1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Oduvanchick [21]
2 years ago
9

Find a vector a with representation given by the directed line segment AB. Draw AB and the equivlent representation starting the

origin. A(2,1), B(0,6)
Mathematics
1 answer:
chubhunter [2.5K]2 years ago
5 0

Answer:

AB = (-2, 5)

Step-by-step explanation:

The vector V is of the form, V = (B1 - A1, B2 - A2)

A = (2, 1);  B = (0, 6)

V = (0 - 2, 6 - 1)

V = (-2, 5)

You might be interested in
A plane ticket barcelona costs £175 the price decreases by 6% work out the new price
Bond [772]

Answer: £164.50

175 decreased by 6% = 164.5

Absolute change (actual difference):

164.5 - 175 = - 10.5

Step-by-step explanation:

175 - Percentage decrease =

175 - (6% × 175) =

175 - 6% × 175 =

(1 - 6%) × 175 =

(100% - 6%) × 175 =

94% × 175 =

94 ÷ 100 × 175 =

94 × 175 ÷ 100 =

16,450 ÷ 100 =

164.5

£164.50

6 0
3 years ago
Read 2 more answers
You work at a pioneer historical site. On this site you have handcarts. One cart has a handle that connects to the center of the
Gelneren [198K]

Answer:

a)  see below

b)  radius = 16.4 in (1 d.p.)

c)  18°. Yes contents will remain. No, handle will not rest on the ground.

d)  Yes contents would spill.  Max height of handle = 32.8 in (1 d.p.)

Step-by-step explanation:

<u>Part a</u>

A chord is a <u>line segment</u> with endpoints on the <u>circumference</u> of the circle.  

The diameter is a <u>chord</u> that passes through the center of a circle.

Therefore, the spokes passing through the center of the wheel are congruent chords.

The spokes on the wheel represent the radii of the circle.  Spokes on a wheel are usually evenly spaced, therefore the congruent central angles are the angles formed when two spokes meet at the center of the wheel.

<u>Part b</u>

The <u>tangent</u> of a circle is always <u>perpendicular</u> to the <u>radius</u>.

The tangent to the wheel touches the wheel at point B on the diagram.  The radius is at a right angle to this tangent.  Therefore, we can model this as a right triangle and use the <u>tan trigonometric ratio</u> to calculate the radius of the wheel (see attached diagram 1).

\sf \tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle

Given:

  • \theta = 20°
  • O = radius (r)
  • A = 45 in

Substituting the given values into the tan trig ratio:

\implies \sf \tan(20^{\circ})=\dfrac{r}{45}

\implies \sf r=45\tan(20^{\circ})

\implies \sf r=16.37866054...

Therefore, the radius is 16.4 in (1 d.p.).

<u>Part c</u>

The measure of an angle formed by a secant and a tangent from a point outside the circle is <u>half the difference</u> of the measures of the <u>intercepted arcs</u>.

If the measure of the arc AB was changed to 72°, then the other intercepted arc would be 180° - 72° = 108° (since AC is the diameter).

\implies \sf new\: angle=\dfrac{108^{\circ}-72^{\circ}}{2}=18^{\circ}

As the handle of the cart needs to be no more than 20° with the ground for the contents not to spill out, the contents will remain in the handcart at an angle of 18°.

The handle will not rest of the ground (see attached diagram 2).

<u>Part d</u>

This can be modeled as a right triangle (see diagram 3), with:

  • height = (48 - r) in
  • hypotenuse ≈ 48 in

Use the sin trig ratio to find the angle the handle makes with the horizontal:

\implies \sf \sin (\theta)=\dfrac{O}{H}

\implies \sf \sin (\theta)=\dfrac{48-r}{48}

\implies \sf \sin (\theta)=\dfrac{48-45\tan(20^{\circ})}{48}

\implies \theta = 41.2^{\circ}\:\sf(1\:d.p.)

As 41.2° > 20° the contents will spill out the back.

To find the <u>maximum height</u> of the handle from the ground before the contents start spilling out, find the <u>height from center of the wheel</u> (setting the angle to its maximum of 20°):

\implies \sin(20^{\circ})=\dfrac{h}{48}

\implies h=48\sin(20^{\circ})

Then add it to the radius:

\implies \sf max\:height=48\sin(20^{\circ})+45\tan(20^{\circ})=32.8\:in\:(1\:d.p.)

(see diagram 4)

------------------------------------------------------------------------------------------

<u>Circle Theorem vocabulary</u>

<u>Secant</u>: a straight line that intersects a circle at two points.

<u>Arc</u>: the curve between two points on the circumference of a circle

<u>Intercepted arc</u>: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.

<u>Tangent</u>: a straight line that touches a circle at only one point.

7 0
2 years ago
In the triangle below,
Greeley [361]

Answer:

12.3

Step-by-step explanation:

You will use cosine to solve for y because you are given the hypontenuse and need to find the adjacent side.

cos 35 degrees = adjacent/hypontenuse

cos 35 = y/ 15

15( cos35 ) = y

y=12.287

=12.3

7 0
3 years ago
Find the value of the expression (3x−12)−(12xy−10)(3x-12)-(12xy-10) for x=3x=3 and y=6y=6
Rina8888 [55]
Hi!

Put in the values for x and y.

(3 · 3 - 12)-(12 · 3 · 6 - 10)

Solve

(9 - 12)-(216 - 10)
-3 - 206
-209

The answer is -209

Hope this helps! :)

4 0
3 years ago
Read 2 more answers
Brian multiplied his average speed of 14.73 miles per hour by the amount of time he spent cross-country skiing. His product was
Gekata [30.6K]

Answer:

12.2*1=12.2

12.2*0.45=5.49

5.49+12.2=17.69

Step-by-step explanation:

5 0
2 years ago
Other questions:
  • These four teenagers have come to some decisions. Which is likely to have the
    10·1 answer
  • PLEASE HELP<br> factor 12n - 18.
    10·2 answers
  • What is the measure of ∠ABC
    12·1 answer
  • 4q-2r/3m=7 solve for q
    10·1 answer
  • You have a 10% off coupon for the paper towels that are 6.99. The tax rate is 8%. Find the discount amount and tax amount
    13·1 answer
  • a pile of steel plates is 2.75 feet high. if the plates are 0.375 inch thick. how many are there in the pile.
    13·1 answer
  • 2(b + c)2-3 (b - c)? if b = 8 and c =<br>=-4​
    6·1 answer
  • Of two consecutive integers, twice the smaller is four less than the greater. Find the integers. Provide and equation if you don
    15·1 answer
  • Brainliest is on the line here
    9·1 answer
  • Complete the double number line to show the other values of fat and protein.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!