Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
First, identify the three vectors in component form (remember to have the direction angle for each vector account for the quadrants they are in!):
[tex]u=\langle90\cos220^\circ,90\sin220^\circ\rangle\\v=\langle 60\cos110^\circ,60\sin110^\circ\rangle\\w=\langle 40\cos30^\circ,40\sin30^\circ\rangle[/tex]
Secondly, we add them:
[tex]u+v+w=\langle90\cos220^\circ+60\cos110^\circ+40\cos30^\circ,90\sin220^\circ+60\sin110^\circ+40\sin30^\circ\rangle\approx\langle-54.824,18.531\rangle[/tex]
Thirdly, find the magnitude of the new vector:
[tex]||u+v+w||=\sqrt{(-54.824)^2+(18.531)^2}\\||u+v+w||\approx57.871[/tex]
And finally, find the direction of the new vector:
[tex]\theta=tan^{-1}(\frac{18.531}{-54.824})\\\theta\approx-18.675^\circ\approx-19^\circ[/tex]
Because our new vector is in Quadrant II, our found direction angle is a reference angle, telling us that the actual direction of our vector is 19° clockwise from the negative x-axis, which would be 180°-19°=161°
Thus, B is the best answer
Problem 2
To find the component form of a vector, we simply subtract the initial point from the terminal point. In this case, our initial point is at (7,-1) and our terminal point is at (1,6). We subtract the horizontal and vertical components separately:
[tex]\langle1-7,6-(-1)\rangle=\langle-6,7\rangle[/tex]
Thus, A is the correct answer
Problem 3
Again, subtract the initial point from the terminal point to find the vector, and then apply scalar multiplication:
[tex]-\frac{1}{2}v=-\frac{1}{2} \langle-8-8,10-4\rangle=-\frac{1}{2}\langle-16,6\rangle=\langle8,-3\rangle[/tex]
Thus, C is the correct answer
Problem 4 (top one in 4th image)
Remember that scalar multiplication only affects the magnitude of the vector and not the direction. Thus, [tex]-3u=-3\bigr[20\langle\cos30^\circ,\sin30^\circ\rangle\bigr]=-60\langle\cos30^\circ,\sin30^\circ\rangle[/tex], which means our magnitude is -60 and our direction remains 30°.
Thus, B is the correct answer
Problem 5 (fake #6, bottom one in 4th image)
Basically, whatever is in front of the i represents the horizontal component, and whatever is in front of the j represents the vertical component, so:
[tex]u=-3i+8j=\langle-3,8\rangle[/tex]
Thus, B is the correct answer
Problem 6 (real one, 5th image)
Recall:
Two vectors are said to be orthogonal if their dot product is 0 and are perpendicular to each other (form a 90° angle)Two vectors are said to be parallel if the angle between the vectors is 0° or 180° i.e. cosθ=-1Knowing these facts, let us compute the dot product:
[tex]u\cdot v=(-4*28)+(7*-49)=(-112)+(-343)=-455[/tex]
Since the dot product of the two vectors is not 0, then the vectors are not orthogonal, so we can eliminate choices A and B
To check if the vectors are parallel, find the angle between them:
[tex]\displaystyle\theta=cos^{-1}\biggr(\frac{u\cdot v}{||u||\:||v||}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{(-4)^2+(7)^2}\sqrt{(28)^2+(-49)^2}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{16+49}\sqrt{784+2401}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{65}\sqrt{3185}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{207025}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{455}\biggr)\\\\\theta=cos^{-1}(-1)\\\\\theta=180^\circ[/tex]
So, since the angle between the two vectors is 180°, this implies that cosθ=-1, and the two vectors must be parallel.
Thus, D is the correct answer
Related Questions
Which of the following is formula that represents The Pythagorean
Theorem?
Answers
Look at the diagram for the answer
Hope that helps!
The price of an item has risen to $228 today. Yesterday it was $95. Find the percentage increase.
Answers
Answer:
140% increase
Step-by-step explanation:
Percent increase = [(final - initial) ÷ initial] · 100
[(228 - 95) ÷ 95] · 100
[133 ÷ 95] · 100
1.4 · 100
140
BRAINLIEST please if this helped!NEED HELP ASAP
In the diagram, m ZAFB = 78°
Which angle is complementary to ZAFB and what is its measure?
Answers
Answer:
Angle BFC is complimentary to AFB. Its measure is 12.
Step-by-step explanation:
Complementary angles add up to 90 degrees. When these two angles combine, it adds up to 90. 90-78 = 12. This angle's measure is 12.
Plot 1 goes from 0 to 8. There are 2 images above 5, 2 above 6, 4 above 7, and 5 above 8. Plot 2 goes from 0 to 8. there are 5 images above 1, 2 images above 2, 4 images above 3, 3 images above 4, 1 image above 5, 1 image above 6, and 1 image above 8.
Use visual clues to decide which plot has the highest measure. No calculations should be necessary, although you may use them to verify your answers.
Highest mean:
✔ Plot 1
Highest median:
✔ Plot 1
Highest range:
✔ Plot 2
Highest interquartile ranges:
✔ Plot 2
Answers
Answer: the answer is 45
Step-by-step Step-by-step explanation:
so it says a pilot goes from 0 to 8 and then two images above so you add to to eat and then you add 5 to 2:30 for me to 522 the artistic 24 + 27 + 5 then you answer 8 + 2028 and then you add 5 + 1 + 2 + 2 + 4 + 3 + 3 + 4 + 1 + 5 + 16 + 18 and you get 45
Answer:
A, A, B, B
Step-by-step explanation:
Find the value of sin20 × sin30 × sin40 × sin80.
Please I need answers...
Answers
Answer:
3/16
Step-by-step explanation:
Prove that sin 20 ×sin40 × sin60 × sin80 = 3/16.
We have to prove sin 20 × sin40 × sin60 × sin80 = 3/16.
Consider LHS
sin 20 × sin 40 × sin60 × sin80
Sin Values
In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function is used to find the unknown angle or sides of a right triangle.
We know the trigonometric values of sin function
Proof
Consider LHS
sin 20 × sin 40 × sin60 × sin80
= sin60 [sin20 × sin40 × sin80]
= √3/2[sin20 × sin(60 – 20) × sin(60 + 20)]
= √3/2[sin 3(20)/4]
= √3/2[sin 60/4]
= √3/2[√3/2 × 4]
= √3/2 × √3/8 = 3/16
∴ LHS = RHS
Hence proved
*50 points* Pls help. Pls answer both part A and Part B. Look at the picture for question.
Answers
Answer:
Eleanor has made an error in Step 1
She clearly intended to multiply both sides by 2, but forgot to multiply the [tex]-9x[/tex] part of the RHS.
Step 1 should be: [tex]x+18=8(2x-6)-18x[/tex]
Correct solution
Given: [tex]\dfrac12(x+18)=4(2x-6)-9x[/tex]
Step 1: [tex]x+18=8(2x-6)-18x[/tex]
Step 2: [tex]x+18=16x-48-18x[/tex]
Step 3: [tex]x+18=-48-2x[/tex]
Step 4: [tex]66=-3x[/tex]
Step 5: [tex]x=-22[/tex]
A circle has an area between 100-150 square inches,what are some possible lengths for a diameter of this circle
Answers
Answer:
it would range between 11.28379... to 13.819765...
Step-by-step explanation:
the circle's area formula is pi * radius^2
so you make to equation, plugging the 100 and 150 into the circle's area
you get square root of (100/pi) which gets 11.28379... for the area of 100
you do the same with 150 to get square root of (150/pi) which gets 13.819765...
those are the diameter of the circle since the diameter is double the radius which i already multiplied afterwards. so if you need the radius divide the number ive given you
Find the length of the midsegment of the trapezoid.
Answers
Answer:
So 18+-10=8, 18+-8=10. So the answer is 8 I guess.
What is the smallest number which is reversed when 2 is added to its double?
Answers
Answer:
We know that to reverse a number, we should swap the numbers in TENS and ONES position. Therefore, the general form of its reverse 'ba' is (10 \times b) + a. Let us try to find the sum of both these numbers. Therefore, the sum of two-digit numbers and their reverse is always a multiple of 11.
Step-by-step explanation:
#carryonlearning
Brainlest me please
Donna received a $90 gift card for a coffee store. She used it in buying some coffee that cost $7.59 per pound. After buying the coffee, she had $59.64 left on her card. How many pounds of coffee did she buy?
Answers
Answer: 4 pounds
Step-by-step explanation:
First, we will see how much the coffee cost by subtracting what was left by the total gift card.
$90 - $59.64 = $30.36
Now, we will divide how much the coffee cost by how much one pound costs. This will give us how many pounds she bought, and the answer to your problem
$30.36 / $7.59 = 4
She bought four pounds of coffee.
Help me in math pls ty
Answers
Answer:
See below ↓↓↓↓↓↓
Step-by-step explanation:
5.
12 2/3 - 5/738/3 - 5/7266/21 - 15/21251/21 or 11 20/216.
11 1/3 - 3/534/3 - 3/5170/15 - 9/15161/15 or 10 11/157.
9 1/6 - 2 3/455/6 - 11/4110/12 - 33/1277/12 or 6 5/128.
25 1/4 - 3/525.25 - 0.624.6524 13/25 or 613/259.
4 1/2 - 1 4/64 1/2 - 1 2/39/2 - 5/327/6 - 10/617/6 or 2 5/610.
6 1/8 - 2 2/349/8 - 8/3147/24 - 64/2483/24 or 3 11/24i need help with this
Answers
Answer:
Step-by-step explanation:
Circumference is given by the formulas :
[tex]2\pi r[/tex] or [tex]\pi d[/tex]
Since we are given the diameter we can use the second one :
We are told to use 3.14 for π :
C = (3.14)×(16)
C = 50.24
Area of a circle is given by the formula:
[tex]\pi r^{2}[/tex]
To work out r we simply half the diamter:
16÷2 = 8
Now we put this into the area formula:
π(8)² = 64π
We are told to use 3.14 as pi so:
64π = 64×3.14 = 200.96
Answer:
Circumference = 50.24 in
Area = 200.96 in²
Step-by-step explanation:
First, let us find the circumference of the circle.
For that, let us use this formula.
C = π d
Given that,
d ⇒ diameter ⇒ 16 in
Let us find now.
C = π d
C = 3.14 × 16
C = 50.24 in
And now let us find the area of the circle.
Before that, let us find the radius.
d = 2r
16 = 2r
Divide both sides by 2.
8 in ⇒ radius
Let us use the below formula to find the area of the circle.
A = π r²
A = 3.14 × 8 × 8
A = 200.96 in²
NEED AN ANSWER RIGHT NOW I HAVE ALMOST NO TIME PLEASE
The zeros of a quadratic relationship are 3 and 7. The optimal value is -3. Is the optimal value a maximum or minimum? Explain.
TYSM IF SOMEONE HELPS
Answers
Answer:
Minimum
Step-by-step explanation:
The zeros of a quadratic equation are the points at which the parabola intersects the x-axis.
[tex]\sf x=3 \implies x-3=0[/tex]
[tex]\sf x=7 \implies x-7=0[/tex]
[tex]\sf \implies y=a(x-3)(x-7)[/tex] (for some constant a)
[tex]\sf \implies y=ax^2-10ax+21a[/tex]
The optimal value is the y-coordinate of the vertex.
[tex]\sf \implies vertex=(x,-3)[/tex]
The x-coordinate of the vertex is the midpoint of the zeros:
[tex]\sf x=\dfrac{7-3}{2}+3=5[/tex]
[tex]\sf \implies vertex=(5,-3)[/tex]
Therefore, the vertex will be in Quadrant IV and so the parabola opens upwards into Quadrant I.
So the optimal value is a MINIMUM since the vertex is the minimum point of the curve.
Additional Information to create the equation of the quadratic
Vertex form of quadratic equation: [tex]\sf y=a(x-h)^2+k[/tex]
where (h, k) is the vertex
[tex]\sf \implies y=a(x-5)^2-3[/tex]
[tex]\sf \implies y=ax^2-10ax+25a-3[/tex]
To find the value of a, compare the constants of both equations:
[tex]\sf 21a=25a-3[/tex]
[tex]\sf \implies -4a=-3[/tex]
[tex]\sf \implies a=\dfrac34[/tex]
So the final equation is:
[tex]\sf factor \ form \implies y=\dfrac34(x-3)(x-7)[/tex]
[tex]\sf standard \ form\implies y=\dfrac34x^2-\dfrac{15}{2}x+\dfrac{63}{4}[/tex]
[tex]\sf vertex \ form \implies y=\dfrac34(x-5)^2-3[/tex]
find the area of a trapezoid
Answers
Answer:
see explanation
Step-by-step explanation:
the area (A) of a trpezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
b₁, b₂ are the parallel bases and h the perpendicular height between them
(1)
b₁ = 12, b₂ = 8 , h = 5
A = [tex]\frac{1}{2}[/tex] × 5 × (12 + 8) = 2.5 × 20 = 50 cm²
(2)
b₁ = 6 , b₂ = 4 , h = 3
A = [tex]\frac{1}{2}[/tex] × 3 × (6 + 4) = 1.5 × 10 = 15 cm²
(3)
b₁ = 7 , b₂ = 4 , h = 4
A = [tex]\frac{1}{2}[/tex] × 4 × (7 + 4) = 2 × 11 = 22 cm²
Answer:
see explanation
Step-by-step explanation:
the area (A) of a trpezoid is calculated as
A = \frac{1}{2}21 h (b₁ + b₂ )
b₁, b₂ are the parallel bases and h the perpendicular height between them
(1)
b₁ = 12, b₂ = 8 , h = 5
A = \frac{1}{2}21 × 5 × (12 + 8) = 2.5 × 20 = 50 cm²
(2)
Match each value to what it represents. 25 = 32 1. 32 power 2. 5 exponent 3. 2 base
Answers
Answer:
The power is 32 because that is what 2 to th 5 is , 2 is the base as its the number being multiplied 5 times which leaves 2 as the exponent.
Find the value of k so that the quadratic inequality x² + 14x + k < 0 only for x is an element of [-11,–3]
Answers
Answer:
x²+14x+33<0.
Step-by-step explanation:
1) according to the condition x=-11 and x=-3 are zeros of the function y=ax²+bx+c;
2) if -3;-11 are zeros, then (-3)*(-11)=c ( already a=1; b=14). Then
3) x²+14x+33<0.
The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.
On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4).
Which graph represents g(x)?
On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8).
On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10).
On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).
Answers
it goes through the point (2, 10), has a vertex at (5, 1) and goes through the point (8, 10)
I WILL GIVE BRAINLIEST + 25 POINTS PLEASE HELP
Answers
Answer:
25
Step-by-step explanation:
Answer:
50.24 square yards
Step-by-step explanation:
Area of the circle
A = πr²A = 3.14 x (4)²A = 3.14 x 16A = 50.24 square yardsCAN SOMEBODY HELP ME SOLVE THE EQUATION
Answers
Tables A, B, and C.
The only non-linear graph is D. Do not overthink questions like this, this is where schools try to trick you. You are given plot points, plot them and see if they are straight lines (linear) on the graph. If there is a bend (non-linear or peyronie's disease).
Which of the following are composite numbers? Select ALL that apply. 4 9 15 3 5 answers.
Answers
Answer:
4 and 9
Step-by-step explanation:
Composite numbers are whole numbers that can have more than 2 factors.
b – 12 = 36
A.b = 34
B.b = 48
C.b = 26
D.b = 28
Answers
What are the domain and range of the function f(x) = 3x + 5
Answers
Step-by-step explanation:
Here,let x = 1,2,3 and 4
Then,
Domain =(1,2,3,4)
Again,
f(1)= 3*1 + 5
=3 + 5
=8
f(2)=3*2 + 5
=6 + 5
=11
f(3)=3*3 + 5
=9 + 5
=14
f(4)=3*4 + 5
=12 + 5
=17
Therefore, Range=(8,11,14,17)
Please help me I’m not sure how to answer this problem
Answers
Answer:
12/13
Step-by-step explanation:
P(not a queen) = 48/52 = 12/13
Answer:
48/52
Step-by-step explanation:
Out of a 52 card deck there are 4 queens
there is a 48/52 propability you will not be drawn a queen or 92.31% you will not be drawn a queen
Find the area
(Explain)
Answers
Answer:
960 cm²
Step-by-step explanation:
Area of trapezoid: (a + b)(h)/2
A = (20 + 40)(32)/2
A = 60(32)/2
A = 1920/2
960 cm²
BRAINLIEST please if this helped!How many different triangles can you make if you are given the measurement for two angles and the length of a side that is NOT shared?
Answers
Answer:
One triangle
Step-by-step explanation:
I hope this helps :)
Is the sequence An a function? Why or why not?
Answers
Answer: A sequence is a type of function. Remember, a function is any formula that can be expressed in "f(x) = x" format, but a sequence only contains integers at or greater than zero.
Hope this helps! Have a good day! :)
Please helpp!!!!!!!!!!!!!!! I will mark brainlist
Answers
If you into 0 for x you get 4. It is not straight line or constant rate of change because slope is x^2 which is a parabola. If you input -3 you don’t get -5 you get 13. And lastly, y is a function of x means y changes according to the x input, which is the case here.
Answer:
statements 2 & 5 are true
Step-by-step explanation:
1. False because is a quadratic nonlinear equation
2. True, 4 is the ordered to the origin
3. False, the rate not being linear is not constant
4. False, because when the input is -3 the output is 13
[tex]y = (-3)^{2} +4=9+4=13[/tex]
5. True, y depends on x
Hope this helps
Solve For X, using the given triangle.
Please answer quick! Also, keep in mind that this uses stuff like sin, cos, and tan. I'm looking for like trig and whatnot, please help!
Answers
Step-by-step explanation:
[tex] \tan(31) = \frac{x}{33} \\ x = 33 \tan(31) \\ x = 19.82840042791 \\ x = 19.83[/tex]
Answer:
x = 19.8
Step-by-step explanation:
You want to use tangent, since you are trying to find the opposite side and know the adjacent side to the angle.
tan = opposite/adjacent
31tan = x/33
Multiply both sides by 33
33(31tan) = (33) x/33
33(31tan) = x
Find the tan of 31° using a scientific calculator.
tan 31° is about 0.6
Solve for x
33(0.6) = x
x = 19.83
rounded to the the nearest tenth
x = 19.8
. Assuming that the pool is 10 ft deep, approximately how many cubic heters of water will this pool hold when filled? (3.3 feet 1 meter)
Answers
Answer:
The answer is true
Step-by-step explanation:
hope this helps
Let
[tex]Let \\ \displaystyle\sf S = \sum_{k=1}^n \dfrac{n}{n^2+kn + k^2} [/tex] and ,
[tex]\displaystyle \sf T_n =\sum_{k=0}^{n-1}\dfrac{n}{n^2+kn+k^2}[/tex] ,
[/tex]
where n = 1,2,3,4..... Then ,
[tex]A)\quad S_n < \dfrac{\pi}{3\sqrt3} \qquad \qquad B)\quad S_n >\dfrac{\pi}{3\sqrt3}\\\\ C)\quad T_n >\dfrac{\pi}{3\sqrt3}\qquad\qquad D)\quad T_n < \dfrac{\pi}{3\sqrt3}[/tex]
Answers
Answer:
A, D
Step-by-step explanation:
You want to know the bound for the values of Sn and Tn, given their definitions as ...
[tex]\displaystyle S_n=\sum_{k=1}^n{\dfrac{n}{n^2+kn+k^2}}\\\\T_n=\sum_{k=1}^{n-1}{\dfrac{n}{n^2+kn+k^2}}[/tex]
ValuesAll we need to do to determine the correct answer choices is evaluate the sums for some value of n.
For n=2, the value of S2 is ...
S2 = 2/(4+2+1) +2/(4+4+4) = 2/7 +2/12 = 19/42 ≈ 0.4524
For n=2, the value of T2 is ...
T2 = 2/(4+2+1) = 2/7 ≈ 0.2857 . . . . . 1/(3n) less than the value of Sn
Both of these values are less than π/(3√3) ≈ 0.6046.
The correct answer choices are ...
A) Sn < π/(3√3)
D) Tn < π/(3√3)
__
Additional comment
For the purpose here, it is not necessary to determine the limiting value of either Sn or Tn. It is only necessary to demonstrate which side of the given value the terms of either sequence lie.
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