Answers
Answer:
Step-by-step explanation:
[tex]\sf 1.1)\dfrac{Sin \ \theta-Cos \ \theta}{Sin \ \theta + Cos \ \theta}=\dfrac{(Sin \ \theta-Cos \ \theta)}{((Sin \ \theta + Cos \ \theta)}*\dfrac{(Sin \ \theta-Cos \ \theta)}{(Sin \ \theta-Cos \ \theta)}[/tex]
[tex]\sf = \dfrac{(Sin \ \theta-Cos \ \theta)^2}{Sin^2 \ \theta-Cos^2 \ \theta}\\\\=\dfrac{Sin^2 \ \theta+Cos^2 \ \theta-2Sin \ \theta \ Cos\ \theta}{(Sin \ \theta-Cos \ \theta)}\\\\\\\bf Identity: \ (a +b)^2= a^2 + b^2 - 2ab\\\\\\=\dfrac{1-2Sin \ \theta \ Cos \ \theta}{(Sin \ \theta-Cos \ \theta)} = LHS[/tex]
[tex]\sf 1.2) LHS = tan^2 \ x - Sin^2 \ x = \dfrac{Sin^2 \ x}{Cos^2 \ x}-Sin^2 \ x[/tex]
[tex]\sf =\dfrac{Sin^2 \ x}{Cos^2 \ x}-\dfrac{Sin^2 \ x*Cos^2 \ x}{1*Cos^2 \ x}\\\\\\ = \dfrac{Sin^2 \ x - Sin^2 \ x*Cos^2 \ x}{Cos^2 \ x}\\\\\\= \dfrac{Sin^2 \ x *(1 -Cos^2 \ x)}{Cos^2 \ x}\\\\=\dfrac{Sin^2 \ x*Sin^2 \ x}{Cos^2 \ x} \\\\ \bf 1 - Cos^2 \ x = Sin^2 \ x\\\\= \dfrac{Sin^2 \ x}{Cos^2 \ x}*Sin^2 \ x\\\\=tan^2 \ x * Sin^2 \ x = RHS[/tex]
[tex]\sf 1.3) LHS = \dfrac{1-Cos \ x}{Sin \ x}-\dfrac{Sin \ x}{1+Cos \ x} =\dfrac{(1-Cos \ x)(1+Cos \ x)}{Sin \ x*(1+Cos \ x)}-\dfrac{Sin \ x*Sin \ x}{(1+Cos \ x)*Sin \ x}\\[/tex]
[tex]\sf =\dfrac{1 - Cos^2 \ x}{Sin \ x*(1+Cos \ x)}-\dfrac{Sin^2 \ x}{Sin \ x*(1+Cos \ x)}\\\\=\dfrac{Sin^2 \ x}{Sin \ x*(1+Cos \ x)} - \dfrac{Sin^2 \ x}{Sin \ x*(1+Cos \ x)}\\\\=\dfrac{Sin^2 x - Sin^2 \ x}{Sin \ x*(1+Cos \ x)} \\\\= 0 = RHS[/tex]
[tex]\sf 1.4) LHS = Sin x - \dfrac{1}{Sin \ x + Cos \ x}+Cos \ x \\[/tex]
[tex]\sf = \dfrac{Sin \ x *(Sin \ x + Cos \ x) - 1 + Cos \ x * (Sin \ x + Cos \ x)}{Sin \ x + Cos \ x }\\\\\\= \dfrac{Sin \ x * Sin \ x + Sin \ x*Cos \ x -1 + Cos \ x*Sin \ x + Cos \ x*Cos \ x}{Sin \ x + Cos \ x}\\\\\\=\dfrac{Sin^2 \x + Sin \ x \ Cos \ x - 1 + Cos \ x \ Sin \ x + Cos^2 \x}{Sin \ x + Cos \ x}\\\\=\dfrac{Sin^2 \ x + Cos^2 \ x - 1 + Sin \ xCos \x +Sin \ x Cos \ x}{Sin \ x + Cos \ x}\\\\= \dfrac{1 - 1 +2Sin \ x Cos \ x}{Sin \ x + Cos \ x}\\\\= \dfrac{2Sin \ x Cos \ x}{Sin \ x + Cos \ x}[/tex]
Related Questions
Use the fact that 1.5 is the same as 3/2 to select all of the equations below that are equivalent toT
Answers
The equivalent expressions of T=A^1.5 are: T= (A)^3/2 and T= ((A)^1/2)^3
According to the statement
we have to show that the 1.5 is same as 3/2 are equivalent to T.
So,
Equivalent expressions are expressions with the same value.
The Given expression is
T=A^1.5
we can write it as a
T= (A)^3/2
Because we know that the
1.5 = 3/2
So, it become T= (A)^3/2.
And From
T=A^1.5
we can write it as a
T= ((A)^1/2)^3
because we know that the
3/2 = (1/2)^3.
So, The equivalent expressions of T=A^1.5 are: T= (A)^3/2 and T= ((A)^1/2)^3.
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Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new housing project to a processing plant The city does not want the sewer line to cross the farm land. Can a direct line be installed?
● Let 1 unit = 100 feet.
● The entry to the sewer plant is at (2,3)
● The sewage exit from the housing project is at (12,6)
● The sprinkler system extends 200 ft and the center of the land is at (8,3)
Questions: (1) Will the sewer line cross the farmland? If so then at what points?
(2) If the farmer wants to maximize the farming area and does not want to cross the sewer line, what is the longest sprinkler system that could be installed?
Answers
The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;
(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)
(2) The longest installable sprinkler system is approximately 172.4 feet
How can the points where the line crosses the farmland be found?1. The slope of the sewer line is found as follows;
m = (6 - 3)/(12 - 2) = 3/10 = 0.3The equation of the sewer line can be expressed in point and slope form as follows;
(y - 3) = 0.3×(x - 2)y = 0.3•x - 0.6 + 3
y = 0.3•x + 2.4
The equation of the circumference of the sprinkler can be expressed as follows;
(x - 8)² + (y - 3)² = 2²Therefore;
(x - 8)² + (0.3•x + 2.4 - 3)² = 2²
Solving gives;
x= 6.53, or x = 8.48
y = 0.3×6.53 + 2.4 = 4.36
y = 0.3×8.48 + 2.4 = 4.9
Therefore;
The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)2. When the farmland does not cross the sewer line, we have;
sewer line is tangent to circumference of farmland
Slope of radial line from center of the land is therefore;
m1 = -1/0.3
Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;
y - 3 = (-1/0.3)×(x - 8)
Which gives;
y = (-1/0.3)×(x - 8) + 3
The x-coordinate is therefore;
0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3
x ≈ 7.5y = 0.3 × 7.5 + 2.4 ≈ 4.65The longest sprinkler system is therefore;
d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724
Which gives;
The longest sprinkler system is 1.724 × 100 ft. ≈ 172.4 ft.Learn more about the equation of a circle here:
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f(x) = (two-fifths) Superscript x
g(x) = (two-fifths) Superscript x – 3
Which statement about f(x) and its translation, g(x), is true?
The range of g(x) is , {y | y > 0} and the range of f(x) is {y | y > –3}.
The range of g(x) is , {y | y > 3} and the range of f(x) is {y | y > 0}.
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
The asymptote of g(x) is the asymptote of f(x) shifted three units up.
Answers
Answer: The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
Answer:
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
bc I said so
a big water tank contained 200 litres of water. during the day, 88 l 580 ml of water was used and 200 ml leaked. how much water was left in the water tank?
Answers
The quantity of water left in the tank as described in the task content is; 111 l 220ml.
What is the amount of water left in the tank?The tank described in the task content initially contains 200 liters, in which case, 1 liter corresponds to 1000ml.
Hence, when 88l 580ml was used, the remaining quantity of water is; 200l - (88l 580ml) = 111 l 420ml.
And finally, since 200 ml leaked, the quantity of water left is; 111l 220ml.
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A rectangle is 8 feet longer than it is wide. find the dimensions of the rectangle if its area is 345 sq-feet.
Answers
The width of rectangle is 15 feet and the length of rectangle is 23 feet.
According to the statement
Width of rectangle = x
Length of rectangle = x+10
Area of rectangle = 345 sq-feet.
we know that the area of rectangle is
Area of rectangle = L*W
Substitute the values in it then
345 = (x) (x+8)
345= (x)^2 + 8x
(x)^2 + 8x - 345 = 0
By factorisation
(x-15) (x+23) = 0
So, width of rectangle is 15 feet and the length of rectangle is 23 feet.
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Multiply two and six eighths multiplied by six.
A. fourteen and five eighths
B. sixteen and two eighths
C. sixteen and four eighths
D. seventeen and three eighths
Answers
Answer:
C . Sixteen and four eighths.
Step-by-step explanation:
2 6/8 * 6
= 22/8 * 6
= 6*22 / 8
= 132/8
= 16 4/8.
what is the measure.. PLS HELP THIS IS URGENT
Answers
The angle of the given ray is of x = 150º.
What is the angle of the ray?The angle of the ray is given by the sum of the angles that compose the ray.
In this problem, the angles are of 65º, 40º and 45º, hence:
x = 65 + 40 + 45 = 150º
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Determine which graph represents this system of equations to complete the statements that follow. y = -x2 + x + 5, y = -x + 2.
Answers
The solution to the system of equations is (-1, 3) and (3, -1)
How to graph the equations?The system of equation is given as:
y = -x^2 + x + 5
y = -x + 2
Next, we plot the graph of the system using a graphing tool
From the graph, both inequalities intersect at
(-1, 3) and (3, -1)
Hence, the solution to the system of equations is (-1, 3) and (3, -1)
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Answer:
graph 1,
3,-1 and -1,3
Step-by-step explanation:
See screenshot
What is the equation of a circle whose center at (-5, -2) and radius is 2?
Answers
The equation of a circle whose centre ([tex]-5,-2[/tex]) and radius [tex]2[/tex] is [tex]x^{2}+y^{2}+10x+4y+25=0[/tex]
What is equation of a circle?
A circle is a closed curve drawn from a fixed point called centre of the circle. The distance between the centre of the circle and the arc of the circle is called the radius of the circle.
The equation of a circle with centre [tex](h, k)[/tex] radius [tex]r[/tex] is
[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]
Given center = [tex](-5,-2)[/tex] and Radius = [tex]2[/tex]
Put the Given value in the equation:
= [tex](x-(-5))^{2} +(y-(-2))^{2} = 2^{2}[/tex]
= [tex](x+5)^{2} +(y+2)^{2}=2^{2}[/tex]
= [tex](x^{2} +10x+25)+(y^{2}+4y+4)= 4[/tex]
= [tex]x^{2} +y^{2}+10x+ 4y+ 29 = 4[/tex]
= [tex]x^{2} +y^{2}+10x +4y+ 29-4=0[/tex]
= [tex]x^{2} +y^{2}+10x+4y+25=0[/tex]
So, the equation of the circle whose centre is [tex](-5,-2)[/tex] and Radius [tex]2[/tex] is
[tex]x^{2}+y^{2}+10x+4y+25=0[/tex]
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DOES ANYONE KNOW THE ANSWER
Answers
Answer:
D. none
Step-by-step explanation:
we only know about the right angle at the bottom right.
that is not enough information.
we always need 3 pieces of confirmed information of each triangle to be able to say that the 2 triangles are indeed of the same shape and size.
like the other answer options would indicate :
SAS : side - angle - side.
2 sides and the enclosed angle. if we know they are equal, then the rest of the triangles follow automatically.
SSS : all 3 sides. with 3 defined sides there is only one possible shake and size for that triangle.
HL : Hypotenuse and a leg of a right-angled triangle (also 3 pieces of information - 2 sides and the right angle).
since we have only the right angle and nothing else, we cannot prove that the triangles are congruent.
Determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence. In this case, you know the measure of two adjacent sides and the angle opposite to one of them. If it is a valid criterion, explain why. If it is not valid, use GeoGebra to create a counterexample demonstrating that it doesn’t work and give an explanation. (Hint: Try constructing a triangle where the known angle is opposite to the shortest known side.) If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the space below.
Answers
The illustration to determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence is given below.
How to illustrate the information?Congruence of triangles means that two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
In this case, these triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.
To illustrate the question, this will be:
Step 1: Draw a line segment AB
Step 2:Draw an acute angle (let's say 45° ) at A as AX
Step 3: From B draw an altitude on AX BY ⊥ AX
Step 4 Using suitable compass width and taking Y as center cut AX on both sides at C and D
Now BC = BD as BY is perpendicular bisector
Now compare ΔABC and ΔABD. Using suitable compass width and taking B as center cut AX at 2 points C & D directly so BC = BD.
This can illustrate that SSA is not a valid means for establishing triangle congruence.
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Answer:
Below is an example to show whether side-side-angle (SSA) is a legitimate method for proving triangle congruence. How should the information be illustrated? Triangle congruence refers to the property that two triangles are congruent if their three corresponding sides and their three corresponding angles are both equal in size. In this instance, the triangles can be moved around, rotated, flipped, and turned to have a same appearance. They are in alignment with one another when moved. This can serve as an example of why SSA cannot be used to prove triangle congruence.
Step-by-step explanation:
On a plat map are two adjacent rectangular lots. Lot A has a square footage of 46,060, and Lot B has a square footage of 43,005. The common boundary they share is 235 feet long. What is the width of Lot B
Answers
The Width of plot B is 183 ft.
According to the statement
we have given that the Plot A has a square footage of 46,060, and Plot B has a square footage of 43,005. The common boundary they share is 235 feet long.
And we have to find the width of the Plot B
We know that
Area of plot A = 46,060 square footage.
Area of plot B = 43005 square footage.
Common area share by both Plot = 235 feet long.
So, Now
The width of Plot B = Area of plot B / Common area
Substitute the values in it then
width of Plot B = Area of plot B / Common area
width of Plot B = 43005 / 235
width of Plot B = 183 feet.
So, The Width of plot B is 183 ft.
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Solve:
2a + 6 = 12
a =
Answers
Answer:
8
Step-by-step explanation:
because hhhhhh
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jkkkkk
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vvvvv
dddfff
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kkkkkk
lllll.ssss
Now simplify the y-terms to get the equation of the parabolic path. You do not need to expand the x-term. (2 points) Hint: Square both sides to get rid of the square roots
Answers
The simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
How to determine the simplified equation?The complete question is added as an attachment
The equation is given as
[tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex]
Subtract (x - 10)^2 from both sides
[tex](y- 6)^2 = 4^2 - (x - 10)^2[/tex]
Evaluate 4^2
[tex](y- 6)^2 =16 - (x - 10)^2[/tex]
Take the square root of both sides
[tex]y- 6= \sqrt{16 - (x - 10)^2}[/tex]
Add 6 to both sides
[tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
Hence, the simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
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What is the end behavior of the graph
Answers
Answer:
as x is approaching positive infinity, y approaches positive infinity
as x is approaching negative infinity, y is approaching negative infinity
El rio Lempa sirve de linea fronteriza entre Honduras y El Salvador, mide 300km
de largo. ¿Cuántos metros mide este rio?
Answers
Answer:
El río mide:
300000 metros.
Step-by-step explanation:
1 km = 1000 metros
300 km = 300 * 1000 = 300000 metros
...
y square plus 5y equals to 0
Answers
Answer:
y^2 + 5y = 0
y(y + 5) = 0
y = 0, -5
The answer is y = 0 and y = -5.
The given question :
y² + 5y = 0y (y + 5) = 0y = 0, y = -5Richard wants to weed 33% of his garden today. The total garden is 144 square yards. How many square yards should Richard weed to reach his goal?
Answers
to solve is shown below:
What is the multiplicative inverse of -13/14
Answers
The multiplicative inverse of -13/14 as in the task content is; -14/13.
What is the multiplicative inverse of -13/14?The multiplicative inverse of a number x is given as; 1/x.
On this same note, it follows that since, the number whose multiplicative inverse is to be found is: -13/14, the multiplicative inverse is; -14/13.
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Find the five-number summary for the data.
{236, 202, 218, 208, 225, 229, 211, 237, 223, 206, 217, 216, 232, 225, 208}
Answers
Minimum: 202
Quartile (Q1): 208
Median: 218
Quartile Q3: 229
Maximum: 237
What is the Five-Number Summary?The max and min value, the lower and upper quartiles, and the median of a data comprise the five-number summary.
Given the data: 236, 202, 218, 208, 225, 229, 211, 237, 223, 206, 217, 216, 232, 225, 208, we would have the following:
Minimum: 202 (least value)
Quartile (Q1): 208 (center of the first half of the data)
Median: 218 (center of the data when ordered)
Quartile Q3: 229 (center of the second half of the data)
Maximum: 237 (highest value).
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1. sonya's salary increases at a rate of 4% per year. her starting salary is $45,000. what is her annual salary, to the nearest $100, after 8 years of service?
Answers
Her annual salary after 8 years will be $57,600.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. It is frequently symbolized with the percent sign, " %". A % is a number with no dimensions; it has no unit of measurement.To find what is her annual salary, to the nearest $100, after 8 years of service:
Find 4% of 45,000
[tex]\frac{x}{45000} *100=4\\\frac{x}{450} =4\\x =1800[/tex]
So, 4% of $45,000 of $1800.
1st year = $45000
2nd year = 45000 + 1800 = $46800
3rd year = 46800 + 1800 = $48600
4th year = 48600 + 1800 = $50400
5th year = 50400 + 1800 = $52200
6th year = 52200 + 1800 = $54000
7th year = 54000 + 1800 = $55800
8th year = 55800 + 1800 = $57600
Therefore, her annual salary after 8 years will be $57,600.
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The salary of Sonya after 8 years will be $61,600 (nearest $100).
What is compound interest?The interest on the a loan or deposit that is calculated using the both initial principal as well as the accrued interest from prior periods is known as compound interest (sometimes known as compounding interest).
Some features of compounding are-
Compound interest is calculated just on initial principal of a deposit or loan, which also takes into account all of the interest accrued from prior periods.The yearly interest rate is raised to a number of compounded periods minus one, and the starting principal amount is multiplied by both of these factors.The frequency plan for compounding interest can be set to be continuous, daily, or yearly.The quantity of compounding periods has a bigl impact on compound interest calculations.Calculation for the amount after 8 years-
The principal amount is $45,000
Rate of interest is 4% per year.
Time duration is 8 years.
The formula for total amount after compounding is -
[tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period.
t = number of time periods elapsed.
As the rate of interest is applied only one in a year ; n = 1.
Substitute the values in the formula to get the value.
[tex]A=45,000\left(1+\frac{.04}{1}\right)^{8}\\A=45,000\left(1.04}\right)^{8}\\\\A=61585.60[/tex]
Therefore, the salary of Sonya will be $61600 (nearest $100) after 8 years.
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What is the value of the expression below when w = 9 and x = 5?
10w + 4x
Answers
Answer:
110
Step-by-step explanation:
10w + 4x
10 (9) + 4 (5)
90 + 20
110
The answer is 110.
Hope it helps!
Have a nice day:)
In a survey of 456 residents, 279 were opposed to the use of the photo-cop for issuing traffic tickets. What is the best point estimate for the proportion () of all residents opposed to the photo-cop use
Answers
The best point estimate for the proportion of all the residents opposed to the photo cop use is 60% which is the fourth option.
Given that in a survey of 456 residents , 279 were opposed to the use of the photo cop for issuing traffic tickets.
We have to find the best point estimate for the proportion of all residents opposed to the photo cop use.
Total residents=456
Residents who opposed to the use of the photo cop for issuing traffic tickets=279
Proportion=number of residents who opposed/ total residents
=279/456
=0.611
=61.1%
The nearest option is fourth which is 60%.
Hence the best point estimate for the proportion for the proportion of all the residents opposed to the photo cop use is 60% which is option 4.
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Question is incomplete as it should include options which are :
1) 500
2)50%
3)300
4)60%
5)40%
Which of the following statements about angles is NOT correct?
Complementary angles are two angles whose sum is 90 degrees.
The measure of an obtuse angle is always greater than the measure of an acute angle.
The measure of an acute angle and the measure of an obtuse angle added together will always
be supplementary.
Two right angles that share a leg are supplementary.
Answers
ANSWER: The third statement appears to be incorrect.
An insurance office records the number of claims received each day, X, and built the probability distribution table below using the data collected. Find the mean and the standard deviation of the probability distribution using Excel. Round the mean and standard deviation to two decimal places.
Answers
The mean of the data given is 13.4364 and.the standard deviation is 1.788.
How to illustrate the information?It should be noted that the mean is the average of the giving set of numbers. In this situation, the mean is 3.1998.
E(X²) will be:
= (0² × 0.0408) + (1² × 0.1304) .... + (12² × 0.0001)
= 13.4364
Var(X) = 13.4364 - 3.1998²
= 3.198
The standard deviation will be:
= ✓3.198
= 1.788
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Which of the following is 25 9/16 equal to?
Answers
Answer:
Step-by-step explanation:
25.5625
Answer:
25.5625
Step-by-step explanation:
The solution is in the image
A _______ group is another name for a command group
Answers
Answer:
department
Step-by-step explanation:
A "task force" group is another name for a command group.
We have,
A task force is a temporary grouping of individuals or units with a specific objective or mission.
It is typically formed to address a particular task or problem and is led by a designated commander or leader.
Task forces can be assembled from different departments or organizations to collaborate and work together towards a common goal.
Thus,
A "task force" group is another name for a command group.
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Patient a weighs 135.8 pounds.patient b weighs 135 2/5 ibs. which patient has the greater weight or if their weights are equal
Answers
Answer:
patient A has the greater weight
what is the length of side AB of the triangle?
Answers
BC is 3 across & CA is 3 up, but this creates a right-angle triangle. So, Pythagoras Theorem is used to find AB
AB = root 3^2 + 3^2
AB = 3 root 2
or 4.242640687
Thus, AB is 4.24 to 2d.p
(root means square root)
Hope this helps!
Dad has 15 oak and maple boards from the lumber yard. each oak board is 6 centimetres thick. each maple board is 9 centimetres thick. when my dad stacks the boards, the stack is 96 centimetres thick. how many of each type of board does he have?
Answers
Answer:
He has 2 maple boards and 13 oak boards.
Step-by-step explanation:
Assuming all boards are oak : 6*15=90
Maple minus oak = 3
96-90=6 6/3=2 maple boards
Verification : 2*9+6*13 = 96
Answer:
13 oak, 2 maple
Step-by-step explanation:
o = oak
m = maple
o + m = 15
6o + 9m = 96
o + m = 15
o = 15 - m
6o + 9m = 96
6(15 - m) + 9m = 96
90 - 6m + 9m = 96
90 + 3m = 96
3m = 6
m = 2
o + 2 = 15
o = 13
6(13) + 9(2) = 96 (Yes, correct!)
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