Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
Let's think of the boat and wind as vectors:
Boat Vector --> [tex]\langle28cos36^\circ,28sin36^\circ\rangle[/tex]
Wind Vector --> [tex]\langle10cos22^\circ,10sin22^\circ\rangle[/tex]
Now, let's add the vectors:
[tex]\langle28cos36^\circ+10cos22^\circ,28sin36^\circ+10sin22^\circ\rangle[/tex]
Find the magnitude (the true velocity):
[tex]\sqrt{(28cos36^\circ+10cos22^\circ)^2+(28sin36^\circ+10sin22^\circ)}\approx37.78\approx38[/tex]
Find the direction (angle):
[tex]\theta=tan^{-1}(\frac{28sin36^\circ+10sin22^\circ}{28cos36^\circ+10cos22^\circ})\approx32.32^\circ\approx32^\circ[/tex]
Thus, D is the best answer
Problem 2
Recall that the angle between two vectors is [tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})[/tex] where [tex]u\cdot v[/tex] is the dot product of the vectors and [tex]||u||*||v||[/tex] is the product of each vector's magnitude:
[tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})\\\\\theta=cos^{-1}(\frac{\langle-82,47\rangle\cdot\langle92,80\rangle}{\sqrt{(-82)^2+(47)^2}*\sqrt{(92)^2+(80)^2}})\\\\\theta=cos^{-1}(\frac{(-82)(92)+(47)(80)}{\sqrt{6724+2209}*\sqrt{8464+6400}})\\\\\theta=cos^{-1}(\frac{(-7544)+3760}{\sqrt{8933}*\sqrt{14864}})\\\\\theta=cos^{-1}(\frac{-3784}{\sqrt{132780112}})\\\\\theta\approx109.17^\circ\approx109^\circ[/tex]
Therefore, C is the best answer
Related Questions
bord ke aussionas 10 feet of string to make 15 beaded bracelets. She needs binches of string for each Pracelde. Does she have enough string to make all the bracelets? Explain. (1 foot 12 inches).
hi can u show me the math but not in the word form thanks
Answers
Answer:
10x12=120 inches
Step-by-step explanation:
multiply 12 inches by 10 feet
Bernie bought five 30 L buckets of lawn fertilizer. How much fertilizer did he have in all?
Answers
Answer:
5 × 30 L = 150 L
______________
A right triangle has side lengths that are consecutive integers and a perimeter of 12 feet. What are the
angles of the triangle?
А. 30°, 60° and 90°
B. 33.47°, 56.53° and 90°
C. 36.87°, 53.13° and 90°
D. 40.16°, 49.84° and 90°
Answers
Answer:
option c
Step-by-step explanation:
Let the sides of the right angled triangle = x , (x +1) , (x +2)
Perimeter = 12 feet
x + x +1 + x + 2 = 12
x +x + x + 1+2 = 12
Combine like terms
3x+ 3 = 12
Subtract 3 from both sides
3x = 12- 3
3x = 9
Divide both sides by 3
x = 9/3
x = 3
x + 1 = 3 + 1 = 4
x + 2 = 3 + 2 = 5
The sides of the triangle are 3 , 4 ,5
The biggest side will be the hypotenuse.
So, hypotenuse = 5 ft. other legs are 3 and 4
[tex]\text {Sin \ $\theta$ = $\dfrac{opposite \ side \ of \ \theta}{hypotenuse}$ } \\\\\\ = \dfrac{4}{5}\\\\\\Sin \ \theta = 0.8\\\\\theta = Sin^{-1} \ 0.8\\\\\theta = 53.13 \ ^\circ[/tex]
another angle = 180 - [ 90 + 53.13]
= 180 - 143.13
= 36.87°
Pls show work thank you!!!
Answers
[tex]|-16-x|=0\\\\\implies -16-x = 0\\\\\implies x = -16[/tex]
Simplify cos^4x+(2cos^2x)(sin^2x)+sin^4x
Answers
Answer:
cos4(x)+2cos2(x)sin2(x)+sin4(x)
Step-by-step explanation:
1ST TO ANSWER GETS BRAINLIEST
What is the total area of the patio, walkway, and garden?
Answers
Answer:
82 ft²
Step-by-step explanation:
Find the 70th term of the following arithmetic sequence.
17, 20, 23, 26,
Answers
Answer:
Since it starts at 17 and is increasing by 3 each time, the 70th term will be:
17 + 3(70) =
17 + 210 =
227
In conclusion, 227 would be the 70th term in the sequence.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Step-by-step explanation:
Tn = a + (n - 1)d
n = 70, a = 17, d = > 20 - 17 => 3
T_70 = 17 + (70 - 1)3
T_70 = 17 + 69•3
T_70 = 17 + 207
T_70 = 224
The Pythagorean theorem states that a² + b² = c² for a right triangle with leg lengths, a and b, and hypotenuse length, c.
The hypotenuse of a right triangle is 5 units long and has the points (3, 0) and (0, 4) as end points. One of the legs has length 3.
Use the Point and Segment tools to draw a right triangle at demonstrates the other leg length is 4.
Answers
Answer:
Step-by-step explanation:
Draw the third point at (0, 0). This would make the distance from (3,0) to (0,0) equal to 3, and the distance from (0,4) to (0,0) be 4.
If ((x) = x2+ 3x - 2, find f(-2).
Answers
f(x) = x² + 3x - 2
f(-2) = (-2)² + 3*(2) - 2 = 4 - 6 - 2 = - 4
Convert the unit of length. Round the answer to one decimal place if necessary. 180 cm ≈ _____ ft
180 cm ≈ _____ft ?
Answers
Answer:
that would be the circumference of the circle
= 2 pi r
= 2 * pi * 2
= 6.28 feet to 2 DP's.
Step-by-step explanation:
Answer:
6 ft
Step-by-step explanation:
Convert the unit of length. Round the answer to one decimal place if necessary. 180 cm ≈ _____ ft
[tex]Ft=\frac{cm}{30.48}\\\\Ft=\frac{180}{30.48}\\\\Ft=5.90551181\\\\Ft\approx 6[/tex]
180 cm ≈ 6 ft
Hope this helps!
Remington is installing a fence around his
rectangular yard. His yard is 20 feet long
by 45 feet wide. If the fencing he picked
out costs $25 per foot, how much money
will be spent on the fence?
Answers
Answer:
$3,250
Step-by-step explanation:
Find the perimeter of the yard ( the distance around the yard).
A rectangle has two sides of each dimension.
The perimeter is 20 + 20 + 45 + 45 = 130 feet.
Now multiply the total feet by the cost per foot:
130 feet x 25 per foot = $3,250 total.
where does leprechaun come from
Answers
Answer:
A leprechaun (Irish: leipreachán/luchorpán) is a diminutive supernatural being in Irish folklore, classed by some as a type of solitary fairy. They are usually depicted as little bearded men, wearing a coat and hat, who partake in mischief. In later times, they have been depicted as shoe-makers who have a hidden pot of gold at the end of the rainbow.
Answer:
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Answer:
x = 6
Step-by-step explanation:
We know that the angles in a triangle add to 180°, so we can add the angles shown in this triangle together, make them equal to 180° and solve for x.
90° + (4x + 3)° + 63° = 180°
90° + 4x° + 3° + 63° = 180°
4x° + 156° = 180°
4x° = 24°
x = 6
So, x = 6. Hopefully, this helped! If you have any further questions, let me know.
how do you write a solution set when there are infinite solutions
Answers
Answer:
it depends
Step-by-step explanation:
sometimes a teacher will accept "there are infinite solutions" but if you cant you may need to do something else(this applies to basically everything)
for an example lets use x=1
(1,+infinity)
or
(1,-infinity)
(this is being graphed.) (this may not apply to everything)
i hope this helps
Which of the binomials below is a factor of this expression?
121A^2 - 64B^2
A. 121A + 8B
B. 11A + 8B
C. 121A + 32B
D. 11A + 32B
Answers
Answer: 11A+8B
Step-by-step explanation:
For 1-6, classify each triangle by its sides and then by its angle
Answers
Answer:
1) right angled triangle
2) isosceles triangle
3) equilateral triangle
4) scalen triangle
5) isosceles triangle
6) right angled triangle
. There is 40% decresed in price on a sale. It is futher decresed by 5% find the total decreased percentage
Answers
Let x be the original price of the object.
After the 40% discount, the price of the object now becomes;
x-0.4x=0.6x
0.6x is our new price after the first discount.
Now if we want to find the price after the second discount, (5%)
That would come off to be;
0.6x-0.6(0.05)x=0.6x-0.03x=0.57x
Our last price is 0.57x
If you notice, there was a 43% discount in total, as it goes to 57% of its original price.
This is very non intuitive for some people, as they may think there will be a 45% discount.
Which expression represents the product of b and 18?
A. 18(b-18)
B. 18+b
C. 18/b
D. 18b
Answers
Answer:
You're answer is D.18b
Hey there!
The product of a number and 18 means you multiply that number times 18; the result is called the product.
When we multiply a number times a variable, we always write the number before the variable.
For example, we multiply 4 times d, and the result is 4d.
Let's check the options and see if we can spot something like "5a"
The first option: we multiply 18 times the difference of b and 18.
The second option: we add 18 and b
The third option: we divide 18 by b
The fourth option: we multiply 18 times b (That's the right option! We did it :)
Hence, the answer is
[tex]\boxed{\boxed{\bold{18b}}}[/tex]
Hope everything is clear.
Let me know if you have any other questions; if so, please comment.
#LearningDoesn'tEnd
#LearningIsFun
[tex]\rule{200}{2}[/tex]
A company promises to release a new smartphone model every month. Each model's battery life will be 5% longer than the previous model's. If the current model's battery life is 663.0 minutes, what will the latest model's battery life be 7 months from now?
Answers
Answer:
895.05
Step-by-step explanation:
5% of 663 is 33.15, so times 33.15 by the 7 months and the answer to that is 232.05 then add that to the current battier life.
The answer is 895.05
Find the difference of 7 2/3 and 6 3/7
Answers
Answer:
Fraction answer (about):
1 1/4
Decimal answer (about):
1.24
Step-by-step explanation:
7 2/3 - 6 3/7 =
1.2380952381
1.2380952381 = about 1.24
The difference between 7 2/3 and 6 3/7 = 1.24
1.24 in fraction form is about 1 1/4
Have a great rest of your day
#TheWizzer
Answer:26/21
Step-by-step explanation:
What is the slope of the line with equation y-3=-1/2 (x-2)?
Answers
Hello!
This equation is written in Point-Slope Form (y-y₁=m(x-x₁)
Where
y₁=y-coordinate of the point
m=slope
x₁=x-coordinate of the point
In this case, the slope is
[tex]\boxed{\boxed{\bold{\frac{1}{2}}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
:-)
Answer:
C) 1/2
Step-by-step explanation:
woof woof
Nine cards are numbered from 1 to 9 and placed in a box. One card is selected at random and not replaced. Another card is randomly selected. What is the probability of selecting
two prime numbers?
Answers
Answer: 1/6
Step-by-step explanation: There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.
The square root of the cube of 4 is equal to
3 or 4 or 16 or 8 or 2
Answers
Answer:
Step-by-step explanation: 1.587401052
Answer:
8
Step-by-step explanation:
this means
[tex] \sqrt{ {4}^{3} } [/tex]
4³ = 4×4×4 = 64
the square root of 64 is 8.
SU is a midsegment of AQRT.
If OR = z-40 and SU = z - 49, what is the value of z?
I just need one example to understand this because forgot how to do it
Answers
Answer:
z = 58
Step-by-step explanation:
Since SU is a midsegment of QRT, the length of SU is one-half the length of RQ.
[tex] \frac{1}{2} (z - 40) = z - 49[/tex]
[tex]z - 40 = 2z - 98[/tex]
[tex]z = 58[/tex]
Find x on the triangle geometry please help
Answers
Answer:
[tex]\sf x=7\sqrt{6}[/tex]
Step-by-step explanation:
As the base angles of the triangle are the same, then the legs of the right triangle are also equal. Therefore, we can use Pythagoras' Theorem to calculate x.
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse of the right triangle)
Given:
a = 7√3b = 7√3c = xSubstituting the given values into the formula:
[tex]\sf \implies (7\sqrt{3})^2+(7\sqrt{3})^2=x^2[/tex]
[tex]\sf \implies147+147=x^2[/tex]
[tex]\sf \implies x^2=294[/tex]
[tex]\sf \implies x=\sqrt{294}[/tex]
[tex]\sf \implies x=\sqrt{49 \cdot 6}[/tex]
[tex]\sf \implies x=\sqrt{49}\sqrt{6}[/tex]
[tex]\sf \implies x=7\sqrt{6}[/tex]
[tex]\\ \rm\Rrightarrow cos\theta=\dfrac{Base}{Hypotenuse}[/tex]
[tex]\\ \rm\Rrightarrow cos45=\dfrac{7\sqrt{3}}{x}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{\sqrt{2}}=\dfrac{7\sqrt{3}}{x}[/tex]
[tex]\\ \rm\Rrightarrow x=7\sqrt{3}\sqrt{2}[/tex]
[tex]\\ \rm\Rrightarrow x=7\sqrt{6}[/tex]
Three and one fifth of 1 1/2 is what number?
Answers
Answer:
3 1/5 = 16 / 5
1 1/2 = 3 / 2
16 / 5 * 3 / 2 = 48 / 10 = 24 / 5
The correct answer is 24 / 5 = 4 4 /5
(You can check on your calculator)
What part of the expression below should be calculated first 8 x {22 x [15 + (14 x 2)]} A 8+22. B 22×15. C 14x2. D 15+14.
Answers
Answer:
14*2
Step-by-step explanation:
8 x {22 x [15 + (14 x 2)]}
With multiple parentheses work from the inside out
The inner most parentheses are
14*2
A laptop computer is purchased $1500. After each year , the resale value decreases by 25%. What will the resale value be after 5 years ? Round to the nearest dollar
Answers
After 5 years of being decreased by 25% the resale price will be $355
Find the product. Simplify your answer.
(2w–1)(4w–2)
Answers
Answer:
8w² -8w +2
Step-by-step explanation:
(2w-1)(4w-2)
= 8w² -4w -4w + 2
= 8w² -8w +2
rounded to the nearest hundredth how many meters are in 32 ft (1 m = 3.28)
Answers
Answer:
9.76 M
Step-by-step explanation:
32/3.28
9.756097561
9.76