Answer:
a. 25.98i - 15j mi/h
b. 1.71i + 4.7j mi/h
c. 27.69i -10.3j mi/h
Step-by-step explanation:
a. Identify the ship's vector
Since the ship moves through water at 30 miles per hour at an angle of 30° south of east, which is in the fourth quadrant. So, the x-component of the ship's velocity is v₁ = 30cos30° = 25.98 mi/h and the y-component of the ship's velocity is v₂ = -30sin30° = -15 mi/h
Thus the ship's velocity vector as ship moves through the water v = v₁i + v₂j = 25.98i + (-15)j = 25.98i - 15j mi/h
b. Identify the water current's vector
Also, since the water is moving at 5 miles per hour at an angle of 20° south of east, this implies that it is moving at an angle 90° - 20° = 70° east of north, which is in the first quadrant. So, the x-component of the water's velocity is v₃ = 5cos70° = 1.71 mi/h and the y-component of the water's velocity is v₄ = 5sin70° = 4.7 mi/h
Thus the ship's velocity vector v' = v₃i + v₄j = 1.71i + 4.7j mi/h
c. Identify the vector representing the ship's actual motion.
The velocity vector representing the ship's actual motion is V = velocity vector of ship as ship moves through water + velocity vector of water current.
V = v + v'
= 25.98i - 15j mi/h + 1.71i + 4.7j mi/h
= (25.98i + 1.71i + 4.7j - 15j )mi/h
= 27.68i -10.3j mi/h
The Mariana trench, off the coast of Guam in
the Pacific Ocean, is 11 034m deep. Write 11
034 in standard form.
Answer:
11,000 + 30+4
Step-by-step explanation:
what is
- l4l equal to?
Answer: -4
Explanation:
Absolute value is the distance that a number is away from zero. Keep in mind that the absolute value is always positive.
However since the negative sign is on the outside of the function , you leave it on the final answer. Therefore the answer is -4
What is the explicit formula for this arithmetic sequence?
-12,-17, -22, -27, ...
Answer:
Step-by-step explanation:
An explicit arithmetic formula in standard form is
[tex]A_n=a_1+d(n-1)[/tex] where n is the position of a number in thesequence, a1 is the first number in the given sequence, and d is the common difference. The common diff here is -5 since we have to subtract 5 from each term to get to the next one in the sequence. The first number is -12. So
a1 = -12
d = -5 and the explicit formula is
[tex]A_n=-12-5(n-1)[/tex] and you could simplify it a bit to
[tex]A_n=-12-5n+5[/tex] and finally to
[tex]A_n=-5n-7[/tex] which is a linear representation. Arithmetic sequences can all be simplified down to represent lines.
Một xí nghiệp sản xuất độc quyền hai loại sản phẩm. Biết hàm cầu của hai loại sản phẩm trên lần lượt là 1 2 Q 40 2 ; Q 35 D D 1 2 1 2 P P P P và hàm chi phí kết hợp là 2 2 1 1 2 2 1 2 C Q 6Q Q +Q +15Q 150 . Q Trong đó, P,Q 1,2 i i i lần lượt là đơn giá và sản lượng của sản phẩm thứ i . a) (CLO1.3, CLO2.2, CLO4.2) Tìm mức sản lượng của mỗi loại sản phẩm để xí nghiệp có lợi nhuận tối đa. Khi đó, giá bán các sản phẩm là bao nhiêu? b) (CLO1.3, CLO2.2, CLO4.2) Tính chi phí cận biên cho từng loại sản phẩm tại mức tối ưu tìm được ở câu a).
simplify (3³ × 3⁴) ÷ 3²
Which are the solutions of x2 = -13x – 4?
Answer:
x=3.75
Step-by-step explanation:
Please help me i'm struggling!
Answer:
B
Step-by-step explanation:
y = 2x - 4
y + 4 = 2x
x = y/2 + 4/2
x = y/2 + 2
—-
y = x/2 + 2
Answer:
y = x/2 + 2
This is the answer because I got it right on my test.
If polygon ABCD rotates 70° counterclockwise about point E to give polygon A'B'C'D', which relationship must be true? A. BB' = DD' B. m∠ABC < m∠A'B'C' C. m∠ABC > m∠A'B'C' D. A'E' = AE
Answer:
A'E' = AE
Step-by-step explanation:
Transformation is the movement of a point from its initial position to a new position. Types of transformation are rotation, reflection, translation and dilation. If an object is transformed then all its points are also transformed.
Rigid transformations are transformations that preserves the shape an size of an object (i.e. the side length and angles). Examples of rigid transformations are rotation, translation and reflection.
Since rotation is a rigid transformation, the side lengths and angles of polygon A'B'C'D' would be the same as that of polygon ABCD. Therefore:
A'E' = AE
PLEASE HELP ME WITH THIS
If the graphs of the linear equations in a system are the same line, what does that mean about the possible solution or solutions of the system? А.) There is exactly one solution
B.) There is no solution.
C.) There are infiriitely many solutions
D.) The lines in a system cannot graph the same line.
((PLEASE HELPPP))
Help please!!!!help help help
Answer:
ask the goggle not 1 you help in thi aap bro your aand me same thing make sorry
Answer:
{-2,-1, 0, 1, 8}
Step-by-step explanation:
Domain is the input values ie. x values
{-2,-1, 0, 1, 8}
Answer right Brainliest!
Answer:
The right answer is D) If graphed, the ordered pairs would form a straight line
PLEASE ANSWER THIS QUESTION IM BEGGING YOU !
Answer:
5/36
Step-by-step explanation:
There are 12 tiles
P( blue) = blue /total = 5/12
We put the first tile back so there are still 12 tiles in the bag
P(yellow) = yellow/total = 4/12 = 1/3
P( blue, yellow) = 5/12 * 1/3 = 5/36
I need help ASAP!! Please.
Answer:
x = 8
Step-by-step explanation:
What is the length of leg s in the right triangle shown?
Answer:
D. 5
Step-by-step explanation:
Applying,
cos∅ = adjacent/Hypotenuse
From the diagram,
Given: ∅ = 45°, adjacent = s, hyptenuse = 5√2
Therefore,
cos45° = s/5√2
make s the subject of the equation
s = cos45°×5√2
s = (1/√2)(5√2)
s = 5
Hence the right answer is D. 5
find x if the mean of the number is 13 ,2x,0,5x,11 and 9
Answer:
45/7
Step-by-step explanation:
ok lets first find the total sum. there are 5 numbers so 13*5=65
2x+0+5x+11+9=65
7x=45
x=45/7 or 6.42857143
Find the value of x.
Answer:
Step-by-step explanation:
When two chords intersect inside the circle, the product of their segments are equal.
BE * ED = AE * EC
x *3x = 4 *3
3x² = 12 {Divide both sides by 3}
x² = 12/3
x² = 4
x = √4
x = 2
Answer:
The value of x is 2.
Step-by-step explanation:
We know that , when the two chords are intersect inside the circle, the product of their segment are equal.
So, BE × ED = AE × EC
putting the values
x × 3x = 4 × 3
multiply the values
3 x ² = 12
divide 12 by 3
x ² = 12 / 3
x ² = 4
Taking the square root of 4
x = √4
x = 2
The value of x is 2.
Solve the system algebraically.
2x + y - 10 = 0
x-y-5=0
What is the value of y?
-5/3
5
Answer:
5 is the value of y
PLZ FRIEND ME!!
Un arco de 50 m de longitud subtiende un ángulo central θ en un círculo de 35 m de radio. Encuentre la medida de θ.
Answer:
θ = 81.89°
Step-by-step explanation:
Si tenemos un círculo de radio R, el perímetro de este círculo estará dado por:
P = 2*pi*R
donde pi = 3.14
Ahora, si en lugar de el círculo completo solo queremos la longitud de un dado arco, definido por un ángulo θ, el largo de ese arco estará dado por:
L = (θ/360°)*2*pi*R
Notar que cuando θ = 360° (es decir, el ángulo del círculo completo) el largo del arco será igual que el perímetro, lo cual deberíamos esperar.
Ahora sabemos que:
El arco tiene 50m de longitud.
El radio del círculo es 35m
queremos encontrar el valor de θ
Reemplazando esos valores en la ecuación de arriba obtenemos:
50m = (θ/360°)*2*3.14*35m
Ahora solo debemos resolver esto para θ
50m = (θ/360°)*219.8m
(50m/219.8m) = (θ/360°)
(50m/219.8m)*360° = θ = 81.89°
Which inverse of the difference of 1/3 - 1/4?
Answer:
0/1
Step-by-step explanation:
Help please! I really need it
Write the equation of the line in slope-intercept form
Answer:
y=-1x-4
hope you have a great day
Please help me with this one …..
Answer:
is the clean area the desired one (I assume, yes)?
then y <= 3x + 5
if the dotted area is the desired area, then
y >= 3x + 5
Step-by-step explanation:
the factor of x is the slope of the line expressed as y/x ratio.
clearly, the line shows that for x changing by 1 unit y changes by 3 units. so, the slope is 3/1.
that leaves us only with the 2 middle options.
for "y <=" the desired values of y for a given x must be on the line (equal) or below (smaller than the value of the line equation). that is true, if the desired area is the clear one (no dots).
so, "y >=" is true, if the dotted area is desired.
7 √x +4 Is it a polynomial?
Answer:
Phải
Step-by-step explanation:
URGENT PLEASE HELP WILL GIVE BRAINLEIST !!!!!!!!!!
Answer:
4
Step-by-step explanation:
1 change in x and 4 change in y from 1,0 to 0,4 or 4/1
What are the real roots of the function in the graph?
Answer:
-1 and 3
Step-by-step explanation:
The real roots of a function are located where the function passes through the x-axis. In this case, the function passes through x=-1 and x=3, making them the real roots of the function.
A system of equations consisting of a circle and a line is graphed. Which statements about the number of possible solutions are correct? Check all that apply.
A circle and a line always intersect, so the system can have an infinite number of solutions.
A circle and a line can intersect at one point, so the system can have one solution.
A circle and a line can intersect at three points, so the system can have three solutions.
A circle and a line can intersect twice, so the system can have two solutions.
A circle and a line do not have to intersect, so the system can have no solution.
Answer:
the solution is where the two objects intersect ...
1) A line can completely miss the circle (no solutions is possible)
2) a line can "kiss" the circle at one point (one solution)
3) note that a line can not "bend"... it can touch one side of the circle pass
through the center and touch the circle in a second spot (going out) .. two solutions...
those are the three possibility that are in the question that was posted...
three check comments are true
Step-by-step explanation:
A sphere with a radius of 11 Ft so what is its volume FASTTT PLSSSSS
Step-by-step explanation:
volume of the sphere=4/3×π×r³
=4/3×3.14×11³
=5572.4533ft³
Can someone help me?
Answer:1565
Step-by-step explanation:
tehret
Check out this square pyramid: Find the surface area of the square pyramid (above) using its net (below).
Answer:
12 square units
Step-by-step explanation:
Given
See attachment for net
Required
The surface area
The net has the following shapes:
1 Square: (Length =2)4 congruent triangles (Base = 2; Height = 2)So, the surface area is:
Area = Area of Square + 4 * Area of 1 Triangle
[tex]Area = 2 * 2 + 4 * \frac{1}{2} * 2 * 2[/tex]
[tex]Area = 4 + 8[/tex]
[tex]Area = 12[/tex]