The solution for 8 cos 2 ( t ) − 2 sin ( t ) − 7 = 0 for all solutions 0 ≤ t < 2 π is
t ≈ 0.896 rad and t ≈ 5.387 rad.
We can use the trigonometric identity:
cos(2t) = 2cos²t - 1, to rewrite the equation as:
8(2cos²t - 1) - 2sint - 7 = 0
Simplifying and rearranging terms, we get:
16cos²t - 2sint - 15 = 0
Using the identity sin²(t) + cos²(t) = 1, we can substitute sin(t) = ±√(1 - cos²(t)) and get a quadratic equation in terms of cos(t):
16cos²(t) - 2(±√(1 - cos²(t))) - 15 = 0
Solving for cos(t), we get:
cos(t) = ±√(17)/4
Since 0 ≤ t < 2π, we can use the inverse cosine function to find the solutions in this interval:
t = cos⁻¹(√(17)/4) and t = 2π - cos⁻¹(√(17)/4)
Therefore, the solutions are:
t ≈ 0.896 rad and t ≈ 5.387 rad.
To learn more about cos : https://brainly.com/question/23720007
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1. Noah had $ 5.25 and Lin had $ 8.95. How much did they have altogether?
2. Diego had $ 21.32 and gave $ 9.50 to Elena. How much did he have left?
3. Andre deposited $ 24.50 into his bank account each week for 5 weeks. What was the total amount Andre deposited?
4. Four friends did a job together that paid $ 85.20. How much should each get if they all get an equal amount?
1. 5.25 + 8.95 = 14.20
2. 21.32 - 9.50 = 11.82
3. 24.50 × 5 = 122.5
4. 85.20 ÷ 4 = 21.3
Hope this helped! Please comment if you have any questions regarding how I got my answers. Stay safe.
Two skateboarders are trying to build a ramp with an angle of 41°and a height of 3 ft. Which expression gives the length or
ramp?
22 foot ladder is placed against a vertical wall of building with the bottom of the ladder standing on level ground 9 feet from the base of the building how high up the wall does the ladder reach
Answer:
20.1 feet
Step-by-step explanation:
We solve the above question using the Pythagoras Theorem
The Pythagoras Theorem =
Opposite² + Adjacent ² = Hypotenuse²
From the above question,
Opposite side = Height of the wall = x
Adjacent side = Distance from the base of the building = 9 feet
Hypotenuse = Length of the ladder = 22 feet
Hence:
x² + 9² = 22²
x² = 22² - 9²
x = √22² - 9²
x = √403
x = 20.0748599 feet
Approximately = 20.1 feet
Therefore, the height of the wall = 20.1 feet
write a polynomial in standard form that represents the area of the shaded region.
Which quotient is greater than 3?
Question 4 options:
42 ÷ 19
40 ÷ 18
38 ÷ 14
36 ÷ 11
Answer:
36/11
Step-by-step explanation:
Answer:
36/15
Step-by-step explanation:
Solve for x.
7x - 3 = 6x -
x = 1/4
x=1
x=-1
x = -1/4
Someone help me please I can’t figure this answer out whatsoever
Answer:
Hello! :) have a good day!
The answer is x = -1/4
A brace is needed at the corner of a table, as shown in the diagram.
9 in
6 in.
What is the approximate length of the brace? A. 130 inches
B. V45 inches
C. 117 inches. D.12 inches
E. 15 inches
Answer: it’s 30
Step-by-step explanation: I got it right on my exam
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2150. What was the rate charged per hour by each mechanic if the sum of the two rates was $145 per hour?
Answer:
Step-by-step explanation: 20x+15(160-x)=2625
20x+2400-15x=2625
5x=225
x=45
160-x=115
rate of first mechanic= $45/hr
rate of second mechanic=$115/hr
Help please !!!! thnk you!!!!
x = 2
The line of symmetry is the line at which the parabola is the same on each side. With the line x = 2 , each side of the parabola is the same.
I am not a professional, simply using prior knowledge!
Note- It would mean the world to me if you could mark me brainliest!
Please help what is the answer
PLEASE ANSWER QUICK I WILL GIVE BRAINLISEST
The relative humidity is 100%, and the temperature is hot. In a few sentences, explain how the weather would change if the temperature drops and becomes cool.
Answer:
ohhh no typon hope it helps
Answer:
When the temperature drops the molecules form closer together causing the weather to feel cool. When the temperature drops the humidity drops as well causing there to be less chance of rain and why snow occurs instead of rain when humidity and temperature drops.
Step-by-step explanation:
If this helped you please rate this comment, give it a like, and maybe mark it as branliest!
A right triangle is described as having an angle of measure six less than negative two times a number, another angle measure that is three less than negative one-fourth the number, and a right angle. What are the measures of the angles in degrees?
I NEED HELP ASAP!!! I'LL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!!
Answer:
y=2 and x=3
Step-by-step explanation:
Answer:
y=2 and x=3 I think
Step-by-step explanation:
This circle graph shows how Jimmy spent his time during the last 24 hours.
How much more time did he spending watching T.V. and Talking on the Phone than he did Going to School?
8 hours
5 hours
1.92 hours
1.2 hours
Answer:
Excess time = 1.2 hour
Step-by-step explanation:
Given:
Total time = 24 hours
Talking on phone = 17 %
Sleeping = 33%
Going to school = 25%
Studying = 4%
Eating = 8%
Computation:
Watching TV percent = 100% - Talking on phone - Sleeping - Going to school - Studying - Studying - Eating
Watching TV percent = 100% - 17% - 33% - 25% - 4% - 8%
Watching TV percent = 13%
Time taken by school = 24 x 25%
Time taken by school = 6 hour
Time taken by watching T.V. and Talking on the Phone = 24 x (13% + 17%)
Time taken by watching T.V. and Talking on the Phone = 7.2 hour
Excess time = 7.2 - 6
Excess time = 1.2 hour
A and B together complete a work in 20days. They worked together for 5days and B leaves. How long will A takes to finish the remaining work if A alone can finish the work 36days.
Answer:
27 days
Step-by-step explanation:
A alone, rate per day = 1/36
A and B together, rate per day = 1 / 20
Total Workdone for 5 days :
1/ 20 * 5 = 5 / 20 = 1/4
Fraction of work left :
1 - 1/4 = 3/4
3 / 4 * 36 /1
= (3 * 36) / 4
= 108 / 4
= 27 days
On a map ,the distance between two towns is 2.6 cm .The scale of the map is 1 cm :50 km. What is the actual distance between the two towns ?
A-100km
B-70km
C-130km
D-150km
And how
Answer:
C-130km
Step-by-step explanation:
50 km = 5 000 000 cm
=> Actual distance between 2 towns = 2.6 x 5 000 000 = 13 000 000 cm = 130 km
=> C-130 km will be the correct ans.
Answer:
C - 130
Step-by-step explanation:
We have two towns that have a distance of 2.6cm, at the same time we know the scale of the map is 1cm : 50km and the question being asked is the actual distance between the two towns.
What we have to do to find the answer is multiply 2.6 by 50, since we know that one centimeter is equal to 50 kilometers on the scale, this is what we must do.
50 * 2.6
Therefore, the distance between the two towns is 130 kilometers.
Place the circles in order from the circle with the largest area to the circle with the smallest area.
Answer:
explain how like uh 0Oo. done
Step-by-step explanation:
The street signs in a subdivision are in the shape of
circles. Each street sign has an area of 452.16 square
inches. What is the approximate circumference of each
sign? Use 3.14 for .
F 38
G 72
H 75
J 144
Find the solution set of the inequality
8x - 8 ≤ -72
Answer:
x ≤ -8
Step-by-step explanation:
8x-8 ≤ -72
+8 +8
8x ≤ -64
divide by 8
8x/8 ≤ -64/8
x ≤ -8
Subtract.
(6x + 5) - (x+3)
O A. 5x + 2
B. 5x shig
C. 6x+8
0 D. 6x + 2
does this make sense more food less active less weight
Answer:
no
Step-by-step explanation:
because more food less active
so if you eat more food, and you are less active you don't exercise off the weight
So you would gain weight not lose weight
Can you please help me on this it says fully simplify using only positive exponents 5x8y7/25x4y
Answer:
1/5x^12 * y^8.
Step-by-step explanation:
((5x^8*y^7/25)x^4)(y)
=1/5x^12 * y^8.
5. Which of the following ways would NOT be a correct way to name this angle?
A. СВА
B. CAB
C. ABC
E. B
Answer:
B
Step-by-step explanation:
If 12 blueberries weigh 7.2 grams, find the weight of 32 blueberries.
Answer:
The weight of 32 blueberries is 19.2
Step-by-step explanation:
We need to find what one blueberry weigh:
7.2 divided by 12 = 0.6
0.6 x 32 = 19.2
yes yes - drop the answer or ill drop ur ip
GRADE 7 MATHEMATICS (QUARTER 2)
SUBJECT TEACHER:
GENERAL INSTRUCTION
SCORE:
Read and analyze carefully the given questions.
IL You may refer to your module pages 22 - 27.
Directions: Choose the letter of the best answer and write in the space provided before the number,
1. In the expression x2, 2 is what we call
A Base
B. Exponent
C. Multiply
D. Divide
2. Find the product of (x) (**)
A x?
B. 22
Сх
D. X
3. What is the product if 2x is multiplied by 5x?
A 10x
B. 7x2
C. 10x
D. 3x
4. Divide 32a9bc2 by 4a-0%
A. 8a+b+c2
B. 8ac2 C. 8a 0042
D. Sa+bc
5. Multiply 2x by 13xy
A. 26xy
B. 26x3y2
C. 26x
D. 26xy
6. What is the product of 2x3 +3x2 + 4x and x + 1?
A 2 + 2x + 3x2 + 4x B. 2X* + 5x + 7x2 + 4x C. 5x + 7x3 + 4x + 2x D. 7* *4x3 + 2x + 5x
7. What polynomial is obtained if 27x*y* + 18x2y3 + 9x^y is divide by 3xy?
A 9xy + 6x2y3 + 3y B. 9xy + 6x3y C 9xy + 18xy + 6x
D. 9x+y + xy + 3x
8. What expression will satisfy the given statement: (a + 3)(_) = a + 6a + 9
A a-3
B. -3-a
C. a + 3
D. -3 + a
9. Find the product of (x-1) and (x + 1).
A x² + 1
B. X?- 1
c. x² + x + 1
D. X2 - x + 1
10. What will be the first term of the product of (2x - 1)?
A 4x2
B. 4x
C. 1
D. 2x
11. Multiply (4y - 5d) (4y + 50)
A. 16y2 + 2502
B. 4y + 50 C. 16y2 - 25d2
D. 4y - 50
12. Evaluate ( x - 3)(x2 + 3x + 9)
A. x2 - 81
B. x - 27
C. X + 9x + 27
D. X - 9x + 27
13. Solve (x-6)
A. x2 + 12x - 36
B. x2 + 36 C. X2 - 36
D. x2 - 12x + 36
14. What is the area of the square whose side is 2x + 5?
A 4x2-20%-25 B. 4x2 - 20x + 25 C. 4x2 + 20x - 25
D. 4x2 + 20x + 25
15. Evaluate (x + 4)'
A x + 12x2 + 48x + 64 B. X- 12x2 - 48x - 64 C. X - 12x2 + 48x - 64 D. x + 12x2 - 48x + 64
GRADE 7 MATHEMATICSQUARTER 2 (WEEK 7-8)
Directions: Choose the letter of the best answer and write in the space provided before the number.
Answer:
1) B? (I think that is meant to be an exponet. if it is, you would write it as x^2)
2) I do not know
3) A (it would actually be 10x^2, but 10x is the closest to it
4) A makes the most sense
5) A
6/7/8) I do not know, sorry
9) A makes the most sense
10-15) I am sorry, I cannot solve it
Step-by-step explanation:
I am sorry you have to go through this in 7th grade
Please help me out thank you.
Answer:
A
Step-by-step explanation:
n>= -6 and n<= 3
hope this helps
Answer:
_____________
How far is the portion of her route from A to D? Round to the nearest whole number. Explain. I NEED IT BY TONIGHT SO PLSS SOMEONE HELP ME!
9514 1404 393
Answer:
A to D is about 2087 ft
Step-by-step explanation:
For the portion of the path of interest, the sine and cosine relations apply.
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
__
AB is the adjacent side to the angle marked 33°, with hypotenuse 975 ft.
cos(33°) = AB/(975 ft)
AB = (975 ft)cos(33°) ≈ 817.70 ft
BC is the opposite side in the same triangle.
sin(33°) = BC/(975 ft)
BC = (975 ft)sin(33°) ≈ 531.02 ft
CD is the hypotenuse of the right triangle BCD. The side BC that we know is opposite the given angle, so the sine relation applies.
sin(46°) = BC/CD
CD = BC/sin(46°)
CD = (531.02 ft)/sin(46°) ≈ 738.21 ft
__
Now we know the segments of the path of interest:
A–D = AB +BC +CD
A–D = 817.70 ft + 531.02 ft + 738.21 ft = 2086.93 ft
A–D ≈ 2087 ft
_____
Additional comments
The attachment shows all of the segments computed working counterclockwise from A. The angles in triangle DEF are computed using the Law of Sines from sides DF and DE and angle DEF. Segments EG and GH are computed using the Law of Cosines.
When we get to points F, G, H, we find that there is some inconsistency with the locations that would be computed working clockwise using AB and angle BFA. This inconsistency shows up in an error in the 119° angle in the attached figure.
This means that segments on the back side of the route, along path EFGHA, will vary somewhat depending on how they're computed.
We assume that points B, C, F, G are collinear.
16,-8,4...;6th term
The 6th term of the sequence is______.
Answer:
- [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
1) 16
2) 16 ÷ ( - 2) = - 8
3) - 8 ÷ ( - 2) = 4
4) 4 ÷ ( - 2) = - 2
5) - 2 ÷ ( - 2) = 1
6) 1 ÷ ( - 2) = - [tex]\frac{1}{2}[/tex]
find the area of the figure.
Answer:
Step-by-step explanation:
Split the figure into 2. You didn't provide the measurements, so if you have them, just take it the rhombus and make it into a rectangle and find the area of that. find the area of the rectangle. add the two values together. Based off of the image, I'd say that the rhombus would be 15 units and the rectangle would also be 15 units so the answer would be 30 units
Answer:
30
Step-by-step explanation:
area of a rectangle is width times length so 3 squares times 5 squares gives that part an area of 15 squares squared ooh tahts a fun word to say
umm and then area of a trapezoid is a+b/2 times h
so a and b are the top and bottom sides of the trapezoid so 5 squares on top and 5 squares on bottom so that equals 10 divided by 2 is 5 then times the height would be 3 so 5 times 3 equals 15
so 15 the area of the trapezoid plus the area of the rectangle 15 equals a total area of 30 squares squared