Answers
2 \: { \cos}^{2} \alpha \: - \: 5 \: \cos\alpha \: + \: 2 \: = \: 0 \\ \\ Let \: \: \cos \alpha \: = \: x \\ \\ Hence \: \: , \: \\ the \: given \: expression \: becomes \\ \: a \: Quadratic \: Equation\: - \\ \: \\ 2 {x}^{2 } \: - \: 5x + \: 2 \: = \: 0 \\ \\ 2 {x}^{2} \: - \: 4x \: - \: x \: + \: 2 \: = \: 0 \\ \\ 2x \: (x - 2) \: - \: 1 \: (x - 2) \: = \: 0 \\ \\ (2x - 1) \: (x - 2) \: = \: 0 \\ \\ Solving \: for \: \: x \: \: , \: \: \\ \: We \: get \: \: - \: \\ \\ \: \: x \: = \: \frac{1}{2} \: \: \: \: \: \: and \: \: \: \: \: \: \: \: x \: = \: 2 \\ \\ As \: value \: of \: \cos\alpha \: ranges \: from \: \\ \: \: - 1 \: \: \: to \: \: \: 1 \: \\ \\ Neglect \: \: x \: = \: 2 \\ \\ Hence \: , \: x \: = \: \frac{1}{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \cos\alpha \: = \: \frac{1}{2} \\ \\ \\ \: \: \: || \: \: \: \alpha \: = \: \: 2n \pi \: + \: \frac{\pi}{3} \: \: \: \: or \: \: \: \: 2n \pi \: - \: \frac{\pi}{3} \: \: \: || \\ \:
\: \: \: \: \: \: \: \: \: Ans.\: \: \: \\ \\ \: \:( \: Where \: n \: represents \: any \: Integer\: ) \: \: \: \: \: [/tex]
Related Questions
Tony Hawk was the first skateboarder to do a “900,” a rotation of 900°. How many times did he rotate on the skateboard? times 8. Each arm of this pinwheel is the image of another arm rotated
Answers
900 / 360 = 2.5 rotations
round 49,953 to the nearest hundred
Answers
A three dimensional object was sliced parallel to its base and the result was a triangular cross-section.The same shape resulted from slicing the object perpendicular to its base.What three dimensional object fits this description?
Answers
Answer:
The answer is below!
Step-by-step explanation:
A cone is the three-dimensional shape that gives a triangular cross-section when sliced either parallel or perpendicular to its base.
Explanation:The three-dimensional shape that fits the description of producing a triangular cross-section when sliced both parallel and perpendicular to its base is a cone.
A cone is a solid that has a circular base and a single vertex. When a cone is sliced parallel to its base, the cross-section is a circle. When a cone is sliced perpendicular to its base, the cross-section is a triangle, specifically a right triangle. The right triangle results from the slice passing through the vertex and the base of the cone.
Learn more about Cone here:https://brainly.com/question/10670510
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an art easel with equal sides are opened and placed on a desk, classify the type of triangle formed by the easel and the desk
Answers
[tex](4y + 4x) = [/tex]
What is the sum of y and x
Answers
4x + 4y = 0
Solving
4x + 4y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4y' to each side of the equation.
4x + 4y + -4y = 0 + -4y
Combine like terms:
4y + -4y = 0
4x + 0 = 0 + -4y
4x = 0 + -4y
Remove the zero:
4x = -4y
Divide each side by '4'.
x = -1y
Simplifying
x = -1y
Please help (click to veiw photo)
Answers
m = 300x + 100, so we substitute that into the equation for m.
300x + 100 - n
n = 250x + 200, so we substitute that into the equation for n.
300x + 100 - 250x - 200
Subtract the 250x to get:
50x + 100 - 200
Subtract the 200 to get:
50x - 100, which is option D.
Hope this helps!
The area of a rectangular knitted blanket is 15x2-14x-8. What are the possible dimensions of the blanket? Use factoring.
Answers
Final answer:
The area of a rectangular blanket is 15x² - 14x - 8, and by factoring this expression, we find the possible dimensions to be (5x + 2) units by (3x - 4) units. The variable x represents a dimension and must be a positive value so that the actual dimensions are also positive.
Explanation:
The student is asking about the possible dimensions of a rectangular knitted blanket whose area is given by the polynomial 15x² - 14x - 8. To find the dimensions of the blanket, we need to factor this quadratic expression. Factoring is the process of breaking down a complex expression into simpler ones that, when multiplied together, give the original expression.
Let's factor the given expression:
Find two numbers whose product is 15 (coefficient of x²) multiplied by -8 (constant term) and whose sum is -14 (coefficient of x). These numbers are -20 and +6.Rewrite the middle term (-14x) using the numbers found: 15x² - 20x + 6x - 8.Factor by grouping: (15x² - 20x) + (6x - 8) = 5x(3x - 4) + 2(3x - 4).The expression can now be factored as (5x + 2)(3x - 4).The factored form suggests that the rectangle's dimensions could be (5x + 2) units by (3x - 4) units, where x is a variable representing one of the dimensions. However, since the values of x need to make physical sense in the context of a blanket's size, x will need to be a positive value such that (5x + 2) and (3x - 4) are also positive.
Morty buys and sells computer parts he bought two monitors for $25 each and later sold them for 88 each he bought four cases for $15 each and later sold them for $24 each if you buy five memory modules for $20 each and later sold them for $55 each
Answers
Morty earns a total profit of $337 from buying and selling monitors, cases, and memory modules by calculating the individual profits for each transaction and summing them up.
Explanation:The question is asking for a calculation of the profit Morty makes on buying and selling computer parts. There are three transactions to consider:
Morty buys two monitors for $25 each and sells them for $88 each.He buys four cases for $15 each and sells them for $24 each.He buys five memory modules for $20 each and sells them for $55 each.To find the total profit, we calculate the profit for each transaction:
Profit from monitors: (2 * $88) - (2 * $25) = $176 - $50 = $126Profit from cases: (4 * $24) - (4 * $15) = $96 - $60 = $36Profit from memory modules: (5 * $55) - (5 * $20) = $275 - $100 = $175Then we sum these individual profits for the total profit:
Total profit = $126 + $36 + $175 = $337
The total profit that Morty makes from buying and selling these computer parts is $337.
Morty made a profit of $126 on the monitors, $36 on the cases, and $175 on the memory modules.
Explanation:Morty bought two monitors for $25 each, costing him a total of $50. He later sold them for $88 each, earning a total of $176. He bought four cases for $15 each, costing him a total of $60. He later sold them for $24 each, earning a total of $96.
He also bought five memory modules for $20 each, costing him a total of $100. He later sold them for $55 each, earning a total of $275.
In summary, Morty made a profit of $126 on the monitors, a profit of $36 on the cases, and a profit of $175 on the memory modules.
PLZ HELP!
at the apple orchard workers were asked to put 100 apples in barrels. the following five were filled incorrectly. if the supervisor wrote +5 above a barrel, it meant that the barrel was 5 apples over, -5 meant that a barrel was 5 apples less than 100.
How many TOTAL apples are i the five barrels?
a -480 apples
b 498 apples
c 500 apples
d 520 apples
Answers
Please help I’m doing functions
Answers
-15+13= -2
Hope this helps
XXVI – IV math help hard roman NUMERALS
Answers
IV is 4.
26-4 = 22
22 is XXII in roman numerals.
Hope this helps :)
XXVI=26
VI=6
XXVI-VI=20
In a dog show, there will be a gold, a silver, and a bronze medal awarded. There are
5 finalists. In how many different ways can the 3 medals be awarded?
Answers
60 ways
Explanation
In permutation the order really matters unlike combination where order does not matter.
The question wants you to find how many time you can choose 3 out of 5 with order.
This means we should find 5 permutation 3.
5P3=5!/3!
=(5×4×3×2×1)/(3×2×1)=5×4
=60
Answer:
60 ways
Step-by-step explanation:
There are five finalist and 3 medals.
For getting the first medal, there are 5 choices, any of the finalist can get that.
For getting the second medal, we are left with 4 choices.
For getting the third medal we are left with 3 choices.
Hence, the number of ways 3 medals can be awarded are:
5×4×3=60 ways
write two division equations for 16 times 7/8 = 14
Answers
14/(7/8)=16
14/16= 7/8
The reason that these equations work is because the inverse operation of multiplication is division. Any factors of the the multiplication equation can divide the product by the factor and the answer would be the other factor. Example:
AB=C
C/B= A
C/A=B
The product always has to be the first Number of the equation while either factor follows.
HELPPP PLEASE DUE NOW
Answers
105 = 13x + 66
Subtract 66 from each side
39 = 13x
Divide each side by 13
3 = x
Now for z.
Since two equal angles equal 105º each, multiply it by 2 to get 210.
The whole thing is 360º.
360 - 210 = 50
Divide it by 2 to get one of the angles
50 / 2 = 25
z = 25º
Hope this helps!
the ratio of plates to napkins is 3:12. what is the ratio in simplest form
Answers
What is 8kg-6.075kg=?
Answers
Percy buys tomatoes that cost $0.58 per pound. He pays $2.03 for the tomatoes. Part 1 out of 3 Percy estimates he bought 4 pounds of tomatoes. Is Percy's estimate reasonable? Complete the explanation.
Answers
Percy's estimate is not unreasonable, but it is somewhat high (by more than 10%).
The cost, 0.58/lb, is closer to 0.6, a number that would cause Percy to estimate his purchase at 20/6 = 3 1/3 pounds.
When estimating, it is often useful to make an estimate of the error. This last estimate will be a little low, by about 3% due to the estimated cost and 1.5% due to the estimated total amount paid, for a total of about 4.5% low.
Pls help me lots of points
Answers
Answer:
2 m&ms and 1 hershey's bar
Step-by-step explanation:
if side a=22.3 and angle b=47 ,find c.
A.24.6
B.25.1
C.31.5
D. 32.9
Answers
Answer:
D. 32.9
Step-by-step explanation:
Doug has 5 hours to make an on time delivery 273 miles away if Doug Drives 55 miles per hour will Doug make the delivery dead line explain
Answers
275 > 273 so he will make it in time
????????????????????????
Answers
Hope this helps :)
Name a fraction that is less than or greater than the given fraction draw to justify your answer
Answers
-(m-6)=3m+14 what is m
Answers
[tex] - m + 6 = 3m + 14[/tex]
[tex] - 4m = 8[/tex]
[tex]m = - 2[/tex]
You and your friend are standing back to back. Your friend runs 20 feet forward and then 15 feet right. At the same time, you run 12 feet forward and then 9 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball
Answers
Rewrite the set
F
by listing its elements. Make sure to use the appropriate set notation.
=
F
x
x
is an integer and
<
−
2
≤
x
2
Answers
Evaluate. 6+5|4-3^2| A. -19 C. 31 D. 55
Answers
Answer:
6 + 5|4 - 3²| =
6 + 5|4 - 9| =
6 + 5|-5| =
6 + 5(5) =
6 + 25 = 31
The correct answer is C.
What is the value of G in the center and how do you solve it?
Answers
7 + 3c = -11 --> c = -6
-9 - a/4 = 5 --> a = -56
b/5 +9 = 6 --> b = 75
second, solve:
a/f = -7 --> substitute -56 in for a --> -56/f = -7 --> f = 8
b/e = 3 --> substitute 75 in for b --> 75/e = 3 --> e = 25
3 = c/d --> substitutie -6 in for c --> 3 = -6/d --> d = -2
third solve:
g = d+e+f --> substitute -2 in for d, 25 in for e, and 8 in for f.
g = -2 + 25+8
g = 31
3 = c/d => d = c/3
7+3c = -11 => 3c = -11 - 7 => 3c = -18 => c = -18/3 => c = -6.
Now d = c/3 => d = -6/3 => d = -2.
Lets now find out e:
b/e = 3 => e = b/3
b/5 + 9 = 6 => b = (6-9)*5 => b = -15
Now e = b/3 => e = -15/3 = -5
Now we need to find f:
a/f = -7 => f = a/-7
-9 - a/4 =5 => a= (-9-5)*4 = -56
Now f = a/-7 => f = -56 / -7 = 8
So g = d + e + f
= (-2) + (-5) + 8
= 1
Therefore g = 1
How much popcorn would each person get if 3 people shared 1/3 of a bag of popcorn
Answers
To solve this divide 1/3 and 3 . . .
1/3 divided by 3 = ?
1 x 1 = 1
3 x 3 = 9
Your answer is 1/9.
Each person would get 1/9 of a bag of popcorn if 3 people shared 1/3 of a bag of popcorn.
Hope this helps you.
Have a great day!
maurice has a string that is 15 inches long. he has beads that are 3 inches long. how many beads will fit on the string?
Answers
Simplify each expression. Select the correct answer from the drop-down menu.
−6(3i)(−2i) =
2(3 − i)(−2 + 4i) =
Answers
2(3-I)(-2+4i)= -4 + 28i
the answer is:
−6(3i)(−2i) = -36
2(3 − i)(−2 + 4i) = -4+28i
2i(4 − 5i) = 10+8i
hope this helps! :o)