A worker is constructing a concrete pad that has a radius of 6.3 metres, as shown below. Report a Problem ↻ Reload Image How many metres of wooden forming are needed for the circumference of the pad? 24.6 metres 31.5 metres 39.6 metres 249.2 metres
The circumference of the pad to the nearest tenth is 39.6 meters
Formula for calculating the circumference of a circle?The circumference of a circle is the arc length of the circle, as if it were opened up and straightened out to a line segment. It is also known as the perimeter of a circle.
The formula for calculating the circumference of a circle is expressed as;
C = 2πr
where
π = 3.14
r is the radius of the circle
Given the following parameters
π = 3.14
r = 6.3m
Substitute to have:
C = 2 * 3.14 * 6.3
C = 6.28 * 6.3
C = 39.564
Hence the circumference of the pad to the nearest tenth is 39.6 meters
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Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900. The following table shows the number of sales each salesman had during the first three weeks of this month.
Based on the amount that both Salesmen A and B earn per sale, the number of sales they both had was 12 sales.
How many sales did Salesmen A and B have?Sales commission is a key aspect of sales compensation. It's the amount of money a salesperson earns based on the number of sales they have been able to make.
We are told that;
Salesman A gets $65 per sale.
Salesman B gets $300 and $40 per sale.
Assuming the number of sales to take them both to the same amount is x, the relevant formulas would be:
65x = 300 + 40x
Rearranging gives;
65x - 40x = 300
25x = 300
x = 300/25
x = 12 sales
The amount that salesman A earned is = 65 * 12 = $780
The amount that salesman B earned is = 300 + (40 * 12) = $780
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Use cos a cos b=1/2 [cos (a + b) + cos (a-b)]to derive cos x + cos y= cos 2 (x+y/2) cos (x-y/2) .
The trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
In the question, we are asked to derive the trigonometric identity, cos x + cos y = 2 cos (x + y/2) cos (x - y/2), using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
We are given the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
Substituting a = x + y/2 and b = x - y/2 in this, we get:
cos (x + y/2) cos (x - y/2) = 1/2[cos (x + y/2 + x - y/2) + cos (x + y/2 - x - y/2)],
or, cos (x + y/2) cos (x - y/2) = 1/2[ cos (2x/2) + cos (2y/2) ],
or, 2 cos (x + y/2) cos (x - y/2) = cos x + cos y, which on inter-changing the sides, gives us:
cos x + cos y = 2 cos (x + y/2) cos (x - y/2), which is the required trigonometric identity.
Thus, the trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
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The provided question is incorrect. The correct question is:
"Use cos a cos b=1/2 [cos (a + b) + cos (a-b)]to derive cos x + cos y = 2 cos (x + y/2) cos (x - y/2) ."
Agri-Small Business limited expenses on petrol for their fleet is R 4 850.00 at the end of September and they have a balance of R106 360.00 remaining in their account. The company has used 25% of its September income on salaries, 11% on electricity, rates and taxes, and 42% of the remaining on insurance and investments. The total income and expenditure in September are
a. Income is R 299 596.00 and expenditure is R 193 236.00.
b. Income is R 193 236.00 and expenditure is R 4 850.00.
c. Income is R 106 360.00 and expenditure is R 4 850.00.
d. Income is R 106 360.00 and expenditure is R 299 596.00
The total income and expenditure in September are "Income is R 106 360.00 and expenditure is R 4 850.00." Option C. This is further explained below.
What are the total income and expenditure in September?Generally, the equation for Insurance and investment is mathematically given as
II= 42% of the balance
II = 0.42*0.64A
II= 0.2688A
Generally, the equation for Total After All other exp is mathematically given as
Texp = 0.64A – 0.2688A
Texp= 0.3712A
Total After All other exp = 111210
subbing ahead and equating we have
111210 = 0.3712 A
Therefore
A = 299596
The total income is 299596
Therefore, the calculation for the expense is given as
Expense = 0.25A + 0.11A + 0.2688A + 4850
Expense= 0.6288A + 4850 = (0.6288*299596) + 4850
Expense= 193236
The Expense is 299596
In conclusion, At the end of September, Agri-Small Business's minimal spending on gasoline for their fleet amounted to R 4 850.00, and they still had a balance of R106 360.00 in their account. The majority of the remaining revenue was allocated to insurance and investments by the business, which accounted for 42% of the total. Wages and salaries accounted for 25% of the company's income in September. The overall revenue and expenses for the month of September were as follows: the income was R 106 360.00, and the expenses were R 4 850.00. Option C.
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What is 57, 020, 000 expressed in scientific notation
Answer:
we write in form of (a x 10^n)
5.702 x 10⁷
Answer:
5.702 x 10^7
Step-by-step explanation:
In scientific notation, a number in the ones place is raised to a power of 10: the power will be positive if the original number is huge, and negative if the original number is small.
The number 57,020,000 is a huge number. We simply move the decimal 7 places to the left to get 5.072, and since we moved the decimal 7 places, 10 is raised to the power of 7.
Brainliest, please :) Hope this helps!
9-Volume of Solids
Find the volume of each solid. Round to the nearest tenth,
31)
33)
11 yd
8t
5 yd
5 yd
6 yd
11 yd
10 R
10 %
8 t
32)
34)
8m
6m
5m
4m
10 m
10 m
The volume of the solids are 240 cubic yards and 125.6 cubic cm
How to determine the value of the solids?The complete question is added as an attachment
Solid 1
The shape is a rectangular prism.
The volume of a rectangular prism is
Volume = Length * Width * Height
So, we have
Volume = 8 yd * 5 yd * 6 yd
Evaluate
Volume = 240 cubic yards
Hence, the volume of the solid is 240 cubic yards
Solid 2
The shape is a cylinder.
The volume of a rectangular prism is
Volume = πr²h
So, we have
Volume = 3.14 * 2^2 * 10
Evaluate
Volume = 125.6 cubic cm
Hence, the volume of the solid is 125.6 cubic cm
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9. Raju sells a watch at 5% profit. Had he sold it for 24 more he would have gained 11%. Find the cost price of the watch.
Answer:
400$
Step-by-step explanation:
Let C.P. of the watch = Rs. 100
When profit =5%; S.P. = Rs. (100+5)
= Rs. 105
and when profit = 11%;
S.P. = Rs. (100+11)
=Rs.111
Difference of two selling prices
= Rs. 111-Rs.105 = Rs.6
When watch sold for Rs. 6 more; then C.P. of the watch = Rs.
100
6
When watch sold for Rs. 24 more; then C.P. of the watch = Rs.
100
6
×
24
= Rs.
100
×
24
6
=400
In questions 6 – 9, state the solutions for the quadratic equation depicted in the graph.
Step-by-step explanation:
It is just where it crosses the x axis
6) -3, -4
7) 1, -6
8) -5, -6
9) 3, -2.5
QUESTION 9
Find f(g(2)) for the following:
Given: ƒ (x) = 2x² − 1, g(x)=x+2
-
Find:f(g(2))
Answer:
x = 31
Step-by-step explanation:
Given:
f(x) =
[tex]2 {x}^{2} - 1[/tex]
g(x) = x + 2
We will first find g(2).
g(2) = 2 + 2 = 4
Next we will find f(g(2)).
f(g(2))= f(4) =
[tex]2( {4}^{2} ) - 1 \\ = 2(16) - 1 \\ = 32 - 1 \\ = 31[/tex]
Review the graph of function j(x).
On a coordinate plane, a line starts at open circle (2, 6) and goes down through (negative 2, 2). A solid circle is at (3, 6). A curve goes from solid circle (2, 3) to open circle (3, 4). A line goes from the open circle to closed circle (6, 5).
What is Limit of j (x) as x approaches 3?
3
4
5
6
The limit of j (x) as x approaches 3 is 4.
According to the question, A line begins at an open circle (2, 6) on a coordinate plane and descends through ( -2, 2). At, a complete circle is (3, 6). From a solid circle (2, 3), a curve leads to an open circle (3, 4). From the open circle to the closed circle, a line runs (6, 5).
From the graph, it can be seen that the limit of the function j(x) as the value of x approaches 3 is 4.
A diagram or pictorial representation that organizes the depiction of data or values is known as a graph.
The relationships between two or more items are frequently represented by the points on a graph.
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Answer:
4
Step-by-step explanation:
egg 2023
Land is decreasing at a rate o 17.3 annually. In 2016 there was 3,400 acres. If t represents the number of years since 2016.
The equation that can be used to determine after how many years the town will have of 900 acres of undeveloped land is 900 = 3400 * (0.827)^t
Estimate the equation that can be used to determine after how many years the town will have of 900 acres of undeveloped landFrom the question, the given parameters are:
Initial value = 3400 acres
Rate, r = 17.3%
Final value = 900
An exponential function is represented using the following equation
y = a(1 - r)^t
Substitute the known values in the above equation
y = 3400 * (1 -17.3%)^t
Express 17.3% as decimal
y = 3400 * (1 -0.173)^t
Evaluate the difference
y = 3400 * (0.827)^t
Recall that:
Final value = 900
So, we have
900 = 3400 * (0.827)^t
Hence, the equation that can be used to determine after how many years the town will have of 900 acres of undeveloped land is 900 = 3400 * (0.827)^t
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What is in simplest form?
A.
B.
C.
D.
Answer:
C. 8√3
Step-by-step explanation:
* = multiply or times
To find √192 in its simplest form we need to divide it by a square number like 64.
192/64 = 3
√192 = √64 * √3 = 8√3
A new outlet is being planned with an allocated budget of $50,000 per month for advertising and planned average price of $10.00 per pizza. Estimate the monthly sales (number of pizzas) of this outlet.
Answer:
5,000
[tex]50000 \div 10 = 5000[/tex]
100 POINTS Consider this piecewise function.
Plot f (x) on the graph.
NO LINKS
Answer:
The intervals represent the domain, or the values on the horizontal axis.
When x ≤ -3, the graph should form a straight line at y = 3. Because the interval includes x = -3, the rightmost part of the line should be capped with a closed dot. The line should continue for infinity to the left.
When -3 < x < 4, the graph should form a line with the equation (2x + 1). Because the interval does not include the endpoints, the endpoints should have open dots.
When x ≥ 4, the graph should form a straight line at y = -4. Because the interval includes x = 4, the leftmost endpoint should be a closed dot. The right of the line should continue for infinity.
**The included graph does not take the endpoints into account
Answer:
See attached for graph.
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]f(x)=\begin{cases}3 & \textsf{if }x\leq -3\\2x+1 & \textsf{if }-3 < x < 4 \\ -2 & \textsf{if } x\geq 4 \end{cases}[/tex]
Therefore, the function has three definitions:
[tex]f(x)=3 \quad \textsf{when x is less than or equal to 3}[/tex]
[tex]f(x)=2x+1 \quad \textsf{when x is more than -3 and less than 4}[/tex]
[tex]f(x)=-2 \quad \textsf{when x is more than or equal to 4}[/tex]
When graphing piecewise functions:
Use an open circle where the value of x is not included in the interval.Use a closed circle where the value of x is included in the interval.Use an arrow to show that the function continues indefinitely.First piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies f(-3)=3 \implies (-3,3)[/tex]
Place a closed circle at (-3, 3).
As this piece of the function is f(x) = 3 for any value of x that is less than or equal to -3, draw a horizontal straight line to the left from the closed circle. Add an arrow at the end.
Second piece of function
Substitute the endpoints of the interval into the corresponding function:
[tex]\implies f(-3)=2(-3)+1=-5 \implies (-3,-5)[/tex]
[tex]\implies f(4)=2(4)+1=9 \implies (4,9)[/tex]
Place an open circle at (-3, -5) and (4, 9).
Join the points with a straight line.
Third piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies f(4)=-2 \implies (4,-2)[/tex]
Place a closed circle at (4, -2).
As this piece of the function is f(x) = -2 for any value of x that is more than or equal to 4, draw a horizontal straight line to the right from the closed circle. Add an arrow at the end.
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Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb. write an inequality that represents the number of movies(M) and songs(S) that Caisse downloads each month?
If Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.
Given that Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb.
We are required to find the inequality that represents the number movies and songs that Caisse downloads each month.
Inequality is like an equation that shows the relationship between variables that are expressed in greater than, less than , greater than or equal to , less than or equal to sign.
let the number of movies be x and the number of songs be y.
According to question Caisse cannot download more than 1000 mb, so we will use less than towards equation.
It will be as under:
85x+4y<1000.
Hence if Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.
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distribution has a mean if 18 standard deviation of 4 a value of 24 is how many standard deviations away from the mean
A value of 24 is 2.5 standard deviations away from the mean
'How to determine the number of standard deviations away from the mean?The given parameters about the distribution are:
Mean = 18
Standard deviation = 4
Value = 24
Let the number of standard deviations away from the mean be x.
The value of x is calculated using
Mean + Standard deviation * x = Value
Substitute the known values in the above equation
18 + 4 * x = 24
Subtract 18 from both sides of the equation
4 * x = 6
Divide both sides of the equation by 4
x = 1.5
Hence, a value of 24 is 2.5 standard deviations away from the mean
So, the complete parameters about the distribution are:
Mean = 18
Standard deviation = 4
Value = 24
24 is 2.5 standard deviations away from the mean
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Combined, Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, how many pens does Sanjay have?
Answer:Sanjay has 8
Step-by-step explanation: Because 8x4 equals 32 so thats how much tanya has a 32+8 equals 40. This is what I did I knew 10x4 is 40 so that couldn't be it so then I tried 8 because nine x four is 36 which would be to high so I tried 8 and it was perfect hope this helps.
If Combined, Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, then Sanjay have 8 pens.
What is Equation?Two or more expressions with an equal signs is called as Equation.
Given that Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, We need to find how many pens sanjay has.
Let sanjay has x number of pens.
Tanya has four times as many pens as Sanjay
So 4 times means four multiple of sanjay pens.
Tanya has four times as many pens as Sanjay can be write as 4x.
Combined of tanya and sanjay has 40 pens.
Combined means adding.
x+4x=40
Add the like terms
5x=40
Divide both sides by 5.
x=8
So Sanjay has eight pens and Tanya has 4(8)=32 pens.
Hence Sanjay have eight pens.
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How to find exponential function?
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:[tex]\bold{y=Ce^{kt}}[/tex][tex]\bold{(5,5)}[/tex][tex]\bold{(0, \dfrac{6}{7} )}[/tex][tex]\small\leadsto\bold{Substitute:}[/tex]
[tex]\longrightarrow\sf{ \dfrac{6}{7}= Ce^{k*0}}[/tex]
[tex]\longrightarrow\sf{\dfrac{6}{7}= C*e^0}[/tex]
[tex]\longrightarrow\sf{e^0=1}[/tex]
[tex]\therefore\sf{C= \dfrac{6}{7} }[/tex]
[tex]\therefore\sf{5=Ce^{k*5}}[/tex]
[tex]\\[/tex]
[tex] \bold{Solve \: to \: find \: k:}[/tex]
[tex]\longrightarrow\sf{5 = \dfrac{6}{7} *e^{k5}}[/tex]
[tex]\longrightarrow\sf{ \dfrac{7*5}{6} *e^{5k}}[/tex]
[tex]\longrightarrow\sf{In=( \dfrac{35}{6} ) = 5k}[/tex]
[tex]\longrightarrow\sf{1.76=5k}[/tex]
[tex]\longrightarrow\sf{k=\dfrac{1.76}{5} = 0.352}[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex]\large\sf{\boxed{\sf \dfrac{6}{7}= e^{0.352*t}}}[/tex]
19. At a boardroom meeting, the sales manager is happy to announce that sales have risen from $850,000 to $1,750,000 at a
rate of 4.931998% per year. How many years did it take for the sales to reach $1,750,000?
The number of years it would take sales to reach $1,750,000 is 14.65 years.
What is the number of years?The formula that can be used to determine the number of years it would take for the sales to reach $1,750,000 is:
Number of years : In (FV / PV) / r
Where:
FV = future level of sales - $1,750,000PV = present level of sales = 850,000r = rate of growth - 4.931998%Number of years : In ($1,750,000 / 850,000) / 0.04931998
Number of years : In (2.06) / 0.04931998
Number of years : 14.65 years
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Please help, will mark brainliest.
Divide the interval [3, 5] into [tex]n[/tex] subintervals of equal length [tex]\Delta x=\frac{5-3}n = \frac2n[/tex].
[tex][3,5] = \left[3+\dfrac0n,3+\dfrac2n\right] \cup \left[3+\dfrac2n,3+\dfrac4n\right]\cup\left[3+\dfrac4n,3+\dfrac6n\right]\cup\cdots\cup\left[3+\dfrac{2(n-1)}n, 3+\dfrac{2n}n\right][/tex]
The right endpoint of the [tex]i[/tex]-th subinterval is
[tex]r_i = 3 + \dfrac{2i}n[/tex]
where [tex]1\le i\le n[/tex].
Then the definite integral is given by the Riemann sum
[tex]\displaystyle \int_3^5 \sqrt{8+x^2} \, dx = \lim_{n\to\infty} \sum_{i=1}^n \sqrt{8+{r_i}^2} \Delta x = \boxed{\lim_{n\to\infty} \frac2n \sum_{i=1}^n \sqrt{17 + \frac{12i}n + \frac{4i^2}{n^2}}}[/tex]
Solve this system. Write your answer as an ordered pair.
-5x + y = -3
3x - 8y = 24
[tex]\begin{cases} -5x+y=-3\\ 3x-8y=24 \end{cases} \\\\\\ \stackrel{\textit{using the 1st equation}}{-5x+y=-3}\implies \underline{y=-3+5x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{3x-8(\underset{y}{-3+5x})=24}\implies 3x+24-40x=24\implies 3x-40x=0 \\\\\\ -37x=0\implies \boxed{x=0}~\hfill \underline{y=-3+5(\stackrel{x}{0})}\implies \boxed{y=-3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (0~~,~~-3)~\hfill[/tex]
Answer:
( 0, -3 )
Step-by-step explanation:
-5x + y = -3 ⇒ ( 1 )
3x - 8y = 24 ⇒ ( 2 )
We can make y the subject of equation 1.
y = 5x - 3 ⇒ ( 3 )
Now let us take equation 2.
Here we can replace y with ( 5x - 3 ) to find the value of x.
Value of x.
3x - 8y = 24
3x - 8 (5x - 3) = 24
3x - 40x + 24 = 24
-37x = 0
x = 0
Now let us take equation 3 to find the value of y.
Here we can replace x with 0.
Let us find it now.
y = 5x - 3
y = 5 × 0 - 3
y = 0 - 3
y = -3
Now, let us write the answer as an ordered pair.
( x, y )
( 0, -3 )
Michael is an art elective programme student who
is working on an assignment. He plans to cover a
rectangular sheet of paper of dimensions 126 cm by
108 cm with identical square patterns.
(i) What is the least number of square patterns
that could be formed on the sheet of paper?
(ii) How do you determine what other shapes
can the patterns be if they are to fit the sheet of
paper perfectly? Explain your answer.
Answer:
Step-by-step explanation:
find the prime factors of given numbers:
126= 2*3*3*7- this side can be cut into any number here or combination of numbers as per factors
108= 2*2*3*3*3 - same as above
As per prime factors, the squares can be of sizes:
2×2, 3×3, 6×6, 9×9 and 18×18
The least number can be obtained with the biggest size option 18×18, this will give 7*6=42 square
To maintain essential electricity, a gasoline generator at a Puerto Rico hospital uses 3 gallons of gasoline per hour. a) How many gallons of gas are needed to fuel the generator for 1 full day? 72 2 points b) How much co2 will be produced by running the generator for 1 full day? 2 points
The mass of the CO2 produced IS 630 Kg
What is gasoline?Gasoline is a kind of fuel that is composed mostly of isooctane. In most engines, gasoline is widely used hence the demand for the product is high. We know that the combustion of an alkane (of which gasoline is one) would produce carbon dioxide and water according to a balanced reaction equation.
The balanced reaction equation for the combustion of gasoline is shown in the image attached to this answer.
Since a Puerto Rico hospital uses 3 gallons of gasoline per hour, and there are 24 hours in a day, it the follows that 72 gallons of gasoline are used per day. This 72 gallons is the equivalent of 272.88 L
Now;
Given that the density of gasoline = 748.9 g/L
Mass of gasoline = 748.9 g/L * 272.88 L = 204 Kg
Number of moles of gasoline = 204 * 10^3/114 g/mol = 1789.5 moles
If 2 moles of gasoline produces 16 moles of CO2
1789.5 moles produces 1789.5 moles * 16 moles/2 moles = 14316 moles
Mass of CO2 = 14316 moles * 44 g/mol = 630 Kg
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In the diagram, angle ADE ≈ angle ABC the ratios blank and blank are equal.
Based on the angle-angle similarity theorem (AA), the pair of ratios that are equal is: AE/EC = AD/DB.
What is the Angle-angle Similarity Theorem (AA)?The angle-angle similarity theorem (AA) states that two triangles are similar to each other if they have two corresponding congruent angles, and therefore, the ratios of their corresponding side lengths are equal. This means their corresponding side lengths are proportional in measure.
Given that angle ADE ≅ angle ABC, we also know that:
Angle EAD ≅ CAB.
Thus, this implies that triangle EAD is similar to triangle CAB based on the angle-angle similarity theorem (AA). Therefore, the ratios of their corresponding side lengths are equal.
Thus, the ratios that are equal to each other would be:
AE/EC = AD/DB.
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can you answer this question
Based on the given entries that Jonathan Shaw owes and owns, the Balance Sheet can be drawn below.
What is Jonathan Shaw's balance sheet?The assets will go to the right side of the sheet and the liabilities and equity will go to the left.
Jon's Shop of Gifts Balance Sheet
Assets Liabilities
Cash $2,556 Bank loan $19,000
Accounts Receivable: $450 Accounts Payable - $900
R. Gregory Ceramic supply
Accounts Receivable: $1,860 Accounts Payable - $2,900
R. Gregory Jose's Art Co.
Supplies $1,000 Total liabilities $22,800
Furniture $10,300 Equity
Equipment $20,000 Jonathan Shaw capital $51,166
Automobiles $37,800 Total equity $51,166
Total assets $73,966 Total liabilities and $73,966
equity
The equity can be found as:
= Assets - liabilities
= 73,966 - 22,800
= $51,166
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(05.03 LC)
The equation shows the relationship between x and y:
y = −4x + 9
What is the slope of the equation? (5 points)
Group of answer choices
−9
−4
4
9
need heeeelp please
Answer:
(x, y) = (-√3/2, 1/2)
Step-by-step explanation:
The terminal point for that angle can be read from a unit circle chart.
On the attached chart, the point of interest is the first one above the -x axis on the left side. The chart tells you the coordinates are ...
(x, y) = (-√3/2, 1/2)
PLEASE HELP ALOT OF POINTSThe Pythagorean Theorem states "The square on the hypotenuse of a
right triangle is equal to the sum of the squares on the two legs". Jaylene
produces this image in her notebook and claims that it proves the
Pythagorean Theorem is true. Is this a fair claim? Why or why not?
Answer:
choice C. Yes, this image proves the pythagorean theorem is true because 9 + 16 = 25
Step-by-step explanation:
The question is in the picture
Answer:
16
Step-by-step explanation:
18,903
Find all values of x in the interval [0, 2π] that satisfy the equation. 7 sin(2x) = 7 cos(x)
Answer:
x = {π/6, π/2, 5π/6, 3π/2}
Step-by-step explanation:
The equation can be solved using a double-angle trig identity and factoring.
SimplifyDividing the equation by 7 and substituting for sin(2x), we have ...
7sin(2x) = 7cos(x)
sin(2x) = cos(x)
2sin(x)cos(x) = cos(x)
2sin(x)cos(x) -cos(x) = 0
cos(x)(2sin(x) -1) = 0
Zero product ruleThe product of factors is zero when one or more of the factors is zero.
cos(x) = 0 ⇒ x = {π/2, 3π/2}
2sin(x) -1 = 0 ⇒ x = arcsin(1/2) = {π/6, 5π/6}
Solutions in the given interval are ...
x = {π/6, π/2, 5π/6, 3π/2}
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Additional comment
When the equation is of the form f(x) = 0, then the x-intercepts of f(x) are its solutions. We can rearrange this one to ...
sin(2x) -cos(x) = 0
The solutions identified above match those shown in the graph.