Answers
[tex]\bf 8cos^2(\theta )-3cos(\theta )=0\implies \stackrel{common~factor}{cos(\theta )}[8cos(\theta )-3]=0\\\\ -------------------------------\\\\ cos(\theta )=0\implies \measuredangle \theta =cos^{-1}(0)\implies \measuredangle \theta =90^o\\\\ -------------------------------\\\\ 8cos(\theta )-3=0\implies 8cos(\theta )=3\implies cos(\theta )=\cfrac{3}{8} \\\\\\ \measuredangle \theta =cos^{-1}\left( \cfrac{3}{8}\right)[/tex]
22)
[tex]\bf \begin{cases} y=cos(2x)\\ y=cos^2(x)-1 \end{cases}\implies \stackrel{intersection~at}{cos(2x)=cos^2(x)-1} \\\\\\ 2cos^2(x)-1=cos^2(x)-1\implies 2cos^2(x)-1-cos^2(x)+1=0 \\\\\\ 2cos^2(x)-cos^2(x)=0\implies cos^2(x)=0\implies cos(x)=0 \\\\\\ \measuredangle \theta =cos^{-1}(0)\implies \measuredangle \theta =180^o~~,~~270^o[/tex]
Trigonometric identities are equations that hold true for all permissible values of the involved variables. They are fundamental to many areas of mathematics and have applications in various fields such as physics and engineering.
Explanation:Trigonometric identities are equations that are true for all values of the variables where both sides of the equation are defined. They are fundamental to the study of mathematics, particularly in geometry, calculus and physics.
Some of the basic trigonometric identities include:
Reciprocal identities:sin = 1/csc θcos = 1/sec θtan = 1/cot θPythagorean identities:sin² θ + cos² θ = 11 + tan² θ = sec² θ1 + cot² θ = csc² θ...Trigonometric identities are widely used in solving trigonometric equations and proving other identities, and in many fields such as engineering, physics and computer science.
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Related Questions
what is the answer to the system of equations 2x+y=29 and y=1x+2.
explain why, if answer is a random answer you will be reported and lose points.
this is for free and easy points
Answers
The other equation is 2x+y = 29.
2x+y = 29
2x+x+2 = 29
3x = 27
x = 9
y = x+2 = 9+2 = 11
2x+y = 29
2x+x+2 = 29
3x = 27
x = 9
Hope this helps...
library library currently has 125 audiobook the library plan purchase the same number of books each month after 4 months the library has 20 more audiobook which equation can be used to determine t and a total number of audio books the library will have after and months
Answers
Eliminate the parameter. x = one divided by two t, y = 3t^3 - 1
Answers
Answer:
y = 24x3 - 1
Step-by-step explanation:
None needed YW
The perimeter of parallelogram ABCD is equal to 10 cm. Find the length of diagonal BD if you know that the perimeter of △ABD is 8 cm.
Answers
Let
P1-------------> Perimeter of parallelogram ABCD
P2-------------> Perimeter of △ABD
we know that
P1=10 cm
P1=2*(AD)+2*(AB)=10------------> AB+AD=5-----------> equation 1
and
P2=AD+AB+DB
P2=8 cm------------>AD+AB+DB=8-------- AB+AD=8-DB-----> equation 2
I substitute 1 in 2
(5)=8-DB----------> DB=8-5-----------> DB=3 cm
the answer is DB=3 cm
The length of the diagonal BD is 3 centimeters.
Procedure - Length determination in a parallelogram sideA parallelogram is a quadrilateral where each pair of parallel sides have the same length and can be form by two congruent triangles which share the same side (diagonal).
Expressions for the parallelogramPerimeter equations for the parallelogram are the following:
[tex]AB + BD + AD = 8\,cm[/tex] (1)
[tex]2\cdot AB + 2\cdot AD = 10\,cm[/tex] (2)
Where:
[tex]AB[/tex], [tex]AD[/tex] - Side lengths of the parallelogram, in centimeters. [tex]BD[/tex] - Diagonal length of the parallelogram, in centimeters.Resolution of the systemBy (2) we have the following conclusion:
[tex]AB + AD = 5\,cm[/tex]
And we find the length of the diagonal BD by (1):
[tex]5\,cm + BD = 8\,cm[/tex]
[tex]BD = 3\,cm[/tex]
The length of the diagonal BD is 3 centimeters. [tex]\blacksquare[/tex]
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what's a Fibonacci sequence?
Answers
A Fibonacci Sequence is a series of number . It is the sum of two preceding numbers.
Hope this helps <33
simplest sequence is 1,1,2,3,5,8 and so on
I need this equation solved with the work shown please
Answers
SO THE ANSWER IS 2 1/2
find the distance between :(-1,5)( 3,-2)
Answers
distance= [tex] \sqrt{(3+1)^2+(5+2)^2}= \sqrt{65} [/tex]
Complete the comparison: 26 < ? A. 25 B. 54 C. 13 D. 26
Answers
meaning 26 is less than 54 which is true
A self-service car wash charges $4 for the initial 5 minutes plus an additional $0.75 for each minute after that. Nick only has $10 to spend on washing his car. Let m represent the number of minutes Nick spends washing his car.
Answers
Cost for spending 5 min is $4, any additional minutes will be $0.75 per minutes.
amount of cash Nick will remain with after spending $4 will be:
10-4=$6
the total extra minutes he will spend will be:
6=0.75*m
0.75m=6
thus
m=6/0.75
m=8 min
the total number of minutes that Nick will spend with $10 will be:
8+5=13 min
Nick can spend a total of 13 minutes washing his car at the self-service car wash with his $10 budget, accounting for both the initial charge and the additional cost per minute after the first 5 minutes.
Nick is planning to use a self-service car wash that charges $4 for the initial 5 minutes and an additional $0.75 for each minute after that. With a budget of $10, he wants to calculate the number of minutes (m) he can spend washing his car. The cost for m minutes is given by the equation:
Total Cost = Initial Charge + (Additional Charge per minute * Number of extra minutes)
First, subtract the initial charge from the total amount Nick has:
$10 - $4 = $6
This is the amount remaining for the additional minutes. Next, divide this by the additional charge per minute:
$6 / $0.75 per minute = 8 minutes
Therefore, Nick can spend 8 minutes washing his car after the initial 5 minutes, for a total of 13 minutes.
Alice has a box that is 5 inches long, 5 inches wide, and 5 inches tall. How many 1 inch by 1 inch by 1 inch blocks can Alice fit into the box?
Answers
Hope this helps!:)
~Scarlett
how do you reduce 4/8?
Answers
so you get 2/4 which is equal to 1/2 which is your answer!!
Hope this helps!!
John bought 15 cookies and ate 3 of them. He ate ____% of the cookies.
Answers
Which are the solutions of x2 = –5x + 8?
Answers
hope this helps
Answer:
The solutions are 1.275 and -6.275
Step-by-step explanation:
Given
x^2 = –5x + 8
First, put all terms in the left side of the equal sign, as follows:
x^2 + 5x - 8 = 0
Then, use the quadratic formula with a = 1 (the coefficient of the quadratic term), b = 5 (the coefficient of the linear term) and c = -8 (the independent term).
[tex]x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}[/tex]
[tex]x = \frac{-5 \pm \sqrt{5^2 - 4(1)(-8)}}{2(1)}[/tex]
[tex]x = \frac{-5 \pm \sqrt{57}}{2}[/tex]
[tex]x_1 = \frac{-5 + \sqrt{57}}{2}[/tex]
[tex]x_1 = \frac{-5 + 7.55}{2}[/tex]
[tex]x_1 = 1.275[/tex]
[tex]x_2 = \frac{-5 - \sqrt{57}}{2}[/tex]
[tex]x_2 = \frac{-5 - 7.55}{2}[/tex]
[tex]x_2 = -6.275 [/tex]
What are two items that weigh less than 1 oz
Answers
An ounce is about the weight of 11 pennies. So anything that weighs less than about 11 pennies would weigh less than 1 oz.
You could have a piece of paper, blade of grass, a pill, a quarter, etc.
I hope this helps!
MrEquation
The sum of 5 consecutive even numbers is 200 what is the fifth term in the sequence
Answers
if to write the given sequence as n;n+2;n+4;n+6;n+8, then it is possible to write its sum:
n+n+2+n+4+n+6+n+8=200.
5n=180; n=36.
n=36 it means that the 1st number is 36. The 5th number is n+8=36+8=44.
all the even numbers are: 36;38;40;42;44.
answer: 44.
What is the correct data set for the box & whisker plot shown above??
Answers
Answer: It’s A.
Step-by-step explanation:
for a p e x
Will Give 100 points and brainliest!
An image of a rectangular pyramid is shown below: A right rectangular pyramid is shown. Part A: A cross section of the rectangular pyramid is cut with a plane parallel to the base. What is the name of the shape created by the cross section? Explain your answer. (5 points) Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex, what would be the shape of the resulting cross section? Explain your answer. (5 points)
Answers
Part B: Rectangle cross-section
The Part A cross section will be rectangle and Part B cross section will be triangle .
What is rectangular pyramid ?A rectangular pyramid is a 3-D object with a base shaped like a rectangle and triangle-shaped faces or sides that correspond to each side of the base. Like the other types of pyramids, a rectangular pyramid also has a point on top of the base of the pyramid that is joined together by bringing the top of all the sides which is known as the apx. A rectangular pyramid has a total of 5 faces, 5 vertices, and 8 edges and is of two types a right pyramid or an oblique pyramid.
According to the question
Part A: A cross section of the rectangular pyramid is cut with a plane parallel to the base.
When we cut a cross section parallel to base of the rectangular pyramid which have rectangular base
The cross section will always be a rectangle.
Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex .
When we cut a cross section perpendicular to the base, passing through the top vertex of the rectangular pyramid
The cross section will always be a Triangle.
As the lateral face of a rectangular pyramid is a triangle, so a cross section that passes through the top vertex and the base is also a triangle.
Hence , The Part A cross section will be rectangle and Part B cross section will be triangle .
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Convert the equation 3x + 2y = 14 to slope intercept form
Answers
y=-3/2x+7
I have added a photo of how you show your work.
Answer:
Step-by-step explanation:
y=-3/2x+7
Dam is rowing a boat away from a dock the graph shows the relationship between the time and sams distance from the dock. Evaluate the function for an input of 9
Answers
A and C would not be correct because you are finding the distance for 9 minutes. D is not correct because the y-axis does not even have 3 meters on it, neither does the graph hit y=3.
Answer:
B. After 9 minutes Sam is 80 meters away from the dock.
Step-by-step explanation:
We have been given a graph of function that shows the relationship between the time and Sam's distance from the dock.
Let us see our given options one by one to find the correct choice.
A. After 80 minutes Sam is 9 meters away from the dock.
Upon looking at our graph we can see that y-axis is representing distance in meters and x-axis is representing time in minutes. Range of x is from 0 to 11 So our input cannot be greater than 11.
Therefore, option A is not a correct choice.
B. After 9 minutes Sam is 80 meters away from the dock.
We can clearly see from our given graph that at 9 minutes distance is 80 meters, which means that after 9 minutes Sam is 80 meters away from the dock. Therefore, option B is the correct choice.
C. After 80 minutes Sam is 80 meters away from the dock.
We can see from our graph that range of x is from 0 to 11 minutes, So our input can not be greater than 11. Therefore, option C is not a correct choice.
D. After 9 minutes Sam is 3 meters away from the dock.
We can see from our graph that initial value of our function is 20, which means that at time equals 0 minutes Sam was 20 meters away from dock and this distance is increasing with the time. Therefore, option D is not a correct choice.
check all that apply
Answers
Answer:
A, D, E
Step-by-step explanation:
Squaring both sides of the inequality, we get
x < 25 . . . . . with the restriction x ≥ 0
The listed numbers that are in the range [0, 25) are 1, 18, 24.
a furlong is a unit of length still used today in racing and agriculture. a race that is 8 furlongs is 1 mile. a furlong is 660 feet. how many furlongs are in 1 mile?
Answers
There are 0.125 miles in one furlong.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Examples:
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
We have,
There are 8 furlongs in 1 mile.
Since a furlong is 660 feet, we can convert the number of feet into 1 mile.
Now,
1 mile = 5280 feet
Multiply 660/5280 on both sides.
660/5280 mile = 660 feet
0.125 mile = 660 feet
Therefore,
There are 0.125 miles in one furlong.
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The complete question.
A furlong is a unit of length still used today in racing and agriculture.
A race that is 8 furlongs is 1 mile.
A furlong is 660 feet. how many miles are in 1 furlong?
If a train is moving 72 km/h on a road of 360 km, how much time will it take to arrive?
Answers
72 kilometers is 72,000 meters, and an hour is 60 minutes of 60 seconds each, meaning an hour is 3600 seconds (60m*60s). This means that in 3600 seconds the car travels 72,000 meters. You can figure out how many meters are travelled per second by dividing 72,000 meters by 3,600 seconds, giving you 20 meters per second. This would give you an answer of 80 meters in 4 seconds, not 120 m. I don't know how to account for that disparity, but 80 meters would be the correct answer. If there is any other information in the problem it is probably important."
You want to have $31,664 in cash to buy a car in 4 years. you expect to earn 11.5% per year on your savings. how much do you need to deposit today if this is the only money you save for this purpose?
Answers
You would need to deposit approximately $20,701.27 today if this is the only money you save for the purpose of buying a car in 4 years, considering an expected annual interest rate of 11.5%.
We have,
To determine how much you need to deposit today, we can use the concept of present value (PV).
The present value represents the current value of a future cash flow, accounting for the time value of money and the expected interest rate.
In this case, you want to have $31,664 in cash in 4 years, and you expect to earn an annual interest rate of 11.5%.
Let's calculate the present value using the following formula:
[tex]PV = FV / (1 + r)^n[/tex]
where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods.
Plugging in the values, we have:
[tex]PV = $31,664 / (1 + 0.115)^4[/tex]
Calculating this equation, we find:
[tex]PV = $31,664 / (1.115)^4[/tex]
= $31,664 / 1.530749
PV ≈ $20,701.27
Therefore,
You would need to deposit approximately $20,701.27 today if this is the only money you save for the purpose of buying a car in 4 years, considering an expected annual interest rate of 11.5%.
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A segment has endpoints at (3,−4) and (3,−17) How many units long is the segment?
Answers
Answer:
what the other person said
Step-by-step explanation:
What is the circumference of a circle with a radius of 5.4 inches? Enter your answer as a decimal in the box. Use 3.14 for pi. Round your answer to the nearest tenth. in.
Answers
Answer:
33.9
Step-by-step explanation
I got 100% on my test and just wanted everyone to know that it is correct.
Josef says that the range for the car data is greater than the range for the minivan data because the box in the box plot for the car data is wider. Which explains Josef’s error?
Answers
Choice A
Answer:
its a ik it
Step-by-step explanation:
I wonder if I did #9 right and I’m having trouble with #10
Answers
QUESTION: Add. Write your answer as a mixed number in simplest form.
[tex]6 \frac{7}{9} + 9 \frac{8}{9} [/tex]
1. Rewriting our equation with parts separated
[tex]=6+ \frac{7}{9} +9+ \frac{8}{9} [/tex]
2. Solving the whole number parts
[tex]6+9=15[/tex]
3. Solving the fraction parts
[tex] \frac{7}{9} + \frac{8}{9} = \frac{15}{9} [/tex]
4. Reducing the fraction part, 15/9,
[tex] \frac{15}{9} = \frac{5}{3} [/tex]
5. Simplifying the fraction part, 5/3,
[tex] \frac{5}{3} = 1\frac{2}{3} [/tex]
6. Combining the whole and fraction parts
[tex]15+1+ \frac{2}{3} =16 \frac{2}{3} [/tex]
ANSWER: [tex] 16\frac{2}{3} [/tex]
Hope that helps!
It's correct. The only problem is entering it. Is a fraction OK or do you need to break it down to 16.6666
10
I don't wonder that you are having trouble with this.
Do it in parts.
numerator
3/4 - 3/2 = 3/4 - 6/4 = - 3/4 Notice what happened. You multiplied top and bottom of 3/2 by 2
= 3*2 = 6
2 * 2 = 4
Now do the denominator
1/4 - 3/5 =
5/20 - 12/20
= - 7/20
What do you have?
-3/4 // - 7/20 Now invert and multiply
- 3/4 * - 20 /7
= 60/ 28
= 15 / 7 Where did the two minus' go?
each picnic table seats 6 people how many picnic tables are needed to seat 24 people?
Answers
Final answer:
To seat 24 people at picnic tables that each seat 6, you divide 24 by 6, which equals 4 tables needed.
Explanation:
The question is asking how many picnic tables are needed to seat 24 people, if each table seats 6 people. This is a division problem where we need to divide the total number of people by the number of seats at a single table. You divide 24 (the total number of people) by 6 (the number of seats at one table) to find out the number of tables needed.
Here is the calculation: 24 \/ 6 = 4. Therefore, you would need 4 picnic tables to seat 24 people, assuming each person takes one seat and that there are no empty seats.
How many positive integers between 100 and 999 inclusive are divisible by three or four?
Answers
There are 900 numbers between 100 and 999 (inclusive)
We group the numbers into groups of 3s. So we find one number divisible by 3 in every group.
Number of numbers that can be divided by 3 = 900 ÷ 3 = 300
Number of numbers that can be divided by 3 = 300
We group the numbers into groups of 4s. So we find one number divisible by 4 in every group.
Number of numbers that can divided by 4 = 900 ÷ 4 = 225
Number of numbers that can divided by 4 = 225
Among the group of 4s, there is 1/3 that are already inclusive in divisible by 3.
225 ÷ 3 = 75
Number of numbers that can divided by 4 = 225 - 75 = 150
Total numbers of positive integers divisible by three and fours = 300 + 150 = 450
The total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is 450.
Explanation:The problem is looking for positive integers between 100 and 999 inclusive, that are divisible by three or four. First, we find out how many numbers between 100 and 999 are divisible by 3 by using the formula: (Last Numbers - First Number) divided by the number you are dividing + 1. Hence, [tex](999 - 102) / 3 + 1 = 300.[/tex] Similarly, for numbers divisible by 4: (996 - 100) / 4 + 1 = 225. However, we must subtract out the numbers that are counted twice because they are divisible by both 3 and 4 (i.e., divisible by 12). To find this, we do [tex](996 - 108) / 12 + 1 = 75.[/tex]
In conclusion, we add the numbers divisible by 3 and those divisible by 4 and subtract the ones that are divisible by both (12). Hence, the total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is [tex]300 + 225 - 75 = 450.[/tex]
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Martin put 8 pounds of grapes into a bowl. Four friends each took 2/3 pounds from the bowl. What fraction represents the total amount of grapes removed from the bowl ?
Answers
[tex]\sf 4\times\dfrac{2}{3}=\dfrac{8}{3}[/tex]
We can convert this improper fraction to a mixed number. Three goes into eight two times. 3 * 2 = 6. 8 - 6 = 2. So we have 2 and two thirds leftover, or:
[tex]\sf 2\dfrac{2}{3}[/tex]
So the total amount of grapes that was removed from the bowl is [tex]\sf\dfrac{8}{3}[/tex] or [tex]\sf 2\dfrac{2}{3}[/tex] pounds.
Answer:
-8/3
Step-by-step explanation:
i took the test on edg