Given: Sine (A) = four-fifths, StartFraction pi Over 2 EndFraction < A < Pi and Sine (B) = StartFraction negative 2 StartRoot 5 EndRoot Over 5 EndFraction, pi, Pi < B < StartFraction 3 pi Over 2 EndFraction
What is the value of cos(A – B)?
Negative StartFraction 2 StartRoot 5 EndRoot Over 25 EndFraction
Negative StartFraction StartRoot 5 EndRoot Over 5 EndFraction
StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction
StartFraction 11 StartRoot 5 EndRoot Over 25 EndFraction
Answers
The value of [tex]Cos(A - B)[/tex] will be [tex](\frac{-\sqrt{5} }{5} )[/tex].
What are trigonometric functions ?Trigonometric functions are the periodic functions which denote the relationship between angle and sides of a right-angled triangle.
We have,
[tex]Sin(A) = \frac{4}{5}[/tex] , [tex]\frac{\pi }{2} < A < \pi[/tex]
[tex]Sin(B) = \frac{-2\sqrt{5} }{5}[/tex] , [tex]\pi < B < \frac{3\pi }{2}[/tex]
So,
Using identity ;
[tex]Cos(A - B)= CosA\ *\ Cos B + Sin A\ *\ Sin B[/tex]
So,
First find [tex]SinB[/tex] and [tex]CosA[/tex];
i.e.
[tex]CosB=\frac{-\sqrt{5} }{5}=\frac{-1}{\sqrt{5} }[/tex], [tex]\pi < B > \frac{3\pi }{2}[/tex]
[tex]CosA=\frac{-3}{5}[/tex], [tex]\frac{\pi }{2} < A > \pi[/tex]
Now,
Substituting values,
[tex]Cos(A - B)= CosA\ *\ Cos B + Sin A\ *\ Sin B[/tex]
[tex]Cos(A - B)= ((\frac{-3}{5})\ *\ \frac{-1}{\sqrt{5}} ) +((\frac{4}{5})\ *\ \frac{-2\sqrt{5} }{5} )[/tex]
Simplify,
[tex]Cos(A - B)= (\frac{3 }{5\sqrt{5}} ) -(\frac{8 }{5\sqrt{5}})[/tex]
[tex]Cos(A - B)= (\frac{-5 }{5\sqrt{5}} )[/tex]
[tex]Cos(A - B)= (\frac{-1 }{\sqrt{5}} )[/tex]
Or we can write
[tex]Cos(A - B)= (\frac{-\sqrt{5} }{5} )[/tex]
Hence, we can say that the value of [tex]Cos(A - B)[/tex] will be [tex](\frac{-\sqrt{5} }{5} )[/tex] which is given in option (b).
To know more about Trigonometric functions click here
https://brainly.com/question/6904750
#SPJ3
Related Questions
HURRY PLEASE?!
Determined to finish her milkshake before Diego, Lin now drinks her 12 ounce milkshake at a rate of 13 an ounce per second. Diego starts with his usual 20 ounce milkshake and drinks at the same rate as before, 23 an ounce per second.
Below is a graph of this system.
After how many seconds do both Diego and Lin have the same amount of milkshake left?
[ Select ]
How many ounces do both Diego and Lin have left of their milkshakes at that point?
[ Select ]
Answers
Answer: 24 seconds
4 ounces
Answer:
24 seconds and 4 ounces
Step-by-step explanation:
The point where both lines meet is the point where they are both equal.
The point where both lines meet is (24,4)
Since the x-axis represents seconds the x-coordinate will represent the number of seconds it takes for them to be equal which is 24.
Since the y-axis represents ounces the y-coordinate will represent the number of ounces they have when they are equal which is 4.
student 1 y=-3x+x student 2 y=7x/10 student 3 y=4(2-x) Which students write an equation of a nonlinear function?
Answers
Answer:
its 547632
Step-by-step explanation:
cuz yeeeeeeeeee
PLEASE HELP 6TH GRADE
Answers
A scientist teacher murdered $3980 worth of microscopes and dissension kits for the new science lab a total of 38 microscopes and 47 dissension kids were ordered a microscope cost four times as much as a Ascension kit write a system of linear equations that represents the situation what is the cost of each item
Answers
Answer:
dang
Step-by-step explanation:
._.
2 divided by 1/3 pls
Answers
Answer:
6
Step-by-step explanation:
2/ 1/3= 6
Answer:
= 6
Step-by-step explanation:
you can do the keep, switch, flip strategy
keep 2/1, switch division to multiplication, and flip 1/3 to 3
2 x 3 = 6
Can someone help pls !
Answers
Answer:
(B). [tex]A_{y}[/tex] = [tex]\left[\begin{array}{cc}12&7\\17&-51\end{array}\right][/tex]
Step-by-step explanation:
12x - 13y = 7
17x - 22y = - 51
A = [tex]\left[\begin{array}{cc}12&-13\\17&-22\end{array}\right][/tex]
[tex]A_{x}[/tex] = [tex]\left[\begin{array}{cc}7&-13\\-51&-22\end{array}\right][/tex]
[tex]A_{y}[/tex] = [tex]\left[\begin{array}{cc}12&7\\17&-51\end{array}\right][/tex]
7
Complete the statement. Round to the nearest hundredth if necessary.
39 ft
yd
Answers
Answer:
1.7 mi
Step-by-step explanation:
Car x travels 162 miles in 3 hours: write an equation of the line that describes the relationship between distance and time. Use x for the time in hours and y for the distance in miles
Answers
Answer:
A:The equation y=54x describes the relationship
B: y as 216 and x being 4
If a car travels for 0 hours, it will travel 0 mile(s). This means it will pass through the point (0,0)
.Use the slope to move 3 units to the right of the origin and
162 unit(s) up to find the point
(3,162) that can be used to graph the relationship. Step-by-step explanation:
What is the midpoint of line segment
A (-3,-5)
B (1,-9)
‾
start overline, A, B, end overline?
Answers
HELP PLS
A) 16
B) -4
C) -16
Answers
Answer:
B) -4 is the crct answer may be
Write an recursive rule for the sequence 7,14,21,28
Answers
Given the function f(x) = x2-2, find the average rate of change over the interval -2 sxs 4
Answers
Answer:
The correct answer for that is (98)
You eat 80% of your daily calories at breakfast. Does this statement make sense?
Answers
Answer:
you so dumb
Step-by-step explanation:
Answer:
this statement does make sense
HELP PLEASE FAST ILL MARK BRAINLIEST IF CORRECT 20 points!!
Answers
Answer:
8.49
Step-by-step explanation:
6^2 + 6^2 = 72
√72 = 8.485... = 8.49
Solve the equation - [tex]\frac{w}{5}[/tex] +9=13. What is w?
Answers
Answer:
w = -20
Step-by-step explanation:
-[tex]\frac{w}{5}[/tex] + 9 = 13
Shift the (+9) to the other side of the equation. (+9) will turn into (-9).
-[tex]\frac{w}{5}[/tex] = 13 - 9
= 4
Shift the (÷5) to the other side of the equation. (÷5) will turn into (×5).
-w = 4 × 5
= 20
Multiply both sides of the equation by (-1) so that -w will turn into w.
w = (-1) × 20
w = -20
Machine A makes 12.75 ounces of popcorn in 3 minutes. Machine B makes 18 ounces of popcorn in 4 minutes.
If each machine makes popcorn for 10 minutes, will there be enough popcorn for eight 9-ounce bags? Explain.
Answers
Answer:
Machine A makes popcorn at a rate of 4.25 ozs per minute (12.75oz/3min).
Machine B makes popcorn at a rate of 4.5 ozs per minute (18oz/4min).
Machine A will make 4.25oz/min * 10minutes = 42.5oz of popcorn after 10 minutes
Machine B will make 4.5oz/min * 10 minutes = 45oz of popcorn after 10 minutes
After 10 minutes there will be a total of 42.5oz (Machine A) +45oz (Machine B) = 87.5oz.
So the answer is: Yes there will be (more than) enough popcorn if both machines make popcorn for 10 minutes.
If the question is wondering how many 9oz bags they can fill: 87.5oz/9oz per bag = 9.7222 bags. The machines can fill 9, 9oz, bags with some popcorn leftover.
Step-by-step explanation:
Machine A makes popcorn at a rate of 4.25 ozs per minute (12.75oz/3min).
Machine B makes popcorn at a rate of 4.5 ozs per minute (18oz/4min).
Machine A will make 4.25oz/min * 10minutes = 42.5oz of popcorn after 10 minutes
Machine B will make 4.5oz/min * 10 minutes = 45oz of popcorn after 10 minutes
After 10 minutes there will be a total of 42.5oz (Machine A) +45oz (Machine B) = 87.5oz.
So the answer is: Yes there will be (more than) enough popcorn if both machines make popcorn for 10 minutes.
If the question is wondering how many 9oz bags they can fill: 87.5oz/9oz per bag = 9.7222 bags. The machines can fill 9, 9oz, bags with some popcorn leftover.
Answer:
Yes
Step-by-step explanation:
Divide 12.75 by 3 to get the amount Machine A makes in 1 minute, 4.25 ounces.
Divide 18 by 4 to get the amount Machine B makes in 1 minute, 4.5 ounces
Multiply 4.25 by 10 for a total from Machine A, 42.5 ounces.
Multiply 4.5 by 10 for a total from Machine B, 45 ounces.
Add 42.5 to 45 totalling 87.5
Eight 9-ounce bags require 72 ounces of popcorn. So if both Machines made a total of 87.5 ounces they would have enough popcorn.
I know the answer is 36 but I need to know the working out and I am unsure how to work the question out.
Plz explain
Thanks in advance!! :)
Answers
Answer:
36
Step-by-step explanation:
Since the 3 numbers have a ratio of 2:3:7, that means it simplifies to that. So, there must be a common factor, let’s say x, for each of the numbers. Thus, the numbers are 2x, 3x, and 7x. To find the mean, we add up all of the numbers and divide by the number of numbers: (2x + 3x + 7x)/3 = 12x/3 = 4x = 48. Dividing by 4 on both sides gets x = 12. The median of the numbers is the number in the middle which is 3x. Substituting x = 12, we get: 3(12) = 36.
I hope this helps!!! :)
sharice is putting jars of jam into boxes. she puts 8 jars into each box, and she has a total of 144 jars. sharice wants to know how many boxes she needs.
Answers
she needs 18 boxes.
What is factoring?A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.
Given
Based on the given conditions, formulate: 8 x = 144
Divide both sides of the equation by the coefficient of variable: x = 144/8 out the common factor: x = 18
To know more about factoring refer to :
https://brainly.com/question/25829061
#SPJ2
please please help me!
Answers
Answer:
Option 4
Step-by-step explanation:
It has a negative slope of -[tex]\frac{1}{5}[/tex] (move down one and to the right 5)
Given that f(x) = x2 + 4x – 21 and g(x) = x - 3, find f(x) · g(x) and
express the result in standard form.
Answers
9514 1404 393
Answer:
(f·g)(x) = x^3 +x^2 -33x +63
Step-by-step explanation:
The product of the two functions can be found using the distributive property.
[tex]f(x)\cdot g(x)=(x^2+4x-21)\cdot(x-3)\\\\=(x^2+4x-21)(x)+(x^2+4x-21)(-3)\\\\=x^3+4x^2-21x-3x^2-12x+63\\\\\boxed{(f\cdot g)(x)=x^3 +x^2-33x+63}[/tex]
what is the equation of the line through (2,-1) and (0,5)
A. y= -3x + 5
B. y= 3x - 5
C. y= -3x - 5
D. y= 3x + 5
Answers
Find an equation of the parabola with vertex (2, -1) and directrix y=-7.
Answers
Answer:
the answer to this is y=7x-15
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
Answers
Answer:
x^2 + 11x + 24
Step-by-step explanation:
x^2 + 3x + 8x + 24 =
= x^2 + 11x + 24
What is 3 3/8 divided by 9
Answers
Answer:
0.375
Step-by-step explanation:
Answer:
3/8
Reason:
I just did a question exactly like this, and this was the answer.
Help with this question please ASAP!! :)
Answers
Answer:
options 1, 3, and 6.
Step-by-step explanation:
on the diagram, ∠2 is in the area of line EA and EG. If you are reading it by letters, ∠GEA is equal to ∠2 because they are in the same area. The last option (6) being ∠AEG, the middle angle is E which is the same as ∠GEA and ∠2.
hope this helps!! :))
10 ( y - 2)
what is the answer
Answers
Answer:
10y-20
Step-by-step explanation:
sorry if I am incorrect
Some marbles in a bag are red and the rest are blue. If one red marble is removed,
then one-seventh of the remaining marbles are red. If two blue marbles are removed
instead of one red, then one-fifth of the remaining marbles are red. How many
marbles were in the bag original
Pls give EXPLANATION
Answers
Answer:
22
Step-by-step explanation:
Let r be red and b be blue
1/7(r-1+b)=r-1
1/5(r+b-2)=r
r-1+b=7(r-1)
r+b-2=5r
r-1+b=7r-7
1=7r-7-5r
8=2r
r=4
1/5(4+b-2)=4
2+b=20
b=18
18+4=22
Please help guys!!!!!!
Answers
Answer:I think its 68
Step-by-step explanation:
Answer:
The measure of angle N is 68 degrees.
Step-by-step explanation:
Since this shape is a parallelogram, opposite angles will be equivalent. So to start, set (6x - 2) equal to (4x + 36).
— 6x - 2 = 4x + 36
Next, subtarct the 4x from both sides of the equation as well as add 2 to both sides of the equation an simplify.
— 6x - 4x - 2 + 2 = 4x - 4x + 36 + 2
— 2x = 38
Now, divide both sides of the equation by 2 to find the value of x.
— 2x/2 = 38/2
— x = 19
Finally, substitute 19 for every x in the original equation. Simplify.
— 6(19) - 2 = 4(19) + 36
— 114 - 2 = 76 + 36
— 112 = 112
We now know that these two angles are 112 degrees. If a parallelogram's angles must add up to 360 degrees, then subtract 112 twice from 360 to find the combined total angle measure of N and Q. Then divide that number by 2 to find the measure of N.
— 360 - 112 - 112 = 136
— 136/2 = 68
The measure of angle N is 68 degrees.
Pls helpooooooooo indeddhelpillgovebrqinlyidkwkek
Answers
Answer:
3-7×14 12946.-40
Step-by-step explanation:
mark me as brainliest
A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month is given by C=0.3X^2+8,000. How fast is the cost per month changing when production is changing at the rate of 14 units per month and the production level is 70 UNITS?
Costs are ___ at the rate of $___ per month at this production level.
Answers
Answer:
Costs are changing at the rate of $588 per month at this production level.
Step-by-step explanation:
From the question, we have:
C = 0.3X^2 + 8,000 ........................ (1)
Differentiating equation (1) with respect to time, t, we have:
dC/dt = (0.3 * 2) X (dX/dt)....................... (2)
Where;
X = 70
dX/dt = 14
Substituting this into equation (2), we have:
dC/dt = (0.3 * 2) * 70 * 14
dC/dt = 588
This implies that costs are changing at the rate of $588 per month at this production level.