Answer:
The family of directions of the given vector is represented by [tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].
Step-by-step explanation:
According to the given information, vector stands in the 4th Quadrant ([tex]x > 0[/tex], [tex]y < 0[/tex]) and direction of the vector ([tex]\theta[/tex]) in sexagesimal degrees, is determined by following definition:
[tex]\theta = 360^{\circ} - \tan^{-1} \left(\frac{|y|}{|x|} \right)\pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]
Please notice that angle represents a function with a periodicity of 360°.
If we know that [tex]x = 4[/tex] and [tex]y = -3[/tex], then the direction of the vector is:
[tex]\theta = 360^{\circ}-\tan^{-1}\left(\frac{|-3|}{|4|} \right)\pm 360\cdot i[/tex]
[tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex]
The family of directions of the given vector is represented by [tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].
Write 33/100 in a decimal
Answer:
it is .33
Step-by-step explanation:
take 33 and for each 0 move the decimal point like so
33.
3.3
.33
keep learning (:
320 rounded to the nearest ten
Answer:
320
Step-by-step explanation:
Answer:
the answer is 320
Step-by-step explanation:
twenty is part of the ten times table and is therefore a "ten"
How do you expand ln(1/49^k)
Answer:
There are a few rules that we can use here:
ln(a^x) = x*ln(a)
ln(a) - ln(b) = ln(a/b)
ln(1) = 0
So here we want to expand:
ln(1/49^k)
First we can use the second property to get:
ln(1/49^k) = ln(1) - ln(49^k)
using the third property, we have:
ln(1/49^k) = ln(1) - ln(49^k) = 0 - ln(49^k)
ln(1/49^k) = - ln(49^k)
Now we can use the first property to get:
ln(1/49^k) = - k*ln(49)
Now we can use the fact that:
49 = 7*7 = 7^2
then:
- k*ln(49) = -k*ln(7^2) = -2*k*ln(7)
So we have:
ln(1/49^k) = (-2*ln(7))*k
We can expand it anymore because this is a real number "(-2*ln(7))" times a variable k.
ACTIVITY 1. Evaluate the following (a) sin60° (b) tan 34° (c)cos 124°
Answer:
(a) sin 60° = √ 3/ 2 OR 0.8660
(b) tan 34° = 0.6745
(c) cos 124° = − 0.5591
Jerod hopes to earn $1200 in interest in 4.9 years time from $24,000 that he has available to invest. To decide if it's feasible to do this by investing In an account that compounds monthly, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places
Answer:
The annual interest rate would have to be of 0.1%.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Jerod hopes to earn $1200 in interest in 4.9 years time from $24,000 that he has available to invest.
This means that:
[tex]A(4.9) = 1200 + 24000 = 25200[/tex]
[tex]t = 4.9[/tex]
[tex]P = 24000[/tex]
Compounded monthly:
This means that [tex]n = 12[/tex]
What would the annual rate of interest have to be?
We have to solve for r, so:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]25200 = 24000(1 + \frac{r}{12})^{12*4.9}[/tex]
[tex](1 + \frac{r}{12})^{12*4.9} = \frac{25200}{24000}[/tex]
[tex](1 + \frac{r}{12})^{58.8} = 1.05[/tex]
[tex]\sqrt[58.8]{(1 + \frac{r}{12})^{58.8}} = \sqrt[58.8]{1.05}[/tex]
[tex]1 + \frac{r}{12} = (1.05)^{\frac{1}{58.8}}[/tex]
[tex]1 + \frac{r}{12} = 1.00083[/tex]
[tex]\frac{r}{12} = 0.00083[/tex]
[tex]r = 12*0.00083[/tex]
[tex]r = 0.001 [/tex]
The annual interest rate would have to be of 0.1%.
Cho hình hộp chữ nhật ABCD A B C D
Answer:
A B C D
A×B×C×D
3×3×3×6
162
1. Which of these sentences are propositions? What are the
truth values of those that are propositions?
a) Boston is the capital of Massachusetts.
b) Miami is the capital of Florida.
c) 2 + 3 = 5. d) 5 + 7 = 10.
e) x + 2 = 11. 1) Answer this question.
Answer:I have the same problem
Step-by-step explanation
PLS HELP
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (g o f) (-5)
–6
3
–59
26
Answer:
1st option
Step-by-step explanation:
Evaluate f(- 5) then substitute the value obtained into g(x)
f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then
g(3) = - 4(3) + 6 = - 12 + 6 = - 6
A ball was bounced 3 times between 3:15p and 3:18p, thrown 10 times between 3:20p and 3:30p and bounced 7 times between 4:15p and 4:20p. What is the rate per hour of ball bouncing based on a 2 hour data collection time period.
Answer:
strange phrasing of a question
If one assumes that the "observation" was from 3:00 pm - 5:00 pm (2 hours)
and the ball was ONLY "bounced" 10 times (3+7)
we can can say that the rate was 10 bounces/2 hours or 5 b.p.h. (bounces per hour)
Step-by-step explanation:
The slope of the line below is to use the corners of the labeled point to find a point slope equation of the line.
Plz help
Answer: Choice A) y - 10 = 2(x - 3)
============================================================
Explanation:
We can rule out choices C and D because this diagonal line has a positive slope (as it moves uphill when moving to the right).
So m = 2 must be the slope.
---------
Recall that
y - y1 = m(x - x1)
represents the point slope form of a linear equation.
The point shown on this graph is (3,10) meaning that x1 = 3 and y1 = 10 pair up together.
So,
y - y1 = m(x - x1)
y - 10 = 2(x - 3)
which points to choice A as the final answer
1 gallon = 3.8 liters 1 mile = 1.6 kilometers using the conversion above,a bus that uses that uses 10 liters of gasoline to travel 10 liters of gasoline to travel 100 kilometers would have an efficiency rating closest to a) 15 miles per gallon b) 24 miles per gallon c) 38 miles per gallon d) 60 miles per gallon
9514 1404 393
Answer:
b) 24 miles per gallon
Step-by-step explanation:
The usual metric measure of vehicle fuel efficiency is liters per 100 km. Greater efficiency is indicated by a lower value.
In the US, the measure is usually miles per gallon. Greater efficiency is indicated by a higher value. Since we want the efficiency expressed in miles per gallon, we need to divide distance by fuel consumption.
(distance)/(fuel used) = (100 km)/(10 L)
= (100 km)/(10 L) × (1 mi)/(1.6 km) × (3.8 L)/(1 gal) = (100×3.8)/(10×1.6) mi/gal
= 23.75 mi/gal ≈ 24 mi/gal
a coin is tossed succesively three times times . determine tje probabiliy of getting all three heads
Answer:
Answer : 1/8.
Step-by-step explanation:
Hey there!
Please see the attached picture for your answer.
Hope it helps!
Ayuda por fa con estos ejercicios por fa urgente
Step-by-step explanation:
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+32
3. Solve the system of equations using the elimination method.
5x + 2y = 9
-5x + 4y = 3
please give detailed steps!!
Answer:
x = 1
y = 2
Step-by-step explanation:
5x + 2y = 9
-5x + 4y = 3
==> 6y = 12 ==> y = 12/6 ==> y = 2.
we replace y by its value in the first or the second equation, so will have:
5x + 2×2 = 9
5x + 4 = 9
5x = 5
x = 1
An exterior angle of a regular polygon cannot have the measure of
Select one:
a. 120
b. 40
c. 50
d. 90
e. 30
I need your help once again, Brian
Answer:
3b^2+2b-8
Step-by-step explanation:
(3b-4)(b+2)
FOIL
first:3b*b = 3b^2
outer:2*3b = 6b
inner: -4b
Last: -4*2 = -8
Add together
3b^2 +6b-4b-8
Combine like terms
3b^2+2b-8
Answer:
[tex]3b^2+2b-8[/tex]
Step-by-step explanation:
Again, we can use FOIL to expand this equation:
First: [tex]3b(b)=3b^2[/tex]
Outer: [tex]3b(2)=6b[/tex]
Inner: [tex]-4(b)=-4b[/tex]
Last: [tex]-4(2)=-8[/tex]
We can combine the b terms to get [tex]2b[/tex], and we have our answer as [tex]3b^2+2b-8[/tex]
There are 52 cards in a deck, and 13 of them are hearts. Four cards are dealt, one at a time, off the top of a well-shuffled deck. What is the percent chance that a heart turns up on the fourth card, but not before
Answer:
10.97%
Step-by-step explanation:
There are 52 cards.
13 of them, are hearts.
Then
52 - 13 = 39 cards are not hearts.
4 cards are drawn, we want to find the percent chance that the fourth card is a heart card, but no before.
So the first card can't be a heart card.
because the deck is well-shuffled, all the cards have the same probability of being drawn.
Then the probability of not getting a heart card, is equal to the quotient between the number of non-heart cards (39) and the total number of cards (52), then the probability is:
p₁ = 39/52
The second card also can't be a heart card, the probability is calculated in the same way than above, but now there are 38 non-heart cards and a total of 51 cards (because one card was already drawn) then the probability here is:
p₂ = 38/51
For the third card the reasoning is similar to the two above cases, here the probability is:
p₃ = 37/50
The fourth card should be a hearts card, the probability is computed in the same way than above, as the quotient between the number of heart cards in the deck (13) and the total number of cards in the deck (now there are 49 cards)
then the probability is:
p₄ = 13/49
The joint probability (the probability of these 4 events happening together) is equal to the product between the individual probabilities:
P = p₁*p₂*p₃*p₄
P = (39/52)*(38/51)*(37/50)*(13/49) = 0.1097
The percent chance is the above number times 100%
Percent = 0.1097*100% = 10.97%
g U is the set of in the United States. A is the set of in the United States that have the in their name. B is the set of in the United States that have the in their name. Describe the set in words. Choose the correct answer below. A. is the set of in the United States that have the . B. is the set of in the United States that have the . C. is the set of in the United States that have the . D. is the set of in the United States that have the .
Question isn't well formatted picture if actual question is attached below :
Answer:
A' set of colleges in the United States which Don not have the word community in their name.
Step-by-step explanation:
If a universal set U is defined as :
U =set of colleges in the United States.
A = the set of colleges in the United States that have the word community in their name.
B is the set of colleges in the United States that have the name of an entertainer in their name.
The set A' is called the A complement. The complement of a particular refers to elements in the universal set which are not in A ;
A' = 1 - A'
Therefore, A' set of colleges in the United States which Don not have the word community in their name.
