The boat speeds of 15 km/h and 18 km/h, directions, and the time of travel of 45 minutes gives the angle between their paths as approximately 68°.
How can the angle between the paths of the boats be found?The given parameters are;
Direction of the first boat = Northeast
Speed of the first boat = 15 km/h
Direction of the second boat = Northwest
Speed of the second boat = 18 km/h
Distance between the boats after 45 minutes = 14.0 km.
45 minutes = 0.75 × 1 hour
Distance traveled by the first boat in 45 minutes, d1, is therefore;
d1 = 15 km/h × 0.75 hr = 11.25 km
For the second boat, we have;
d2 = 18 km/h × 0.75 hr = 13.5 km
Using cosine rule, we have;
14² = 11.25² + 13.5² - 2 × 11.25 × 13.5 × cos(A)
Where A is the angle between the paths of the two boats.
Which gives;
[tex]cos(A) = \frac{361}{972} [/tex]
[tex] A= \mathbf{ arccos\left(\frac{361}{972} \right) }\approx 68^\circ [/tex]
The angle between their paths to the nearest degree, A ≈ 68°Learn more about the rule of cosines here:
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[tex] \sqrt{ x} = \sqrt{2} + 1 \: then \: x = [/tex]
helpppp asap
edit:help guys i have examm
Answer:
3+2√2Step-by-step explanation:
Given the expression
√x = √2 + 1
To get x, we will have to square both sides
(√x)² = (√2 + 1)²
x = (√2 + 1)(√2 + 1)
x = √4+√2+√2+1
x = 2+2√2+1
x = 3+2√2
Hence the value of x is 3+2√2
Marco paid $12 for 3jump ropes. If each jump rope costs the same amount, how much does 1 jump rope cost? Write and solve an equation.
Answer:
each jump rope costs 4 dollars
12÷3=4
Answer:
$4
Step-by-step explanation:
Divide: 12 divided by 3=4
Hope this helped!! :)
Stay safe and have a wonderful day/night!!!!!
Brainliest?!?!
if I have 100 baskets and I have 400 hundred apples how many apples will go into each basket
Answer: 4 apples will go into each basket if you want all the baskets to be filled with an equal amount.
Step-by-step explanation:
100x=400
dividing through by 100 we get
x=4
Which equation correctly uses the law of cosines to solve for the length s?
Answer: Choice D
s^2 = 9^2 + 10^2 - 2(9)(10)cos(100)
==========================================================
Explanation:
Consider the pythaorean theorem
a^2 + b^2 = c^2
which is the same as saying
c^2 = a^2 + b^2
If we tack on "-2ab*cos(C)", then we end up with
c^2 = a^2 + b^2 - 2ab*cos(C)
which is one form of the law of cosines. The side c is opposite angle C, and the two are on opposite sides of the equation. The 'a's and 'b's are on the right side with the angle C.
Note if C = 90 degrees, then cos(C) = cos(90) = 0 which means the whole "-2ab*cos(C)" term goes to 0 and we'd be left with the pythagorean theorem again.
In this case, we replace c with s, replace 'a' with 9, replace b with 10, and C with 100.
Answer:
Option (4)
Step-by-step explanation:
Cosine rule states,
(UT)² = (SU)² + (ST)² - 2(SU)(ST)cos(∠UST)
Here, UT is the opposite side of angle UST and two sides SU and ST are the adjacent sides.
∠UST is the included angle between SU and ST.
By this formula,
s² = 9² + 10² - 2(9)(10)cos(100°)
Therefore, Option (4) will be the answer.
Find the area of the shaded segment of the circle
Answer:
≈ 0.8 m²
Step-by-step explanation:
________________________________________________
FORMULA FOR FINDING AREA OF SEGMENT :-
[tex]A = r^{2} [\frac{\alpha }{360} \times \pi - (\sin \frac{\alpha }{2} \times \cos \frac{\alpha }{2} )][/tex]
Where :-
A = Area of the segmentr = Radius of the circleα (alpha) = Angle subtended by arc at the center________________________________________________
Angle subtended by the minor arc at the center = 360° - 300° = 60°
Radius of the circle = 3 m
Area of the segment =
[tex]3^{2} [ \frac{60}{360} \times \pi - (\sin \frac{60}{2} \times \cos \frac{60}{2})][/tex]
[tex]= 9[\frac{1}{6} \times \pi - (\sin 30 \times \cos 30)][/tex]
[tex]= 9[\frac{\pi }{6} - (\frac{1}{2} \times \frac{\sqrt{3} }{2} )][/tex]
[tex]= 9[\frac{\pi }{6} - \frac{\sqrt{3} }{4} ][/tex]
[tex]= 9[\frac{2\pi - 3\sqrt{3} }{12} ][/tex]
[tex]= \frac{9}{12} \times (2\pi - 3\sqrt{3})[/tex]
( Assuming √3 = 1.73 & π = 3.14 )
[tex]= \frac{3}{4} \times (6.28 - 5.19)[/tex]
[tex]= 0.75 \times 1.09[/tex]
[tex]= 0.8175[/tex]
∴ Area of the segment ≈ 0.8 m² (rounding to the nearest tenth)
Which statement is true for brainliest
Answer:
<A≅<Z
Step-by-step explanation:
Hope This Helps!
A jungle has 578 monkeys.
It also has 153 birds.
How many more monkeys than birds are there?
Monkeys
X Х $ ?
Answer:
425 monkeys
Step-by-step explanation:
Subtract the number of birds from the number of monkeys to find the difference between the two.
Find the equation of the line that has a y-intercept of 1 and is perpendicular to the graph of the line 2x + y = 4.
Answer:
y = 1/2x + 1
Step-by-step explanation:
To be perpendicular to a line is to have the product of the slopes be -1. First, we have to put 2x + y = 4 into slope-intercept form to find the slope of the line. We do this by subtracting 2x on both sides to get that y = -2x + 4. Now, the number that multiplied by -2 is equal to -1 is 1/2, so that is the slope of our line. We can substitute these values into the slope-point equation to find the equation. We would get that y - 1 = 1/2 * (x - 0). This simplifies to y = 1/2x + 1.
Which expression can be used to find the volume of the sphere? A sphere with radius 9 inches. V = four-thirds pi r squared = four-thirds (3.14) (9) squared V = four-thirds pi r cubed = four-thirds (3.14) (9) cubed V = four-thirds pi r cubed = four-thirds (3.14) (18) cubed V = four-thirds pi r cubed = four-thirds (3.14) (18) cubed Mark this and retur
Answer:
V = four-thirds pi r cubed = four-thirds (3.14) (9) cubed
Step-by-step explanation:
Ethan is designing a new board game, and is trying to figure out all the possible
outcomes. How many different possible outcomes are there if he spins a spinner with
three equal-sized sections labeled Walk, Run, Stop and rolls a fair die in the shape of
a cube that has six sides labeled 1 to 6?
Answer:
18
Step-by-step explanation:
3x6
Simplify: i^69
Please help fast
Answer: it's just "i"
Step-by-step explanation:
What is the slope of the linear equation represented by the table. NEEDED PLSS
Answer:28/4
Step-by-step explanation:
Change of y over the change of x.
Y is +28
X is +4
find x or solve for x
Answer:
[tex] \huge \boxed{ \boxed{x = 8}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:rectangleequationPEMDAStips and formulas:every angle of a rectangle is 90°let's solve:[tex]step - 1 : define \\ 12x - 6 = 90[/tex]
[tex]step - 2 : solve[/tex]
[tex] \tt add \: 6 \: to \: both \: sides : \\ \tt12x - 6 + 6 = 90 + 6 \\ \tt 12x = 96[/tex][tex] \tt divide \: both \: sides \: by \: 12 : \\ \tt \frac{12x}{12} = \frac{96}{12} \\ \tt \therefore x = 8[/tex]Fallon collected data for her favorite TV show. She recorded the number of viewers and the number of weeks since the show premiered. With the data in hand, she created this scatter plot and drew a line of best fit
What are the slope and the y-intercept of the line of best fit?
Answer:
On the best-fit line for the points {(2,3) (5,7) (1,2) (4,8)}, one point is (0.5,1.25) and another is the y-intercept (0,0.5). Use the formula for the slope of a line, m = (y2 - y1)/(x2 - x1), to find the slope
Step-by-step explanation:
Hope it help
Mark me as brainliest
Answer:
Slope is (6, 10) and (0, 12). The y-intercept is 12.
Step-by-step explanation:
I had this question on Edmentum.
how many 1/5s are in 20?
Answer:
There are 4
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Solve -3.5=x-4 for x using the multiplication propertiy of equality
Answer:
Hello! :) have a good day!
X= 0.5
Answer:
x = 0.5
Step-by-step explanation:
Please help with this it is due today
Answer:
24
Step-by-step explanation:
how can you tell the difference between circumcenter and incenter?
You have 49 dimes and quarters. You have 7 more quarters than dimes.How much money you have in quarters and dimes
Answer:
Step-by-step explanation:
Because you have seven more quarters than dimes, you have 28 quarters, and 21 dimes, which equals 49 dimes and quarters.
You have $9.10
I hope this helps!
Thanks!
A home meal delivery business delivers 34.5 pounds of food each day. How many ounces of food will they deliver in 4 days? (1 lb.= 16 oz) fill in the blank they will deliver ______ ounces of food in 4 days.
Answer:
They will deliver 2208 ounces of food in 4 days.
Step-by-step explanation:
Multiply 34.5 by 16 to get the ounces and got 552. Then multiply 552 by 4 and you'll get the answer.
:))
Jack invested $7,600 in an account paying an interest rate of 6\tfrac{1}{4}6 4 1 % compounded continuously. John invested $7,600 in an account paying an interest rate of 6\tfrac{3}{4}6 4 3 % compounded quarterly. After 19 years, how much more money would John have in his account than Jack, to the nearest dollar?
Answer: John would have $1371.33 more in his account than Jack.
Step-by-step explanation:
Formula to calculate amount after t years if compounded continuously:
[tex]A=Pe^{rt}[/tex]
Formula to calculate amount after t years if compounded quarterly:
[tex]A=P(1+\dfrac{r}{4})^{4t}[/tex]
, where P= Principal amount, r= rate of interest.
Given: P= $7,600
t=19 years
For Jack, [tex]r=6\dfrac{1}{4}\%=\dfrac{25}{4}\%=\dfrac{25}{400}=0.0625[/tex]
For John, [tex]r=6\dfrac{3}{4}\%=\dfrac{27}{4}\%=\dfrac{27}{400}=0.0675[/tex]
Amount in Jack's account after 19 years= [tex]7600e^{0.0625(19)}[/tex]
[tex]=7600e^{1.1875}\\\\=7600(3.27887376794)\\\\\approx\$24,919.44[/tex]
Amount in John's account after 19 years= [tex]7600e^{0.0675(19)}[/tex]
[tex]=7600(1+0.0675)^{19}\\\\=7600(3.45931245291)\\\\\approx\$26,290.77[/tex]
Difference = 26290.77-24919.44 = $ 1,371.33
John would have $1371.33 more in his account than Jack.
Answer:668
Step-by-step explanation: I just did it.
can someone help me how to calculate 15% of R200
Answer:
30
Step-by-step explanation:
formula :15÷100×200
will mark brainliest
(2x+1)+(3x-5)=5x-4 you just have to try some of them out and see which ones work
GIVING BRAINLIEST IM TIMEDDDD
Answer:its the 2nd one
Step-by-step explanation: i remeber because i took this quiz
7 The table below shows the population of
different regions in 1985 and in 2005.
Place
Entire world
China
Population in Population
1985
in 2005
4.9 X 109 6.4 X 109
1.1 X 109 1.3 X 109
7.6 x 108 1.1 x 10
2.4 x 108 3.0 X 108
8.9 X 106 7.2 X 106
India
United States
Bulgaria
a Determine the ratio of the population
of the entire world to that of China in
2005, giving your answer to the nearest
integer
Answer:
In this table the graphic shows that...
Step-by-step explanation:
...the population increased 5,9 x 10 6.
The ratio is 64:13
What is ratio?Ratio is the comparison of two quantities which is obtained by dividing the first quantity by the other. If a and b are two quantities of the same kind and with the same units, such that b is not equal to 0, then the quotient a/b is called the ratio between a and b. Ratios are expressed using the symbol of the colon (:). This means that ratio a/b has no unit and it can be written as a : b
Given data:
Population of china in 2005 =1.3*10^9
population of entire world in 2005 = 6.4*10^9
Now,
ratio= 6.4*10^9/ 1.3*10^9
ratio= 64/13 or 64:13
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8n + ? = 0
A.) - 8/n
B.) 8/n
C.) 1/8n
D.)-8n
D is the correct answer:)
Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 in the account by the end of the summer. He withdraws $35 each week for food, clothes and movie tickets. How many weeks can Keith withdraw money from his account?
6x² + 4x / 6x² + 13x + 6 ( please show work )
Answer: 6x+4x +13x+6 equal
what is the factored form of 4(3x + 12) + 4?
Answer:
12x + 52
Step-by-step explanation:
Distribute.
(4 • 3x + 4 • 12) + 4
12x + 48 + 4
12x + 52
Hangi sayının 10 eksiğinin 7 katı 70'tir ?