The value of sinx is 1 - 3cosx
What is Trigonometry?
Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles. The topic arose in the Hellenistic civilization during the third century BC from geometric applications to astronomical research. Today, four varieties of trigonometry are used: core, plane, spherical, and analytic. The ratio of the sides and angles of a right triangle is the subject of core trigonometry.
Solution:
1/cosx - tanx = 3
we can write tanx as sinx/cosx
this is because we know that sinx = Perpendicular / Hypotenuse
and cosx = Base / Hypotenuse
so if we divide sinx by cosx we will find that it is equal to Perpendicular / Base which is nothing but tanx
1-sinx = 3cosx
sinx = 1 - 3cosx
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What is the quotient of and 3/4 and 5 6?
9/10 is the quotient when 3/4 is divided by 5/6.
What is fraction?The two parts that make up a fraction are the numerator, which is located at the top, and the denominator, which is located at the bottom.
How to divide fractions?When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction and this can be obtained by reversing its numerator and denominator—is and then dividing the fractions. Multiply the two numerators after that. Multiply the two denominators after that, After that we need to simplify the fraction to its lowest form.
Mathematically quotient ,
= (3/4) ÷ (5/6)
It is possible to define an arithmetic operation as one in which we add, subtract, multiply, and divide numbers. It has the fundamental operators +, -,÷,× and.
= (3/4)*(6/5)
= 18/20
= 9/10
so the quotient of 3/4 and 5/6 in lowest form is 9/10.
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Indicate which property is illustrated in Step 3. OA. inverse property of multiplication O B. commutative property of division OC. identity property of addition OD. identity property of division Step 1 Step 2 Step 3 12 6+3+1=(12= 6) +(3+ = 2 + (3+1) = 2+3
Answer:
its a commutative property becaus its just changing the order
Can a person draw Social Security and disability at the same time?
Generally it is not possible. But if someone applying for early retirement after being forced to leave their jobs due to an illness or injury. In order to help them pay their costs until their SSDI claim is approved and the waiting period for those benefits has passed, they can start collecting early retirement payments.
Generally speaking, it is not possible to receive both Social Security retirement benefits and Social Security Disability Insurance (SSDI) at the same time. However, if you fulfill the severe financial requirements while receiving SSDI or retirement payments from Social Security, you can be eligible for Supplemental Security Income (SSI).
To fill the gap between when someone must leave the working due to a disability and when they can receive retirement benefits, the Social Security Administration (SSA) established the SSDI program. Because of this, there is only one option to get SSDI and retirement benefits at the same time.
This happens when a person chooses to retire early between the ages of 62 and their full retirement age but is later granted SSDI payments. Some people do this on purpose by applying for early retirement after being forced to leave their jobs due to an illness or injury. In order to help them pay their costs until their SSDI claim is approved and the waiting period for those benefits has passed, they can start collecting early retirement payments.
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The William’s family drove from Brooklyn to Yonkers. Use the table to determine whether the distance driven is a linear function of the hours traveled. Explain.
The distance driven is a linear function of the hours traveled, due to the constant addition every time the number of hours is increased by one.
What is the condition for a linear function?A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
The points of the function in the table are given as follows:
(1,55), (2,110), (3, 165), (4,220).
(time input, distance output).
The increases to the output when the input time is increased by one are given as follows:
220 - 165 = 55.165 - 110 = 55.110 - 55 = 55.As the increases are constant, the distance driven, in fact, is a linear function of the hours traveled.
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Thank you to whoever replies!
Answer:
Step-by-step explanation:
value of y is 87*
because linear pair always sum up to give 180*
we know 93+y=180
so y=180-93=87
y= 87°
value 'y' and 93° are a linear pair, the sum of the angles is always equal to 180°
180-93 = 87
The fraction of the instructions that used the word off is [tex]\frac{9}{25}[/tex]
How many number less than 100 are divisible by 3?
On solving the provided question, we can say that - there are 67 numbers less than 100 are divisible by 3
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
= n(A ∪ B)
= n(A) + n(B) - n(A ∩ B)
= 33 + 50 - 16
= 67
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Given the following two ordered pairs calculate the rate of the function.
(−9, −4) and (−3, −16)
Enter your answer in the box.
m=
Answer:
m=-2
Step-by-step explanation:
Recall slope (m) can be found using the following:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For this problem, let:
[tex](x_1,y_1)=(-9,-4)\\(x_2,y_2)=(-3,-16)[/tex]
So,
[tex]m=\frac{(-16)-(-4)}{(-3)-(-9)}\\m=\frac{(-16)+4}{(-3)+9}\\m=\frac{-12}{6}\\m=-2[/tex]
What is Pascal's law statement?
Pascal's law statement states that pressure is equal to the force divided by the area on which it acts.
What is Pascal's law statement?According to Pascal's law, pressure applied to a fluid inside of a container will be transmitted without a change in magnitude to every point within the fluid as well as the container's walls. Any point in the fluid experiences equal pressure in all directions.
The force multiplied by the surface area on which it acts produces pressure. Pascal's principle states that a pressure increase on one piston in a hydraulic system causes an equal increase in pressure on another piston in the system.
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What is the nature of roots of x² 6x 9?
The equation x² + 6x + 9 has two real roots, because the discriminant (b² - 4ac) is greater than zero. The two roots can be calculated using the quadratic formula.
The equation x² + 6x + 9 has two real roots, because the discriminant (b² - 4ac) is greater than zero. This can be seen by calculating b² - 4ac, which in this case gives (6² - 4*1*9) = 36 - 36 = 0. A discriminant of zero or higher means that the equation has two real roots. The two roots can be calculated using the quadratic formula, which is x = [-b ± Â√(b² - 4ac)] / 2a. In this case, a = 1, b = 6, and c = 9, so the formula becomes x = [-6 ± Â√(6² - 4*1*9)] / 2, which simplifies to x = [-6 ± Â√0] / 2, or x = [-6 ± 0] / 2. So the two roots are x = -3 and x = -3, which means that the equation has two equal real roots.
x² + 6x + 9
b² - 4ac = (6² - 4*1*9) = 36 - 36 = 0
x = [-6 ± Â√(6² - 4*1*9)] / 2
x = [-6 ± Â√0] / 2
x = [-6 ± 0] / 2
x = -3 and x = -3
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How do I solve for y-intercept?
Answer:
Below
Step-by-step explanation:
At the y-axis intercept, the value of x = 0 <==== put '0' in for 'x' and calculate the y-axis intercept
Use point-slope form to write an equation of the line with the given slope that passes through the given point.
Answer:
Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. ...
Point-slope form = y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is the point given and m is the slope given.
Step-by-step explanation:
The local school district you live in selling bonds for $2000 that pays 5% interest annually that matures in 10
years. How much interest will you earn?
O $2000
O $500
O $750
O $1000
Answer:
$1000
Step-by-step explanation:
5% = 1 year
50% = 10 years
50% = 0.5
Take 2000 times 0.5 = $1000
So, you will earn $1000 interest in 10 years
What percent chance is 1 out of 20?
Based on the given task content; the percent chance is 1 out of 20 is 5%.
How to find percentage?Percentage refers to the amount, number or rate of something, regarded as part of a total of 100.
The percent chance is 1 out of 20
= 1/20 × 100
= 0.05 × 100
= 5%
Un conclusion, 5% is the percent chance is 1 out of 20
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What's the mean of the following number set 2 2 4 6 8 8 10?
The required mean of the given data is 5.71.
What is mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset.
The term "average" is frequently used to describe this measure of central tendency.
So, we have the data set:
2, 2, 4, 6, 8, 8, 10
Mean formula: Sum of terms / Number of terms
Now, calculate the mean as follows:
Mean: Sum of terms / Number of terms
Mean: 40 / 7
Mean: 5.71
Therefore, the required mean of the given data is 5.71.
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What is equidistant from a fixed point?
A set of points equidistant from a fixed point in a plane figure is called a circle where the distance between each of the set of the points and the fixed point forms the radius of the circle.
A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.
In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.
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What does a 3 to 1 slope mean?
3 to 1 slope means, there are three horizontal units for every one vertical unit.
How do one find the slope of a graph?The slope is computed mathematically as "rise over run" (change in y divided by change in x).
In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.
That is to say,
Determine the coordinates of two locations along the line that one choose.Evaluate the differences in these two positions' y-coordinates (rise).Evaluate the differences in these two locations' x-coordinates (run).In order to calculate the difference in y-coordinates (rise/run or slope), divide it by the difference in x-coordinates."Ratios like 3:1 are used to represent slopes. This indicates that there is a 1 unit (foot or meter) vertical shift, either up or down, for every 3 units (feet or meters) of horizontal distance."
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How do you create a unique array?
Minimum Increment operations to make Array unique
Minimum Increment operations to make Array unique.Making elements distinct in a sorted array by minimum increments.Find sum of non-repeating (distinct) elements in an array.Find k closest numbers in an unsorted array.Find k closest elements to a given value.What does the unique function do in Excel?The UNIQUE function will return an array, which will spill if it's the final result of a formula. This means that Excel will dynamically create the appropriate sized array range when you press ENTER .
How does ArrayList work?ArrayList is like an array behind the scenes as it’s backed by an array of type java.lang.Object in java.
Normally arrays are fixed in size which means the number of elements that can be added are fixed and cannot be increased once created. ArrayList can dynamically increase in size once the array that backs is full so, these way we won’t encounter runtime exceptions.
When we say list.get(0), it’s equivalent to array[0]. It can be said the ArrayList is a kind of more convenient way to use dynamic arrays.
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What are the 12 types of sets?
The 12 types of sets are empty set, singleton set, finite set, infinite set, subset, equal set, universal set, power set, proper subset, superset, equivalent set and proper superset.
An empty set does not contain any element, while a singleton set contain only one element.
If the number of elements in a set is finite, the set is a finite set. If the number of elements in a set is not finite, that is not countable it is an infinite set.
A set, say A contain only elements of another set, say B but not necessarily all elements, than set A is a subset of set B.
Whenever a set A is a subset of set B, we say the B is a superset of A. If A and B are two sets, then A is called the proper subset of B if A is a subset of B but B is not a subset of A i.e., A ≠ B.
If a set contains all and only elements of another set, then both set are said to be equal sets.
A universal set contains all elements of related sets.
Power set is the collection of all subsets of a particular set.
The set B is the proper superset of set A, then all the elements of set A are in B, but set B must contain at least one element which is not present in set A.
Equivalent sets are sets that have same number of elements.
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Если большой металлический шар данного радиуса R расплавить и из всего материала вылить одинаковые маленькие шарики радиуса r, то сколько их получится?
R=3см;r=0,5см;π≈3.
Answer: 216 small balls
Step-by-step explanation:
The volume of a ball:
[tex]\displaystyle\\V=\frac{4}{3} \pi R^3[/tex]
Let us calculate the volume of a big metallic ball:
[tex]\displaystyle\\V_{big}=\frac{4}{3} (3)(3^3)\\\\ V_{big}=4(27)\\\\V_{big}=108 \ cm^3[/tex]
Now let us calculate the volume of a big small ball:
[tex]\displaystyle\\V_{small}=\frac{4}{3} (3)(0.5^3)\\\\ V_{small}=4(0.125)\\\\V_{small}=0.5 \ cm^3[/tex]
Thus, the number of identical small balls should work:
[tex]\displaystyle\frac{V_{big}}{V_{small}} =\frac{108}{0.5} \\\\\frac{V_{big}}{V_{small}} =216\ units[/tex]
Deion is building a walkway with a width of xx feet to go around a swimming pool that measures 13 feet by 9 feet. If the total area of the pool and the walkway will be 621 square feet, how wide should the walkway be?
Applying the area of a rectangle, the width of the walkway (x) is: 7 feet.
What is the Area of a Rectangle?
Area of a rectangle = (length)(width)
Total area of the pool and walkway = 621 sq. ft
Length of the pool and walkway = 13 + 2x
Width of the pool and walkway = 9 + 2x
Thus, we will have the equation of the total area as:
(13 + 2x)(9 + 2x) = 300
4x² + 44x + 117 = 621
4x² + 44x + 117 - 621 = 0
4x² + 44x - 504 = 0
Factorize
(x - 7)(x+18) = 0
x = 7
or
x = -18
The width, x, cannot be negative, so, the width of the walkway (x) would be 7 feet.
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Is the square root of 2 equal to 2?
Therefore , the given expression of the problem √2 = 2 is a false statement the true statement is √2 ≠ 2.
What is square root?The number is derived by multiplying the square root of a positive integer by itself.
For instance, the square root of 25 is 5, since 5 x 5 is 25.
As you can see, 5 is also the square root of 25 because (5) (5) = 25.
The square root of a number is always represented by the symbol, which is √.
Here,
The square root symbol, which has the value of 1.414, is used to symbolize the square root of 2, also known as root 2.
Mathematicians frequently utilize this number.
Because Root 2 has an unlimited number of decimals and cannot be stated as a fraction, it is an irrational number.
and 2 has a value of 2.
Thus,
=> √2 ≠ 2
as
=> 1.414 ≠ 2.00
Therefore , the given expression of the problem √2 = 2 is a false statement the true statement is √2 ≠ 2.
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What is the statistical mode of the following numbers 9 10 6 5 6?
The statistical mode of a set of numbers is the number that occurs most frequently in the set. In the set {9, 10, 6, 5, 6}, the number 6 occurs twice, which is more than any other number. Therefore, the mode of this set is 6.
What does the word statistical in math mean?The field of statistics, which is applied mathematics, encompasses the gathering, describing, analyzing, and drawing of conclusions from quantitative data. The fundamental mathematical ideas in statistics include calculus of differential and integrals, linear algebra, and probability theory.
Give a statistical illustration.When attempting to estimate the population of a town, it is vital to determine the percentage of its residents who watch TV. This context makes reference to the sample, which is a condensed selection from the population.
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This meal costs $17.00. a 7% sales tax is applied, followed by an automatic tip of 18%. what is the total with tax and tip?
The total cost for the meal with tax and tip is $22.26.
This can be calculated using the following formula:
Total Cost with Tax and Tip = Meal Cost + (Meal Cost * Sales Tax Rate) + (Meal Cost * Tip Rate)
In this case, the formula would be:
Total Cost with Tax and Tip = 17.00 + (17.00 * 0.07) + (17.00 * 0.18)
This simplifies to:
Total Cost with Tax and Tip = 17.00 + 1.19 + 3.06
Which yields a final total cost of 22.26.
To explain in more detail, the meal cost is the original cost of the meal, which in this case is 17.00. Then, the sales tax rate is applied to the meal cost, which is 7% or 0.07. This gives us an additional cost of 1.19 (17.00 * 0.07). Lastly, the tip rate is applied to the meal cost, which is 18% or 0.18. This gives us an additional cost of 3.06 (17.00 * 0.18). Adding the meal cost of 17.00, the tax cost of 1.19, and the tip cost of 3.06 together gives us a total cost of 22.26.
Therefore, the total cost for the meal with tax and tip is $22.26.
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a researcher wants to study students to see if age of students has a positive relationship with grade point average. the researcher will get both age and grade point average from the college but not identifying individual students. grade point average appears to follow the normal curve. which test statistic would you use?
As our sample size is large and grade point average follows normal curve, we use parametric test.
What is normal curve?The normal curve is a statistical measurement which refer that the available data presented in a large number close to the mean value.
What is parametric test?The test is used to determine an approximate value of a set of data.
hence, we use parametric test for determining an approximate value.
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How do you find the nature of roots with examples?
The nature of the roots of a quadratic equation is known by a value known as the discriminant, which is calculated by seeing the equation and comparing it with the standard equation which is given by -
ax^2 + bx +c , where a , b , c are constants .
The root of the equation is given by -
x= [(-b )± (b^2 - 4ac)] / 2a
Here, the term (b^2 - 4ac) is called the discriminant of the quadratic equation .
This discriminant is the defining factor of the nature of the roots.
Now, here arise three cases-
(i) If (b^2 - 4ac) > 0, the roots are real and distinct .
(ii) If (b^2 - 4ac) = 0 , the roots are real and equal.
(iii) If (b^2 - 4ac) < 0 , the roots are not real and they are imaginary i.e. they are complex in nature and of the form a+ib.
For example , we have an equation x^2 + 2x + 1.
Here, a =1, b=2 and c=1.
Putting these values in the discriminant , we get -
b^2 - 4ac = 4-4(1)(1) = 0.
So, the roots of the equation are real and equal i.e. x=2,2.
Hence, it is the discriminant which determines the nature of roots.
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What is the value of 3 is to 4?
Let x= 3^4. So the value of given expression after applying power rule is x=81.
What is meant by power?
How many times you should multiply a number depends on its power. Exponents and indices are other names for powers. For instance, 82 may also be referred to as "8 to the power 2," "8 to the second power," or just "8 squared."
What is meant by n^5 where n can be any number?
By n^5 means n^5=n*n*n*n*n that is multiplying n five times.
3^4=(3^2)^2
=(9)^2
=81
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What percent is equivalent to 1/50
Answer: 2% is equivalent to 1/50
Step-by-step explanation:
We first need to divide the numerator by the denominator.
1 ÷ 50 = 0.02
Once we have the fraction in a decimal format, the answer is then multiplied by 100 to get the correct percentage:
0.02 × 100 = 2%
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Answer:
corrine got 66006 vote
bill got 53450 vote
Answer:
Bill Randall= 53450 votes.
Corrine Brown= 66006 votes.
Step-by-step explanation:
Bill Randall = X
Corrine Brown = 1x
Bill Randall= x+1x+12556=119456
2x+12556=119456
2x=119456-12556
2x=106900
x=106900/2
x=53450
Corrine brown = 53450+12556
= 66006
Does anyone know how to do this, I'm stuck
Please help me with this question
step by step explanantion
Answer: 148cm²
Step-by-step explanation:
The volume of the cuboid is the length, height, and width multiplied together. Since the problem gives us the volume, we can set an equation.
[tex]l*w*h=120 cm^3[/tex]
Since the area of the base of 30cm², we can get another equation.
[tex]l*w=30cm^2[/tex]
We can plug in our equations.
[tex]30cm^2*h=120cm^3[/tex] [divide both sides by 30cm²]
[tex]h=4cm[/tex]
Now, we know the height of the cuboid.
Since we aren't given a specific length and width, it can be any of the combinations that give 30 cm² when multiplied.
We can have 1,30 or 2,15 or 3,10 or 5,6.
I will work out 5,6 with l=5 and w=6.
The surface area of a cuboid is [tex]2(lw+wh+lh)[/tex].
[tex]2(30+24+20)=2(74)=148cm^2[/tex]
This is one possible answer. There are multiple ones with the pair choices above.