Answer:
a = 8.1
Step-by-step explanation:
Firstly, since we have a triangle, automatically, we have 3 interior angles
Mathematically the sum of these angles = 180
A + B + C = 180
27 + 25 + C = 180
52 + C = 180
C = 180-52
C = 128
We use the sine rule to find a
The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle
Thus, mathematically according to the sine rule;
c/Sin C = a/Sin A
14/sin 128 = a/sin 27
a = 14sin27/sin 128 = 8.0657
which to the nearest tenth is 8.1
Enter the correct answer in the box. Write your answer in the form at + bm = c.
Answer:
t + m ≤ 11
Step-by-step explanation:
The total weight will be the sum of the weights of the bags present. The weight of t bags of topsoil will be 30t; the weight of m bags of mulch will be 30m. We want the total weight to be at most 330. (Weight numbers are in pounds.)
30t +30m ≤ 330
We can remove a factor of 30 to simplify this to ...
t + m ≤ 11
_____
You may be expected to use the un-simplified form of the inequality.
Which of the following points is a solution of the inequality y <-Ixl
You did not give any options but i will try to answer.
y < -lxl basically means that the value of y is less than the absolute value of x time - 1.
So if x = 2, then y is any number less than -2.
And if x is -3. then y is any number less than -3.
Happy to help!
Find the value of n such that 540n is perfect cube.
Answer:
1.35
Step-by-step explanation:
next cube above 540 is 729
to get to 729: 729 / 540 = 1.35
n = 1.35
Which, if any, of the following proofs are correct demonstrations of the validity of this argument? A ⊃ (B ⊃ C) B ⊃ (~C ⊃ ~A) Proof 1 (1) A ⊃ (B ⊃ C) /B ⊃ (~C ⊃ ~A) Premise/Conclusion (2) (A • B) ⊃ C 1 Exp (3) (B • A) ⊃ C 2 Com (4) B ⊃ (A ⊃ C) 3 Exp (5) B ⊃ (~C ⊃ ~A) 4 Contra Proof 2 (1) A ⊃ (B ⊃ C) /B ⊃ (~C ⊃ ~A) Premise/Conclusion (2) B Assumption (3) A Assumption (4) B ⊃ C 1, 3 MP (5) C 2, 4 MP (6) A ⊃ C 3–5 CP (7) B ⊃ (A ⊃ C) 2–6 CP (8) B ⊃ (~C ⊃ ~A) 7 Contra
Answer
Step-by-step explanation:
Answer:
See the argument below
Step-by-step explanation:
I will give the argument in symbolic form, using rules of inference.
First, let's conclude c.
(1)⇒a by simplification of conjunction
a⇒¬(¬a) by double negation
¬(¬a)∧(2)⇒¬(¬c) by Modus tollens
¬(¬c)⇒c by double negation
Now, the premise (5) is equivalent to ¬d∧¬h which is one of De Morgan's laws. From simplification, we conclude ¬h. We also concluded c before, then by adjunction, we conclude c∧¬h.
An alternative approach to De Morgan's law is the following:
By contradiction proof, assume h is true.
h⇒d∨h by addition
(5)∧(d∨h)⇒¬(d∨h)∧(d∨h), a contradiction. Hence we conclude ¬h.
A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. What is the probability that the random sample of 100 male students has a mean GPA greater than 3.42?
Answer: 0.0548
Step-by-step explanation:
Given, A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05.
Let [tex]\overline{X}[/tex] represents the sample mean GPA for each student.
Then, the probability that the random sample of 100 male students has a mean GPA greater than 3.42:
[tex]P(\overline{X}>3.42)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3.42-3.5}{\dfrac{0.5}{\sqrt{100}}})\\\\=P(Z>\dfrac{-0.08}{\dfrac{0.5}{10}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>1.6)\\\\=1-P(Z<1.6)\\\\=1-0.9452=0.0548[/tex]
hence, the required probability is 0.0548.
differentiate with respect to X
[tex] \sqrt{ \frac{cos2x}{1 +sin2x } } [/tex]
Power and chain rule (where the power rule kicks in because [tex]\sqrt x=x^{1/2}[/tex]):
[tex]\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'[/tex]
Simplify the leading term as
[tex]\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}[/tex]
Quotient rule:
[tex]\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}[/tex]
Chain rule:
[tex](\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)[/tex]
[tex](1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)[/tex]
Put everything together and simplify:
[tex]\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}[/tex]
[tex]=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}[/tex]
[tex]=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}[/tex]
[tex]=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}[/tex]
[tex]=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}[/tex]
[tex]=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}[/tex]
[tex]=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}[/tex]
Please HELP best answer will receive a BRAINLIEST. Given the probability density function f ( x ) = 1/3 over the interval [ 4 , 7 ] , find the expected value, the mean, the variance and the standard deviation.
Answer:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
Step-by-step explanation:
For this case we have the following probability density function
[tex] f(x)= \frac{1}{3}, 4 \leq x \leq 7[/tex]
And for this case we can find the expected value with this formula:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
A 4 foot wide painting should be centered on a 10 foot wide wall. How many feet (x) should be on each side of the painting?
Answer:
3 feet
Step-by-step explanation:
To find x, we can write the following equation:
x + 4 + x = 10
2x + 4 = 10
2x = 6
x = 3 feet
Betty has several of the standard six-sided dice that are common in many board games. If Betty rolls one of these dice, what is the probability that: She rolls a three. She rolls an odd number. She rolls a six or odd number.
Answer:
The probability of rolling a 3 is 1/6 because there's only one 3 out of the 6 options that are on a standard die.
The probability of rolling an odd number is 3/6 or 1/2 because 3 out of the 6 numbers on a standard die (1, 3, 5) are odd.
The probability of rolling a six or odd number is 4/6 or 2/3 because out of the 6 numbers on a standard die, there's one 6 and 3 odd numbers and 1 + 3 = 4.
The Box-and-Whisker plot shows the average temperatures in, atlanta, georgia, in march. which statement about the temperatures in atlanta must be true? A. about half the days in march had average temperatures above 60 degrees. B. about half the days in march had average temperatures either below 60 or above 73 degrees C. the coldest day in march was 51 D. the hottest day in march was 84
Answer:
"B. about half the days in march had average temperatures either below 60 or above 73 degrees"
Step-by-step explanation:
To answer this question, note that a box plot is usually divided into quartiles, each representing approximately 25% each.
In the box plot above,
*about 25% (Q1) represents days with temperature of 60° and below. This is about ¼ of the days in March.
*About 25% (Q2) represents days with temperature between 61° and 68°. That's about ¼ of the days in March
*About 25% (Q3) represents days with temperature between 70° and 73°. That's about ¼ of the days in March
*About 25% (Q4) represents days with temperature between 74° and 82°. That's about ¼ of the days in March
*Coldest day in March has a temperature of 54°
*Hottest day in March is 82°
From the options given, the only statement that is true is "B. about half the days in march had average temperatures either below 60 or above 73 degrees"
¼ of the Days in March has temperatures below 60° (Q1), while ¼ of the days in March has temperatures above 73° (Q4). Therefore, ¼+¼ = ½ of the days in March having average temperatures either below 60 or above 73 degrees.
Answer:
b
Step-by-step explanation:
About half of the days in March had average temperatures either below 60 or above 73 degrees.
State sales tax S S is directly proportional to retail price p p . An item that sells for 142 142 dollars has a sales tax of 12.32 12.32 dollars. Find a mathematical model that gives the amount of sales tax S S in terms of the retail price p p .
Answer: [tex]S=0.087p[/tex] .
Step-by-step explanation:
Equation for direct proportion:
y=kx
, where x= independent variable ,
y=dependent variable.
k= proportionality constant
Here, State sales tax S is directly proportional to retail price p.
Also, dependent variable= S, independent variable =p
Required equation: S= kp
Put S= 12.32 and x= 142
[tex]S=12.32=k(142)\\\\\Rightarrow\ k=\dfrac{12.32}{142}\approx0.087[/tex]
Hence, the required equation is [tex]S=0.087p[/tex] .
(3/4) URGENT!! PLEASE HELP! -50 POINTS- WILL MARK BRAINLEST ASAP AND 5 STARS IF CORRECT!!! please no wrong answers for the points.
Answer:
D
Step-by-step explanation:
The graph above is your graph.
As x increase, y decreases
As x decrease, y increases.
However, there is a small portion of the graph where both x and y were positive.
But I'm guessing it should be D.
Answer:
D
Step-by-step explanation:
[tex]f(x)=-x^3+2x^2-x+3[/tex]
As the highest power is 3, it is odd, as [tex]x[/tex] approaches to [tex]-\infty[/tex] [tex]y[/tex] approaches to [tex]\infty[/tex]
First, we have [tex]x \rightarrow-\infty[/tex], [tex]y \rightarrow \infty[/tex]
Plotting the graph, you can easily conclude the answer to the question.
And as [tex]x \rightarrow \infty[/tex], [tex]y \rightarrow -\infty[/tex]
Yesterday at 1:00 P.M., Maria’s train was 42 miles north of Gull’s Beach, traveling north at an average speed of 90 mph. At the same time on the adjacent track, Elena’s train was 6 miles north of Gull’s Beach, traveling north at an average speed of 101 mph. To the nearest hundredth of an hour, after how much time will the trains meet up? 0.23 hours 0.31 hours 3.27 hours 4.36 hours
Answer:b
Step-by-step explanation:
Answer:
3.27 hours
Step-by-step explanation:
Calculate the difference in speed and distance between the trains.
The relative speed:
101 - 90 = 11 mph
Difference in distance:
42 - 6 = 36 miles
[tex]time=\frac{distance}{speed}[/tex]
[tex]t=\frac{36}{11}[/tex]
[tex]t = 3.27[/tex]
A car was sold at a 12% discount, which amounts to $1800. How much would the car sell for after the discount?
Answer:
1584$
Step-by-step explanation:
Original price is 1800$ (100%)
Discount percent: 12%
=> The price after discount is 100 - 12 = 88% of original price
=> The price after discount is 1800 x 88% = 1800 x 88/100 = 1584$
Answer:
13200
Step-by-step explanation:
12% - 1800
100% - x
X = (1800x100)/12 = 15000 - original price
15000-1800 = original price - discount = 13200 price after discount
The total cost for my brother's bowling party was $140. It cost $50to reserve a bowling lane plus the cost of renting shoes for the 9 people attending.
Answer:
$10 to rent shoes for 9 people
Step-by-step explanation:
Total amount of the party = $140
A bowling lane = $50
$140 - $50 = $90
$90 divided by 9 = 10
$10 to rent shoes for 9 people
A circular chicken house has an area of 40m². What length of chicken wire is required to fence the house without any wire left over?
please answer this correctly
How far apart are the gift shop and the science lab
Please answer this correctly without making mistakes
The answer is 86.4 km
Explanation:
The graph shows the gift shop is to the east of the science lab, and, between the gift shop and the science lab it is the art supply. Besides this, the description of the graph provides the distance between the art supply and the science lab, which is 40.0, as well as, the distance between the art supply and the gift shop, which is 46.4 kilometers.
In this context, it is possible to calculate the distance from the science lab to the gift shop by adding the partial distances, considering the art supply as a middle point in the map. This means the distance from the lab to the gift shop = 40.0 km (distance from the lab to the art supply) + 46.4 km (distance from the art supply to the gift shop) = 86.4 km.
On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least 50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"? 4x + 8y 50 4x + 8y ≥ 50
Answer:
4x + 8y ≥ 50
Step-by-step explanation:
Lorenzo must score at least 50 points to earn a B. He cannot score any less, therefore you use the greater than or equal to sign (≥).
Answer:
4x+8y>=50 is the required inequality.
Step-by-step explanation:
Here,
4 marks (multiple choice) and 8 marks (word problem) are the marks of each questions in the exam.
also x and y represents the number of correct and wrong answer respectively.
according to the question the person must have The points equal to or more than 50 points so, the inequality must be 4x+8y>=50.
so, theanswer is 4x+8y>=50.
hope it helps...
3x to the 2nd power +4y to the 2nd power x=2 y=1 z=-3
Answer:
Step-by-step explanation:
3(2)^2 + 4(1)^2
3(4) + 4
12+4= 16
Answer:
[tex]\huge\boxed{16}[/tex]
Step-by-step explanation:
[tex]3x^2+4y^2\ \text{for}\ x=2;\ y=1.\\\\\text{Substitute:}\\\\3(2)^2+4(1)^2=3(4)+4(1)=12+4=16\\\\\text{Used PEMDAS}[/tex]
A housepainter mixed 3 1/2 pints of blue paint in a bucket with 1 1/6 pints of white paint. How much paint was in the bucket? The answer should be written as a proper mixed number and should be simplified, if possible.
Answer:
4 2/3 :)
Step-by-step explanation:
The total paint in the bucket in the simplified mixed fraction is [tex]6\frac{2}{3}[/tex] pints.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, A housepainter mixed [tex]3\frac{1}{2}[/tex] pints of blue paint in a bucket with [tex]1\frac{1}{6}[/tex] pints of white paint.
So, The total paint in the bucket is the sum of the pints of both paints which
is, = [tex](3\frac{1}{2} + 1\frac{1}{6})[/tex] pints.
[tex]= (\frac{7}{2} + \frac{7}{6})[/tex] pints.
[tex]= \frac{21 + 7}{6}[/tex] pints.
[tex]= \frac{28}{6}[/tex] pints.
[tex]= 6\frac{2}{3}[/tex] pints.
learn more about fractions here :
https://brainly.com/question/10354322
#SPJ2
Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xey + yez + zex, (0, 0, 0), v = 4, 3, −1
Answer: 6 / √26
Step-by-step explanation:
Given that f(x, y, z) = xe^y + ye^z + ze^x
so first we compute the gradient vector at (0, 0, 0)
Δf ( x, y, z ) = [ e^y + ze^x, xe^y + e^z, ye^z + e^x ]
Δf ( 0, 0, 0 ) = [ e⁰ + 0(e)⁰, 0(e)⁰ + e⁰, 0(e)⁰ + e⁰ ] = [ 1+0 , 0+1, 0+1 ] = [ 1, 1, 1 ]
Now we were also given that V = < 4, 3, -1 >
so ║v║ = √ ( 4² + 3² + (-1)² )
║v║ = √ ( 16 + 9 + 1 )
║v║ = √ 26
It must be noted that "v" is not a unit vector but since ║v║ = √ 26, the unit vector in the direction of "V" is ⊆ = ( V / ║v║)
so
⊆ = ( V / ║v║) = [ 4/√26, 3/√26, -1/√26 ]
therefore by equation D⊆f ( x, y, z ) = Δf ( x, y, z ) × ⊆
D⊆f ( x, y, z ) = Δf ( 0, 0, 0 ) × ⊆ = [ 1, 1, 1 ] × [ 4/√26, 3/√26, -1/√26 ]
= ( 1×4 + 1×3 -1×1 ) / √26
= (4 + 3 - 1) / √26
= 6 / √26
Someone please explain this!!!!
Answer:
23) x ≥ -140.
24) k > -9.
25) v ≥ 9.
26) m > 16.
Step-by-step explanation:
23) -14 ≤ [tex]\frac{x}{10}[/tex]
[tex]\frac{x}{10}[/tex] ≥ -14
x ≥ -140
Since it is a ≥ sign, you will put a shaded circle at -140, and the line will stretch infinitely to the right of the circle.
24) -20 < k - 11
k - 11 > -20
k > -9
Since it is a > sign, you will put a non-shaded circle at -9, and the line will stretch infinitely to the right of the circle.
25) -6v ≤ 54
6v ≥ 54
v ≥ 9
Since it is a ≥ sign, you will put a shaded circle at 9, and the line will stretch infinitely to the right of the circle.
26) 8 < [tex]\frac{m}{2}[/tex]
[tex]\frac{m}{2}[/tex] > 8
m > 16
Since it is a > sign, you will put a non-shaded circle at 16, and the line will stretch infinitely to the right of the circle.
Hope this helps!A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 4 m from the dock
Answer:
-1.031 m/s or [tex]\frac{-\sqrt{17} }{4}[/tex]
Step-by-step explanation:
We take the length of the rope from the dock to the bow of the boat as y.
We take x be the horizontal distance from the dock to the boat.
We know that the rate of change of the rope length is [tex]\frac{dy}{dt}[/tex] = -1 m/s
We need to find the rate of change of the horizontal distance from the dock to the boat = [tex]\frac{dx}{dt}[/tex] = ?
for x = 4
Applying Pythagorean Theorem we have
[tex]1^{2} +x^{2} =y^{2}[/tex] .... equ 1
solving, where x = 4, we have
[tex]1^{2} +4^{2} =y^{2}[/tex]
[tex]y^{2} = 17[/tex]
[tex]y = \sqrt{17}[/tex]
Differentiating equ 1 implicitly with respect to t, we have
[tex]2x\frac{dx}{dt} = 2y\frac{dy}{dt}[/tex]
substituting values of
x = 4
y = [tex]\sqrt{17}[/tex]
[tex]\frac{dy}{dt}[/tex] = -1
into the equation, we get
[tex]2(4)\frac{dx}{dt} = 2(\sqrt{17} )(-1)[/tex]
[tex]\frac{dx}{dt} = \frac{-\sqrt{17} }{4}[/tex] = -1.031 m/s
Find the coordinate vector [Bold x ]Subscript Upper B of x relative to the given basis BequalsStartSet Bold b 1 comma Bold b 2 comma Bold b 3 EndSet.
Answer:
3
Step-by-step explanation:
3
The sum of three consecutive even integers is 90. Find the Integers.
Answer:
28, 30, 32
Step-by-step explanation:
Their average will be 90/3 = 30. That is the middle integer.
The three integers are 28, 30, 32.
_____
Comment on the working
It often works well to use the average value when working consecutive integer problems. The average of an odd number of consecutive integers is the middle one. The average of an even number of consecutive integers is halfway between the middle two.
There are 42 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 6 min. (Give answers accurate to 3 decimal places.)
(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?
1
(b) If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV?
2
Answer:
A) 0.99413
B) 0.00022
Step-by-step explanation:
A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:
Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes
Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:
μ = n*μ_s ample = 42 × 5 = 210 minutes
While the standard deviation for the population would be:
σ = √nσ_sample = √(42 × 6) = 15.8745 minutes
To find the z-score, we will use the formula;
z = (x - μ)/σ
Thus;
z = (250 - 210)/15.8745
z = 2.52
From the z-distribution table attached, we have;
P(Z < 2.52) ≈ 0.99413
B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.
Thus, total time is now 250 + 10 = 260 minutes
Similar to the z-formula in A above, we have;
z = (260 - 210)/15.8745
z = 3.15
P(Z > 3.15) = 0.00022
Vector has x and y components of -8.80 cm and 18.0 cm, respectively; vector has x and y components of 12.2 cm and -6.80 cm, respectively. If - + 3 = 0, what are the components of ? x = cm y = cm
Question:
Vector A has x and y components of −8.80 cm and 18.0 cm , respectively; vector B has x and y components of 12.2 cm and −6.80 cm , respectively. If A − B +3 C = 0, what are the components of C?
Answer:
x = ___ cm
y = ___ cm
Answer:
x = 7.0cm
y = -8.27cm
Step-by-step explanation:
For a vector F, with x and y components of a and b respectively, its unit vector representation is as follows;
F = ai + bj [Where i and j are unit vectors in the x and y directions respectively]
Using this analogy, let's represent vectors A and B from the question in their unit vector notation.
A has an x-component of -8.80cm and y-component of 18.0cm
B has an x-component of 12.2cm and y-component of -6.80cm,
In unit vector notation, these become;
A = -8.80i + 18.0j
B = 12.2 i + (-6.80)j = 12.2i - 6.80j
Also, there is a third vector C. Let the x and y components of C be a and b respectively. Therefore,
C = ai + bj
Now,
A - B + 3C = 0 [substitute the vectors]
=> [-8.80i + 18.0j] - [12.2 i -6.80j] + [3(ai + bj)] = 0 [open brackets]
=> -8.80i + 18.0j - 12.2 i + 6.80j + 3(ai + bj) = 0
=> -8.80i + 18.0j - 12.2 i + 6.80j + 3ai + 3bj = 0
=> -8.80i + 18.0j - 12.2 i + 6.80j + 3ai + 3bj = 0 [collect like terms and solve]
=> -8.80i - 12.2 i + 3ai + 6.80j + 18.0j + 3bj = 0
=> -21.0 i + 3ai + 24.8j + 3bj = 0 [re-arrange]
=> 3ai + 3bj = 21.0i - 24.8j
Comparing both sides shows that;
3a = 21.0 -------------(i)
3b = -24.8 -----------(ii)
From equation (i)
3a = 21.0
a = 21.0 / 3 = 7.0
From equation (ii)
3b = -24.8
b = -24.8 / 3
b = -8.27
Therefore, the x-component and y-component of vector B which are a and b, are 7.0cm and -8.27cm respectively.
There are two pennies lying flat on a table. One of the pennies is fixed to the table, while the other one is being rolled around the fixed one staying tangent to it all the way. How many spins will it make by the time it returns to the starting point ?
Answer:
well if you want my answer even though it could not be right so dont get mad at me if i am wrong but i think that it is all mostly based on how far they are from each other the further it is the more it will roll the closer it is the less it it will roll
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
rolling it shows its circumference and the other pennine has the ame circumference
The surface area of a given cone is 1,885.7143 square inches. What is the slang height?
This question is not complete. This is because it lacks the appropriate diagram containing necessary information to solve this question.
Please find attached the appropriate diagram to solve for this question
Complete Question :
The surface area of a given cone is 1,885.7143 square inches. What is the slant height?
Answer:
25 inches
Step-by-step explanation:
In the diagram, we are given the following information
Height of the cone = 20 inches
Radius of the cone = 15 inches.
The formula for the slant height of a cone represented by l =
l² = r² + h²
l = √(r² + h²)
l = √(15² + 20²)
l = √(225 + 400)
l = √625
l = 25 inches
Therefore, the slant height of this cone = 25 inches
INTEGERS YES OR NO 74 3.49 - 4/7 (the - is suupose to be inbetween both numbers, not just the 4 is negative) -148.29 - 8/1
Answer:
The integers are the numbers such that:
- The distance between consecutive integers is always of 1 unit and the integer numbers only have zeros after the decimal point, such that the set is: Z = {..., 0, 1, 2, 3, 4, ......}
74) No digits after the decimal point, so this is an integer.
3.49) we have digits after the decimal point, so this is not an integer.
4/7) 4 is smaller than 7, so 4/7 is smaller than one and larger than zero,
one and zero are consecutive integer numbers, so 4/7 can not be an integer number.
You also can solve the division and find that the quotient has digits after the decimal point.
148.29) This number has digits after the decimal point, so this is not an integer number.
8/1) here we have 8 divided by one, we know that:
8/1 = 8
8 has no digits after the decimal point, so this is an integer.