Find all solutions to the equation.sin^2x + sin x = 0Thanks in advance!
Answers
Given:
\(sin^2x+sinx=0\)To solve the function, factor the function using sin(x):
\(sin(x)*[sin(x)+1\rbrack=0\)That means, in order to the produtct be zero, or sin(x) or [sin(x)+ 1] = 0
So, let's solve each situation.
\(\begin{gathered} sin(x)=0 \\ By\text{ taking the inverse:} \\ x=sin^{\left\{-1\right\}}\left(0\right) \\ x=\pi n,\text{ n is a integer} \end{gathered}\)Or:
\(\begin{gathered} sin(x)+1=0 \\ \text{ Subtracting 1 from both sides:} \\ sin(x)+1-1=0-1 \\ sin(x)=-1 \\ \text{ Taking the inverse:} \\ x=sin^{-1}(-1) \\ x=\frac{3}{2}\pi+2\pi n \end{gathered}\)Answer:
x = πn, 3/2 π + 2πn, for n integer n.
Related Questions
On a coordinate plane, circle has its center at the point (3, −6). The point (−1, −2) is on circle .
Which of these statements are correct? Choose ALL that are correct.
Responses
The line = − 1 is tangent to circle at P
The line = − 1 is tangent to circle at P
The area of the circle is 32 square units
The area of the circle is 32 square units
The radius of the circle is 4√2
The radius of the circle is 4√2
The range of the circle is (−6 − 4√2) ≤ ≤ (−6 + 4√2) -
The range of the circle is (−6 − 4√2) ≤ ≤ (−6 + 4√2) -
The point (4, −0.5) is on the circle.
The point (4, −0.5) is on the circle.
The equation of the circle is ( − 3)² + ( + 6)² = 32
Answers
We can conclude that the equation of the circle is (x - 3)² + (y + 6)² = 32, where (3, -6) is the center and 4√2 is the radius. Option 3 and 6 are correct options.
Based on the information given, we know that circle has its center at the point (3, -6) and a radius of 4√2. We also know that the point (-1, -2) and (4, -0.5) are on the circle.
Using the distance formula, we can confirm that the distance between the center of the circle and each of these points is indeed 4√2.
This equation can be simplified to x² - 6x + y² + 12y + 1 = 0 by expanding and combining like terms. This is the equation of circle , and any point that satisfies this equation will be on the circle. Option 3 and 6 are correct options.
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According to the Rational Root Theorem, which statement about f(x)=8x3−4x2+6x+3 is true?
Group of answer choices
Any rational root of f(x) is a multiple of 8 divided by a multiple of 3.
Any rational root of f(x) is a factor of 8 divided by a factor of 3.
Any rational root of f(x) is a multiple of 3 divided by a multiple of 8.
Any rational root of f(x) is a factor of 3 divided by a factor of 8.
Answers
The rational root theorem is used to determine the possible roots of a function.
The true statement is: (d) Any rational root of f(x) is a factor of 3 divided by a factor of 8.
The function is given as:
\(\mathbf{f(x) = 8x^3 - 4x^2 + 6x + 3}\)
The possible roots of a function
\(\mathbf{f(x) = qx^n + ax^{n-1} +.....+ p}\)
are
\(\mathbf{Roots = \pm\frac{Factors\ of\ p}{Factors\ of\ q}}\)
By comparison: p = 3 and q = 8
So, we have:
\(\mathbf{Roots = \pm\frac{Factors\ of\ 3}{Factors\ of\ 8}}\)
Hence, the true option is (d) Any rational root of f(x) is a factor of 3 divided by a factor of 8.
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4) Amy traveled to the recycling plan
back. It took one hour less time to get
there than it did to get back. The average
speed on the trip there was 50 km/h. The
average speed on the way back was 40
km/h. How many hours did the trip there
take?
Answers
The time taken by Amy to travel to the place was t = 4 hours.
What is average speed?A measure of average speed is the amount of distance travelled in a given amount of time. It is determined by dividing the overall mileage by the overall time required to cover that mileage.
In physics and other sciences, average speed is frequently employed to describe how objects move. For instance, it is possible to estimate how long it will take to go a certain distance or assess a car's fuel economy by looking at its average speed over a given distance. By dividing the whole distance travelled by the total time required, average speed may also be used to characterise the speed of an object that is moving at various speeds at different points along its path.
Let the time taken to get back = t + 1.
Now, it took one hour less time to get there thus time = t.
Now, average speed is given as:
average speed = total distance / total time
Substituting the values:
50 km/h = d / t
d = 50t .........(1)
40 km/h = d / (t + 1)
d = 40(t + 1)......(2)
Setting the value of d as equal we have:
50t = 40(t + 1)
50t = 40t + 40
10t = 40
t = 4
Hence, the time taken by Amy to travel to the place was t = 4 hours.
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Each side of a quilt square measures approximately 4.25 inches. If there are about 2.54 centimeters in 1 inch, how long is each side of the square in centimeters? Use complete sentences to explain your reasoning.
Answers
Answer: approximately 10.8 centimeters
Step-by-step explanation:
We have a square, where each side measures approx. 4.25 in
Now we know that 1in ≈ 2.54 cm
Then, in 4.25 in, we have 4.25 times 1 inch, so we have 4.25 times the length of 2.54 cm
So the approximate measure of the sides in centimeters is:
4.25*(2.54)cm = 10.8 cm
So we have that each side measures approximately 10.8 centimeters
HELP ASAP PLEASE MY DAD AND MOM ARE BOTH VERY MAD AT ME RIGNT NOW SO PLEASE HURRY UP
The line plot represents data collected from a used bookstore.
A horizontal line labeled Cost in Dollars starts at 1 with tick marks every one unit up to 8. There are two dots above 2 and 6. There are three dots above 3 and 5. There are four dots above 4. The graph is titled Cost of Used Books.
Which of the following describes the spread and distribution of the data represented?
The data is almost symmetric, with a range of 9. This might happen because the bookstore offers a sale price for all books over $6.
The data is skewed, with a range of 9. This might happen because the bookstore gives away a free tote bag when you buy a book over $7.
The data is bimodal, with a range of 4. This might happen because the bookstore sells most books for either $3 or $6.
The data is symmetric, with a range of 4. This might happen because the most popular price of a book at this store is $4.
Answers
With a range of 4, the data is bimodal. This is possible because most novels at the bookstore cost $3 or $6. The correct option is C.
What does bimodal data mean?"Bimodal" is a term that is commonly used to characterise the distribution of goods and services.
The line plot reveals two modes or peaks in the data, one at $3 and the other at $6, for a total spread of $4 from $3 to $6.
This implies that the bookstore offers the majority of its books for $3 or $6, and that these prices are well-liked by customers.
There is no indication of symmetry and skewness in the data, and no information about any promotions or sales that might influence the
distribution of prices is given. As a result, the bimodal distribution is the most probable explanation for the observed pattern in the data.
With a range of 4, the data is bimodal. This is possible because most novels at the bookstore cost $3 or $6. The correct answer is (C).
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Find the scale factor of ΔABC to ΔFGH.
Answers
Answer:
4:3
Step-by-step explanation:
AC=8
FH=6
8/6=4/3=4:3
if a1=5 and an=nan-1-4 then find the value if a3
Answers
EXPLANATION
If a_1 = 5 and a_n = n*a_n-1 - 4 the value of a_3 is given by the following relationship:
\(a_2=\text{ 2}\cdot5\text{ - 4 = 10-4=6}\)\(a_3=2\cdot6-4=12-4=8\)The answer is 8
Alan purchases a $41.30 jacket and a $27.55 hoodie. how much would it cost him if there was a 10% discount as well as nine % sales tax?
Answers
well, the jacket and hoodie will cost him 41.3 + 27.55 = 68.85, let's get the 10% and chop it off from it.
\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 68.85}}{\left( \cfrac{10}{100}\right)68.85}\implies 6.885~\hfill \begin{array}{llll} 68.85-6.885\\ 61.965 \end{array}\)
now, let's get 9% from 61.965 and chop it off from it.
\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{9\% of 61.965}}{\left( \cfrac{9}{100}\right)61.965}\implies 5.57685~\hfill \begin{array}{llll} 61.965-5.57685\\ 56.38815\\ \stackrel{\textit{rounded up}}{56.39} \end{array}\)
In 92,542 what’s ten times that amount
Answers
Answer:
945,420
Step-by-step explanation:
Which sum does the model below represent?
+
+
+
+
ĐO
oo ooo
0 4+(-7) = -3
O 4+ 7 = 11
O 8+(-3) = 4
O 11+ (-4) = -3
Answers
Answer:
THIS ANSWER IS CORRECT
----------------------------------------------
Step-by-step explanation:
BRAIN LESS ANSWER
King of Diamonds Industries has bonds on the market making annual payments, with 14 years to maturity, and selling for R1 482,01. At this price, the bonds yield 7%. What is the coupon rate?
Answers
The coupon rate of the bonds by King of Diamonds Industries would be 7 %.
How to find the coupon rate ?The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:
= (Coupon payment x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value / (1 + rate )^ number of years
1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14
103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x (1 - ( 1 + 0.07) ^ ( - 14) )
Using a calculator, C is $ 70.
This means that the coupon rate is:
= 70 / 1, 000
= 7 %
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The circle graph shows the result of a survey. In what way is this graph misleading? Explain.
Answers
Step-by-step explanation:
because the total sum of each percent is 90%
and it must be 100% as it is a full circle
Expanded form of 13.028
Answers
Answer:
Expanded form of 13.028
Step-by-step explanation:
13028/1000
.
A woman deposits $300 in a savings account that pays 6% annually. If she withdraws all the money in the account after 120 days, how much does she withdraw (rounded to the nearest dollar)?
Answers
The woman will withdraw $300 given 6% interest rate annually.
We can use the formula for simple interest to solve this problem:
I = Prt
where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years. Since the interest rate is given as an annual rate, we need to convert it to a daily rate by dividing by 365:
r = 0.06/365 = 0.00016438356
The time in years is 120/365 = 0.3287671233 years. Now we can plug in the values and solve for I:
I = 300 * 0.00016438356 * 0.3287671233 = 0.01699999999
The interest earned is $0.017, which is negligible. Therefore, the woman will withdraw the entire principal plus any interest earned, which is:
300 + 0.017 = $300.02
Rounding to the nearest dollar, the woman will withdraw $300.
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Use thUse the transformations on the function f(x) = x| to select the correct graph of
e transformations on the function f(x) = x| to select the correct graph of
Answers
Answer:
the graph that starts at (0,1) and has a rise/run of 1/3
Step-by-step explanation:
cynthia besch wants to buy a rug for a room that is 25ft wide and 33ft long. She wants to leave a uniform strip of floor around the rug. she can afford to buy 513 square feet of carpeting. what dimensions should the rug have
Answers
The dimensions of the rug would be 27 feet long and 19 feet wide with a 6 foot space around the carpet uniformly.
How to find the dimension of the rug?She wants to buy a rug for a room that is 25 ft wide and 33 ft long.
She wants to leave a uniform strip of floor around the rug.
she can afford to buy 513 square feet of carpeting.
Cynthia room area = lw
where
l = lengthw = widthTherefore,
Cynthia room area = 25 × 33
Cynthia room area = 825 ft²
She wants to leave a uniform strip of floor all around the rug and has affordability to buy 513 square feet of carpet.
Therefore, the dimension the rug should have is as follows:
(25 - 6) (33 - 6) = 513
19 × 27 = 513 ft²
Therefore, the dimensions of the rug would be 27 feet long and 19 feet wide with a 6 foot space around the carpet uniformly.
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Charlene was making some chocolate squares for her class party. She had 8 packages of the mix. Each package called for cup of milk. How many whole cups of milk would Charlene use for all 8 packages?
Answers
The number of whole cup of milk that Charlene would use for all 8 packages would be = 8 cups of whole milk.
What is a square?A square is a type of quadrilateral that has four sides with four angle 90° at each edge.
The number of chocolate square mixture Charlene would use for the party = 8 packages.
The number of packages that require a cup of milk = 1
Therefore the number of whole cups of milk that would be used for the whole 8 packages would be = 8×1 = 8 cups of whole milk.
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¿Escuadra de 40 x48?
Answers
Answer:
1920
Step-by-step explanation:
Trust Me
Use the graph to estimate the x- and y-intercepts.
Answers
Answer:
x- intercept is 6 y- intercept is -18
Step-by-step explanation:
Just use the graph, this graph is hard to get the answer but you just have to estimate.
Problem 21 pls helps
Answers
Answer:
f(-10) = -2
Step-by-step explanation:
\( y =\frac{20}{x}\)
Replace y by f(x)\(\implies f(x)=\frac{20}{x}\)
Plug x = -10\(\implies f(-10)=\frac{20}{-10}\)
\(\implies f(-10)=-2\)
Answer:
-2
Step-by-step explanation:
sub -10 in place of x and divid to give you -2
u
n n
+ + +
=
+ − +
, khi → +∞.
Answers
Answer:
45678
Step-by-step explanation:
u
n n
+ + +
=
+ − +
, khi → +∞.
if the sides if a square are increased by 3 m, the area becomes 64 m^2. Find the length if a side if the original square
Answers
Answer:
5 m
Step-by-step explanation:
Set up an equation using the square area formula, A = s²
Let x represent the original side length:
(x + 3)² = 64
Simplify:
x² + 6x + 9 = 64
Subtract 64 from both sides:
x² + 6x - 55
Factor by finding 2 factors of -55 that add up to 6:
(x + 11)(x - 5) = 0
Solve for the 2 solutions:
x + 11 = 0
x = -11
x - 5 = 0
x = 5
The side length cannot be be negative, so the answer is 5.
The side length of the original square is 5 m.
If you divide 7/8 by 3/4 , Will the the quotient be Greater than or less than 3/4
Answers
Answer:
greater.
Step-by-step explanation:
7/8 divided by 3/4 is equals to 7/6, therefore it is greater than 3/4
Answer:
greater
Step-by-step explanation:
because you have to keep change and flip and you answer would get you 28 over 24 or 1 4/24 hope that helped have a blessed day
Evaluate the question (7 x 4) - (2 + 8).
Answers
Answer:
10 is the answer
Step-by-step explanation:
hope it helps
Answer:
18
Step-by-step explanation:
(7⋅4)−(2+8)
(28)−(2+8)
28−(10)
28−1⋅10
28-10
18
The makers of a soft drink want to identify the average age of its consumers. A sample of 25 consumers was taken. The average age in the sample was 31 years with a standard deviation of 3.8 years.The Margin of error of the 99% confidence interval for the average age of the consumers is a.1.90 years b.2.13 years c.4.10 years d.1.65 years
Answers
Answer:
a.1.90 years
Step-by-step explanation:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1-0.99}{2} = 0.005\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).
So it is z with a pvalue of \(1-0.005 = 0.995\), so \(z = 2.575\)
Now, find the margin of error M as such
\(M = z*\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
In this question:
\(n = 25, \sigma = 3.8\)
So
\(M = 2.575*\frac{3.8}{\sqrt{25}} = 1.90\)
So the correct answer is:
a.1.90 years
Ethan had planned to visit his local post office on Saturday to exchange $400
or euros. The exchange rate for that day was $1 = 1.25 E
However, due to unforseen circumstances, Ethan arrived at the post office after
it closed on that day. He therefore had to wait until the following Monday to
exchange his $400 for euros. The exchange rate on Monday was $1 = 1.20 E
a) How many fewer euros did he receive due to this delay? |20
b) What percentage loss was caused by this delay?
Answers
The amount of fewer euros he would receive as a result of the delay is 20 E.
The percentage loss that was caused by the delay is -4%.
What is the fewer euros received and the percentage loss?
Exchange rate is the rate at which one unit of a currency can buy another currency. In this question, the value of Euros appreciated by Monday. This is because $1 buys less Euros on Mondays. On the hand, dollars depreciates in value.
Amount of fewer Euros received = value of euros if it were exchanged on Friday - value of euros if it was exchanged on Monday
Value of euros if it were exchanged on Friday = 1.25 x 400 = 500 E
Value of euros if it was exchanged on Monday = 1.20 x 400 = 480 E
Difference = 500 E - 480 E = 20 E
Percentage loss = (Euros received on Monday / Euros that would have been received on Friday) - 1
Percentage loss = (480 / 500) - 1 = -0.04 = -4%
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true/false.
____1.When the non-Standard unit used is small few unit's are
needed to fill a container when the non-standard the non-standard units used is bigger more units are needed to fill the container.
____2.Objects with shape can have the same volume.
____3. To find the volume of rectangular prism multiply the length,width and height.
_____4. Volume is measured in square unit's.
_____5. the amount of space inside an object is called the volume of the object.
____6. The volume of a rectangular prism is equal to the product of its length, width, and height V = 1xwxh cubic units.
____7. Standard units give a consistant and accurate measure of a container.
____8. Non-Standard units cannot be used to measure volume.
____9. Volume is measured in cubic units, such as cubic centimeters.
Answers
1. It is false that when non-Standard unit used is small few unit's are
needed .
2. Objects with different shapes can have the same volume. True
3. Length, width and height and multiplied to find volume of a rectangular prism. True
4. It is false that volume is measured in square unit.
5. It is true that Volume is a measure of the amount of space inside an object.
6. The formula for volume of a rectangular prism is V = l × w × h. True
7. It is true that Standard units give a consistent and accurate measure of a container.
8. It is false that Non-Standard units cannot be used to measure volume.
9. Volume is measured in cubic units. True
What is volume of an object?Volume can be defined as the amount of space inside and object. the object can be in different form such as cone, rectangular prism, cylinder and many other shapes. Even though shapes are different, It is possible for different shapes or objects to have the same volume when measure.
Measurement of volume can be through standard measurement and non standard measurements such as a cup of rice. However, for consistency and the sake of accuracy, it is advisable to always use standard measurements of volume where possible to avoid error that may occur in non standard measurement. The acceptable and recognized unit of volume is cubic meter (\(m^3\)).
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The table provides various values, including select minimums and maximums, of a particular cosine function f (x).
Answers
The cosine function f (x) is a periodic function that oscillates between -1 and 1. Knowing the range of values helps to better understand the behavior of the cosine function and make predictions about its values.
It is expressed as f (x) = cos(x), where x is the angle in radians. The cosine function has a period of 2π, meaning its values repeat every 2π units. The cosine function can be used to model a wide range of phenomena, including the oscillations of sound waves and the regular fluctuations in temperature.The table of values for the cosine function contains select minimums and maximums. The minimum value is -1, which occurs when x = 3π/2. This can be seen in the formula, as cos(3π/2) = -1. The maximum value is 1, which occurs when x = 0 or x = 2π. In other words, cos(0) = 1 and cos(2π) = 1.These minimums and maximums are important because they establish the range of values for the cosine function. Knowing the range of values helps to better understand the behavior of the cosine function and make predictions about its values.
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factorise x³-4x²+x+6
Answers
The binomial factors of x³- 4x²+x+6 are (x+2), (x+3), and (x-1).
Using the splitting and grouping the terms:
x³ + 4x² + x - 6
= x³ + 2x² + 2x² + x - 6 [Splitting 4x² = 2x² + 2x²]
= (x³ + 2x²) + (2x² + x - 6)
= x² (x + 2) + (2x² + 4x - 3x - 6)
= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]
= x² (x + 2) + (x + 2) (2x - 3)
= (x + 2) ( x² + 2x - 3)
= (x + 2) ( x² + 3x - x - 3)
= (x + 2) [x (x + 3) - 1 (x + 3)]
= (x + 2) (x + 3) (x - 1)
Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)
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There are two apples and two are taken away, five and another seven apples are added. How many apples are left if 8 - 6 are taken away?
Answers
Answer:
4-6 apples are left.
Step-by-step explanation:
2-2+5+7=12
12-8=4
12-6=6
4-6 apples are left.