Answers
Answer:
\(\displaystyle \sin\Big(\frac{x}{2}\Big) = \frac{7\sqrt{58} }{ 58 }\)
\(\displaystyle \cos\Big(\frac{x}{2}\Big)=-\frac{3 \sqrt{58}}{58}\)
\(\displaystyle \tan\Big(\frac{x}{2}\Big)=-\frac{7}{3}\)
Step-by-step explanation:
We are given that:
\(\displaystyle \sin(x)=-\frac{21}{29}\)
Where x is in QIII.
First, recall that sine is the ratio of the opposite side to the hypotenuse. Therefore, the adjacent side is:
\(a=\sqrt{29^2-21^2}=20\)
So, with respect to x, the opposite side is 21, the adjacent side is 20, and the hypotenuse is 29.
Since x is in QIII, sine is negative, cosine is negative, and tangent is also negative.
And if x is in QIII, this means that:
\(180<x<270\)
So:
\(\displaystyle 90 < \frac{x}{2} < 135\)
Thus, x/2 will be in QII, where sine is positive, cosine is negative, and tangent is negative.
1)
Recall that:
\(\displaystyle \sin\Big(\frac{x}{2}\Big)=\pm\sqrt{\frac{1 - \cos(x)}{2}}\)
Since x/2 is in QII, this will be positive.
Using the above information, cos(x) is -20/29. Therefore:
\(\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{1 + 20/29}{2}\)
Simplify:
\(\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{49/29}{2}}=\sqrt{\frac{49}{58}}=\frac{7}{\sqrt{58}}=\frac{7\sqrt{58}}{58}\)
2)
Likewise:
\(\displaystyle \cos \Big( \frac{x}{2} \Big) =\pm \sqrt{ \frac{1+\cos(x)}{2} }\)
Since x/2 is in QII, this will be negative.
Using the above information, cos(x) is -20/29. Therefore:
\(\displaystyle \cos \Big( \frac{x}{2} \Big) =-\sqrt{ \frac{1- 20/29}{2} }\)
Simplify:
\(\displaystyle \cos\Big(\frac{x}{2}\Big)=-\sqrt{\frac{9/29}{2}}=-\sqrt{\frac{9}{58}}=-\frac{3}{\sqrt{58}}=-\frac{3\sqrt{58}}{58}\)
3)
Finally:
\(\displaystyle \tan\Big(\frac{x}{2}\Big) = \frac{\sin(x/2)}{\cos(x/2)}\)
Therefore:
\(\displaystyle \tan\Big(\frac{x}{2}\Big)=\frac{7\sqrt{58}/58}{-3\sqrt{58}/58}=-\frac{7}{3}\)
Related Questions
15 - 4j = 43
Help me
Answers
Answer:
I did not understand your question so this is what I know. If it is correct pls mark me brainliest.
Step-by-step explanation:
15 + -4j = 0
Solving for variable 'j'.
Move all terms containing j to the left, all other terms to the right.
Add '-15' to each side of the equation.
15 + -15 + -4j = 0 + -15
Combine like terms: 15 + -15 = 0
0 + -4j = 0 + -15
-4j = 0 + -15
Combine like terms: 0 + -15 = -15
-4j = -15
Divide each side by '-4'.
j = 3.75
Simplifying
j = 3.75
The solution of the linear equation with single variable 15 - 4j = 43 will be negative 7.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation with a single variable 'j' is given below.
15 - 4j = 43
Simplify the equation, then the value of the variable 'j' will be calculated as,
15 - 4j = 43
-4j = 43 - 15
j = 28 / (-4)
j = - 7
The arrangement of the direct condition with a single variable 15 - 4j = 43 will be negative 7.
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Find the length of the missing side please help
Answers
Step-by-step explanation:
7. Since they are similar triangles we have:
\( \frac{10}{8} = \frac{x}{12} \\ \\ x = 15\)
So DF is 15
8. They are also similar. So:
\( \frac{14}{7} = \frac{x}{5} \\ x = 10\)
So PR is 10
The price of an oven was increased by 20% to £156.
What was the price before the increase?
Answers
Answer:
Step-by-step explanation:
Before the increase it was 100%
So 20+100=120
156/120*100=130$
Don’t do it like 20/100 *156 and then minus it from 156 because you will get a wrong answer
(This was answered by another person on a another question.)
Answer:
130
Step-by-step explanation:
x * 1.2 = 156
x = 156/1.2
x = 130
I need help with a math problem
Answers
What is the area model of 37 times 9
Answers
Answer:
333
Step-by-step explanation:
Please Help Me!
Milk is on sale for 40% off when it is normally $3.75 per gallon. How much will a gallon of milk cost?
The discounted price for milk is $_____(Round to the nearest cent.)
Answers
Answer:
$2.25 is the discounted price for each gallon.
Step-by-step explanation:
So you take 40% and convert it into decimal form, which is 0.4. Then you take $3.75 x 0.4 = 1.5. Then subtract $1.50 from $3.75, and that equals $2.25 each gallon.
Have a nice day!
5x+3=4x. solve for x
Answers
As per given by the question,
There are given given that the equation,
The equation is,
\(5x+3=4x\)Now,
For finding the value of x,
The given equation can be written as;
\(5x+3-4x=0\)Now,
\(\begin{gathered} 5x+3-4x=0 \\ x+3=0 \\ x=-3 \end{gathered}\)Hence, the value of x is -3.
The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm².
The height of the open box is (x - 2) cm.
I have attached a pic
(I already did part (a) and (bi) and you may use the answers to help you do the (bii) question)
+ the answer for (bi) if you can’t see it, it is 4.28 and -6.78
This is the question:
b) (ii) Hence calculate the volume of the box, stating the units of your answer.
Answers
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.
What is volume?Volume is the measure of the amount of 3-dimensional space occupied by an object or substance. It is usually measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in mathematics, physics, chemistry, and engineering, and is used to calculate the amount of material needed for a given project.
The volume of the box can be calculated by multiplying the area of the base with the height of the box. The area of the base is 58 cm² and the height of the box is x - 2 cm. Therefore, the volume of the box can be expressed as:
Volume = 58 cm² x (x - 2 cm)
= 58 cm³
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.
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Every month, Tara writes a cheque for $25 to pay off part of a loan. She has enough in her current account to pay no more than $450 towards the loan. Write and solve an inequality to find how many months can Tara send payments for the loan
Answers
The number of months that tara can send her payments for the Loan is; 18 months
How to find the time period of a Loan?
We are told that;
Tara has to pay $25 each month to pay the loan.
She has $ 450 in her account to pay the loan.
For us to find the number of months she can pay the loan, we will apply the unitary method as;
$25 she can pay in 1 month
The number of months to pay $1 is; 1/25 months
The number of months to pay $450 is; (1/25) * 450 = 18 months.
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Please help me, I don't know this one.
Answers
Given the function y = -5x + 4, what is the range of the function if the domain is {-2, 0, 5}?
Answers
Answer:
90 hours
Step-by-step explanation:
{14, 4, -21} is the range of the function if the domain is {-2, 0, 5}
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
To find the range of the function, we need to plug each value in the domain into the given function and see what output (y-value) we get.
When x = -2:
y = -5(-2) + 4 = 14
When x = 0:
y = -5(0) + 4 = 4
When x = 5:
y = -5(5) + 4 = -21
So the range of the function is {14, 4, -21}.
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Estimate the error if T_6 |(trapezoid rule with n = 6) was used to calculate ^3_0 cos(2x)dx |error| 0.2250| b) |error| 0.2000| |error| 0.2750| |error| 0.3000| e)|error| 0.250|
Answers
To estimate the error when using the trapezoid rule with n = 6 to calculate the integral of cos(2x) from 0 to 3, we'll need to find the maximum value of the second derivative of the function in the given interval and apply the error formula for the trapezoid rule. Hence, the correct option is (e).
Follow the following steps:
Step 1: Find the second derivative of cos(2x)
First derivative: -2sin(2x)
Second derivative: -4cos(2x)
Step 2: Find the maximum value of the second derivative in the interval [0, 3]
Since cos(2x) ranges from -1 to 1, the maximum value of -4cos(2x) is 4.
Step 3: Apply the error formula for the trapezoid rule
The error formula is |error| = (b - a)³ * M / (12n²)
Where a = 0, b = 3, M = 4 (maximum value of the second derivative), and n = 6.
|error| = (3 - 0)³ * 4 / (12 * 6²)
|error| = 27 * 4 / (12 * 36)
|error| = 108 / 432
|error| = 0.25
So, the estimate of the error when using the trapezoid rule with n = 6 to calculate the integral of cos(2x) from 0 to 3 is 0.25 . Hence, correct answer is (option e).
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Rewrite the following as single exponent using product rule:
9^6 x 9^1
Answers
The answer is 9^7
pls tell me which one is the correct one
Answers
Answer:
Option B
Step-by-step explanation:
Given expression is,
(x² - 18x + 180)
Which is in the form of (ax² + bx + c)
To factorize the given expression, we will split b in two parts \(b_1\) and \(b_2\) so that,
\(b=b_1+b_2\)
And \(c=b_1\times b_2\)
If b = 18,
\(b_1=10\) and \(b_2=8\)
c = 10 × 8 = 80
Therefore, (x² - 18x + 180) = x² - 10x - 8x + 80
= x(x - 10) - 8(x - 10)
= (x - 8)(x - 10)
Option B is the correct option.
8x^3y^3(10x^5)= Having trouble getting the answer I keep getting it wrong Pls Help me!
Answers
Answer:
80x⁸y³ is your answer. Hope it helps <3
The number of kilograms of water in a persons body varies directly as the persons mass. A person with a mass of 90 kg contains 60 kg of water . How many kilograms of water are in a persson whose mass of 75 kg
Answers
Answer:
There are 33 and 1/3 kg of water in a
person with mass of 50 kg
Step-by-step explanation:
Hope this helped
Use the graph of the function f shown to the right to answer parts (a)-(n) (a) Find f(-7) and f(2) f(-7)= f(2)= GETT (-6,0) (-39) (-2,6) 44 12 -1.9) (0-3) -7.-6) -61 -12 2-6) (6,6) (4.0)
Answers
Given the graph of the function f shown to the right as shown below: Graph of the function fIn order to find f(-7) and f(2) of the given function, we need to follow the given steps.(a) Find f(-7) and f(2)For f(-7):
We observe that the given graph passes through (-7,-39), hence to find f(-7), we need to substitute x = -7 in the equation of the given function f(x).f(-7) = -39. Therefore, f(-7) = -39For f(2):We observe that the given graph passes through (2,12), hence to find f(2), we need to substitute x = 2 in the equation of the given function f(x).f(2) = 12Therefore, f(2) = 12.
Thus, the required values are: f(-7) = -39 and f(2) = 12.
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Analyze the proportion below and complete the instructions that follow.
2x+5 x-5
3
4
Solve the proportion for x
A. -7
B. -4
C-2
D. -1
Answers
Answer:
A
Step-by-step explanation:
(2x + 5)/(3) = (x - 5)/(4)
Multiplying both sides by 12 to eliminate the fractions, we get:
4(2x + 5) = 3(x - 5)
Expanding the brackets, we get:
8x + 20 = 3x - 15
Subtracting 3x and 20 from both sides, we get:
5x = -35
Dividing both sides by 5, we get:
x = -7
Therefore, the solution to the proportion is x = -7.
So, the correct option is A) -7.
Sarah used 2.5 cups of cheese in a dish that serves 10 people. Arun used 1.6 cups of cheese in a dish that serves 8 people. 1 How many cups of cheese are needed for 1 serving of Aruns dish?
Answers
Data:
Cheese: c
People: p
Sarah:
c=2.5 cups
p=10
Arun:
c=1.6 cups
p=8
To find the number of cups of cheese that Arun need to a serving you divide the 1.6 cups into 8 (8 servings):
\(\frac{1.6}{8}=0.2\)Then, Arun needs 0.2 cups of cheese for 1 serving.Determine the average and rms values for the function y(t)=25+10sin6πt over the time periods (a) 0 to 0.1 s, (b) 0.4 to 0.5 s, (c) 0 to 1/3 s, and (d) 0 to 20 s. Comment on the nature and meaning of the results in terms of analysis of dynamic signals.|
Answers
Comment: RMS value is equal to the average value. This means that the signal does not have any high-frequency content. It can be inferred that the function y(t) does not oscillate. When the RMS value is less than the average value, it means that the signal has a lesser amount of high-frequency content.
Average and rms values for the function y(t)=25+10sin6πt over the time periods (a) 0 to 0.1 s, (b) 0.4 to 0.5 s, (c) 0 to 1/3 s, and (d) 0 to 20 s are as follows:
a) For t=0 to t=0.1s:
Average value, y_avg = 25
RMS value, y_RMS = 25.1987
Comment: RMS value is greater than the average value. This means that the signal has a considerable amount of high-frequency content. It can be inferred that the function y(t) oscillates rapidly.
b) For t=0.4 to t=0.5s:
Average value, y_avg = 25
RMS value, y_RMS = 28.2843
Comment: RMS value is greater than the average value. This means that the signal has a considerable amount of high-frequency content. It can be inferred that the function y(t) oscillates rapidly.
c) For t=0 to t=1/3 s:
Average value, y_avg = 25
RMS value, y_RMS = 23.7176
Comment: RMS value is less than the average value. This means that the signal has a lesser amount of high-frequency content. It can be inferred that the function y(t) oscillates slowly.
d) For t=0 to t=20 s:
Average value, y_avg = 25
RMS value, y_RMS = 25
Comment: RMS value is equal to the average value. This means that the signal does not have any high-frequency content. It can be inferred that the function y(t) does not oscillate. Comment on the nature and meaning of the results in terms of analysis of dynamic signals.The results indicate that the function y(t) oscillates rapidly at the start and end of the time period and slowly in the middle. When the RMS value is greater than the average value, it means that the signal has a considerable amount of high-frequency content.
On the other hand, when the RMS value is less than the average value, it means that the signal has a lesser amount of high-frequency content.
Furthermore, if the RMS value is equal to the average value, it means that the signal does not have any high-frequency content.
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On a chemistry quiz, there are 5 multiple choice questions with 4 choices each. What is the probability that you get a 100% if you strictly guess.
Answers
Answer:
0.097%
Step-by-step explanation:
Since this is a series of events probability question, in order to calculate the probability you need to first find the probability of getting each individual answer right and then multiplying those probabilities together. This will give you the probability of getting 100% on the entire test. Since the questions are multiple-choice with 4 choices and only 1 correct choice then the probability of getting one right is 1/4 or 25%. Now that we have that probability we simply need to multiply it 5 times for each individual question.
1/4 * 1/4 * 1/4 * 1/4 * 1/4 = 1/1024 or 0.0009765 or 0.097%
Order from greatest to least, 19/4, 45/10, 4 3/5.
Answers
Answer:
45/10, 4 3/5, 19/4
Step-by-step explanation:
19/4 = 4.75
45/10 = 4.5
4 3/5 = 23/5 = 4.6
4.75 > 4.6 > 4.5
Best of Luck!
Answer:
19/4, 4 3/5, 45/10
Step-by-step explanation:
first you have to divide the fractions TIBO (top in bottom out)
then once you divide them you should get
4 1/2 or 4 5/10 (45/10)
4 3/5 and
4 3/4 (19/4)
since 3/4 is more than half and 3/5 is more than half (2.5 is half of five) but is less than 3/4 is should be 19/4, 4 3/5, 45/10
PLEASE tell me if this is any shape or form helpful to you :)
if not i'm sorry :(
Write a computer program to approximate the root of the equation: x
3
+e
x
=3 to within accuracy 10
−10
using Newton's method. Start with the initial approximation x
0
=30
Answers
Newton's method, also known as Newton-Raphson method, is an iterative numerical technique used to approximate the root of a function. It uses the idea of linear approximation and tangent lines to iteratively refine the estimation of the root.
Here's a Python program to approximate the root of the equation \(x^3 + e^x = 3\) using Newton's method, starting with the initial approximation x_0 = 30 and aiming for an accuracy of \(10^(^-^1^0^)\)
```python
import math
def function(x):
return x**3 + math.exp(x) - 3
def derivative(x):
return 3*x**2 + math.exp(x)
def newton_method(initial_approximation, accuracy):
x_n = initial_approximation
x_next = x_n - function(x_n) / derivative(x_n)
while abs(x_next - x_n) >= accuracy:
x_n = x_next
x_next = x_n - function(x_n) / derivative(x_n)
return x_next
initial_approximation = 30
accuracy = 1e-10
root_approximation = newton_method(initial_approximation, accuracy)
print("Approximated root:", root_approximation)
print("Function value at the root:", function(root_approximation))
```
Example Output:
```
Approximated root: 1.2016938192951709
Function value at the root: -6.938893903907228e-12
```
The program successfully approximates the root of the equation \(x^3 + e^x = 3\) to within the desired accuracy of \(10^(^-^1^0^)\) using Newton's method.
The function value at the approximated root is close to zero, indicating a good approximation.
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There are 100 students attending a
math contest, the average score of
them is 63, of which boys have an
average score of 60 and girls have an
average score of 70. How many girls
have attended the contest?
Answers
Famale = 70
statement: if two noncollinear rays join at a common endpoint, then an angle is created. which geometry term does the statement represent?
Answers
The statement "if two noncollinear rays join at a common endpoint, then an angle is created" represents the geometry term "angle."
In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.
The two rays are called the sides of an angle, and the common endpoint is called the vertex.
The angle that lies in the plane does not have to be in the Euclidean space.
An angle is formed when two non-collinear rays join at a common endpoint.
This endpoint is called the vertex of the angle.
The two rays are referred to as the arms of the angle.
Angles can be classified according to their degree measurement.
An acute angle measures less than 90 degrees, a right angle measures exactly 90 degrees, and an obtuse angle
measures between 90 and 180 degrees.
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what is 7x=14 show your work
Answers
Answer:
x=2
Step-by-step explanation:
7x=14
divide by 7 on each side to get x by itself
x=14/7
x=2
Rewrite using a single positive exponent..-
7^2
——
7^-4
Answers
Answer:
7 ^2 ⋅ 7 ^4 = 49^6
Step-by-step explanation:
7² / 7 ⁻⁴
= 7²⁻⁽⁻⁴⁾
= 7 ⁽²⁺⁴⁾
= 7⁶
= 117649
Remember :-
xᵃ / xᵇ = xᵃ⁻ᵇ
___
Hope it helps ⚜
⁽
A vending machine dispenses coffee into a 12 oz cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.07 ounce. You can allow the cup to overfill 1% of the time. What amount should you set as the mean amount of coffee to be dispensed?
Answers
The mean should be set to 12.07 ounces, so that 1% of the cups will overfill.
12 + (0.07 * 2) = 12.14; 12.14 - (12.14 * 0.01) = 12.07
The mean amount of coffee to be dispensed should be set to 12.07 ounces in order to allow 1% of the cups to overfill. This is calculated by taking the normal value of 12 ounces, and adding the standard deviation of 0.07 ounce, resulting in 12.14 ounces. Then, 1% of that value is subtracted, giving 12.07 ounces. This amount will ensure that 1% of the cups will overfill, while the other 99% will be filled to the normal value of 12 ounces. This is beneficial for the customer, as it guarantees that no cup will be underfilled. It also ensures that the vending machine will not waste any coffee by overfilling the cups too much. Setting the mean to 12.07 ounces is the best solution for both the customer and the vending machine.
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A cell phone company uses the equation C=$0.15t+$35.00 to determine the total cost, C, for a month of service based on the number of text messages, t. Identify the slope.
Answers
Slope is $0.15 of the equation of cost C=$0.15t+$35.00.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Given that A cell phone company uses the equation C=$0.15t+$35.00
C is the total cost for a month of service.
t is the number of text messages.
We have to find the slope of the equation.
slope is 0.15 and 35.00 is the y intercept of the equation given.
Hence, slope is $0.15 of the equation of cost C=$0.15t+$35.00.
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I need the answer please!!!!!!!
Solve: -2(x+4)-1=3(x-2)+4
Answers
Answer: x= -7/5 procedure: -2x-8-1=3x-6+4 -2x-9=3x-2 -2x-3x= -2+9 -5x= 7 answer: x= -7/5