At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 15 km/h. How fast (in km/hr) is the distance between the ships changing at 4:00 p.m.? (Round your answer to three decimal places.)
Answers
Distance is the product of speed and time. The rate at which the distance between the ships changes at 4:00 p.m is 27.293 km/h.
What is the distance?Distance is the product of speed and time. It is given by the function,
[tex]\rm Distance = Time \times speed[/tex]
Given at noon the distance between two ships is 170 km. Furter ship A is moving towards the east at a speed of 40 km/h, therefore, the distance covered by Ship A in 4 hours will be,
[tex]\rm \text{Distance covered by Ship A in 4 hours} = 4 \times 40 = 160\ km[/tex]
The distance covered by Ship B in 4 hours will be,
[tex]\rm \text{Distance covered by Ship B in 4 hours} = 4 \times 15= 60\ km[/tex]
At 4 pm the distance between the two ships is the hypotenuse of the red triangle as shown below,
[tex]\rm Hypotenuse = \sqrt{10^2 + 60^2} = \sqrt{100+3600 }= 60.827\ km[/tex]
The rate of change in the distance between the two ships can be written as,
[tex]\rm \text{Rate of change of distance} = \dfrac{170-60.827}{4} = 27.293\ km/h[/tex]
Hence, the rate at which the distance between the ships changes at 4:00 p.m is 27.293 km/h.
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Related Questions
what is the slope of a line (0,2) (-1,-3)
Answers
Answer:
The slope of the line is 5.
Step-by-step explanation:
You need to use the slope formula.
Slope Formula: y2 - y1 / x2 - x1
Your coordinates: (0,2) and (-1, -3)
Do -3 - 2 / -1 - 0
This is because the -3 is your y2 and the 2 is your y1
**Same goes with x but different numbers since it is the x coordinates.**
Now, do -3 - 2 first.
The negatives turn into a positive meaning you have to add the two.
But the bigger number 3 is negative so, your answer should contain a negative.
-3 -2 = -5
Do -1 - 0
This should be an addition problem but contain a negative answer.
-1 -0 = -1
-5/-1 as final.
The negatives cancel, and 5/1 is 5
Your slope is 5.
Answer:
The slope of the line is 5
Step-by-step explanation:
Slope(m) formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
y₂ = -3
y₁ = 2
x₂ = -1
x₁ = 0
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{-3-2}{-1-0} \\\\m=\frac{-5}{-1}\\\\m=5[/tex]
Hope this helps!
(17a ^ 3 * b ^ 2)/(15b ^ 3 * c ^ 2) * (18b ^ 4 * c ^ 3)/(8a ^ 2 * b * c ^ 2) =
Answers
Answer: (51ab^2)/(20c)
STEP
1
:
Equation at the end of step 1
((17•(a3))•(b2)) ((18•(b4))•(c3))
————————————————•————————————————
((15•(b3))•(c2)) ((23a2•b)•c2)
STEP
2
:
Equation at the end of step
2
:
((17•(a3))•(b2)) ((2•32b4)•c3)
————————————————•—————————————
((15•(b3))•(c2)) 23a2bc2
STEP
3
:
(2•32b4c3)
Simplify ——————————
23a2bc2
Dividing exponential expressions :
3.1 b4 divided by b1 = b(4 - 1) = b3
Dividing exponential expressions :
3.2 c3 divided by c2 = c(3 - 2) = c1 = c
Dividing exponents:
3.3 21 divided by 23 = 2(1 - 3) = 2(-2) = 1/22
Equation at the end of step
3
:
((17•(a3))•(b2)) 9b3c
————————————————•————
((15•(b3))•(c2)) 4a2
STEP
4
:
Equation at the end of step
4
:
((17•(a3))•(b2)) 9b3c
————————————————•————
((3•5b3)•c2) 4a2
STEP
5
:
Equation at the end of step
5
:
(17a3 • b2) 9b3c
——————————— • ————
(3•5b3c2) 4a2
STEP
6
:
17a3b2
Simplify —————————
(3•5b3c2)
Dividing exponential expressions :
6.1 b2 divided by b3 = b(2 - 3) = b(-1) = 1/b1 = 1/b
Equation at the end of step
6
:
17a3 9b3c
————— • ————
15bc2 4a2
STEP
7
:
Dividing exponential expressions :
7.1 a3 divided by a2 = a(3 - 2) = a1 = a
Dividing exponential expressions :
7.2 b3 divided by b1 = b(3 - 1) = b2
Dividing exponential expressions :
7.3 c1 divided by c2 = c(1 - 2) = c(-1) = 1/c1 = 1/c
Final result :
51ab2
—————
20c
The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side than from the larger side of the rectangle. The perimeter of the rectangle is equal to 56cm. Find the lengths of each side of the rectangle
Answers
Answer:
smaller side: 10 cmlarger side: 18 cmStep-by-step explanation:
The given relationships can be translated to equations using L and W for the length and width of the rectangle. The distance from the center to the short side is L/2, and the distance from the center to the long side is W/2.
SetupP = 2(L +W) . . . . . formula for the perimeter
56 = 2(L +W) . . . . . the perimeter is 56 cm
L/2 = 4 + W/2 . . . . . distance to short side is 4 cm longer
__
SolutionDividing the first equation by 2 gives ...
28 = L +W
Multiplying the second equation by 2 gives ...
L = 8 + W
Substituting for L in the first equation, we have ...
28 = (8 +W) +W . . . . . . use L=8+W
20 = 2W . . . . . . . . .subtract 8
10 = W . . . . . . . . divide by 2
L = 8 +10 = 18 . . . . . find the length
__
The smaller side is 10 cm; the larger side is 18 cm.
A sample of 36 people yielded the information about their health insurance in the table to the right.
Two people who provided information for the table were selected at random, without replacement. Find the probability that neither had traditional insurance.
Answers
The probability that neither of the two people selected have traditional insurance is 0.33.
What is the probability that neither had traditional insurance?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that neither of the two people selected have traditional insurance = (number of people that chose manage care plan + number of people who dont have any insurance) / total number of people surveryed x [(number of people that chose manage care plan + number of people who dont have any insurance) / total number of people surveryed - 1]
21/36 x 20/35 = 0.33
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How do I find the area of the blue shape? Don't worry about the other colored one.
Answers
Answer:
80 cm²
Step-by-step explanation:
Let's break down the composite shape into two parts. (Image attached)
Let "a" represent the area of the smaller square.Let "b" represent the area of the bigger square⇒ The side length of "a" is 4 cm.
⇒ The side length of "b" is 8 cm.
First, let's find the area of square "a". Keep in mind that the area of a square is the side multiplied by itself.
⇒ (Side)² = A
⇒ (4)² = Area of "a"
⇒ (4)(4) = Area of "a"
⇒ 16 cm² = Area of "a"
Next, find the area of square "b". Keep in mind that the area of a square is the side multiplied by itself.
⇒ (Side)² = A
⇒ (8)² = Area of "b"
⇒ (8)(8) = Area of "b"
⇒ 64 cm² = Area of "b"
Finally, let's sum up the area of square "a" and "b" to find the area of the composite shape.
⇒ Area of composite shape = Area of "a" + Area of "b"
⇒ Area of composite shape = 16 + 64
⇒ Area of composite shape = 80 cm²
Find the surface area
Answers
Answer:
The answer is : 8160 m
Step-by-step explanation:
100% correct
Find the area of the figure.
Answers
answer:
4.5m²
explanation:
1. find area of the circle
A(circle)=πr²
A=π(2.3²)
A=16.62m²
2. find area of the square
the diameter of a circle is twice its radius. when you multiply 2.3 by two, you get 4.6. since the circle reaches to the sides of the square, the diameter is also the length of a side on the square.
A(square)=s²
A=4.6²
A=21.16m²
3. subtract the two areas
to find the area of the shaded sector, we need to subtract the area of the circle from the area of the square.
A(shaded)=21.16-16.62
A=4.54097487m²
(be sure to round as necessary)
--
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The sum of two numbers is 55. Their difference is −1. Find the numbers.
Answers
Step-by-step explanation:
lets say the first is x and the second is y then we can say
x+y=55 ......1
x-y= -1 .......2
by adding 1 with 2 then
x+y+x-y=55+(-1)
==> 2x= 55-1=54
==> x= 54/2=28
if we put x=28 in the 2nd equation then
28-y= -1
==> y=29
Find the area
A. 100
B. 112
C. 224
D. 46
Answers
Answer:
a). 100
Step-by-step explanation:
Finding d₁ and d₂
d₁ = r₁ x 2 = 5 x 2 = 10d₂ = r₂ x 2 = 10 x 2 = 20Finding Area
A = 1/2 x d₁d₂A = 1/2 x 10 x 20A = 1/2 x 200A = 100Two stores sell cherries at different prices per pound.
• Store P sells 3.5 pounds of cherries for $13.30.
• The graph below shows the cost to purchase different weights of cherries at Store Q.
.
Cost (dollars)
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
Phillip needs to purchase 10 pounds of cherries. Which statement below is true?
A Phillip will spend $8.00 less on cherries at Store P than at Store Q.
B Phillip will spend $8.00 more on cherries at Store P than at Store Q.
Phillip will spend $6.00 less on cherries at Store P than at Store Q.
Phillip will spend $6.00 more on cherries at Store P than at Store Q.
Answers
Answer:
can you post the question but more clear please because I didn't understand
Calculate the following measures:
Answers
angle PSQ = 65 (central angle is 130, which means arc PQ is 130, and half of the arc is the inscribed angle)
angle AQS = 35 (congruent to angle SPR)
arc QR = 50 (180-130)
arc RS = 70 (35*2=70)
arc PS = 110 (35*2, making arc SR 70, subtract all arcs from 360 to get 110.
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A truck carries a load of 50 boxes;some are 20kg boxes and the rest are 25kg boxes. if the total weight of all boxes is 1175 kg, how many of each type are there?
Answers
total number of boxes= 50
weight of all the boxes= 1175
some boxes= 25kg
and the rest= 20kg
to find:how many of each type are there.
solution:Let the number of the 20kg boxes = x
and the number of the 25kg boxes = (50-x)
so,
20×(x) + 25×(50-x)
= 1175
20x + 1250 - 25x
= 1175
- 5x = - 75 => x = (-75)/(-5)
= 15
(50–15)
= 35
therefore, 20 kg boxes are 15 and 25 kg boxes are 35.
Help I don't understand this math. Whoever gets the right answer gets Brainlist! :)
Do the graph and table to find the equation that represents the relationship for each of the 2 questions! :)
Answers
Answer:
1) y=x-4
2)y=x+2
Step-by-step explanation:
You can see on the first one y is just 4 less than x
You can see that the second one (graph) has a slope. As by the points, if you increase x by 0.5 you increase y by one.
Thus, y=x+2
Hope this helped! I can't see much of the question :)
Josephine can correct her students' test papers in 9 hours, but if her teacher's assistant helps, it would take them 7 hours. How long, in hours and minutes, would it take the assistant to do it alone? (Write your answer in mixed units. Enter a zero in any unneeded blanks.)
Answers
Using the together rate, it is found that it would take the assistant 31 hours and 30 minutes to do it alone.
What is the together rate?It is the sum of each separate rate.
In this problem, the rates are given as follows:
Josephine: 1/9.Assistant: 1/x.Together: 1/7.Hence:
[tex]\frac{1}{9} + \frac{1}{x} = \frac{1}{7}[/tex]
[tex]\frac{x + 9}{9x} = \frac{1}{7}[/tex]
[tex]9x = 7x + 63[/tex]
2x = 63
x = 31.5.
It would take the assistant 31 hours and 30 minutes to do it alone.
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how long would it take an investment of $25000 to amount to $40 000 at a flat rate of 9.5% per annum?
Answers
Answer:
it will take approximately 6.32 annum(years) to reach $40000
Step-by-step explanation:
9.5% of $25000 = $2375
$40000 - $25000 = $15000 so you need to make an interest of $15000 overall to reach $40000
since you make $2375 each year therefore
$15000 ÷ $2375 will give you the number of years to reach $40000
hence 15000 ÷ 2375 = 6.315
approximately = 6.32 annum(years)
Please help me with this question. Worth 90 points.
Answers
Answer:
3510000
Step-by-step explanation:
Answer:
3510000
Step-by-step explanation:
234,000×6percent
that answer*3percent then substract that 3 percent from . the number before multiplied it by three percent
Madelyn has 4 pairs of red socks, 6 times as many pairs of blue socks 1 as white pairs of socks, and I as many white pairs as red pairs. How many pairs of socks does she have in all? How many socks does Madelyn have?
Answers
The Total Number of socks is 10 in all, bear in mind that there is no blue socks hence it will not add to the total amount of socks
Addition of NumbersNote : 1 pais = 2 socks
Given Data
Red Socks = 4 pairs = 4*2 = 8 socks 6 times as many pairs of blue socks = 0 1 as many pairs of white socks = 2 socksThe statement " 6 times as many pairs of blue socks" is equivalent to no socks, since we have no blue socks, hence 6*0 = 0
Let us find the total socks
= 8+0+2
= 10 socks
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Ama and Kwame shared an amount of money.
If Ama received one third of the money. Which
fraction is for Ama's share?
Answers
2/3
Or two thirds
Explanation:
1-1/3 is 2/3
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Brainliest and 100 points! I need this answer ASAP.
What is the equation of the graphed function?
Enter your answer in the box.
f(x)=______________
Answers
Answer:
f(x) = x² - 4x + 2 or f(x) = (x - 2)²
Step-by-step explanation:
The parabola touches the x-axis at only one pointIf we use y = a(x − h)² + k, we can see from the graph that h = 2 and k = 0This gives us y = a(x − 2)²What is the value of "a"?
We also see that the y-intercept is (0, 4)We can plug it into the equation4 = a(0 - 2)²4a = 4a = 1So, our quadratic equation will be :
y = 1(x - 2)²y = x² - 4x + 2 or y = (x - 2)²Answer:
f(x)=(x-2)^2
Step-by-step explanation:
They deleted my first answer, the one you marked brainliest :/
Promise this is correct, but i don't know how to explain it. The person above me did it wonderfully though. Hope this helped <3, Have a great day!
A demolition crew can do a job in 10 days. Another demolition crew can do the same job in 15 days. How many days would it take the two crews to do the job if they work together?
Answers
Answer:
6 days
Step-by-step explanation:
In one day, one demolition crew:
One day = [tex]\frac{1}{10} x[/tex] with x = the entire job
Other demolition crew:
One day = [tex]\frac{1}{15} x[/tex]
Together, they do it in [tex]\frac{1}{10}x\\[/tex] + [tex]\frac{1}{15}x[/tex] = [tex]\frac{3}{30}x + \frac{2}{30}x = \frac{5}{30}x[/tex] [tex]= \frac{1}{6}x[/tex] in one day
So [tex]\frac{1}{6}x[/tex] x 6 = x
so it takes 6 days to complete the work together.
The volume of a sphere is 9,198.11 ft3. To the nearest foot, what is the radius of the sphere? Use 3.14 for π.
Answers
Step-by-step explanation:
Using the formula
V=4
3πr3
Solving forr
r=(3V
4π)⅓=(3·9.2
4·π)⅓≈1.29978
Moving with a speed of v km/hour, a steam boat travels the distance between the
points A and B, which is 200 km, in t hours.
Find the formula which describes t as a function of v.
Answers
Answer:
t = 200/v
Step-by-step explanation:
The relationship between speed, distance, and time is ...
d = vt
Solving for t gives ...
t = d/v
For a distance of d=200 km, the time in hours will be ...
t = 200/v . . . . . . where v has units of km/hour
Find the distance between the two points in simplest radical form.
(-1,-1) and (5,-9)
Answers
[tex]\sqrt{ { (x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \\ = \sqrt{( {5 - ( - 1)}^{2} + {( - 9 - ( - 1)}^{2} )} \\ \\ = \sqrt{ {(5 + 1)}^{2} + {( - 9 + 1)}^{2} } \\ \\ = \sqrt{ {(6)}^{2} + {( - 8)}^{2} } \\ \\ = \sqrt{36 + 64} \\ \\ = \sqrt{100} \\ \\ = 10 \: units[/tex]
Hope it helpsYou and your friend are standing on the baseline of a
basketball court. You bounce a basketball to your friend, as shown in the diagram. What is the
distance between you and your friend? Round your answer to the nearest tenth.
Answers
The distance between you and your friend rounded to the nearest tenth is 10.7 feet.
How to find the length of a triangle using cosine rule?The distance between you and your friend can be found using cosine rule.
Therefore,
c² =a² + b² - 2ab cos C
Therefore,
let
x = distance between him and his friend
x² = 7² + 6² - 2 × 7 × 6 cos 110°
x² = 49 + 36 - 84 × -0.34202014332
x² = 49 + 36 + 28.7296920394
x² = 113.729692039
x = √113.729692039
x = 10.6644124076
x = 10.7 ft
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A ball is dropped from a helicopter 100m from the ground. As the ball falls, the magnitude of it's associated velocity is
Answers
As the ball falls, the velocity of the ball increases with increase in distance
Velocity and MotionGiven Data
Distance = 100mIt should be noted that when an object falls, it velocity increases from zero to the maximum just before it hits the ground from the initial point of lunch.
Note: For a projectile the ball might reach a zero velocity at maximum height
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d fewer than the quotient of 5 and 2
Answers
Answer:
[tex]\frac{5}{2} - d[/tex]
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Write an equation in standard form of the hyperbola described.
Vertex (10, 0); focus (-26, 0); center (0,0)
Answers
Check the picture below, so the hyperbola looks more or less like the one below, let's find the conjugate axis or namely the "b" component.
[tex]\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=0\\ k=0\\ a=10\\ c=26 \end{cases}\implies \cfrac{(x-0)^2}{10^2}-\cfrac{(y-0)^2}{b^2} \\\\\\ c^2=a^2+b^2\implies 26^2=10^2+b^2\implies 676=100+b^2\implies \underline{576=b^2} \\\\\\ \cfrac{(x-0)^2}{10^2}-\cfrac{(y-0)^2}{576}\implies \boxed{\cfrac{x^2}{100}-\cfrac{y^2}{576}}[/tex]
gggggggggggggggggggggg
Answers
Answer:
12/25
Step-by-step explanation:
lashonda had 4 fiths of 1 acre of land, and 3/5 of the 4 fiths of land is corn.
If you multply 3/5 by 4/5 you will get you answer: 12/25 or 0.48
need help really please someone
Answers
Answer:
2 5/7
Step-by-step explanation:
First we need to make the 4 2/7 top heavy so it is easier to subtract :)
4 2/7 = 3 9/7
Now we can subtract :)
3 9/7 - 1 4/7 = 2 5/7
Have an amazing day!!
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Answer:
The answer is 2 5/7
Step-by-step explanation:
What is Y equals 3X +20
Answers
Or maybe you’re asking what the equation is? Y=mx+b is the slope intercept form.
Answer:
y = 3x + 20
This is an equation, in slope-intercept form, which represents a the placement of a line. The 3 in the equation represents the slope of the line, and the 20 represents the y-intercept.
