Answers
Answer:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{3\sqrt{22}-\sqrt{371}}{40}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \cos(\alpha)=\frac{\sqrt{11}}{8}\text{ and } \sin(\beta)=\frac{\sqrt7}{5}[/tex]
Where both α and β are in QI.
And we want to find cos(α + β).
First, let's determine the side lengths for each angle.
For α, we are given that its cosine is √(11)/8.
And since cosine is the ratio of the adjacent side to the hypotenuse, the adjacent side to α is √11 and the hypotenuse is 8.
Therefore, the opposite side will be:
[tex]o=\sqrt{8^2-(\sqrt{11})^2}=\sqrt{53}[/tex]
Hence, for α, the adjacent side is √11, the opposite side is √53, and the hypotenuse is 8.
Likewise, for β, we are given that its sine is √7/5.
And since sine is the ratio of the opposite side to the hypotenuse, the adjacent side of β is:
[tex]a=\sqrt{5^2-(\sqrt{7})^2}=\sqrt{18}=3\sqrt{2}[/tex]
In summary:
For α, the adjacent is √11, the opposite is √53, and the hypotenuse is 8.
For β, the adjacent is 3√2, the opposite is √7, and the hypotenuse is 5.
Using an angle addition identity, we can rewrite our expression as:
[tex]\cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)[/tex]
And since both α and β are in QI, all trig ratios will be positive.
Using the above information, we can substitute in the following values:
[tex]\displaystyle \cos(\alpha +\beta)=\Big(\frac{\sqrt{11}}{8}\Big)\Big(\frac{3\sqrt2}{5}\Big)-\Big(\frac{\sqrt{53}}{8}\Big)\Big(\frac{\sqrt7}{5}\Big)[/tex]
Finally, simplify:
[tex]\displaystyle \cos(\alpha +\beta)=\frac{3\sqrt{22}}{40}-\frac{\sqrt{371}}{40}=\frac{3\sqrt{22}-\sqrt{371}}{40}\approx -0.1298[/tex]
Related Questions
What is the domain of the function y= (square root) x+6-7
Answers
Answer:
the third choice. x>_-6
Step-by-step explanation:
1. When you have the square root of (x+6), it shifts the graph 6 units to the left.
2. So the x values would start and include -6 and continue growing to the right.
3. So the domain (x values) of the equation is x is greater than or equal to -6
Solve this equation 53y - 55 = 42y
Answers
11y=55
Y=55/11 =5
Sophia buys an apple that weighs 0.45 pound, a grapefruit that weighs pound, a navel orange that weighs pound, and a pear that weighs 0.5 pound. What is the order of the fruit from least
Answers
Answer:
The order of fruit from least to greatest weight is -
Apple , pear, navel orange, grapefruit
Step-by-step explanation:
P.S - The exact question is -
Given - Sophia buys an apple that weighs 0.45 pound, a grapefruit that weighs [tex]\frac{3}{4}[/tex] pound, a navel orange that weighs [tex]\frac{5}{8}[/tex] pound, and a pear that weighs 0.5 pound.
To find - What is the order of the fruit from least weight to the greatest weight ?
Proof -
Weight of apple = 0.45 pound
Weight of grapefruit = [tex]\frac{3}{4}[/tex] pound = 0.75 pound
Weight of navel orange = [tex]\frac{5}{8}[/tex] pound = 0.625 pound
Weight of a pear = 0.5 pound
As,
0.45 < 0.5 < 0.625 < 0.75
So, The order of fruit from least to greatest weight is -
Apple , pear, navel orange, grapefruit
Xander goes to the movies with his family. Each family member buys a ticket and two boxes of popcorn. There are five members of his family. Let t represent the cost of a ticket and p represent the cost of a box of popcorn. Explain how each expression describes the situation in a different way.
Answers
Answer:
t + 2p = cost of 1 family member
Step-by-step explanation:
Because there are 5 family members who buy 1 ticket and 2 boxes of popcorn, we must multiply the cost of one family member by five .
5(t + 2p) = total cost of the whole family.
We can distribute 5 and the above equation will become.
5t + 2(5)p ⇒ 5t + 10p = total cost of the whole family.
Hope that helps! :)
Answer:
Step-by-step explanation:
t + 2p = cost of 1 family member
since there are 5 family members who bought one ticket and 2 popcorn, we simply multiply the cost of 1 family member by 5.
5(t + 2p) = total cost of the whole family.
We can distribute 5 and the above equation will become.
5t + 2(5)p ⇒ 5t + 10p = total cost of the whole family.
HELP MARK BRAINLY
what's the surface area of this figure
Answers
Answer:
I THINK ITS 400 TRY IT OUT:)
Ron is x years old. His brother, Ray, is y years older than him. How old was Ray when Ron was first born?
Answers
Answer:
Ray was y years old when Ron was born
Step-by-step explanation:
Hey there!
The correct answer is y years old.
If he is y years older, that means that when Ron was 0, or when he was just born, Ray was y years older.
Have a terrificly amazing day! :D
*EXTRA POINTS* find the volume please :))
Answers
Answer:
904.32 ft^3
Step-by-step explanation:
Sphere Volume Formula: [tex]\frac{4}{3}[/tex][tex]\pi r^{3}[/tex]
Plug in the numbers:
[tex]\frac{4}{3}\pi 6^{3}[/tex]≅904.78
what is the answer to 6−2(3x−5)=−8
Answers
Answer:
x = 4
Step-by-step explanation:
So first we distribute:
6-6x+10=-8
Combine like terms:
16-6x=-8
Now subtract 16 to -8:
-6x=-24
Divide -6 to both sides:
x=4
–3y9 number of terms
Answers
Answer and Step-by-step explanation:
[tex]-3y^{9}[/tex]
This value above is ONE term. Even though it is made up of more values and stuff, it is all one term BECAUSE they are all connect, so the -3 is with the y by multiplication, and the 9 is with -3y as an exponent of y.
#teamtrees #PAW (Plant And Water)
axis of symetry x^2+4+1
Answers
Answer- x=0
What two expressions represent 3/12?
Answers
Answer:
A and C
3x1/12= 3/12
3x1/2= 3/12
Solve graphically.
5x+7y=1 and x+4y=-5
Answers
Answer:
{x,y} = {3,-2}
Step-by-step explanation:
Then the intersection point is (3, -2). Then the solution of the equations will be (3, -2).
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The equations are given below.
5x + 7y = 1
x + 4y = -5
Convert the equation into an intercept form. Then we have
From equation 1, then we have
5x + 7y = 1
x / (1/5) + y / (1/7) = 1
From equation 2, then we have
x + 4y = -5
x / (-5) + y / (-5/4) = 1
The lines are drawn below.
Then the intersection point is (3, -2). Then the solution of the equations will be (3, -2).
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
what is the surface area of the figure?
Answers
Answer:
96
Step-by-step explanation:
first off you know that it is a square pyramid, so you can assume that all base lengths are 6.
i am going to find the base first. it is 36 because 6*6-36 save this in your mental memory
next, we have to find the 4 triangles
we know that they are 5 by 6 but you have to divide them by 2
so 30/2=15 and there are 4 of them
15*4=60
now add together 60 and 36 and you get 96
hope this helps!
Jaedon bought 3 toy cars for $11.70. How much would 10 cars cost?
Answers
Answer:
39
Step-by-step explanation:
11.70 divided by 3 is 3.9, and the unit rate. Multiply by 10 for the answer.
The pair of polygons below are similar. Give the scale factor of figure A to figure B
Answers
Answer:
which one?
Step-by-step explanation:
which number do you want solved?
62% of trees were saved from a fire. If this represents 1420 trees, how many trees were originally in the forest?Round to the nearest whole tree.
Answers
Answer:
2290 trees
Step-by-step explanation:
Given data
Let the total number of trees be x
62% of the total trees x is 1420 trees
mathematically
62/100x= 1420
0.62x= 1420
divide both sides by 0.62
x= 1420/0.62
x= 2290.32
To the nearest whole tree= 2290 trees
URGENT DUE TOMORROW
Please show working out in an equation form if possible
Answers
a) We were told that relationship between the value of the car and its age is linear. This means that it can be represented with a linear equation such as
y = mx + c
y is the dependent variable and in this case, it is the value of the car, V
x is the independent variable and in this case, it is the age of the car, a
The above equation is the slope intercept form equation where
m represents slope
c represents y intercept
The formula for determining slope is expressed as:
m = (y2 - y1)/(x2 - x1)
We were told that a 5 year old car is worth 14000. This means that
When x1 = 5, y1 = 14000
Also, the same car is worth 11400 after 2 years. This means that the car is worth 11400 after 7 years. Thus,
when x2 = 7, y2 = 11400
Thus,
slope, m = (11400 - 14000)/(7 - 5) = - 2600/2
m = - 1300
We would find the y intercept, c by substituting m = - 1300, x = 5 and y = 14000 into the slope intercept equation. Thus,
14000 = - 1300 * 5 + c
14000 = - 6500 + c
c = 14000 + 6500
c = 20500
Thus, by substituting m = - 1300 and c = 20500 into the slope intercept equation, the linear equation representng this scenario is
y = - 1300x + 20500
By replacing with the given variables,
V = - 1300a + 20500
b) When the car was new, it means that a = 0. By substituting a = 0 into the equation, we have
V = - 1300 * 0 + 20500
V = 20500
The value of the car was $20500 when it was new
Can someone please answer this for me
Answers
Answer:
3.5
Explanation:
Take any two points of the line and simply use the formula slop = y2-y1/x2-x1
Two points that I consider
(x1, y1) = (5,0)
(x2,y2) = (7,7)
Now using the above mentioned formula,
y2-y1/x2-x1 = 7-0/7-5 = 7/2= 3.5
Hence slop of line is 3.5
Thanks for joining brainly community!
PLEASE HELP FAST I WILL GIVE BRAINLIST AND EXTRA POINTS FOR YOU TO DRAW THE GRAPH
Answers
Answer:
literally straight on the x axis
Solve the inequation; 5x²+82>262
Answers
-82. -82
5x^2>180
5x^2/5>180/5
X^2>36
Sqrtx^2>sqrt36
X>+/-6
How wide is an 80" widescreen TV (MEASURED DIAGONALLY) if it has a height of 48”?
Answers
Answer:
64"
Step-by-step explanation:
Pythagoras theorem
√(80²-48²)
√4096
=64
Answer:
Width = 64"
Step-by-step explanation:
It forms a right angled triangle. We can use Pythagorean theorem to find the base of the triangle
Base² + altitude² = Hypotenuse²
base² + 48² = 80²
base² + 2304 = 6400
base² = 6400 - 2304
base² = 4096
base = √4096
base = 64
Width = 64"
A baker needs 15 lb of cream cheese that contains 20% fat to fill a big order. But his supplier delivers one cream cheese that contains 10% fat, and another that contains 35% fat. How many pounds of each should the baker combine to fill the order?
Answers
Answer:
6 2/3 lbs of each
Step-by-step explanation:
.10x + .35x = 15(.20)
.45x = 3
x = 3/4.5
x = 6.67
Answer:
Step-by-step explanation:
[.1x+.35(15-x)]/15=.2
.1x+5.25-.35x=3
-.25x+5.25=3
-.25x=-2.25
x=9
So he will use 9lbs of 10% and 6lbs of 35%.
EMERGENCY! NEED QUICK
if
Answers
Answer:
100 degrees
Step-by-step explanation:
hi again,
By the linear pair theorem, Angle B + Angle E will equal 180 degrees
Angle B + 128 = 180
Angle B = 52
By the triangle Sum Theorem, Angle A + Angle B + Angle C = 180
48 + 52 + Angle C = 180
100 + Angle C = 180
Angle C = 80
Like I said, by the linear pair theorem, Angle C + Angle F will equal 180 degrees
80 + Angle F = 180
Angle F = 100
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Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Work out the area of this semi circle Take pi to be 3.142 and write down all the digits given by your calculator
Answers
Answer:
628.4cm²
Step-by-step explanation:
Find the diagram attached
Area of the semi circle = πr²/2
r is the radius = 10cm
Area of the semi circle = π(10)²/2
Area of the semi circle = 3.142(100)/2
Area of the semi circle = 314.2×2cm²
Area of the semi circle =628.4cm²
Hence the area of the semicircle is 628.4cm²
Please Help!! Brainliest Answer! Thank you!
Answers
Answer:
D. 157.5
Step-by-step explanation:
Formual for sum of interior angles
(n-2)*180
so 14*180=2520
but that is the sum
divide that by 16 (2520/16) = 157.5
if g(x)=x^2-5, determine g(h+1)
Answers
what is the axis of symmetry of the graph of the function f(x)=3x^2+12x-4
Answers
Answer:
Step-by-step explanation:
Use the equation x = -b/2a => x = -12/6 = -2.
a=3, b=12
x=-12/(2)(3)
x=-2
What is b PLSSSS ANSWER
WILL GIVE BRAINLIEST
Answers
Answer: -15 divided by 0.3 is the same as -15/3/10 but to solve we can do -15 times 10/3 witch is -150/3=-50
Step-by-step explanation:
ITS AN ANGLE QUESTION PLS HELP
Answers
Answer:
The values of [tex]f[/tex] and [tex]g[/tex] are, respectively:
[tex]f = 6\,cm[/tex], [tex]g = 8\,cm[/tex]
Step-by-step explanation:
The area of the triangle ADE is:
[tex]A_{ADE} = 60\,cm^{2}-48\,cm^{2}[/tex]
[tex]A_{ADE} = 12\,cm^{2}[/tex]
The area of the triangle is defined by the following formula:
[tex]A_{ADE} = \frac{1}{2}\cdot AD\cdot DE[/tex] (1)
If we know that [tex]A_{ADE} = 12\,cm^{2}[/tex] and [tex]DE = 4\,cm[/tex], then the length of the line segment [tex]AD[/tex] is:
[tex]AD = \frac{2\cdot A_{ADE}}{DE}[/tex]
[tex]AD = 6\,cm[/tex]
And the area of the rectangle is:
[tex]A_{ABCD} = AD\cdot CD[/tex] (2)
If we know that [tex]A_{ABCD} = 48\,cm^{2}[/tex] and [tex]AD = 6\,cm[/tex], then the length of the line segment [tex]CD[/tex] is:
[tex]CD = \frac{A_{ABCD}}{AD}[/tex]
[tex]CD = 8\,cm[/tex]
Hence, the values of [tex]f[/tex] and [tex]g[/tex] are, respectively:
[tex]f = 6\,cm[/tex], [tex]g = 8\,cm[/tex]