if tan A=4/3 and tan B=3/5 calculate and simplify the following
Answers
the value of the expression sin A cos B - cos A sin B is √34/5. use the trigonometric identities
what is expression ?
Trigonometric identities are mathematical equations that relate the values of trigonometric functions to one another. They are true for all possible values of the variables involved, and can be used to simplify and solve trigonometric equations.
In the given question,
To solve this problem, we need to use the properties of trigonometric functions to find the values of other trigonometric functions for angles A and B.
We know that:
tan A = opposite/adjacent = 4/3
tan B = opposite/adjacent = 3/5
Using the Pythagorean theorem, we can find the hypotenuse of the right triangles for angles A and B:
For angle A: hypotenuse = √(opposite² + adjacent²) = √(4² + 3²) = 5
For angle B: hypotenuse = √(opposite² + adjacent²) = √(3² + 5²) = √34
Now, we can use the definitions of sine, cosine, and tangent to find their values for angles A and B:
sin A = opposite/hypotenuse = 4/5
cos A = adjacent/hypotenuse = 3/5
sin B = opposite/hypotenuse = 3/√34
cos B = adjacent/hypotenuse = 5/√34
We can simplify these values by rationalizing the denominators:
sin B = 3√34/34
cos B = 5√34/34
Finally, we can use the trigonometric identities to find the value of the expression:
sin A cos B - cos A sin B
Substituting the values we found:
sin A cos B - cos A sin B = (4/5)(5√34/34) - (3/5)(3√34/34)
Simplifying:
sin A cos B - cos A sin B = √34/5
Therefore, the value of the expression sin A cos B - cos A sin B is √34/5.
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if tan A=4/3 and tan B=3/5 calculate and simplify the following expression sin A cos B - cos A sin B ?
Related Questions
1. Bailey withdrew $135 from her checking account. Write an algebraic expression that describes answer asap
Answers
Answer:
x - 135 where x is the money you have in your bank
Step-by-step explanation:
Answer:
X-135
Step-by-step explanation:
$135 from her checking account.=x
Help please i need the answer to this
Answers
Answer:
5
Step-by-step explanation:
The slope is the one with the x next to it
Answer:
the answer is m=5
Solve the equation.
-9x + 1 = -x + 17
Answers
Answer:
x = -2
Step-by-step explanation:
alot to explain soo
Answer: B. X = -2
Step-by-step explanation:
-9x + 1 = -x + 17 (add x to both like terms).
-8x + 1 = 17 (subtract 1 from both sides).
-8x = 16 (divide 8 by both sides)
X = -2
Hope this helped. :)
true or false (and state why): if a sample from a population is large, a histogram of the values in the sample will be approximately normal, even if the population is not normal.
Answers
By the central limit theorem, with a large random sample, the sample histogram will not closely resemble the normal curve but with a large random sample, the probability density function of the sample mean closely resembles the normal curve.
The central limit theorem for samples says that if we keep drawing larger and larger samples and calculating their means, the sample forms their own normal distribution (the sampling distribution). The normal distribution will have the same mean as the original distribution and a variance that equals the original variance divided by the sample size. The variable n is the number of values that are averaged together,and not the number of times the experiment is done.
Hence,with a large random sample, the sample histogram will not resemble the normal curve but with a large random sample, the probability density function of the sample mean will closely resemble the normal curve.
The complete question is-
true or false: (justify/explain your answer) state whether a or b is the true statement below and then explain why the other statement is false. a. with a large random sample, the sample histogram will closely resemble the normal curve. b. with a large random sample, the probability density function of the sample mean will close resemble the normal curve.
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a sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. what is the independent variable? multiple choice sales manager salesperson number of contacts amount of sales
Answers
The point on the y-axis that lies on the line passing through point g and is parallel to line df is (0, -slope of df * xg + yg).
To find the point on the y-axis that lies on the line passing through point g and is parallel to line df, we first need to determine the slope of line df. Once we have the slope, we can find the slope of the line passing through point g and parallel to line df. Then, we can use point-slope form to write the equation of this line and solve for the y-intercept, which will give us the point on the y-axis that we are looking for.
Assuming that the coordinates of point g and the endpoints of line df are given, we can find the slope of line df using the slope formula:
slope of df = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of line df.
Next, since the line passing through point g is parallel to line df, it will have the same slope as line df. So we can use the slope we just found to write the equation of the line passing through point g:
(y - yg) = slope of df * (x - xg)
where (xg, yg) are the coordinates of point g.
Now we can solve for the y-intercept by setting x = 0 (since we want the point on the y-axis):
(y - yg) = slope of df * (0 - xg)
y - yg = -slope of df * xg
y = -slope of df * xg + yg
So the point on the y-axis that lies on the line passing through point g and is parallel to line df is (0, -slope of df * xg + yg).
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The independent variable in the context of this problem is given as follows:
Number of contacts.
What are dependent and independent variables?In the case of a relation, we have that the independent and dependent variables are defined as follows:
The independent variable is the input.The dependent variable is the output.In the context of this problem, we have that the input and the output are given as follows:
Input: number of contacts.Output: amount of money earned.Hence the number of contacts represents the independent variable in the context of this problem.
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URGENT!! WILL MARK BRAILIEST! GOD BLESS. PLEASE SHOW ALL WORK. The age of Vicky and Krishna total 27 years. In 4 years, Krishna’s age plus twice Vickey’s age will be 43. What are Vickey and Krishna’s ages?
Answers
9514 1404 393
Answer:
Vickey is 4Krishna is 23Step-by-step explanation:
Let v represent Vickey's age now. Then Krishna's age now is 27-v. In 4 years, the sum of their ages is ...
(27 -v +4) +2(v +4) = 43
27 -v +4 +2v +8 = 43 . . . . eliminate parentheses
v +39 = 43 . . . . . . . . . . . . . collect terms
v +39 -39 = 43 -39 . . . . . . subtract 39 from both sides
v = 4 . . . . . . . . . . . . . . . . . simplify; this is Vickey's age
27 -v = 23 . . . . . Krishna's age
Vickey's age is 4; Krishna's age is 23.
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The maximum area is 640,000.
Given fencing yards = 3200
let the length be x and the width be y
The parameter of the rectangle is given as;
2(L + B),that is
2(x + y) = 3200
x + y = 1600
y = 1600-x
let the area of the rectangle be A, then
A = x y
A = x(1600-x)
A = 1600x - x^2
finding the maximum derivative of A with respect of x
da/dx = 1600 - 2x
set da/dx to zero,
1600 - 2x = 0
1600 = 2x
x = 1600/2
x =800
substitute the value of x = 800 in to y
y = 1600 - 800
y = 800
The maximum area is 800 x 800
Therefore Maximum area = 640,000.
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If 2 sides of a triangle are 18 inches and 25 inches, then which of the following is NOT a possibility for the 3rd side of the triangle?
5 inches
11 inches
32 inches
40 inches
Answers
If it takes 8 hours to drive 435 miles, how many
hours would you expect it would take to drive 650
miles if you travel at the same rate? (Round to
hundredths.)
Answers
Answer:
11.95
Step-by-step explanation:
435 divided by 8 is 54.375
650 divided by 54.375 is 11.95 (Rounded)
Answer: 11.95 hours
Step-by-step explanation:
\(\dfrac{435\ miles}{8\ hrs}=\dfrac{650\ miles}{x}\\\\\\435x=8(650)\\\\\\x=\dfrac{8(650)}{435}\\\\\\x=\large\boxed{11.95}\)
Andy buys x cakes
Betty buys 4 times as many cakes as andy
colin buys 3 more cakes than andy
each cake costs 65p
the total cost of the cakes is £52.65
How many cakes did each person buy?
Andy:
Betty:
Colin:
Answers
Each person buys a number of cakes
Andy: 13Betty: 52Colin:16What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy
So,
Andy has = x Cakes
Betty have = 4x Cakes
Clin has = x +3 Cakes
Since each cake costs 65p and the total cost of the cakes is £52.65
thus,
0.65( x + 4x + x +3) = 52.62
x + 4x + x +3 = 81
6x = 78
x = 13
Therefore,
Andy has = 13 cakes
Betty has = 4x = 4*13 = 52 cakes
Colin has = x + 3 = 16 cakes
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Write and equation a solve!
Marry had $115 to spend on clothes. She found a pair of shoes fo $55 and then pants for $15 each. how many pairs of pants can she buy?
Answers
2. You’re left with $60
3. Each pants are $15 each, so you do $60 divided by $15.
This should equal 4 pairs of pants
Hope this helps :D
I need the second one because i can't figure it out ;--;
Answers
Answer:
vertex form: y=a(x-h)^2+k ⇒ (a, h, k) = (-1/4, -2, 4)factored form: y=a(x+6)(x-2) ⇒ a = -1/4standard form: y=ax^2+bx+c ⇒ (a, b, c) = (-1/4, -1, 3)Step-by-step explanation:
We don't know how you did the first way, so the only way we can make sure another way is different is to do it two ways.
1) First, we'll make use of the vertex-form equation. The given zeros are at -6 and +2, so the line of symmetry is x = (-6+2)/2 = -2. Then vertex form of the equation will look like ...
y = a(x +2)^2 +k
We have two unknown values, so we need to make use of two points to find them.
Using (2, 0):
0 = a(2 +2)^2 +k
0 = 16a +k
Using (-4, 3):
3 = a(-4+2)^2 +k
3 = 4a +k
Subtracting the second equation from the first, we get
0 -3 = (16a +k) -(4a +k)
-3 = 12a
a = -1/4
Substituting into the first of our equations, ...
0 = 16(-1/4) + k = -4 +k
k = 4
So, the equation is ...
y = (-1/4)(x +2)^2 +4
__
2) Using factored form, we can write the equation as ...
y = a(x +6)(x -2) . . . . for zeros x=-6 and x=2
We can find 'a' by using the third point:
3 = a(-4+6)(-4-2) = a(2)(-6) = -12a
a = 3/-12 = -1/4
So, the equation is ...
y = (-1/4)(x +6)(x -2)
__
3) You can also make use of the standard form equation. This gives rise to three equations in the three coefficients.
y = ax^2 +bx +c
0 = a(-6)^2 +b(-6) +c = 36a -6b +c
3 = a(-4)^2 +b(-4) +c = 16a -4b +c
0 = a(2)^2 +b(2) +c = 4a +2b +c
These can be solved by your favorite method to give ...
a = -1/4, b = -1, c = 3
So, the equation is ...
y = (-1/4)x^2 -x +3
If 9 - X= 2, what does x equal?
Answers
Answer:
x=7
Step-by-step explanation:
find the midpoint of the line segment joining the points (5 -3) and (-1 7)
Answers
Answer:
Step-by-step explanation:
(5 - 1)/2 4/2= 2
(-3 + 7)/2= 4/2= 2
(2, 2) is the midpoint
Which expression is equivalent to (4mn/m^-2n^6)^-2
Answers
The expression that is equivalent to (4mn/m^-2n^6)^-2 is \(\frac{n^{10}}{16m^{6}}\)
How to determine the equivalent expression?The expression is given as:
(4mn/m^-2n^6)^-2
Apply the law of indices
\((4m^{1 + 2}n^{1-6})^{-2\)
Evaluate the sum and the differences
\((4m^{3}n^{-5})^{-2\)
Apply the negative exponent
\(\frac{1}{16m^{2*3}}}n^{5*2}\)
Evaluate
\(\frac{1}{16m^{6}}n^{10}\)
Rewrite as:
\(\frac{n^{10}}{16m^{6}}\)
Hence, the expression that is equivalent to (4mn/m^-2n^6)^-2 is \(\frac{n^{10}}{16m^{6}}\)
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PLEASE HELP ILL MARK BRAINEST!!!!
Answers
Answer:
(-3,8) would NOT fit the table.
Answer: (-3,8)
Step-by-step explanation: click on the file
Question 4 A family has two cars. The first car has a fuel efficiency of miles per gallon of gas and the second has a fuel efficiency of miles per gallon of gas. During one particular week, the two cars went a combined total of miles, for a total gas consumption of gallons. How many gallons were consumed by each of the two cars that week
Answers
Complete question is;
A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During one particular week, the two cars went a combined total of 1850 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
Answer:
Car 1 consumed 30 gallons of gas.
Car 2 consumed 20 gallons of gas.
Step-by-step explanation:
Let x be number gallons consumed by car 1
Let y be number of gallons consumed by car 2
We are told that total gas consumption of 50 gallons. Thus;
x + y = 50 - - - - - eq(1)
We are told that the first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas and they went a combined total of 1850 miles. Thus;
35x + 40y = 1850 - - - - eq2
Let's make y the subject in eq(1),
y = 50 - x - - - - eq(3)
Putting 50 - x for y in eq 2 gives;
35x + 40(50-x) = 1850
35x + 2000 - 40x = 1850
-5x + 2000 = 1850
-5x = -150
x = 150/5
x = 30 gallons
Substitute 30 for x into eq 3,we have;
y = 50 - 30
y = 20 gallons
Thus;
Car 1 consumed 30 gallons of gas.
Car 2 consumed 20 gallons of gas.
PLEASE HELP W THIS WILL GIVE BRAINLIST TO BEST ANSWER AND EXTRA POINTS
!!!!!ONLY A!!!!
Answers
Answer: 1545
Step-by-step explanation: not 100 but i hope this helps you :D
Somebody help me this is on my final and I don’t wanna fail it please somebody help me
Answers
Answer:
D
Step-by-step explanation:
they both equal each other. 5x+7=9x-63
then you would take 70 divided by 4
which equals 17.5
Answer:
A
Step-by-step explanation:
5x + 7 + 9x -63 = 180
14x - 56 = 180
+ 56 +56
14x = 236
divide both sides by 14
x = 16.85
Rocky Mountain Tire Center sells 10,000 go-cart tires per year. The ordering cost for each order is $35, and the holding cost is 40% of the purchase price of the tires per year. The purchase price is $25 per tire if fewer than 200 tires are ordered,$17 per tire if 200 or more, but fewer than 8,000, tires are ordered, and $13 per tire if 8,000 or more tires are ordered.
a) How many tires should Rocky Mountain order each time it places an order?
b) What is the total cost of this policy?
Answers
a) Rocky Mountain should order 200 tires each time it places an order.
b) The total cost of this policy is $17,160.
a) To determine how many tires Rocky Mountain should order each time, we need to consider the different price levels and find the point where it is most cost-effective to order. Let's analyze the three price levels:
If fewer than 200 tires are ordered: The purchase price is $25 per tire.
If 200 or more, but fewer than 8,000 tires are ordered: The purchase price is $17 per tire.
If 8,000 or more tires are ordered: The purchase price is $13 per tire.
Since the ordering cost is $35 per order, it is most cost-effective to order the maximum quantity that falls within the second price level, which is 200 tires.
b) To calculate the total cost of this policy, we need to consider the ordering cost and the holding cost. The holding cost is 40% of the purchase price per tire per year. Let's calculate the total cost:
Total holding cost = (Purchase price per tire * Quantity ordered * Holding cost rate) / 2 = (($17 * 10,000 * 0.4) / 2) + (($13 * 2,000 * 0.4) / 2) = $34,000 + $5,200 = $39,200
Total cost = Total ordering cost + Total holding cost = (Ordering cost per order * Number of orders) + Total holding cost = ($35 * (10,000 / 200)) + $39,200 = $1,750 + $39,200 = $40,950
Therefore, the total cost of this policy is $40,950.
Rocky Mountain Tire Center should order 200 tires each time it places an order, resulting in a total cost of $40,950 for this policy. This ordering quantity and cost analysis allows Rocky Mountain to make efficient and cost-effective decisions in managing their inventory.
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Fedex typically deleviers 2,400 packages per day and uses 75 trucks for delivery. If the number of trucks used per day is proportional to the number of packages delivered, how many packages would be delivered if there are 100 trucks avilable?
A 3.200 packages
B 1.800 packages
Answers
Answer:
A
Step-by-step explanation:
Can someone help me with this please asap
Answers
Answer:
The answer is 4
Step-by-step explanation:
because all of the angles need to add up to 180 so 17 x 4 is 68 and 68 - 8 = 60 and 60 x 3 = 180 so the answer would be 4
Answer:
4
Step-by-step explanation:
Since all the sides are congruent, so is the angles and in a triangle all angles add up to 180. To find the angle of one of them divide 180 by 3 which is 60.
Then put the equation equal to 60
17x - 8 = 60
17x = 68
x = 4
Convert the following function to Standard Form by using the Area Model.
f(x) = (x+3)²+8
A. f(x) = x² + 6x + 17
B. f(x) = x² + 6x +9
C. f(x) = (x + 3)(x +8)
D. f(x) = x² +17
Answers
Answer:
im just getting points sorry
Step-by-step explanation:
Please help,
Graph - x - 2y =4
Answers
Please help, how do you write 4.06 in word form and expanded form?
Answers
Answer:
four and six one hundredths
406/100
4.06 = (4 x 1) + (0/10) + (6/100)
Given the function f(x) = x2 - x + 7, find each of the following.
f(6)=
f(- 9)=
f(0)
Answers
Answer:
37, 79, 7
Step-by-step explanation:
f(6) = 6² -6 +7
36-6+7 is 37
f(-9) = -9² -9+7
81-9+7 is 79
f(0) = 0² -0+7
0-0+7 is 7
...................................................................
Answers
Answer:
b=2 and c=6
Step-by-step explanation:
According to the question,
a+b=c
Let b=2 and c =6 then, we get,
4+2=6
or, 6=6
proved
Natasha is 12 years old. Her teacher is 36 years old. Which ratio represents Natasha's age in 4 years to her teacher's age in 4 years? *
Answers
Answer:
I’m pretty sure it’s 1:3
Step-by-step explanation:
a spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min. at what rate is the volume of the snowball decreasing when the diameter is 8 cm
Answers
20.11 cm3/min is the rate at which the snowball's volume is decreasing.
Given,
The decreasing diameter when the spherical ball is melting = 0.2 cm/min
We have to find the rate in decrease in volume of snowball when diameter is 8 cm.
Here,
Volume of sphere, V = 4/3 π r³ = 4/3 π (D/2)³ = 1/6 π D³
Considering differences according to time,
dV/dt = d/dt (1/6 π D³) = 1/6 π × 3D² dD/dt
dV/dt = 1/2 π D² dD/dt
Substituting
D is 8 cm, and the diameter is changing at a rate of 0.2 cm/min.
dV/dt = 1/2 π D² dD/dt
dV/dt = 1/2 × π × 8² × 0.2 = 20.11 cm³/min
Therefore,
Decreasing snowball volume at a rate of 20.11 cm3/min
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Sam has 3x + 4 dollars saved. Tessa has saved 7x + 16 dollars. Together they
have $110 saved. How much money have they each saved individually?
Answers
Step-by-step explanation:
3x + 4 + 7x + 16 = 110
10x = 90
x = 9
therefore, Sam = $31 and Tessa = $79
Topic: Algebraic Equations
If you like to venture further, do check out my insta (learntionary) where I constantly post math tips! Thanks!
Answer:
Sam: 31
Tessa: 79
Step-by-step explanation:
3x+4+7x+16=110
10x+20=110
10x=110-20
10x=90
x=9
Money Sam saved
=3(9)+4
=27+4
=31
Money Tessa saved
=7(9)+16
=63+16
=79