Answer:
Step-by-step explanation:
This requires some serious work before we even begin. First off, we will convert the km to meters:
32 km = .032 m
46 km = .046 m
And then we have to deal with the angle given as 40 degrees west of north. An angle 40 degrees west of north "starts" at the north end of the compass and moves towards the west (towards the left in a counterclockwise manner) 40 degrees. That means that the angle that is made with the negative x axis is a 50 degree angle. BUT the way angles are measured in standard form are from the positive x-axis, therefore:
40 degrees west of north = 50 degrees with the negative x axis = 130 degrees with the positive x axis. 130 is the angle measure we use. Phew! Now we're ready to start. Adding vectors requires us to use the x and y components of vectors in order to add them.
[tex]A_x=.032cos90.0[/tex] so
[tex]A_x=0[/tex] (the 90 degrees comes from "due north")
[tex]B_x=.046cos130[/tex] so
[tex]B_x=-.030[/tex] and if we add those to get the x component of the resultant vector, C:
[tex]C_x=-.030[/tex] And onto the y components:
[tex]A_y=.032sin90.0[/tex] so
[tex]A_y=.032[/tex]
[tex]B_y=.046sin130[/tex] so
[tex]B_y=.035[/tex] and if we add those together to get the y component of the resultant vector, C:
[tex]C_y=.067[/tex] Note that since [tex]C_x[/tex] is negative and [tex]C_y[/tex] is positive, the resultant angle (the direction) will put us into QII.
We find the magnitude of C:
[tex]C_{mag}=\sqrt{(-.030)^2+(.067)^2}[/tex]
We will round this after we take the square root to the thousandths place.
[tex]C_{mag}=.073m[/tex] and now for the angle:
[tex]\theta=tan^{-1}(\frac{.067}{-.030})[/tex] which gives us an angle measure of -67, but since we are in QII, we add 180 to that to get that, in sum:
The magnitude of the resultant vector is .073 m at 113°
What is the measure of
A shopkeeper bought Rice cooker for Rs. 5000 and sold it to a customer for Rs. 5,085 with 13% VAT.
Find his profit or loss percent.
Answer:
number to get a better price
Answer:
if I'm not wrong,then this is the equation
Step-by-step explanation:
CP=5000
SP=5085
VAT=13℅
now,
VAT amount=VAT℅ OF SP
=13℅ OF 5085
=13/100*5085
=rs.661.05
again,
profit℅= SP-CP/CP*100℅
=85/500*100
=17℅ answer
(a) The radius of a circle is 5.6 cm. Find the angle in degrees subtended by an arc of 22 cm at the
centre of the circle.
DO NO A PLEASE
Answer:
225 degrees
Step-by-step explanation:
Given the following data;
Radius, r = 5.6 cmLength of arc = 22 cmTo find the angle in degrees subtended by an arc;
Mathematically, the length of the arc of a circle is given by the formula;
S = rA
Where;
S is the length of the arc.A is the angle measured in radians.Substituting the values into the formula, we have;
22 = 5.6 * A
[tex] A = \frac {22}{5.6} [/tex]
A = 3.9286 radians.
Next, we would convert the value of the angle in radians to degrees;
Conversion:
[tex] 1 \; radian = \frac {180}{\pi} \; degrees [/tex]
[tex] 3.9286 \; radians = X \; degrees [/tex]
Cross-multiplying, we have;
[tex] X = \frac {180}{\frac {22}{7}} * 3.9286 [/tex]
[tex] X = \frac {180 * 7}{22} * 3.9286 [/tex]
[tex] X = \frac {1260}{22} * 3.9286 [/tex]
[tex] X = 57.2727 * 3.9286 [/tex]
X = 225.0015 ≈ 225 degrees
Write an inequality, in slope-intercept form, for the graph below. If necessary,
use "<=" for < or ">" for >.
Can anyone pls help ?
Given:
The graph of a linear inequality.
The boundary line passes through the points (0,-2) and (1,1), and the shaded region lies above the boundary line.
To find:
The inequality for the given graph.
Solution:
The boundary line passes through the points (0,-2) and (1,1), so the equation of the boundary line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-2)=\dfrac{1-(-2)}{1-0}(x-0)[/tex]
[tex]y+2=\dfrac{1+2}{1}(x)[/tex]
[tex]y+2=3x[/tex]
Subtract 2 from both sides.
[tex]y=3x-2[/tex]
The boundary line is a solid line and the shaded area lies above the boundary line, so the sign of inequality must be [tex]\geq [/tex].
[tex]y\geq 3x-2[/tex]
Therefore, the required inequality is [tex]y\geq 3x-2[/tex].
Answer:
y>3x-2
Step-by-step explanation:
.............................
6. Márcia cortou quatro tiras retangulares de mesma largura, cada qual de um dos lados de uma folha de papel que media 30 cm por 40 cm. O pedaço de papel que sobrou tem 68% da área da folha original. Qual é a largura das tiras? A) 5 cm B) 4 cm C) 3 cm D) 2 cm E) 1 cm 40 30 5 10 D) 10 E) 5
Answer:
b
Step-by-step explanation:
i had it
Grace bought a property valued at $200,00.00 and 20% down and a mortgage amortized over 10 years. She makes equal payments due at the end of every months. Interest on the mortgage is 4% compounded semi-annually and the mortgage is renewable after five years. a) What is the size of each monthly payment? b) What is the outstanding principal at the end of the five-year term? c) What is the cost of the mortgage for the first five years?
Answer:
Size of each monthly payment = $161.69 per month
Step-by-step explanation:
Given:
Value of property = $20,000
Downpayment = 20%
Number of payment = 12 x 10 = 120
Interest rate = 4% = 4% / 12 = 0.33 %
Computation:
Loan balance = 20,000 - 20%
Loan balance = $16,000
A] Size of each monthly payment [In Excel]
Size of each monthly payment = PMT(0.33%,120,16000,0)
Size of each monthly payment = $161.69 per month
What is the factor of
[tex] {x}^{4} - x[/tex]
Plz
which kind of triangle is shown?
A. Acute isosceles
B. Right scalene
C. Right isosceles
D. Acute scalene
Answer: B
Step-by-step explanation:
Acute isosceles: angle less than 90, 2 equal sides
Right scalene: right angle, different side lengths
RIght isosceles: right angle, 2 equal sides
Acute scalene: angle less than 90, different side lengths
find the missing side
Answer:
28.3
Step-by-step explanation:
tan = opposite/adjacent
tan (58) = 1,600335
opposite = tan * adjacent
opposite = 1,600335 * 15 = 24,005018
For the Pytagorean theorem
x = √24,005018^2 + 15^2 = 28,306199 = 28.3
The width of a rectangle measures (2h-6) centimeters, and its length measures (7h+8) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
18h +4
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w) where l is the length and w is the width
=2( 7h+8 + 2h-6)
Combine like terms
= 2( 9h+2)
Distribute
= 18h +4
Sine and cosine ratios! help!!
Find the length of the segment indicated. Round your answer to the nearest 10th of necessary.
Answer:
Step-by-step explanation:
Just using pythagorean theorem,
13.2²+16.9²=c²
174.24+285.61=c²
c²=√459.85
c= 21.4441134114
c = 21.4 (nearest tenth)
Rhonda walked diagonally across a rectangular playground with dimensions 60 m by 45 m. She started at point C. Determine the angle, to the
nearest degree, between her path and the longest side of the playground.
B
45m
D
60 m
Answer:
37degrees
Step-by-step explanation:
In order to get the required angle, we will use the SOH, CAH, TOA identity.
Let;
Adjacent = 60m
Opposite = 45m
According to TOA:
tan theta = opp/adj
tan theta = 45/60
tan theta = 0.75
theta = arctan 0.75
theta = 36.86
Hence the angle, to the nearest degree, between her path and the longest side of the playground is 37degrees
what is 20(y)+2(x) if y=2 and x=9
btw this is me
Answer: 20(y)+2(x) = 20(2) + 2(9) = 40 + 18 = 58
Answer:
58
Step-by-step explanation:
If y=20 and X=9, then the equation=20 × 2 + 2 ×9= 40 + 18=58.
What is the greatest common factor of 15n^5, 30n^3, and 45n^2
Answer:
15n^2 as it the highest expression that is common among these three.
Ed takes five 100-point tests in his algebra class. He scores 87, 85 and 87 points on the first three tests. If the scores of his last two tests differ by three points and he has a 90% average on his five tests, what was his highest test score?
PLS ANSWER QUICK WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
When we take an average of something, we have to add up all the data on the somethings and then divide by the number of somethings we have. Ed takes 5 tests, and we have scores for them; we also have his current average. What we don't know for sure are 2 of the 5 test scores, but we have enough to determine what they are.
If one test has a score of x, and the other test is 3 points less than that, the score on that last test is x - 3. Putting all of that together into an average problem:
[tex]\frac{87+85+87+x+(x-3)}{5}=90[/tex] and simplfiying a bit:
[tex]\frac{256+2x}{5}=90[/tex]. Multiply both sides by 5 to get
256 + 2x = 450; subtract 256 from both sides to get
2x = 194 and divide by 2:
x = 97
The one test score was a 97 and the other one, which was 3 less than that, was a 94.
Hi~! can someone help me with this~?
It costs 3 bowls and a jug 13.70, the jug costs $4.10 more that the bowl, how much does the jug cost-?
Thank u~!
Answer:
$6.50
Step-by-step explanation:
Let the cost of a bowl and a jug be $b and $j respectively.
3b +j= 13.70 -----(1)
j= b +4.10 -----(2)
Substitute (2) into (1):
3b +b +4.10= 13.70
4b +4.10= 13.70 (simplify)
4b= 13.70 -4.10 (-4.10 on both sides)
4b= 9.60
b= 9.60 ÷4 (÷4 on both sides)
b= 2.40
Substitute b= 2.40 into (2):
j= 2.40 +4.10
j= 6.50
Thus, the jug costs $6.50.
What is the units digit of 7⁷?
Answer:
[tex]7^{7}[/tex] = 823543
the unit position (the first) is equal to "3"
Step-by-step explanation:
A cylinder has a volume of 132x cubic feet and height of 4 feet. What is the area of the base?
* Square feet
Answer:
33π square feet
Step-by-step explanation:
Volume = base area × height
132π = base area × 4
or, base area = 132π/4
or, base area = 33π
Answered by GAUTHMATH
please help i've been stuck on this for a while
Answer:
SSS Postulate
Step-by-step explanation:
The first says 2 sides are the same
The second says 2 sides are the same
The last says 2 sides are the same
Side side side
SSS Postulate
Which of the following values are in the range of the function graphed below? Check all that apply
Answer:
B, C, D
Step-by-step explanation:
In this problem, the range is what the output, or y, can be. The origin, or the middie of the graph, is when x=0 and y=0. From the 10s on the screen, we can gather that 5 lines = a distance of 10 on the graph. Using this information, we can say
5 lines = distance of 10
divide both sides by 5 to find the distance for each line
1 line = distance of 2
The function goes from y=0 to three lines down, for a distance of 6. The range is therefore [-6,0] as all values from -6 to 0 on the y axis are included on the graph, including 0 and -6. In this range, -6, -2, and -1 are all included.
A boat covers a certain distance downstream in 3 hrs and the same distance upstream in 5 hrs. If the speed of the boat in still water is 8km/hour, find the speed of the stream.
help me please I am struggling to solve this question
Answer:
The stream's speed is 2 km/hr. We don't need to know the distance.
Step-by-step explanation:
Let the stream's speed = x
rate * time = d
The distance is the same going upstream as it is coming back down stream.
d_upstream = d_downsteam
(8 + stream)*3 = (8 - stream)*5
(8 + x)*3 = (8 - x)*5 Remove the brackets
24 + 3x = 40 - 5x Subtract 24 from both sides.
3x = 40 - 24 - 5x
3x = 16 - 5x Add 5x to both sides
3x + 5x = 16
8x = 16 Divide by 8
x = 16/8
x = 2
1. A football goal post casts a shadow 120 inches long. You are 5 feet 6 inches tall and cast a shadow 16.5 inches long. Find the height of the goal post in feet. Round your answer to the nearest whole number.
Answer:
40 feets
Step-by-step explanation:
Given that :
Person's height = 5feet 6 inches ;
Person's height in inches ;
1 foot = 12 inches ;
5 feets = (12 * 5) = 60 inches
Person's height = 60 + 6 = 66 inches
Height of person's shadow = 16.5 inches
Height of post shadow = 120 inches
Height of goal post = x
(Height of goal post / height of post shadow) = (person's height / person's shadow)
x / 120 = 66 / 16.5
Cross multiply :
16.5x = 120 * 66
16.5x = 7920
x = 7920 / 16.5
x = 480 inches
To feets ;
1 foot = 12 inches
480 inches = 480/12 feets = 40 feets
Which of the following is 1 2 over 4 in its simplest form?
Answer:
its 3
Step-by-step explanation:
3 is your answer I hope this help
Answer:
i don' know
Step-by-step explanation:
Need help ASAPPPPPPP
Answer:
A) 5
Step-by-step explanation:
51+48+15x+6=180
105+15x=180
15x=75
x=5
james cuts 2 of his neighbor's lawn the first is 1000 m long and 100 m wide what is the area
Step-by-step explanation:
The formula for area is l x b. This stands for length and breadth. I can multiply 1000(100) to get 100,000m. The area of the lawn is 100,000 m.
HOPE IT HELPS YOU
MARK ME BRAINLIEST
Please help me anyone
Answer:
Quelles caractéristiques ces mots ont-ils en commun ? Cliquez sur tout ce qui s'applique.
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
Step-by-step explanation:
The point M(-6, -4) is translated 2 units right. What are the coordinates of the resulting point, M′?
Answer:
(-4, -4)
Step-by-step explanation:
On a 2D graph, moving to the right means going up the x axis, to the left means down the x axis, up means up the y axis, and down means down the y axis.
The point is translated 2 units to the right. This means that it is going up the x axis by two units. As it is going up, we can say that it is increasing. Therefore, on a coordinate (x,y), going up the x axis means we add to the x value. For the point (-6, -4), we add 2 to the x value, or -6, to get -6+2 = -4 as our new x value.
Our new end value is (-4, -4)
write an equation for a line parallel to: y = -3x + 2.
Answer:
y = 1/3x + 2
Step-by-step explanation:
I NEEEDDDD HELPPPP ASAPPPP ITS URGENTTTT!!!
Answer:
(x-13)^2+(y+16)^2=12.56
Step-by-step explanation:
