sin(x - 20)° = cos(5x - 10)°
Expand 5x - 10 in terms of x - 20:
5x - 10 = 5x - 100 + 90
… = 5 (x - 20) + 90
and recall that for all θ, cos(θ + 90)° = - sin(θ)°, so
sin(x - 20)° = cos(5 (x - 20) + 90)°
sin(x - 20)° = - sin(5 (x - 20))°
Replace (x - 20)° = y ° to make this a bit easier to read:
sin(y °) = - sin(5y )°
Expand the right side in terms of powers of sin:
sin(5θ) = 5 sin(θ) - 20 sin³(θ) + 16 sin⁵(θ)
so the equation becomes
sin(y °) = -5 sin(y °) + 20 sin³(y °) - 16 sin⁵(y °)
16 sin⁵(y °) - 20 sin³(y °) + 6 sin(y °) = 0
Replace z = sin(y °) to get a polynomial equation:
16z ⁵ - 20z ³ + 6z = 0
Factorize the left side:
2z (8z ⁴ - 10z ² + 3) = 0
2z (2z ² - 1) (4z ² - 3) = 0
Solve for z :
• 2z = 0 → z = 0
• 2z ² - 1 = 0 → z ² = 1/2 → z = ± 1/√2
• 4z ² - 3 = 0 → z ² = 3/4 → z = ± √3/2
Solve for y in each case above:
• z = sin(y °) = 0 → y = 0 + 360n or y = 180 + 360n
(where n is any integer)
These solutions can be combined into one family, y = 180n.
• z = sin(y °) = -1/√2 → y = 225 + 360n or y = 315 + 360n
• z = sin(y °) = 1/√2 → y = 45 + 360n or y = 135 + 360n
These solutions can also be combined, y = 45 + 90n.
• z = sin(y °) = -√3/2 → y = 240 + 360n or y = 300 + 360n
• z = sin(y °) = √3/2 → y = 60 + 360n or y = 120 + 360n
These can be combined as y = 60 + 180n or y = 120 + 180n.
Solve for x in each case:
• y = x - 20 = 180n → x = 20 + 180n
• y = x - 20 = 45 + 90n → x = 65 + 90n
• y = x - 20 = 60 + 180n → x = 80 + 180n
• y = x - 20 = 120 + 180n → x = 140 + 180n
what is x
I'm confused
Answer:
x = 3
Step-by-step explanation:
the diagonals bisect each other so:
6x + 2 = 20
subtract 2 from both sides of the equation:
6x = 18
x = 18/6
x = 3
Tara and Mallory are practicing their passing at a volleyball practice. Tara bumps the ball from a height of 3 feet above the ground with an initial upward velocity of 12 feet/second. at the same time, mallory serves the ball from a height of 3.25 feet above the ground with an initial upward velocity of 9 feet/second.
if x represents the number of seconds since each ball is passed and y represents the height of the ball, which system of equations models the projectile motion of the two balls? recall that the acceleration due to gravity is -32 feet/second
Answer:
The system of equation that models the projectile of the two balls is option;
C. y = -16·x² + 12·x + 3
y = -16·x² + 9·x + 3.25
Step-by-step explanation:
The general equation for vertical (upward) motion under gravity is presented as follows;
h - h₀ = u·t + 1/2·g·t²
Where;
h = The final height reached
h₀ = The initial height
u = The initial velocity
g = The acceleration due to gravity ≈ -32 feet/second
t = The time taken
We can rewrite the above equation with different letters for the variables as follows;
h = y,
h₀ = y₀, and
t = x
Therefore, we have;
y - y₀ = u·x - 1/2 × 32 × x²
y = u·x - 1/2 × 32 × x² + y₀ = u·x - 16· x² + y₀
y = u·x - 16· x² + y₀ = -16·x² + u·x + y₀
y = -16·x² + u·x + y₀
For Tara, we have;
u = 12 feet/second
y₀ = 3 feet
Therefore, we get;
y = -16·x² + 12·x + 3
For Mallory, we have;
u = 9 feet/second
y₀ = 3.25 feet
Therefore, we get;
y = -16·x² + 9·x + 3.25
The correct option is therefore;
y = -16·x² + 12·x + 3
y = -16·x² + 9·x + 3.25
Meggie starts with 100$ in her account.she wants to deposit 5$ per week . write an equation in slope intercept form to represent this situation
Answer:
y = 5x + 100
Step-by-step explanation:
Aretha had 9 pencils. She gave her
sister 1/3 of the pencils. How many
pencils did Aretha give her sister?
Answer:
3
Step-by-step explanation:
9 divided by 3 is 3
HELP ASSAP I NEED TO FINISH THIS TEST AND TIS THE LAST ONE
Answer:
a=4
b=5
Step-by-step explanation:
What is the resulting cross section if the cheesecake was sliced parallel to its points?
Answer:
Rectangle
Step-by-step explanation:
Jermaine earned 175 points by finishing 5 levels of video games. At this rate, how many points will he earn if he finishes 12 levels of the video game?
Answer:
420 points
Step-by-step explanation:
5 levels of video games = 175 points
1 level = 175 ÷ 5
= 35 points
Therefore,
12 levels of video games = 35 × 12
= 420 points
The Federal Reserve System publishes data on family income based on its Survey of Consumer Finances. When the head of the household has a college degree, the mean before-tax family income is $ 85,050. Suppose that 56% of the before-tax family incomes when the head of the household has a college degree are between $75,000 and $95,100 and that these incomes are normally distributed. What is the standard deviation of before-tax family incomes when the head of the household has a college degree
Answer:
The standard deviation is $13,052.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When the head of the household has a college degree, the mean before-tax family income is $ 85,050.
This means that [tex]\mu = 85,050[/tex]
Suppose that 56% of the before-tax family incomes when the head of the household has a college degree are between $75,000 and $95,100 and that these incomes are normally distributed.
They are equally as far from the mean, one above, and one below. This means that when [tex]X = 95100[/tex], Z has a pvalue of 0.5 + (0.56/2) = 0.78. So when X = 95100, Z = 0.77. We use this to find [tex]\sigma[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.77 = \frac{95100 - 85050}{\sigma}[/tex]
[tex]0.77\sigma = 10050[/tex]
[tex]\sigma = \frac{10050}{0.77}[/tex]
[tex]\sigma = 13052[/tex]
The standard deviation is $13,052.
please help me if you can!
Answer:
A is 55°
Step-by-step explanation:
To solve this, you need to remember that the sum of the angles inside a triangle is equal to 180 degrees.
Also, noting that this is an isosceles triangle. That means that a and b are equal. With that in mind, we can simply say:
a + b + c = 180
a ≡ b ∴ 2b + c = 180
2(4x + 31)° + (2x + 58)° = 180°
8x° + 62° + 2x° + 58° = 180°
Let's just stop right here, and note that normally you can treat symbols of measurements just like variables. We've done the same here, applying the distributive property with the ° symbol. Note though that it's currently part of every single term, so I'm going to factor it out:
(8x° + 62° + 2x° + 58°) / 1° = 180° / 1°
8x + 62 + 2x + 58 = 180
10x + 120 = 180
10x = 60
x = 6
Again noting that A and B are identical due to this being an Isosceles triangle, we can say:
A = (4x + 31)°
A = 24° + 31°
A = 55°
We can also check our answer. The sum of the angles should be 180, and two of those angles should be 55. That means that angle C should be 180 - 2 * 55, or 180 - 110 = 70. Let's test it:
70 = 2x + 58
70 = 12 + 58
70 = 70
So we know that our answer is correct.
M=-3/2(-5,1) standard form
Not sure............but i think it is 8x-1y= -11
Laura wants to learn more about her new high school. Which of the following is a statistical question Laura could ask?
A. What is the address of the school
B. Who is the principal
C. How old are the students at the school
D. Does the high-school have a jazz band
Answer:
D.
Step-by-step explanation:
There is no explanation
Can someone please answer this!!
Lucy started to run on a treadmill after setting its timer for 77 minutes. The display says that she has finished 79% of her run. How many minutes have gone by? Round your answer to the nearest tenth.
Answer:
60.8
Step-by-step explanation:
Step 1: Go on g oogle
Step 2: Type "79% of 77"
Step 3: Round your answer 60.83 to 60.8 because it said round to the nearest tenth.
In ΔRST, s = 3.5 cm, r = 5.4 cm and ∠R=49°. Find all possible values of ∠S, to the nearest 10th of a degree.
Answer:
29.3
Step-by-step explanation:
Sin(49)/5.4 = Sin(S)/3.5
Cross multiply.
0.4891636168
Sin^-1(0.4891636168) = 29.28562335
Round to nearest tenth.
29.3
A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 23.4 pounds and a standard deviation of 6.8 pounds. Step 1 of 2 : If a sampling distribution is created using samples of the amounts of weight lost by 63 people on this diet, what would be the mean of the sampling distribution of sample means
Answer:
The mean of the sampling distribution of sample means would be of 23.4 pounds.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
What would be the mean of the sampling distribution of sample means?
By the Central Limit Theorem, the population mean, that is, of 23.4 pounds.
Sally has a clock with a minute hand that extends to the clock's edge. The 10 points
minute hand is 5.25 inches long. What is the CIRCUMFERENCE of the
clock? *Hint* the minute hand is the radius. *
16.485 inches
32.97 inches
about 86.55 inches
None of the above
Answer:
no se ingles así que no se pero te doy gracias por los puntos
At a Dance Team fundraiser, there is a pie toss going on and Claudia is
tossing pies at her coach.
The path of a pie models a quadratic, and the height is shown in this table.
What is the maximum height of the pie?
PLEASE JUST HELP ITS ACTUALLY AN EMERGENCY I WILL GIVE 3K ON BLOXBURG FOR THIS
cut off the topright rectangle so there are 2 rectangles.
That will make it look like this
2x3=6
+
5x3=15
=
21
The area of that shape would be 21 square feet
21 square ft
u got 3K i only got 1K cuz i be spending it on my house and emotes and food ;-;
A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective. Step 1 of 2: Suppose a sample of 2346 floppy disks is drawn. Of these disks, 1971 were not defective. Using the data, estimate the proportion of disks which are defective. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer:
The proportion of disks which are defective is 0.16.
Step-by-step explanation:
The proportion of defective disks is the number of defective disks in the sample divided by the size of the sample.
In this question:
2346 disks.
1971 not defective, so 2346 - 1971 = 375 defective.
[tex]p = \frac{375}{2346} = 0.16[/tex]
The proportion of disks which are defective is 0.16.
I will mark you brainalist
Answer:
-3,3 this is because that is where both of the lines intersect making them both a solution for both equations.
Step-by-step explanation:
Answer:
B. (-3, 3)
Step-by-step explanation:
Point of intersection of both the lines is the solution to both the equations.
Both the lines are intersecting each other at point (-3, 3)
So, ordered pair of solution is (-3, 3)
The table shows the prices for the same cereal, sold in different weights. Which size box is the best buy, in terms of price per ounce?
A. 9 oz
B.18 oz
C.28 oz
D.38 oz
Answer:
c
Step-by-step explanation:
ESPERO TE A YDUE :)
someone help please with b (the slope is 5)
I need help ASAP I’m confused with this problem
Answer:
I believe it's A
Step-by-step explanation:
not sure but
Simplify -5( 7 + x ) + 2 5/6x.
Level 2: Find the area of the shape:
8 ft
6 ft
14 ft
5 ft
5 ft
Area:
ft2
Help please!!!!
Step-by-step explanation:
a triangle is the area of 2
HELPPPPPP
Order the following numbers from least to greatest.
10 square number 5
10square number -99
10 square number -17
10 square number 14
10 square number -5
10 square number 30
Answer:
10^-99
10^-17
10^-5
10⁵
10¹⁴
10³⁰
Mac Cosmetic sells a lip gloss for $15.50, but it only costs the company $6 to make it what is the percentage markup on the lip gloss?
Answer:
158%
Step-by-step
$15.50 - $6 = $9.50 < Profit
Now To find The Percentage of the markup on the lip gloss?
You Divide $9.50 by $6 And You Will Get This 1.58333333333
For A Percent You Move The Decimal Point Back Two Spots And You Get
158%
I Hope You Understand and i hope i helped you
7. Which of these expressions are equivalent to 10x + 11? Select the three that apply.
A. 5(2x + 10)+1
B. 7(x + 2) + 3x - 3
C. 3(3x + 4) + X-1
D. 2(6x + 4) + 2x + 5
E. 2(6x + 5) - 2x + 1
Answer:
B
Step-by-step explanation:
7 times 1x equals 7x. Then 7 times 2= 14. Thirdly, 7x plus 3x equals 10x. Lastly, 14 -3 equals 11. So 10-+11 altogether
Taylor has 5 yards of gold ribbon to decorate
8 costumes for the school play. She plans to
use the same amount of ribbon for each
costume. How many yards of ribbon will she
use for each costume?
The width of a kitchen is 4.2 metres.
Kitchen cupboard widths are 60cm.
How many kitchen cupboard will fit in 4.2 metres?
Enter the number only
Given:
The width of a kitchen is 4.2 metres.
Kitchen cupboard widths are 60 cm.
To find:
The number of kitchen cupboard that will fit in 4.2 metres.
Solution:
Let x be the number of kitchen cupboard that will fit in 4.2 metres.
Width of 1 cupboard = 60 cm
Width of x cupboards = 60x cm
We know that, 1 m = 100 cm.
Width of a kitchen = 4.2 metres
= 4.2×100 cm
= 420 cm
Now, the width of the x cupboards is equal to width of the kitchen.
[tex]60x=420[/tex]
[tex]x=\dfrac{420}{60}[/tex]
[tex]x=7[/tex]
Therefore, the number of kitchen cupboard that will fit in 4.2 metres is 7.