If a and b are acute angles such that tan (a+b)= 1.73 and tan(a-b) =1/1.73, find a and b
Answers
[tex] \LARGE{ \underline{ \boxed{ \orange{ \rm{Solution:)}}}}}[/tex]
Given,tan (a + b) = 1.73 [tex]\approx[/tex] √3tan (a - b) = 1 / 1.83 [tex]\approx[/tex] 1 / √3To find:Value of a and b in degrees....?Solution:☃️ Refer to the trigonometric table....
Then, proceeding
⇛ tan 60 ° = √3
⇛ tan 60° = tan (a + b)
⇛ 60° = a + b
Flipping it,
⇛ a + b = 60° --------(1)
And,
⇛ tan 30° = 1 / √3
⇛ tan 30° = tan (a - b)
⇛ 30° = a - b
Flipping it,
⇛ a - b = 30° ---------(2)
Now adding eq.(1) and eq.(2),
⇛ a + b + a - b = 60° + 30°
⇛ 2a = 90°
⇛ a = 90° / 2
⇛ a = 45°
Putting value of a in eq.(1),
⇛ 45° + b = 60°
⇛ b = 15°
☄ So, Our Required answers:
a = 45°b = 15°━━━━━━━━━━━━━━━━━━━━
Related Questions
What is the difference between {2,3} and {{2,3}}
Answers
[tex]\{2,3\}[/tex] is a set containing two elements - numbers 2 and 3
[tex]\{\{2,3\}\}[/tex] is a set containing one element - a set [tex]\{2,3\}[/tex]
56:31
Rona mixes 2 pounds of meat with some chopped vegetables to make a mixture. She divides the mixture into 4 equal portions. Each portion weighs 3 pounds. Which equation and solution shows the total amount of chopped vegetables she used in the mixture?
Answers
Answer:
The equation is (2+x) / 4 = 3
Total amount of chopped vegetables = 10 pounds
Step-by-step explanation:
Meat=2 pounds
Vegetables=x
Mixture= 2+x
She divides the mixture into 4 equal portions
(2+x)/4
Each portion weighs 3 pounds
(2+x)/4=3
Solve the equation
(2+x)/4=3
Cross product
(2+x) = 4 × 3
2+x=12
x=12-2
=10
x=10 pounds
Total amount of chopped vegetables = 10 pounds
who is going to win the race?
Answers
Answer:
The correct answer is
Step-by-step explanation:
Red team is going to win the race as they have covered more area than other teams. I am a 100% sure of this answer.Hope this helps....Have a nice day!!!!Answer:
Red Team
Step-by-step explanation:
In the diagram of the right triangle shown find the value of c.
Answers
Answer:
Hey there!
20^2+25^2=c^2
400+625=c^2
1025=c^2
Square root 1025 is the correct answer, so option C.
Let me know if this helps :)
Answer: B
Step-by-step explanation:
URGENT PLZ HELP THANK YOU!
Answers
Answer:
[tex](-5)^{11}[/tex]
Step-by-step explanation:
We can use the exponent rules. If we have [tex]\frac{a^b}{a^c}[/tex], then it will simplify to [tex]a^{b-c}[/tex].
b is 5, c is -6, and a is -5 so:
[tex]-5^{5-(-6)}\\-5^{11}[/tex]
Hope this helped!
The pH of 0.0001 M solution of Ca(OH)2 is
Answers
Step-by-step explanation:
Since Ca(OH)2 is Basic, we need to find pOH:
pOH = - log [OH-]
pOH = - log(0.0001)
pOH = - ( - 4)
pOH = 4
Since, pH + pOH = 14
Therefore,
pH of 0.0001M sol. of Ca(OH)2 = 10
If 3sinA+4cosA=5 then find the value of cosA
Answers
Answer:
Cos A =1.4
Step-by-step explanation:
3sinA=5-4cosA; square both sides: 9sin^2(A)=25-40cosA+16cos^2(A);
9-9cos^2(A)=25-40cosA+16cos^2(A); 25cos^2(A)-40cosA+16=0=(5cosA-4)^2.
cosA=4/5 so sinA=3/5 (√(1-16/25) and sinA+cosA=7/5=1.4.
Suppose triangle TIP and triangle TOP are isosceles triangles. Also suppose that TI=5, PI=7, and PO=11. What are all the possible lengths TP$? Enter the possible values, separated by commas.
Answers
====================================================
Explanation:
A drawing may be helpful to see what's going on. Check out the diagram below. This is one way of drawing out the two triangles. The locations of the points don't really matter, and neither does the the orientation of how you rotate things. What does matter is we have the right points connected to form the segments mentioned.
----------
For now, focus on triangle TIP only. In order to have this be isosceles, we must make TP = 5 or TP = 7.
If TP = 5, then it's the same length as TI.
If TP = 7, then it's the same length as PI.
In either case, we have exactly two sides the same length (the other side different) which is what it means for a triangle to be isosceles.
----------
Let's consider triangle TOP. For it to be isosceles, we must have two sides the same length. We already locked in TP to be either 5 or 7 in the previous section above. So there's no way that TP could be 11 units long to match up with PO = 11.
If TP = 5, then OT must also be 5 units long so that triangle TOP is isosceles.
If TP = 7, then OT = 7 for similar reasoning.
Either way, TP only has two choices on what it could be.
----------
In short, we basically just write the first two values given to us to get the two triangles to be isosceles. We can't use TP = 11 as it would make triangle TIP to be scalene (all sides are different lengths).
Answer:
So we all cheat AOPS huh
Step-by-step explanation:
On a time limit answer asap pls
Answers
Answer:
160°
Step-by-step explanation:
Take notice that m∠1 and m∠2 are supplementary angles, meaning their angle measures will add up to 180°.
Since we know m∠2, we can find m∠1 easily.
180-20=160°
Hope this helped!
Plz help me this is probably easy but im just not seeing it plz help me ASAP
Answers
Answer: is attatched to the photo I sent
Step-by-step explanation:
I admit, this is tricky, just remember to think about it as where the shapes are the most similar. I'm not exactly sure how to explain it, but where it reflects like a mirror is the "copy"
The example I'm thinking of attached too, but these over lap so its diffucult
convert American $553 in Nepal rupees
Answers
Answer:
65,994.52 Nepalese Rupee
Step-by-step explanation:
using conversion rate 1 usd = 119.74 nepalese rupee
553*119.74
Is the given equation a quadratic equation? Explain. x(x−6)=−5
The equation is not a quadratic equation because there is no x2-term.
The equation is a quadratic equation because there is an x2-term.
The equation is not a quadratic equation because the expression is not equal to zero.
The equation is not a quadratic equation because there is a term with degree higher than 2.
I think the answer is A but im not sure.
Answers
Answer:
The equation is a quadratic equation because there is an x2-term.
Step-by-step explanation:
x(x−6)=−5
Distribute
x^2 -6x = -5
The equation is a quadratic equation because there is an x^2-term.
Answer:
Your required answer is option A.
Step-by-step explanation:
Here,
The given equation is;
x(x-6)=-5
now,
while finding x.
either or,
x=-5 (x-6)=-5
x= 1 (shifting-6 in next side)
now, the value of x is -5,1.
so, it's a quadratic equation.
( in quadratic equation the variable always has two values after solution)
Hope it helps..
Line a and t are parallel. What is the value of x?
7x - 48
5x
pls help me
Answers
Answer:
x = 24
Step-by-step explanation:
We know that lines s and t are parallel. Then by definition, the two labelled angles, which are same-side angles, are congruent and equal in measure.
Then, we set the expressions equal to each other:
7x - 48 = 5x
Subtract 5x from both sides:
7x - 5x - 48 = 0
2x - 48 = 0
Add 48 to both sides:
2x = 48
Divide by 2:
x = 48/2 = 24
Thus, x = 24.
~ an aesthetics lover
A piece of aluminum occupies a volume of 13.0 milliliters and weighs 52.9 grams. What is its density of the aluminum rounded to the nearest hundredth?
Answers
Which equation has a constant of proportionality equal to 3? A. y= 8/5 x B. y= 1/3 x C. y= 1/4 x D. y= 18/6 x PLEASE HELP ME :c
Answers
Answer:
(D) [tex]y=\frac{18}{6}x[/tex]
Step-by-step explanation:
We will be able to know if an equation has a constant of proportionality of 3 if the constant which is being multiplied by x is equal to 3.
[tex]\frac{8}{5} =1.6[/tex] so no for A.
[tex]\frac{1}{3} = 0.\overline{33}[/tex] so no for B too.
[tex]\frac{1}{4} = 0.25[/tex] so no for C as well.
[tex]\frac{18}{6} = 3[/tex], so D works.
Hope this helped!
PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answers
Answer:
last option
Step-by-step explanation:
Let's call the original angle x° and the radius of the circle y. The area of the original sector would be x / 360 * πy². The new angle, which is a 40% increase from x, can be represented as 1.4x so the area of the new sector is 1.4x / 360 * πy². Now, to find the corresponding change, we can calculate 1.4x / 360 * πy² ÷ x / 360 * πy² = (1.4x / 360 * πy²) * (360 * πy² / x). 360 * πy² cancels out so we're left with 1.4x / x which becomes 1.4, signifying that the area of the sector increases by 40%.
What Is the answer to it?
Answers
Answer:
2(x + 10)
Step-by-step explanation:
The sum of x and 10 is x + 10
The product of 2 and x + 10 means multiply them, thus
2 × (x + 10)
= 2(x + 10) ← parenthesis indicates x and 10 are added before being multiplied by 2
Arc length practice
Answers
Answer:
[tex]\large\boxed{s = 4\pi}[/tex]
Step-by-step explanation:
The arc length is determined by the formula [tex]s=r\theta[/tex], where s is the arc length, r is the radius, and [tex]\theta[/tex] is the value of the central angle (in radian formatting).
By substituting the values for the radius and the central angle, you can solve for the arc length.
[tex]\text{The radius is half of the diameter -} \: \boxed{\frac{4}{2}=2}[/tex].
The central angle is converted to radian form by multiplying the angle in degrees by the fraction of π/180 - 360° * π/180 = 360π/180 = 2π.
Now, substitute the values and solve for s.
s = (2)(2π)
[tex]\large\boxed{s = 4\pi}[/tex]
A sum of $46875 was lent out at simple interest and at the end of 1 yr 8 month, the total amount was $50000. Find the rate interest per year.
Answers
Answer:
4%
Step-by-step explanation:
As indicated in the question, this is a simple interest question.
The formula for Simple Interest =
I = Principal × Rate × Time
In the above question, we were given the following values.
A = Total value / amount of money = $50000
Principal = $46875
Rate = ??
Time = 1 yr and 8 months
= 1 year +(8/12)
Time = 1.6666666667 years
We are asked to solve for the rate interest per year. Hence, the formula to use to solve this question is given as:
r = (1/t)(A/P - 1)
r = (1/1.6666666667)(50000/46875 - 1)
r = 0.04
Converting to percentage, rate = 0.04 × 100 = 4%
Therefore, the rate interest per year is 4%
4. Alejandro Juarez is paid $829 every two weeks. a. What is Alejandro's yearly salary?
b. How much would Alejandro earn in one month?
Answers
Answer:
1. 21,554 PER YEAR
2. 1658 PER MONTH
Step-by-step explanation:
a.
so there are approximately 52 weeks per year
and alejandro juarez gets 829$ per 2 weeks
1..............LETS FIGURE OUT HOW MUCH HE EARNS PER WEEK
SO 829/2=414.5
so he gets 414.5 $ PER WEEK
2............LETS MULTIPLY THE AMOUNT OF MONEY PER WEEK BY THE WEEKS
SO 414.5*52=21554
SO ALEJANDRO JUAREZ EARNS 21,554$ PER YEAR
B.
SO WE ALREDY KNOWS ALEJANDRO EARNS 414.5$ PER WEEK
AND THERE ARE APPROXIMATELY 4 WEEKS IN A MONTH
SO 414.5*4=1658
SO HE EARNS 1658$ PER MONTH
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
ABC is an eqilateral triangle with sides 10cm find the length of the prependicular from A to BC
Answers
All sides are equal in an equilateral triangle and the perpendicular bisects the side too.
so BC will be bisected and the segments be 5 each.
you can use Pythagoras theorem to find the altitude length, hypotenuse will be one side of the triangle.
[tex] 5^2+h^2=10^2[/tex]
$h^2=100-25=75$
$h=\sqrt{75}=5\sqrt3$
10q-30q is equivalent to
Answers
Answer:
please mark my answer brainliest
Step-by-step explanation:
10q (1-3)
Porfavor, necesito ayuda con estos ejercicios.
Answers
Lo siento, no hablo español pero utilicé Google Translate .
HAHAHAHAHA
Describe the relationship between GF and CD when the two lines are perpendicular to AB. Also describe the relationship between GF and CD is not perpendicular to AB
Answers
IF GF and CD are perpendicular to AB, one can say that they will or do not intersect each other. But if CD is not perpendicular to AB, GF and CD, do intersect at one (single) point.
What is the relationship about?In the congruent relationship above, one can say that two lines intersect to create a linear pair of congruent angles, and thus one can say that the lines are perpendicular in nature.
Therefore, in the case above, IF GF and CD are perpendicular to AB, one can say that they will or do not intersect each other. But if CD is not perpendicular to AB, GF and CD, do intersect at one (single) point.
Learn more about perpendicular lines from
https://brainly.com/question/379998
#SPJ1
Expand the following using the Binomial Theorem and Pascal’s triangle. Show your work. (x + 2)6 (x − 4)4 (2x + 3)5 (2x − 3y)4 In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5
Answers
Answer:
The answer is below
Step-by-step explanation:
Expansion using pascal triangle:
a) (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)
= x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64
b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴
=x⁴-16x³+96x²-256x+256
c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ =
= 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴
= 16x⁴- 96x³ + 216x² - 216x + 81
Expansion using binomial where [tex]C(n,r)=\frac{n!}{(n-r)!r!}[/tex]
a) (x + 2)⁶ = C(6,0)[x⁶2⁰] + C(6,1)[(x⁵)(2)¹] + C(6,2)[(x⁴)(2²)] + C(6,3)[(x³)(2³)] + C(6,4)[(x²)(2⁴)] + C(6,5)[(x)(2⁵)] + C(6,6)[(2⁶)]
= x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)
= x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64
b) (x-4)⁴ = C(4,0)[x⁴] + C(4,1)[(x³)(-4)] + C(4,2)[(x²)(-4)²] + C(4,3)[(x)(-4)³] + C(4,4)[(x⁰)(-4)⁴]
= x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴
=x⁴-16x³+96x²-256x+256
c) (2x + 3)⁵ = C(5,0)[(2x)⁵] + C(5,1)[(2x)⁴(3)] + C(5,2)[(2x)³(3)²] + C(5,3)[(2x)²(3)³] + C(5,4)[(2x)(3)⁴] + C(5,5)[(2x)⁰(3)⁵]
= (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵
= 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
d) (2x-3y)⁴ = C(4,0){(2x)⁴(-3y)⁰} + C(4,1)[(2x)³(-3y)] + C(4,2)[(2x)²(-3y)²] + C(4,3)[(2x)(-3y)³] + C(4,4)[(2x)⁰(-3y)⁴]
= 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴
= 16x⁴- 96x³ + 216x² - 216x + 81
In the expansion of (3a + 4b)⁸, the only possible variable terms are a⁵b³, b⁸, a⁴b⁴, a⁸, ab⁷ because for each of them, the sum of there powers is eight. If the sum of the powers is not 8 then it is not correct.
For a²b³, the sum of the power is 5, for ab⁸ the sum of power is 9 and for a⁶b⁵ the sum of the power is 11 therefore thy are not correct.
As per the question expand the bimonoidal theorem and the pascal triangle. Showing the (x+2)6 (x-4)4 (2x+3)5 (2x-3y)4.
Expansion using pascal triangle:a) (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶) = x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4) =x⁴-16x³+96x²-256x+256c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ = 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴ = 16x⁴- 96x³ + 216x² - 216x + 81.Learn more about the use the binomial theorem.
brainly.com/question/11995132.
calculate the amount and compound interest on rupees 4000 at the rate of 8% per annum compounded annually for 2 years
Answers
Step-by-step explanation:
To calculate the compound interest we use the formula
C = A - PWhere
A is the amount
P is the principal
C is the compound interest
To find the amount we use the formula
[tex]A = P(1 + \frac{r}{100} ) ^{n} [/tex]where P is the principal
r is the rate
n is the period
From the question
P = 4000 rupees
rate = 8%
n = 2 years
Substitute the values into the above formula
That's
[tex]A = 4000( 1 + \frac{8}{100} )^{2} [/tex][tex]A = 4000 ({1 + 0.08})^{2} [/tex][tex]A = 4000 ({1.08})^{2} [/tex]A = 4665.6
The amount is 4665.60 rupeesSince the amount is found we can now find the compound interest
C = 4665.60 - 4000
C = 665.6
The compound interest is 665.60 rupeesHope this helps you
Help please on this question. I’d appreciate it if you answered.
Answers
Ok so the letters overwrap all of the alphabets and the other terms are in.
Answer:
see below
Step-by-step explanation:
Consonants and vowels do not overlap
There are no consonants that are vowels and no vowels that are consonants
That means the circles will never touch
Point E is on line segment DF. Given DE
EF.
6 and DF =9, determine the length EF
Answers
Answer:
3Step-by-step explanation:
IF point E lies on the line segment DF, this means that all the points DEF are collinear and DE+EF = DF.
Given parameter
DE = 6
DF = 9
Required
EF
Substituting the given parameter into the expression above to get the required will be;
DE+EF = DF.
EF = DF-DE
EF = 9-6
EF = 3
Hence the length of EF is equivalent to 3
convert 28km into cm
Answers
Answer:
28km to cm = 2,800,000cm
Step-by-step explanation:
In order to convert km to cm you have to times it by 100,000
So... 28 x 100,000 = 2,800,000
Hope this helps
Answer:2,800,000cm
Step-by-step explanation:
To convert a larger unit into a smaller unit, you must first check how much does the smaller unit need to make the larger unit. Then multiply the given larger unit to the amount of smaller unit that is equal to 1 of the larger unit.
Because: 100,000cm = 1km
So = 28km×100,000 =2,800,000cm
What is another way to write 100,203 in other forms
Answers
Answer:
You can write in
Step-by-step explanation:
Lakhs
First write 100,203.
Put ones,tens,hundreds,thousands,ten thousands and lakh on top of each number from the extreme left.
This is how you can write 100,203 in another way. You can't write in any other way than this one.
Hope this helps....
Have a nice day!!!!
