Given:
[tex](\sin x)^2+(\cos x)^2=1[/tex]
[tex]\cos \theta = \dfrac{4\sqrt{2}}{7}[/tex]
To find:
The value of [tex]\sin \theta[/tex].
Solution:
We have,
[tex]\cos \theta = \dfrac{4\sqrt{2}}{7}[/tex]
Putting this value in the Pythagorean identity, we get
[tex](\sin \theta)^2+(\cos \theta)^2=1[/tex]
[tex](\sin \theta)^2+\left(\dfrac{4\sqrt{2}}{7}\right)^2=1[/tex]
[tex](\sin \theta)^2+\dfrac{16(2)}{49}=1[/tex]
[tex](\sin \theta)^2+\dfrac{32}{49}=1[/tex]
[tex](\sin \theta)^2=1-\dfrac{32}{49}[/tex]
[tex](\sin \theta)^2=\dfrac{49-32}{49}[/tex]
[tex](\sin \theta)^2=\dfrac{17}{49}[/tex]
Taking square root on both sides, we get
[tex]\sin \theta=\pm \sqrt{\dfrac{17}{49}}[/tex]
[tex]\sin \theta=\pm \dfrac{\sqrt{17}}{7}[/tex]
The given value of [tex]\sin \theta[/tex] is positive. So, [tex]\sin \theta= \dfrac{\sqrt{17}}{7}[/tex].
Therefore, the value of value [tex]\sin \theta[/tex] is [tex]\sin \theta= \dfrac{\sqrt{17}}{7}[/tex].
Hey can you help me fast!!
Questions 7 and 8 please. Really need help thank you!!
Answer:
7) sin 60° = 25√3/Z
0.8660 = 25√3/Z
Z = 50
8) using the Pythagorean theorem:
50² = (25√3)² + y²
2500 = 1875 + y²
y² = 625
y = 25
Answer:
z = 50
y = 25
Step-by-step explanation:
Using the 30, 60, 90 triangle rule
you can figure this out.
The rule says
With a 30, 60, 90 triangle
Given the shorter leg, (side across the 30 degree angle,
To find longer leg (side across the 60 degree angle):
Multiple shorter leg by radical 3.
To find hypotenuse (side across the 90 degree angle):
Multiple shorter leg by 2.
Thus
Shorter leg (side opposite 30 degree): 25
Longer leg (side opposite 60 degree):
25 radical 3
Hypotenuse(side opposite 90 degree): 50
Triangle ABC has the following measurements.
m
write an equation and solve for x
Answer:
4y
Step-by-step explanation:
can you figure out the missing number in this sequence?
2, 5, 9, 14, 27
Answer:
The missing number in the sequence is 20
Step-by-step explanation:
The difference between the numbers are as follows: 3,4,5,6,7
The missing number of the given sequence is 13.
The given sequence is,
2, 5, 9, 14, 27
We can see that the difference between each consecutive number is increasing.
The difference between 2 and 5 is 3,
The difference between 5 and 9 is 4,
The difference between 9 and 14 is 5,
And the difference between 14 and 27 is 13.
Therefore, it's possible that the next number in the sequence could have a difference of 14 or more.
So,
To determine the missing number,
We can look at the pattern of the differences between the numbers in the sequence.
Since the difference between 14 and 27 is 13,
We can assume that the difference between the missing number and 27 is at least 14.
Therefore, we can subtract 14 from 27 to get our missing number, which is 13.
To learn more about sequence visit:
brainly.com/question/12373434
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Simplify fully125y2/10xy
Answer:
12.5y/x
Step-by-step explanation:
125y²/10xy = 12.5y/x
Find the volume of the solid shown in the figure
Answer:
The answer to the question is 603.186
Thannnnkkk youuuuuuuuu of youuuu helpp
Help me with Math
( graphs )
PLEASEEE
Which angle type is NOT shown in the diagram?
A) acute
B) obtuse
C) right
D) straight
Help.Right answer gets brainliest.
Answer:
D it should be D i had a similar question
Toby found a $52 wallet on the clearance
rack for 60% off. If sales tax is 6.25%, how
much will he pay in total?
A.$22.10
B.$23.75
C.$28.50
D.$33.15
Answer:
A. $22.10
Step-by-step explanation:
52 x 0.4 = 20.8
20.8 x 1.0625 = 22.1
Rahim was asked to make p the subject of this formula
Q = 5/3 -7
He started his answer as follows
3Q = p - 21 hence p =
Complete Rahim's final answer.
Answer:
p = 63
Step-by-step explanation:
3Q = p - 21
transfer the -21 to the left as the value of Q. Since it was negative, when we transfer it to the left it will turn to poditve so,
3(21) = p
multiply 3 and 21 so 3 multiplied by 21 is equal to,
63 = p, then the answer is p = 63
Please help me with these two questions I am having trouble
Answer:
1. 8820.26 yds^2
2. 101.265 m^2
Step-by-step explanation:
For both problems you need to use the equation π*r^2 which is the area of a circle and where r is the radius of the circle. The radius is also equal to 1/2 the diameter so using this we can figure out the are of the first circle
For the second problem we have to find the area of the circle with and without the sidewalk around it and subtract them from each other
How would you write 12-^3 using a positive exponent?
12^3
12^0
12^3/1
1/12^3
Answer:
[tex] \frac{1}{ {12}^{3} }[/tex]
Step-by-step explanation:
[tex] {12}^{ - 3} = \frac{1}{ {12}^{3} } \\ [/tex]
Consider the function f(x) =2x-6 find f(2)
Step-by-step explanation:
✧ [tex] \underline{ \underline{ \large{ \tt{G \: I \: V \: E\: N}}} } : [/tex]
f ( x ) = 2x - 6✧ [tex] \underline{ \underline{ \large{ \tt{T\: O \: \: F\: I\: N\: D}}}}: [/tex]
value of f ( 2 )✧ [tex] \underline{ \underline{ \large{ \tt{S \:O \: L \: U \: T \: I \: O \: N}}}} : [/tex]
❀ [tex] \large{ \text{When \: x = 2 ,\: f}(2) = 2 \tt{ \times 2 - 6}}[/tex]
⟼ [tex] \large{ \text{f(2) = 4 - 6 = \boxed{ \large{ \text{ - 2}}}}}[/tex]
♨ [tex] \boxed{ \boxed{ \large{ \text{OUR\: FINAL \: ANSWER : \boxed{ \underline{ \bold{ \text{ - 2}}}}}}}}[/tex]
Hope I helped ! ♡
Have a wonderful day / night ! ♪
Let me know if you have any questions regarding my answer! ☄
☃ [tex] \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}[/tex] !! ♕
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
If 10% of a number is 12 and 45% of the same number is 54, find 35% of that number.
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 42
Explanation:
120 x .35 = 42
I hope this helped!
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- Zack Slocum
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42 is your answer
Answer:
let no be x
10% of x=12
x=1200/10=120
again
45% of x=54
x=5400/45=120
here
35% of 120=35/100×120=42
Stonehenge is one of the most famous historical sites in the world. It is believed to
be a burial site built around 2000BC. It covers an area of 804m2. What is the radius
of Stonehenge
Answer: Radius is 15.9975 meters.
Step-by-step explanation:
The formula to find radius of circle is r=[tex]\sqrt{A/\pi }[/tex] so plug in our known variables and solve...
r=[tex]\sqrt{804/\pi }[/tex]
r=[tex]\sqrt{255.9211}[/tex]
r=15.9975
Write an exponential equation that represents the given situation. You invest $1000 and it increases 12% each year. Can you teach me it because i need to show my work, thank you
Answer:
FV= 1,000*(1.12^n)
Step-by-step explanation:
Giving the following information:
Initial investment= $1,000
Increase rate= 12% = 0.12
We need to formulate an exponential equation to show the value in n years.
To calculate the Future Value, we need to use the following formula:
FV= PV*(1+i)^n
Being:
FV= Future Value
PV= Initial Investment
i= increase rate
n= number of periods
FV= 1,000*(1.12^n)
For example, for one year:
FV= 1,000*(1.12^1)
FV= $1,120
For 3 years:
FV= 1,000*(1.12^3)
FV= $1,404.93
A gym owner has some yellow weights and some red weights. The yellow weights are 6 kilograms each, and the red weights are 8 kilograms each. The owner has 4 weights, and they weigh 28 kilograms in all. How many of each color weight does he have?
Answer:
The store owner has two of each color weights
Step-by-step explanation:
joey took a total of 12 pages of notes during 3 hours of class. after attending 4hours of class, how many pages of notes will joey have in his notebook
HELPPP
Answer:
If he kept taking notes at the same pace, he would have 16 pages of notes in his notebook.
Step-by-step explanation:
By dividing the number of pages of notes taken by the time spent taking them, you can find his rate of note-taking, which is 4 pages an hour. By adding another hour of notes, he should have 16 pages of notes. But if this question is asking for 4 more hours, the answer would be 28 pages.
i need help please this is quite hard for me
What is the spread of the data?
A. 15 to 30 years
B. 18 to 25 years
C. 21 to 25 years
D. 18 to 21 years
What is the common ratio of the sequence?
-2, 6, -18, 54,...
a. −3
b. −2
c. 3
d. 8
Answer:
A -3
Step-by-step explanation:
-2 x -3 = 6
6 x -3 = -18
-18x -3 = 54
3) Write an explicit
formula for the
sequence:
45, 41, 37, 33
Answer and Step-by-step explanation:
f(n) = 45 - 4(n - 1)
This is the explicit formula for the sequence.
45 is the initial amount, which is why it is by itself.
The change in the sequence is take away 4, so this becomes a negative 4, which is then multiplied by (n - 1), where n is the term in the sequence.
#teamtrees #PAW (Plant And Water)
please show your work.
Answer:
1. 8.19, 2. 25.96, 3. 3.95
Step-by-step explanation:
use soh cah toa
1. cos is adjacent/hypotenuse
cos73=x/28
multiply both sides by 28
28cos73=x=8.186
2. sin is opposite over hypotenuse
sin68=x/28
multiply both sides by 28
28sin68=x=25.961
3. sin is opposite over hypotenuse
sin26=x/9
myltiply both sides by 9
9sin26=x=3.945
Solve the proportion (last was wrong, i apologize to those who answered my previous one!!)
11/s = s/-6
Answer:
x=±√(-66)
(there is no real solution)
Step-by-step explanation:
Answer:
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jrgjgk
Step-by-step explanation:
jgjk
HELP PLEASE PLEASE!!!
Answer:
a) 20 feet
Step-by-step explanation:
8ft shadow - 5ft
32ft shadow - [tex]\frac{32}{8}[/tex] × 5ft = 20ft
Answer:
A
Step-by-step explanation:
Ratio from shadow to object
8:5
Given Shadow of tree = 32ft, (8x4)
Height of Tree = 5x4 = 20ft
A
thank you for hurrying here is the very last one Explain how you would find the perimeter of this triangle.
Step-by-step explanation:
Use the method of TOA CAH SOH.
[tex]tan(51.3) = \frac{opp}{adj} \\ \tan(51.3) = \frac{u}{4} \\ u = 4 \tan(51.3) [/tex]
[tex] cos(51.3) = \frac{adj}{hypo} \\ \cos(51.3) = \frac{4}{v} \\ v \cos(51.3) = 4 \\ v = \frac{4}{ \cos(51.3) } [/tex]
Perimeter of triangle = Sum of all sides =
[tex]u \: + \: v + 4[/tex]
Answer:
use right angeled triangle method.
A pair of sandals cost $34.00, and 5% tax is charged on the purchase. How much tax is paid?
Answer:
1.70 of tax is paid
Step-by-step explanation:
34(1+0.05) = 35.7
35.7-34= 1.70
1 represents out 100%
do 5% in decimal form which is 0.05
One of the measures of a triangle is 30º. If the sum of the other 2 angles is 150º and the differnce their measures is 18º what are the of the unkown angles
Answer: 84° & 66°
Step-by-step explanation:
find our variables...
difference in two unknown angles is 18 so...
Let's use a, b, & c to set up
a=30 b=b c=b-18
150=b+c
150=b+(b-18)
150=2b-18
168=2b
84=b
Use our known b to find c...
c=b-18
c=84-18
c=66
Adding all three up to make sure they give us 180 degrees is a good way to check our work.
a+b+c=
30+84+66=180