495 dollars
To do this, take 495 and subtract 75. This is how we get the inequality
495-75=m
From here it is simple, just subtract 75 from 495 to get 420
Add: 34.05 + 9.068
Thank you in advance
Answers
please help me please
Answers
[tex] \frac{76}{90} [/tex]
-_-
Pls help and show ur work ASAP I’ll add extra points
Answers
Answer:
Slope: 7/5 , Y-int: 1/5
Step-by-step explanation:
To find the slope, lets use the points (-3,-4) and (2,3)
The slope formula is (y2-y1)/(x2-x1) so we will plug in the numbers.
(3-(-4))/(2-(-3))=7/5. 7/5 is the slope (you can also do rise over run)
We find the y-int in many ways but i will show two.
We can make an equation in point-slope form. The formula is: y-y1=m(x-x1) and we use the point (-3,-4).
y-(-4)=7/5(x-(-3))
y+4=7/5x+21/5 (then move the 4 to the other side)
y=7/5x+1/5
The 1/5 is our y-int since we now have it in slope intercept form!
The other method we can use is putting it into slope intercept form first and using (-3,-4) to find the missing variable.
Slope intercept form is y=mx+b, let m be slope, b is y int, and (x,y) is our point
-4=(7/5)(-3)+b
-4=-21/5+b (move -15/7 to other side)
1/5=b !
we get the same answer I hope this helps sorry its long
Find the 53" term of the following arithmetic sequence.
3, 11, 19, 27, ...
Answers
Answer:
419
Step-by-step explanation:
a=3
d=11-3=8
[tex]a_{n}=a+(n-1)d\\n=53\\a_{53}=3+(53-1)*8\\=3+52*8\\=3+416\\=419[/tex]
Which variable expression represent the word phrase? The sum of 10 and the product of 7 and a number
Answers
Answer:
Step-by-step explanation:
y = 7x + 10
slope-intercept form of a linear equation
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $2.25 and each soda costs $1.50. At the end of the night, you made a total of $225.75. You sold a total of 126 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. What equations did you use to solve this? How many hot dogs were sold and how many sodas were sold?
A.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas.
B.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 77 hot dogs and 49 sodas.
C.
2.25x + 1.50y = 126 and x + y = 225.75 : -283.5 hot dogs and 509.25 sodas.
D.
There is not enough information
Answers
The equations and the number of hotdogs and sodas sold are: x+ y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas.
Two equations can be derived from this question:
2.25x + 1.50y = 225.75 equation 1
x + y = 126 equation 2
Where:
x = number of hotdogs sold
y = number of soda sold
In order to determine the value of y, multiply equation 2 by 2.25
2.25x + 2.25y = 283.50 equation 3
Subtract equation 1 from 3
57.75 = 0.75y
y = 77
Substitute for y in equation 2
x + 77 = 126
x = 49
To learn more about simultaneous equations, please check: brainly.com/question/23589883
Answer:
The correct answer is A) x + y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas
Step-by-step explanation:
hope this helps
Find the Value for X,Y and z using Gauss-Jordan Inversion method
2X+3Y=4
X+2Y=2
Answers
Answer:
x = 2 y = 0
Step-by-step explanation:
Answer:
Step-by-step explanation:
Joe ran 2 miles in 16 minutes. At this rate how long did it take him to run 5 miles.
Answers
Answer:
40min
Step-by-step explanation:
Since the ratio is 2:16, we want simplify. both 2 and 16 are dividable by 2.
2 / 2 = 1
16 / 2 = 8.
Now we can use the ratio 1 mile per 8 min. We want the rate of how many min to miles, so we'd multiply 5 by 8 which equals 40.
Therefore it takes him 40min to run 5 miles.
Hope this helps!
i need help i don’t understand this i’m a freshman in highschool doing a mi
Answers
Hope that helps :)
