Answer:
72
Step-by-step explanation:
When a kite is flying, the string makes an angle of 22° with the horizontal, and the string is 200m long. How high is the kite?
Answer: Check the picture below.
Make sure your calculator is in Degree mode.
the question "how long is the kite?" is not quite clear, i suppose it was asking how far it was from the ground (b) or horizontally (a). I calculated both, I hope this helps
Question:
If x =
[tex] \frac{ \sqrt[3]{m + 1{ }} + \sqrt[3]{m - 1} }{ \sqrt[3]{m + 1} - \sqrt[3]{m - 1} } [/tex]
Then the value of x³-3mx²+3x is:
No link please, Tq
[tex] \text{Given Equation is } \frac{x}{1} = \frac{ \sqrt[3]{m + 1{ }} + \sqrt[3]{m - 1} }{ \sqrt[3]{m + 1} + \sqrt[3]{m - 1} }[/tex]
[tex]\text{On Applying componendo and dividendo, we get:-}[/tex]
[tex] \frac{x + 1}{x - 1} = \frac{( \sqrt[3]{m + 1} + \sqrt[3]{m - 1} )+ ( \sqrt[3]{m + 1}) - \sqrt[3]{m - 1} }{ (\sqrt[3]{m + 1} + \sqrt[3]{m - 1}) - ( \sqrt[3]{m + 1}) - \sqrt[3]{m - 1} } [/tex]
[tex] \implies \: \frac{x + 1}{x - 1} = \frac{2( \sqrt[3]{m + 1)} }{2( \sqrt[3]{m - 1)} } \\ \\ \implies \frac{ x + 1}{x - 1} = \frac{ \sqrt[3]{m + 1} }{ \sqrt[3]{m - 1} } [/tex]
[tex] \text{On Cubing both sides, we get} \\ \frac{(x + 1) {}^{3} }{(x - 1) {}^{3} } = \frac{m + 1}{m - 1} [/tex]
[tex]\text{Again, Applying componendo and dividendo, we get:-}[/tex]
[tex] \frac{(x + 1) {}^{3} + (x - 1) {}^{3} }{(x + 1) {}^{3} - (x - 1) {}^{3} } = \frac{m + 1 + m - 1}{m + 1 - (m - 1)} [/tex]
[tex] \implies \frac{ {x}^{3} + 1 {}^{3} + 3 {x}^{2} \times 1 + 3x \times {1}^{2} + ( {x}^{3} - 1 {}^{3} - 3x {}^{2} \times 1 + 3x \times 1 {}^{2} ) }{x {}^{3} + 1 {}^{3} + 3 {x}^{2} \times 1 + 3x \times {1}^{2} - (x {}^{3} - 1 {}^{3} - 3 {x}^{2} \times 1 + 3x \times {1}^{2}) } = \frac{2m}{2} [/tex]
[tex] \implies \frac{2x {}^{3} + 6x}{ {6x}^{2} + 2 } = \frac{m}{1} [/tex]
[tex] \implies \frac{2(x {}^{3 } + 3x) }{2(3 {x}^{2} + 1) } = \frac{m}{1} [/tex]
[tex] \implies \: x {}^{3} + 3x = 3m {x}^{2} + m \\ \\ \implies {x}^{3} - 3mx {}^{2} + 3x \\ = m[/tex]
Hope This Helps!!
Based on the calculations, the value of [tex]x^3-3mx^2+3x[/tex] is equal to m.
Given the following data:
[tex]x=\frac{\sqrt[3]{m+1} +\sqrt[3]{m-1}}{\sqrt[3]{m+1} +\sqrt[3]{m-1}}[/tex]
How to evaluate the fraction.In order to simplify the given mathematical expression, we would apply the componendo and dividendo rule because it would the number of expansions as follows:
[tex]\frac{x}{1} =\frac{\sqrt[3]{m+1} +\sqrt[3]{m-1}}{\sqrt[3]{m+1} -\sqrt[3]{m-1}}\\\\\frac{x+1}{x-1} =\frac{(\sqrt[3]{m+1} +\sqrt[3]{m-1})+(\sqrt[3]{m+1} -\sqrt[3]{m-1})}{(\sqrt[3]{m+1} +\sqrt[3]{m-1})-(\sqrt[3]{m+1} -\sqrt[3]{m-1})}\\\\\frac{x+1}{x-1} =\frac{\sqrt[3]{m+1} +\sqrt[3]{m-1}+\sqrt[3]{m+1} -\sqrt[3]{m-1}}{\sqrt[3]{m+1} +\sqrt[3]{m-1}-\sqrt[3]{m+1} +\sqrt[3]{m-1}}\\\\\frac{x+1}{x-1} =\frac{2(\sqrt[3]{m+1})}{2(\sqrt[3]{m-1})} \\\\\frac{x+1}{x-1} =\frac{\sqrt[3]{m+1}}{\sqrt[3]{m-1}}[/tex]
Taking the cube of both sides, we have:
[tex](\frac{x+1}{x-1})^3 =(\frac{\sqrt[3]{m+1}}{\sqrt[3]{m-1}})^3\\\\\frac{(x+1)^3}{(x-1)^3}=\frac{m+1}{m-1}[/tex]
Applying the componendo and dividendo rule, we have:
[tex]\frac{(x+1)^3+(x-1)^3}{(x-1)^3-(x-1)^3}=\frac{m+1+(m-1)}{m-1-(m-1)}\\\\\frac{(x+1)^3+(x-1)^3}{(x-1)^3-(x-1)^3}=\frac{2m}{2} \\\\\frac{(x+1)^3+(x-1)^3}{(x-1)^3-(x-1)^3}=m\\\\\frac{2x^3+6x}{6x^2+2} =m\\\\\frac{2(x^3+3x)}{2(3x^2+1)} =m\\\\\frac{x^3+3x}{3x^2+1} =m\\\\x^3+3x=m(3x^2+1)\\\\x^3+3x=3mx^2+m\\\\x^3-3mx^2+3x=m[/tex]
Read more on componendo and dividendo here: https://brainly.com/question/134857
please help fast! I have no idea what I'm supposed 2 do
Answer:
Constant of proportionality: [tex]\frac{1}{3}[/tex]
Equation: [tex]y=\frac{1}{3}x[/tex]
Step-by-step explanation:
The constant of proportionality is the ratio between y and x, according to the following formula
constant of proportionality = k = y/x
Take the given pairs and replace the data.
1.
[tex]k=\frac{\frac{2}{3}}{2}[/tex]
[tex]k = \frac{1}{3}[/tex]
2.
[tex]k = \frac{1}{3}[/tex]
3.
[tex]k=\frac{\frac{10}{3}}{10}[/tex]
[tex]k = \frac{1}{3}[/tex]
4.
[tex]k = \frac{4}{12}[/tex]
[tex]k = \frac{1}{3}[/tex]
As you can see, the constant is the same for all the pairs.
constant of proportionality = [tex]\frac{1}{3}[/tex]
Now, in order to know the equation make a graph of the given data.
The graph is in the picture
Since it is a line, use the equation of the line in point slope form
[tex]y- { y }_{ 1 } = m \left( x- { x }_{ 1 } \right)[/tex]
where (x1, y1) = any pair of the data
m = slope = constant of proportionality
Replace the data in the equation
[tex]y-1 = \dfrac{ 1 }{ 3 } \left( x-3 \right)[/tex]
Use the distributive property to multiply [tex]\frac{1}{3}[/tex] by x - 3
[tex]y-1=\frac{1}{3}x-1[/tex]
Add 1 to both sides
[tex]y = \dfrac{ 1 }{ 3 } x-1+1[/tex]
Add −1 and 1 to get 0
[tex]y=\frac{1}{3}x[/tex]
or
[tex]y=\frac{x}{3}[/tex]
Which step could be used to help isolate the variable in the following equation? 5. 6j – 0. 12 = 4 1. 1j.
For the expression 5.6j - 0.12 = 4 + 1.1j, the value of variable j is 0.92.
What is the property of equality?
The operations of addition, subtraction, multiplication, and division do not change the truth value of any equation is called the property of equality.
The given expression is 5.6j - 0.12 = 4 + 1.1j.
To solve the above expression, we will use the following steps.
Step 1:
By the subtraction property of equality, subtract 1.1j on both sides. We get the expression,
[tex]5.6j - 0.12 -1.1j = 4 + 1.1 j - 1.1 j[/tex]
[tex]4.5 j -0.12 = 4[/tex]
Step 2:
By the addition property of equality, add 0.12 on both sides. We get the expression,
[tex]4.5j -0.12 + 0.12 = 4 + 0.12[/tex]
[tex]4.5 j = 4.12[/tex]
Step 3:
By the division property of equality, divide the above expression by 4.5. We get the expression,
[tex]\dfrac {4.5j}{4.5 }= \dfrac {4.12}{4.5}[/tex]
[tex]j = \dfrac {4.12}{4.5}[/tex]
[tex]j = 0.92[/tex]
Hence we can conclude that the value of variable j is 0.92.
To know more about the property of equality, follow the link given below.
https://brainly.com/question/13130806.
I need to find out the leng of XZ
Answer:
16.84?
Step-by-step explanation:
12.6/cos(29)=16.84
Jeanne Williams sells welding equipment and is paid a commission of 9.5% on the first $25,000 of sales in a month and 12.4% of sales from $25,001 to $70,000 in a month. A commission of 15.1% is paid on all sales over $70,000 in a month. Her sales last month were $43,000 and $54,000 this month. What total commission earnings did Jeanne have for the two months?
Answer:$3,170 is the answer
Step-by-step explanation:
Lebo is saving money to buy some new clothes in january she saved R131,in febuary R246 and in march R394.estime how much money she had at the beginning of April
Answer:
If R is supposed to be $ then the answer is $771 or estimated is $780
Step-by-step explanation:
131 = 130
246 = 250
394 = 400
Solve the equation ( 32
3) (33) = 36
=
X
Answer: D. -30
Step-by-step explanation: EDGE 2022 I GOT 100%
Here are 10 numbers 3,7,2,4,7,5,7,1,8,8,
A) write down the mode
B) work out the median
C) calculate the mean
D) what is the range
Can you please help me???
Han's cell phone plan costs $200 to start. Then there is a $50 charge each month.
Is there a proportional relationship between time and the cost of the cell phone plan? Explain how you know.
Answer:
no. A proportional relationship has a starting value of 0.
Step-by-step explanation:
The starting value of 200 means the relationship cannot be proportional. The starting value is always zero in a proportional relationship.
what was the effect of Spanish rule on the French Huguenots?due tomorrow
choices are:
A) The French were driven from Fort Caroline. They could not practice their religion and their leader and his men were massacred.
B) The French were able to take advantage of weaknesses in the Spanish Army and to take over their fort at St. Augustine.
C) The Spanish moved the Huguenot cemetery away from their fort, because they didn’t like the French names.
what is the factored form of 24v – 84?
Answer:
10
Step-by-step explanation:
b
Heya ~
I need help please . . . .
I am just going to show the image, so y'all won't get confuse.
ANSWERS CHOICES ~
[tex]4[/tex]
[tex]3[/tex]
[tex]-3[/tex]
make a explanation to this.
Thanks ~
Answer:
y = -3
Step-by-step explanation:
y = x - 7
when x = 4
y = 4 - 7
y = -3
Answer:
See below.
Step-by-step explanation:
If x is 4, then replace x with 4 and simplify.
y=4-7
y=-3
-hope it helps
At the movies, Fred and his five friends bought some snacks. They each bought a small popcorn for $3.25. They bought 3 bags of candy to share for $2.50. 2 of the boys bought a soda for $3. Write the expression that you can use to find out how much money they spent at the movies on snacks.
3.25 • 5 + 2.50 • 3 + 2 • 3 = x
16.25 + 7.50 + 6 = x
29.75 = how much they spent all-together
write the following linear equation in slope intercept form. y-5=-2(x+3)
Answer:
y = -2x -1
Step-by-step explanation:
y-5=-2(x+3)
Distribute -2 × x and -2 × 3
y - 5 = -2x -6
y + 5 = -2x -6
y = -2x - 1
Two trains, Train A and Train B, weigh a total of 290 tons. Train A is heavier than Train B. The difference of their weights is 122 tons. What is the weight of each train?
Answer:
Train A is 168 tons and Train B is 122 tons
Step-by-step explanation:
Help please, will give brainliest!!
Answer:
[tex]{2}^{3} = 2 \times 2 \times 2 = 8[/tex]
Step-by-step explanation:
*We're focusing on 2 to the power of 3.
2^3 is represented as 2 x 2 x 2, 2 is being multiplied by itself 2 times.
When we multiply, we find the product of 8.
Therefore,
[tex] {2}^{3} = 2 \times 2 \times 2 = 8[/tex]
How much bigger is the area of a circle with a radius of 5 cm than a circle with a radius of 3 cm?
The area of a circle with a radius of 5 cm is 50.272 [tex]cm^2[/tex] bigger than a circle with a radius of 3 cm.
Given the following data:
Radius A = 5 cm.Radius B = 3 cm.How to calculate the area of a circle.Mathematically, the area of a circle is given by the formula:
[tex]Area = \pi r^2[/tex]
Where:
r is the radius of a circle.For circle A:
[tex]Area = 3.142 \times 5^2\\\\Area = 3.142 \times 25[/tex]
Area = 78.55 [tex]cm^2[/tex].
For circle A:
[tex]Area = 3.142 \times 3^2\\\\Area = 3.142 \times 9[/tex]
Area = 28.278 [tex]cm^2[/tex].
Now, we can calculate the difference:
Difference = [tex]78.55-28.278[/tex]
Difference = 50.272 [tex]cm^2[/tex].
Read more on circle here: brainly.com/question/14478195
The midpoint of AB is M(2, 0) If the coordinates of A are (-3, 3) what are the coordinates of B
Answer:
(7, -3)
Step-by-step explanation:
If M is the midpoint you can use the same translation from A to M as M to B.
The movement from A to M is 5 units up and 3 units left, or (x+5, y-3). If we do the same movement to point M (Which is (2) +5, (0) -3) we will get (7, -3).
Answer:
the coordinates of B is B(7,-3)
Step-by-step explanation:
Solution,
Here, M(2,0) is the midpoint of a line segment joining the points A(-3,3)
and B(a,b)
Let,
(x,y)=(2,0)
(x1,y1)=(-3,3)
(x2,y2)=(a,b)
Now,
Using midpoint formula
[tex]x=\frac{x_1+x_2}{2} ,y=\frac{y_1+y_2}{2} \\\\2=\frac{-3+a}{2} ,0=\frac{3+b}{2} \\\\[/tex][Cross multiply]
[tex]4=-3+a,0=3+b\\\\4+3=a,0-3=b\\\\a=7,b=-3[/tex]
Solve this problem 3 Times 7
Answer:
3 times 7 is 21
Step-by-step explanation:
Answer:
3x7=21
Step-by-step explanation:
7+7+7=21 or 3+3+3+3+3+3+3=21
Brainliest
Help plss, thank you.
Which expressions are equivalent to this exponential expression?.
The expression is equivalent to [tex]5^2[/tex].
Given
Expression; [tex]\rm \dfrac{(5^2)^{-3}\times 5^4}{5^{-4}}[/tex]
Exponential expression;The definition of exponential form is a way of writing a number that is multiplied by itself more than once.
To solve the exponential equation follow all the steps given below.
Therefore,
The expression is equivalent to;
[tex]\rm =\dfrac{(5^2)^{-3}\times 5^4}{5^{-4}}\\\\=\rm \dfrac{(5)^{-6}\times 5^4}{5^{-4}}\\\\=\rm \dfrac{(5)^{-6+4}}{5^{-4}}\\\\=\rm \dfrac{5^{-2}}{5^{-4}}\\\\=5^{-2+4}\\\\=5^2[/tex]
Hence, the expression is equivalent to [tex]5^2[/tex].
To know more about expression click the link given below.
https://brainly.com/question/11865504
The length of a rectangular table is represented by the function L(x) = 3x The width of the table is represented by the function (x) = 4x2 - 6x +5. What is the area of the table in terms of 2
O LOW)(x) = 7x2-3x+8x
O (LOW)(x) = 122-18x+15
O (LW) = 122-182? +15x
O LOW)(x) = 122 +182 +15x
from the conclusion that I'm of and dont I feel like the answer is letter C I'm not sure
woop woop more questions
Answer:
5m+4
Step-by-step explanation:
Open the bracket
i.e 5m+5-1
5m+4.
Type the integer that makes the following addition sentence true:
- 6 + = −8
Answer:
-2
-Step-by-step explanation:
As, -6+(-2)= -6-2=-8
Thus, solved.
Hope it helps...
Which is the best estimate of 75.2 x 9?
Answer:
676.8
Step-by-step explanation:
#carry on learning
Lindsey, Derek, and Tessa went on a 5-mile hike to see a huge waterfall. They put some snacks and water in a backpack before they started, and each person carried the backpack an equal distance during the hike.
How far did each person carry the backpack?
Write your answer as a proper fraction or mixed number.
Answer:2.5
Step-by-step explanation:5/2=2.5
Fiona enlarges a parallelogram that has a perimeter of 17 meters. A small parallelogram has a left side length of 3. 5 meters. A larger parallelogram has a left side length of 21 meters. Not drawn to scale What is the perimeter of the enlarged parallelogram? 30 meters 73. 5 meters 102 meters 105 meters.
Answer:D
Step-by-step explanation:got it right on my test
Answer:
The answer is C i got a 100 on the test
Step-by-step explanation:
The figure shows a rectangle ABCD where the diagonals AC and BD intersect at E.
Given that BEC = 52°, find
(I) ADB
(ii) ACD
Answer:
(i) 64°
(ii) 26°
Step-by-step explanation:
Answer:
(i) m<ADB = 64°
(ii) m<ACD = 26°
Step-by-step explanation:
I use this to mean the measure of angle ADC: m<ADC
(i)
m<BEC = 52°
<DEA and <BEC are vertical angles, so they are congruent.
m<DEA = m<BEC = 52°
Polygon ABCD is a rectangle. When the diagonals, AC and BD, of a rectangle are drawn, 4 triangles are formed. Each two opposite triangles are congruent, and all 4 triangles are isosceles.
Triangle ADE is an isosceles triangle with congruent sides ED and EA. That makes opposite angles ADB and DAC congruent. Also the sum of the measures of the angles of a triangle is 180°.
m<ADB + m<DAC + m<DEA = 180°
m<ADB = m<DAC; m<DEA = 52°
2m<ADB + 52° = 180°
2m<ADB = 128°
m<ADB = 64°
(ii)
Angles DEC and BEC form a linear pair. That means the angles are supplementary, and the sum of their measures is 180°.
m<DEC + m<BEC = 180°
m<DEC + 52° = 180°
m<DEC = 128°
Triangle DEC is an isosceles triangle with congruent sides ED and EC. That makes opposite angles ACD and BDC congruent.
m<ACD + m<BDC + m<DEC = 180°
2m<ACD + 128° = 180°
2m<ACD = 52°
m<ACD = 26°
The stock of Company A gained 3.5% today to $16.56 . What was the opening price of the stock in the beginning of the day?
well, the opening price was "x", which oddly enough is the 100%, however during the trading of the day the company gained 3.5%, so that'd be 100% + 3.5% = 103.5%, and we know that that is 16.56, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 16.56&103.5 \end{array}\implies \cfrac{x}{16.56}=\cfrac{100}{103.5}\implies 103.5x=1656 \\\\\\ x=\cfrac{1656}{103.5}\implies x=16[/tex]