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A vector is 2.5 kilometers per hour at a bearing of of 50° West of North.

Find the magnitude of its vertical component.

lyl = v sin ©

A. lyl = - 1.9
B. lyl = 1.6
C. lyl = 2.5
D. lyl = 50°​

Answer:

150 cm

Step-by-step explanation:

The information in the question includes;

The length of rope P = 3 × The length of rope Q

The length of rope P - 10 cm  = 4 × (The length of rope Q - 10 cm)

Let p represent the original length of rope P and let q represent the original length of rope Q, we have;

p = 3·q...(1)

p - 10 = 4·(q - 10)...(2)

Expanding equation (2) gives;

p - 10 = 4·q - 40

∴ p = 4·q - 40 + 10 = 4·q - 50

p = 4·q - 50...(3)

Equating the values of p in equation (1) and equation (3) gives;

p = 3·q, and p = 4·q - 50, therefore, by the substitution property of equality, we have;

3·q = 4·q - 50

50 = 4·q - 3·q = q

q = 50

p = 3·q

∴ p = 3 × 50 = 150

The original length of P before it was cut, p = 150 cm.

Answer:

13 exercises

Step-by-step explanation:

The number of exercises in the exam = 20

The points received for questions solved correctly = 8 points

The points taken off for exercises solved wrong = 5 points

The number of points Ben has = 13 points

Let 'c' represent the number of exercises he solved correctly and let 'w' represent the number of exercises he solved wrong, we have;

0 < c + w ≤ 20...(1)

8·c - 5·w = 13...(2)

Given that 5·w has either a 0 or 5 as the unit digit, and x3 = x8 - 5, such as 13 = 18 - 5, we have that the last digit of 8·c is 8, and the last digit of 5·w is 5

The products of 8 with '8' as the unit are, 8 × 6, 8 × 11, and 8 × 16

Therefore, when c = 6, and w = 7, we get;

8 × 6 - 5 × 7 = 13

The number of exercises Ben solved, c + w = 6 + 7 = 13 < 20

When c = 11, we get;

8 × 11 - 5 × 15 = 13

11 + 15 = 26 > 20

The number of exercises Ben solved = 13 exercises

Answer:

A and D

Step-by-step explanation:

Look at the answer choices as (x,y) so if you multiply the x for the x spot and the y for the y spot, you make sure the it is greater than or equal to 3 and if it is, select that answer.

Answer:

{}, {s} {q} {l} {r} {s,q} {s, l} {s, r} {q, l} {q, r} {l, r} {s, q, l} {s,l,r} {s, q, r} {q, l, r} {s, q, l, r}

Answer:

a=2

b=10.5

c=4

d=17.5

Step-by-step explanation:

so 3.5 miles per hour and the columns are miles and then hours

so an equation can be 3.5 (mi/hr) * t (time) = distance

so for a): 3.5*t=7

t=2

b) 3.5*3=distance

distance is 10.5

c) 3.5*t=14

t=4

d) 3.5*5=d

d= 17.5

Answer:

A = 112cm²

Step-by-step explanation:

Area of a triangle = (bh) / 2

b = base length and h  = height

The triangle shown has a given base length of 14cm and a given height of 16cm

Hence area = ( 16 * 14 ) / 2

16 * 14 = 224

224 / 2 = 112

A = 112cm²

Step-by-step explanation:

since both cords are equal, so are arc length

4x + 18 = 7x - 51

3x - 21 = 0

x = 7

arc RS = 4(7) + 18

Answer:

The directional derivative of f at A in the direction of [tex]\vec{u}[/tex] AD is 7.

Step-by-step explanation:

Step 1:

Directional of a function f in direction of the unit vector [tex]\vec{u}=(a,b)[/tex] is denoted by [tex]D\vec{u}f(x,y)[/tex],

[tex]D\vec{u}f(x,y)=f_{x}\left ( x ,y\right ).a+f_{y}(x,y).b[/tex].

Now the given points are

[tex]A(8,9),B(10,9),C(8,10) and D(11,13)[/tex],

Step 2:

The vectors are given as

AB = (10-8, 9-9),the direction is

[tex]\vec{u}_{AB} = \frac{AB}{\left \| AB \right \|}=(1,0)[/tex]

AC=(8-8,10-9), the direction is

[tex]\vec{u}_{AC} = \frac{AC}{\left \| AC \right \|}=(0,1)[/tex]

AC=(11-8,13-9), the direction is

[tex]\vec{u}_{AD} = \frac{AD}{\left \| AD \right \|}=\left (\frac{3}{5},\frac{4}{5} \right )[/tex]

Step 3:

The given directional derivative of f at A [tex]\vec{u}_{AB}[/tex] is 9,

[tex]D\vec{u}_{AB}f=f_{x} \cdot 1 + f_{y}\cdot 0\\f_{x} =9[/tex]

The given directional derivative of f at A [tex]\vec{u}_{AC}[/tex] is 2,

[tex]D\vec{u}_{AB}f=f_{x} \cdot 0 + f_{y}\cdot 1\\f_{y} =2[/tex]

The given directional derivative of f at A [tex]\vec{u}_{AD}[/tex] is

[tex]D\vec{u}_{AD}f=f_{x} \cdot \frac{3}{5} + f_{y}\cdot \frac{4}{5}[/tex]

[tex]D\vec{u}_{AD}f=9 \cdot \frac{3}{5} + 2\cdot \frac{4}{5}[/tex]

[tex]D\vec{u}_{AD}f= \frac{27+8}{5} =7[/tex]

The directional derivative of f at A in the direction of  [tex]\vec{u}_{AD}[/tex] is  7.

68Answer:

10

Step-by-step explanation:

68/2=34

24+10=34

Answer: 12.48

Step-by-step explanation:

38x38+bxb=40x40

1444+b=1600

1600-1444=156

[tex]\sqrt156[/tex]=12.48

The base of the house is 12.48 foot far from the foot of the ladder.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

It is given that A 40-foot ladder reaches 38 feet up the side of a house.

We need to find that How far from the base of the house is the foot of the ladder.

Using Pythagoras theorem, we get;

[tex]38^2 + b^2 =40^2\\\\1444 + b^2 = 1600\\ \\b^2 = 1600 - 1444 \\\\b^2= 156\\\\b = 12.48[/tex]

Therefore, the base of the house is 12.48 foot far from the foot of the ladder.

Learn more about Pythagoras theorem;

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Answer:

m = w - t

£108

Step-by-step explanation:

m = Money Billy has to spend per week :

m = wage, w - tax, t

Hence,

m = w - t

Given;

Wage = £150 ; tax = £42

m = £150 - £42

m = £108

Answer:

Length = 6cm

Step-by-step explanation:

You would get 6cm as the length, because 6 ÷ 3 = 2, that is your width. So in the same way, you would divide 18 by 3 and get 6, thus the length of the second rectangle is 6 centimeters

Hope it helps :D

6 cm po tama to mag quandary pi akyu

Answer:

B

Step-by-step explanation:

For this problem, let us find the respective speeds of Jasmine and Caroline and compare the two. All we have to do is divide #minutes by #miles to find the time spent per one mile.

Jasmine:

[tex]\frac{42.5}{5} =\\\\[/tex]

[tex]8.5[/tex] minutes per mile

Caroline:

[tex]\frac{26.4}{3} =\\[/tex]

[tex]8.8[/tex] minutes per mile

Since Caroline takes longer to run a mile than Jasmine, We now know that Jasmine ran at a faster pace:

[tex]8.8-8.5=0.3[/tex]

B. Jasmine ran at a faster pace because she ran 0.3 minutes faster per mile.

I hope this helps! Let me know if you hae any questions :)

Answer:

The axis of symmetry is (0,0)

Step-by-step explanation:

This is the picture

Answer:

a = 18

Step-by-step explanation:

3(x+6)-x = 2x + a

Distribute

3x +18 -x = 2x+a

2x +18 = 2x+a

Subtract 2x from each side

18 = a

Answer:

21

Step-by-step explanation:

If lines m and n are equal, line t intersects both of them at the exact same angle. This means that 6x+3=7x-19. Start moving the variables to one side. 3=x-19. Then move the numbers to the other side of the equation. x=21.

Answer:

15 cm

Step-by-step explanation:

[tex]\frac{12}{24}[/tex] = [tex]\frac{x}{30}[/tex]

cross multiply and solve for x

or just notice that the fraction reduces to 1/2 and 15 is half of 30

the answer is in the picture

Answer:

c

Step-by-step explanation:

the value of x can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

The triangle is an isosceles triangle

An isosceles triangle has two opposite sides. If the two angles are equal , it means the triangle is an isosceles. Thus the value of the base is also 7

7²  + 7²

49 + 49

= 98

√98 = 9.899 = 7√2

Answer:

338 feet

Step-by-step explanation:

350 - 12 = 338

Answer:

[tex]x=68[/tex]

Step-by-step explanation:

In the figure, we shown all four exterior angles of the polygon. The sum of the exterior angles of any polygon is equal to [tex]360^{\circ}[/tex].

Therefore, we have:

[tex]79+(x+10)+(x-1)+(2x)=360,\\79+x+10+x-1+2x=360,\\88+4x=360,\\4x=272,\\x=\boxed{68}[/tex]

Answer:

150 in^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Givens

L = 9

W = 4

H = 3

Formula

SA = 2*L*w + 2*L*H + 2 * H * W

Solution

SA = 2 * 9*4 + 2*9*3 + 2*3 * 4

SA = 72 + 54 + 24

SA = 150 in^2

Answer:

p = -29/2

Step-by-step explanation:

2p + 38 = 9

Subtract 38 from each side

2p + 38-38 = 9-38

2p = -29

divide by 2

2p/2 = -29/2

p = -29/2

Answer:

p=-14.5

Step-by-step explanation:

2p + 38 = 9

      -38    -38

2p = -29

[tex]\sqrt{2}[/tex]    [tex]\sqrt{2}[/tex]

p = -14.5

Answer:

In 10 hours, the population is 6050 bacteria. In 20 hours, the population is 732050 bacteria.

Step-by-step explanation:

Bacterial populations can be assumed to grow exponentially. In 5 hours, since the population will have multiplied by 11, in 10 hours it will have multiplied by 121 (11^2) and by 14641 (11^4).

50 * 11 * 11 = 6050

50 * 11 * 11 * 11 * 11 = 732050

Answer:

Step-by-step explanation:

550 = 50 [tex]x^{5}[/tex]

11 =   [tex]x^{5}[/tex]

ln(11) = 5 ln(x)

x = [tex]e^{ln(11)/5}[/tex]

x = 1.615

10 hours ....

A= 50 ([tex]1.615^{10}[/tex] )

A= 50 ([tex]1.615^{10}[/tex] )

A=6050

20 hours ....

A= 50 ([tex]1.615^{20}[/tex] )

A= 50 ([tex]1.615^{20}[/tex] )

A=732,050

Answer:

For this type of problem, it is best to use Venn diagrams as shown in the picture. The areas where the circles intersect are the mutual events that occur together. The area where all circles intersect is denoted as x. These are the students who play all sports. Assuming all of the students play sports in the school, all of the numbers in the circles should add up to 405. The remaining area would be the difference. The solution is as follows:

Students who play tennis and hockey: 45 - x

Students who play hockey and softball: 60 - x

Students who play only tennis and softball: 39 - x

Students who only play tennis:

251 - 45 + x - 39 +x -x = x + 167

Students who only play hockey:

157 - x - 45 + x - 60 + x = x + 52

Students who only play softball:

111 - x - 60 + x - 39 + x = x + 12

The sum of all of these should be 405:

45-x+60-x+39-x+x+167+x+52+x+12 = 405

Solving for x,

x = 30

Therefore, there are 30 pupils who play all sports; 15 pupils who play tennis and hockey; 30 pupils who play hockey and softball; 9 pupils who play tennis and softball; 197 pupil who only play tennis; 82 pupils who only play hockey; and 42 pupils who only play softball.

Step-by-step explanation:

Hope this is correct, if it is wrong then please feel free to critique me and I wil correct my mistake(s). I'm sorry in advance if it is incorrect.

i hope you guys didn't have to suffer thru the rest like I did c,:

here is THE REST OF THE ANSWERS!

Step-by-step explanation:

THE ENTIRE PICTURE ABOVE IS CORRECT, BUT AFTER THAT THE NEXT ANSWERS ARE.....

8. angle LNO is congruent to angle NLM because of CPCTC

9. segment ON is parallel to segment LM because of converse of the alt. int. angles theorem

10. segment LO is parallel to segment MN because of converse of the alt. int. angles theorem

11. LMNO is a parallelogram because of the def. of a parallelogram

I just did all of these on edg. 2022 and they're correct. have a great day/night you guys and good luck!

We will use the converse of alternate interior angles theorem  to prove LMNO is a Parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are of equal measure.  

The proof is as follows:

Statements                                                   Reasons

1) LO ≅ MN                                                        Given

2) ON ≅ LM                                                       Given

3) LN ≅ LN                                                     Reflexive property

4) Δ LON ≅ Δ NML                                       SSS congruency rule

5) ∠ NLO ≅ ∠ LNM                                         CPCTC

and ∠ MLN ≅ ∠ LNO              

6) LM ║ ON and LO ║ MN   converse of alternate interior angles theorem

7) LMNO is a Parallelogram                  Property of Parallelogram  

For more references on Parallelogram, click;

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Answer:

D

Step-by-step explanation:

you will be multiplying Matrix C with Matrix D so, after using the rule for multiplication of matrices

[ 5x2 +9x4 + 7x1 5x(-4) + 9x0 + 7x7]

[ 10 + 36 + 7 -20 + 0 + 49 ]

[ 53 29]

hope this helps.

Brainly is an awesome app, but there is an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from tutors.

The product of matrices C and D is [53 29]. Therefore, option D is the correct answer.

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined. If AB and BA are both defined, it is not necessary that AB = BA.

Given that, C=[5 9 7] and D= [tex]\left[\begin{array}{ccc}2&-4\\4&0\\1&7\end{array}\right][/tex]

Here, CD = [5×2+9×4+7×1 5×(-4)+9×0+7×7]

= [10+36+7 -20+49]

= [53 29]

Therefore, option D is the correct answer.

To learn more about the product of matrices visit:

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