Use the given information to find (a) sin (s +t), (b) tan (s+t), and (c) the quadrant of s+t cos s=3/5 and cos t= 15/17, s and t quadrant I
Step-by-step explanation:
Let find the other trig function first, just sin s and sin c.
Use pythagoren identity to find sin a.
[tex]1 - \cos {}^{2} (s) = \sin {}^{2} (s) [/tex]
cos s=3/5 so cos^2(s)=9/25
[tex]1 - \frac{9}{25} = \sin {}^{2} (s) [/tex]
[tex] \frac{16}{25} = \sin {}^{2} (s) [/tex]
[tex] \frac{4}{5} = \sin(s) [/tex]
Since this is in the first quadrant, it is positve.
Let do the the same thing for sin t.
[tex]1 - \frac{169}{289} = \sin {}^{2} ( {}^{} t) [/tex]
[tex] \frac{120}{289} = \sin {}^{2} (t) [/tex]
[tex] \frac{2 \sqrt{30} }{17} = \sin(t) [/tex]
Now, we can compute
a.
[tex] \sin(s + t) = \sin(s) \cos(t) + \cos(s) \sin(t) [/tex]
[tex] \frac{4}{5} \times \frac{13}{17} + \frac{3}{5} \times ( \frac{2 \sqrt{30} }{17} )[/tex]
[tex] \frac{52}{85} + \frac{6 \sqrt{30} }{85} [/tex]
[tex] \sin(s + t) = \frac{52 + 6 \sqrt{30} }{85} [/tex]
b
[tex] \tan(s + t) = \frac{ \tan(s) + \tan(t) }{1 - \tan(s) \tan(t) } [/tex]
Tan s is 4/3
Tan t is 2 times root of 30/ 13
So we have
[tex] \frac{ \frac{4}{3} + \frac{2 \sqrt{30} }{13} }{1 - \frac{8 \sqrt{30} }{39} } [/tex]
[tex] \tan(s + t) = \frac{52 + 6 \sqrt{30} }{39 - 8 \sqrt{30} } [/tex]
c. They are all in 1st quadrant
A cylindrical chemical tank is 12 feet high and has a diameter of 45 feet. How many cubic feet of
liquid could the tank hold?
Answer:
6075π ft^3
Step-by-step explanation:
The formula for a cylinder is πr^2 * h
were:
h = height
and r = radius
and because the radius is always 1/2 of the diameter, the radius is 22.5.
So now we plug everything in:
π*22.5^2 * 12
= π*506.25 * 12 =
π * 6075 =
6075π
please don't forget to add the units.
Daniel and his family are going on a summer vacation for 6 weeks exactly. Daniel estimates that he will need 6 loaves of bread to feed him during this time. Calculate how much bread Daniel will actually need, and state whether you agree or disagree with Daniel's estimate based on this calculation.
Answer:
Daniel will need 9 loaves of bread (108 slices)
Step-by-step explanation:
Daniel eats 18 slices of bread a week.
2 slices per week day (2 x 5 = 10)
4 slices per weekend day (4 x 2 = 8)
10 + 8 = 18
he will be there 6 weeks
18 x 6 = 108.
There are 12 slices of bread per loaf.
108 divided by 12 = 9.
Therefore, he will need 9 loaves of bread.
Find the volume of a cone
Select the polynomial that is a perfect square trinomial. 9x2 9x 1 36b2 − 24b 8 16x2 24x 9 4a2 − 10a 25.
The polynomial that is a perfect square is 16x^2 + 24x +9. Option C shows the polynomial which is a perfect square.
What is square?The square can be defined as a two-dimensional figure that has 4 equal sides.
Given are the equations of the areas of the polynomial.
Option C: [tex]16 x^2 + 24x +9[/tex]
We can write the above equation as,
[tex](4x)^2 + 2 \times 4x \times 3 + (3)^2[/tex]
[tex](a+b)^2 = a^2 + 2ab+b^2[/tex]
Here a = 4x and b = 3, so
[tex]16x^2 + 24x+9 = (4x+3)^2[/tex]
The simplification of the area of a polynomial is (4x+3)^2 which represents the area of a square.
Hence the polynomial that is a perfect square is 16x^2 + 24x +9. Option C shows the polynomial which is a perfect square.
To know more about the area of the square, follow the link given below.
https://brainly.com/question/1658516.
A fish tank in the shape of a cube has a side length of 15 inches. How much water does the fish tank hold when completely filled with water?
The amount of water the fish tank can hold is 3375 inches³.
Volume of a cubev = l³
where
l = length
Therefore,
length = 15 inches
How much water the tank can hold is the volume of the tank. Therefore,
v = l³
v = 15³
v = 15 × 15 × 15
v = 3375 inches³
learn more on cube here: https://brainly.com/question/2965400
Please help me pick me choose me
Answer:
D
Step-by-step explanation:
can u guys do this one?
Answer:
24% i think
Step-by-step explanation:
18/75 right?
sooo we cant convert the denominator to 100 so lets just divide it with..nanana. calculator
its
0.24
now move the decimal point two places to the right
24%
The Family Fair Committee wants to show a good
family movie at their next event. They want to
select a movie that will appeal to families with
young children. Which of the following samples
would be the BEST representation of that
population?
A. Ask 100 people at local Senior Citizen Bingo
night
B. Ask 100 students who are in the local Band.
C. Ask 100 parents at the local playground.
D. Ask 100 Dads at the high school football
game.
O
OA
The best representation of the population is; C. Ask 100 parents at the local playground
What is the statistics Population?
In statistics, a population is the entire group that you want to draw conclusions about. Whereas, a sample is the specific group that you will collect data from.
Now, the family committee want to select a movie that will appeal to families with young children. Thus, it will be best for them to ask the parents of children as that will be a true representation of what the families would like to watch.
In conclusion, the only correct option is option C to ask 100 parents at the local playground
Read more about population at; https://brainly.com/question/7301139
pls help me :) i really dont like math
Answer:
Yes!
Step-by-step explanation:
Yes, every diameter of a circle is also a chord because a chord of a circle is any line connecting 2 parts of the circle's circumference.
Can 9 40 41 make a triangle
Answer:
yes
Step-by-step explanation:
Hi there!
We want to see if 9, 40, and 41 can be the sides of a triangle that can exist
We can use triangle inequalities to figure that out
For triangle inequalities, if the lengths of the sides are a, b, and c, then a+b>c, b+c>a, and c+a>b, then the lengths can make a triangle
Let's say that a=9, b=40, and c=41
Now substitute these values into the inequalities:
a+b>c
9+40>41
49>41
This is a true statement.
b+c>a
40+41>9
81>9
This is also a true statement.
41+9>40
50>40
This is a true statement as well.
Since all three of the inequalities ended up being true (all three NEED to be true in order for the given lengths to make a triangle), then we can confirm that 9, 40, and 41 can make a triangle
Hope this helps!
See more on this topic here: https://brainly.com/question/17357347
60% of the students in a school of 800 students take a bus. how many students take the bus?
Answer:
480
Step-by-step explanation:
60% of 800
= [tex]\frac{60}{100}[/tex] × 800
= 0.6 × 800
= 480 ← number of students who take the bus
help meh out and ill give u brainlyst
Answer:
A
Step-by-step explanation:
the a part is right circle that one
Answer:
Your answer is letter a. 3/8
You have 20 juice boxes. You want to distribute the juice boxes among 6 friends, giving the same number to each. How many juice boxes can you give to each friend?
Answer:
the answer is 3
Step-by-step explanation:
20 divided by 6 gives you 3.33333333 but if you estimate it gives you 3
If the total number of juice boxes is 20 and to distribute the juice boxes among 6 friends, The number of juice boxes can you give to each friend will be 3.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
You are given 20 juice cartons, which you distribute to each of your friends. You want to give the same number of juice boxes to each of your six friends.
We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.
The number of juice boxes can you give to each friend is,
=20/6
=3.333 ≈ 3
Thus, if the total number of juice boxes is 20 and to distribute the juice boxes among 6 friends, The number of juice boxes can you give to each friend will be 3.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ5
what does Squared mean
Answer:
If something is squared it is multiplied by itself
Step-by-step explanation:
If 4 was squared it would be like 4 times 4 which is 16
Find the value of x. Round your answer to the nearest tenth.
Answer:20
Step-by-step explanation:
using the spinner above, what is the probability that you will land on red or blue?
Answer: 3/4
Step-by-step explanation:
The probability that you will land on either red or blue is equal to the sum of the probability that you will land on red and the probability you will land on blue.
The probability you will land on red is 1/2 and the probability that you will land on red is 1/4 by the image.
Therefore, the probability you will land on either is 1/4 + 1/2 = 3/4
Given R
0
3
2
-9
and S.
-4
5
0
2
What is X if X + R = S?
Answer:
B step by step is the answer
56 ft =___yd___ft
please help me this is due tomorrow
Answer:
18 yd 2 ft
Step-by-step explanation:
56÷3=18 R2
18x3=54+2=56
Answer:
56 ft = 18 yd and 2 ft
Step-by-step explanation:
3 feet = 1 yard
Therefore, to find how many yards and feet are in 56 yards, divide 56 by 3:
⇒ 56 ÷ 3 = 18 remainder 2
Therefore,
56 ft = 18 yd and 2 ft
First plot 1 and -6 on the number line below.
Then answer the parts below.
-10
-5
0
5
10
Х
$
?
(a) Choose the correct statement.
O 1 is located to the left of -6.
O 1 is located to the right of -6.
(b) Use<, >, or to complete the statement.
1 ?
-6
area of a regular heptagon
Answer:
32.71
Step-by-step explanation:
32xcot([tex]\frac{108°}{7} \\[/tex]) = 32.70521
If startfraction 1 over 64 endfraction = 4 superscript 2 s minus 1 baseline times 16 superscript 2 s 2, what is the value of s?
The value of s after calculation will be s=-1
What will be the value of s?It is given that
startfraction 1 over 64 endfraction = 4 superscript 2 s minus 1 baseline times 16 superscript 2 s 2
So the mathematical form will be
[tex]\dfrac{1}{64} =4^{2s-1} \times 16^{2s+2}[/tex]
[tex]4^{-3} =4^{2s-1} \times 16^{2s+2}[/tex]
[tex]4^{-3} =4^{2s-1} \times 4^{2(2s+2)[/tex]
[tex]4^{-3} =4^{2s-1+2(2s+2)[/tex]
[tex]4^{-3} =4^{2s-1+2(2s+2)[/tex]
[tex]-3=2s-1+2(2s+2)[/tex]
[tex]-3=2s-1+4s+4[/tex]
[tex]-3=6s+3[/tex]
[tex]-6=6s[/tex]
[tex]s=-1[/tex]
Thus the value of s after calculation will be s=-1
To know more about Simplification follow
https://brainly.com/question/723406
Answer:-1 is the answer
Step-by-step explanation:
Which expression is equivalent to j (j) (j) (j) (j) (j) (j) (j) (j) (j) (j) (j) (j)?
13 Superscript j
13j
j Superscript 13
j + 13
Answer:
j^13
Step-by-step explanation:
j*j*j*j*j*j*j*j*j*j*j*j*j= j^13
Answer:
j^13
Step-by-step explanation:
Got it right on the quiz
Are these shapes similar? Choose all that apply. ( Multiple choice answer )
No, the corresponding sides are not proportional.
Yes, the corresponding sides are proportional.
No, the corresponding angles are not congruent.
Yes, the corresponding angles are all congruent.
Answer:
Yes, the corresponding sides are proportional.
Yes, the corresponding angles are all congruent.
Step-by-step explanation:
The sides are proportional with a ratio of 0.6. The angles are all right angles, making them congruent. Therefore, the two shapes are similar.
I hope this helps!
Plssss help if you know how to do it I can’t figure it out
Answer:
bbbbbbbbbbbb
...........
.........
the team won 3/8 of its games and lost the rest. what as the teams win:loss ratio
Answer:
3:8 mark brainli.st
Step-by-step explanation:
What is the answer to this please help me cause I’m new to all of this kind of math and I’m not really the type of person to like math.
Answer:
12/16 then we have to simplify by finding the largest number that goes into both so from looking i can see that its 4
3/4
Hope This Helps!!!
Estimating sums 331+55
Answer:
round to 330 and 60, add and get 390
Step-by-step explanation:
Answer:
390?
Step-by-step explanation:
Round to nearest 10th
330+60=390
HELPPP FOR BRIANLEST!!!!
Answer:
12/17
Step-by-step explanation:
total number of marbles that are purple (11) plus the total number of marbles that are not small (15) minus the number of marbles that are both purple and not small (2)
11 + 15 - 2 = 24
over the total number of marbles (34)
24/34 simplifies to 12/17
answer 13/17
Step-by-step explanation:
you add all the numbers up in the table, which would be 34 and then add up the ones that are big and the ones that are purple, which would be 26 so 26/34 then you simplify.
so 26/34=13/17
calculate 100% if 50% is 32
Answer:
64
Step-by-step explanation:
100% is twice 50%, which is 32.
64 is twice 32, so is 100%