Given sec A= and that angle A is in Quadrant I, find the exact value of csc A in
simplest radical form using a rational denominator.
Need help :(
Answers
The required value is [tex]\csc A=\dfrac{5}{4}[/tex].
Important information:
[tex]\sec A=\dfrac{5}{3}[/tex]Angle A is in Quadrant I.We need to find the exact value of csc A.
Trigonometric Ratios:Formulae used: If angle A is in Quadrant I.
[tex]\cos A=\dfrac{1}{\sec A}[/tex]
[tex]\sin A=\sqrt{1-\cos^2 A}[/tex]
[tex]\csc A=\dfrac{1}{\sin A}[/tex]
Using these formulae, we get
[tex]\cos A=\dfrac{3}{5}[/tex]
And,
[tex]\sin A=\sqrt{1-\left(\dfrac{3}{5}\right)^2}[/tex]
[tex]\sin A=\sqrt{1-\dfrac{9}{25}}[/tex]
[tex]\sin A=\sqrt{\dfrac{16}{25}}[/tex]
[tex]\sin A=\dfrac{4}{5}[/tex]
Now,
[tex]\csc A=\dfrac{1}{\sin A}[/tex]
[tex]\csc A=\dfrac{1}{\frac{4}{5}}[/tex]
[tex]\csc A=\dfrac{5}{4}[/tex]
Thus, the required value is [tex]\csc A=\dfrac{5}{4}[/tex].
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The required value of cscA is 1.25
Given,
[tex]secA=\frac{5}{3}[/tex]
Trigonometrical ratios:
In the first quadrant, all ratios are positives.
[tex]sin A=\frac{P}{H}[/tex]
And the value of hypotenuse is,
[tex]P=\sqrt{H^2-B^2} \\=\sqrt{5^2-3^2} \\=\sqrt{16}\\ P=4[/tex]
So, the sine A is,
[tex]sinA=\frac{P}{H}\\ =\frac{4}{5}[/tex]
So, the rational denominator is,
[tex]cscA=\frac{H}{P}\\ =\frac{5}{4}\\=1.25[/tex]
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Related Questions
Order the set of integers from least to greatest 5, -3, -12, 9
Answers
Answer:
-12, -3, 5, 9
Step-by-step explanation:
ok. So the numbers are 5, -3, -12, and 9.
In these numbers, there are 2 negatives. They are -12 and -3.
In negatives, the bigger the number is, the number is smaller.
So we first put
-12, -3 as our 2 first. Then the other ones are 5 and 9.
and you obviously know that 5 is less than 9. try it out. 9-5 =4 which is positive
So then you put 5, 9
And our full answer is
-12, -3, 5, 9
Identify the slope from the table
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Answers
Answer:
-4
Step-by-step explanation:
‘X’ adds by one while ‘y’ adds by -4
-1/4 ÷ -3/8
Please Hurry
Answers
Answer:
2 /3 (decimal form ≅ 0.6666667 )
Step-by-step explanation:
Unary minus: -1 /4
= -1 /4
Unary minus: -3 /8
= -3 /8
Divide: the result of step No. 1 : the result of step No. 2 = -1 /4 : (-3 /8 ) =
-1 /4 x -8 /3 = -1 (-8) divided by 4(3) = 8 /12 = 4(2 ) divided by 4(3) = 2 /3
The two figures shown are congruent. Which statement is true?
Answers
Answer:reflection image of the other
Source:trust me bro
Use this scenario to answer questions 3-4: Peter was a waiter that was paid at a rate of $8 per hour plus tips. He earned a total of $200 including $54 in tips.
Given the scenario above, write an equation to represent the scenario. Let h = the number of hours
Free brainliest included! :)
Answers
The temperature in Minsk was recorded over a period of four hours. The
equation
y = -5x + 54
describes the temperature over this time, where y is the temperature in
degrees Fahrenheit (°F) and x is the number of hours since measurements
started. Which of the following statements correctly describes the
temperature?
A. It was -5°F after four hours, and it is rising by 54 degrees per
hour.
B. It was 54°F when the temperature was first measured, and it is
dropping by 5 degrees per hour.
c. It was -5°F when the temperature was first measured, and it is
rising by 54 degrees per hour.
O D. It was 54°F after four hours, and it is dropping by 5 degrees per
hour
Answers
Answer:
D.) it was 54 degrees Fahrenheit when the temperature was first measured, and it is dropping by 5 degrees per hour
Step-by-step explanation:
I took the quiz
Answer:
D
Step-by-step explanation:
I took the test
If Jack weighs more that Jill, and they run up the same hill, who has done more work?
If Jack and Jill weigh the same, and Jill runs up the hill in half the time as Jack, who had more power??
Answers
Answer:
1. Jack, because he weighs more and has to use move power to move.
2. Jill
Step-by-step explanation:
Answer:
omg lol. Okay well for the first one the answer is jack does more work going up the hill.
For the second one Jill has more power.
The number that represent the parts per 100 is called the part
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Answer: Is their a graph or something that goes with this. I dont understand.
Step-by-step explanation:
Answer:
What do you want to find?
Step-by-step explanation:
I don't understand...
Add more details and then I'll answer
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Answers
Answer: photo
Step-by-step explanation:
I am not sure but hope it helps
Sam earns $54 275 in a year.
He pays no income tax on the first $8200.
He pays 18% income tax on everything he earns over $8200.
a Work out how much income tax he pays.
b Work out what percentage of his income he pays in tax.
If the income tax rate is increased to 21%, how much more tax will Sam pay?
Answers
Answer:
he would pay $8,293.5 in income tax.
b:
Step-by-step explanation: he pays 15.280515891294% of his pay in tax. if the income rate was increased to 21% then he would pay 9,675.75 in taxes. Which is 1,382.25 more than 18% tax.
The weight of one ticket is approximately 1.67 × 10-4 g. Write the numerical value without scientific notation.
Answers
Answer:
0.000167 g
Step-by-step explanation:
[tex]1.67 \times {10}^{ - 4} \: g\\ \\ = 0.000167 \: g[/tex]
solve the following inequality showing all steps -3n+7<4
Answers
[tex]\textsf{Hey there!}[/tex]
[tex]\mathsf{-3n + 7 < 4}\\\\\textsf{SUBTRACT by 7 on your sides}\\\mathsf{-3n+7-7<4-7}\\\mathsf{Cancel\ out: 7-7\ because\ that\ gives\ you\ 0}\\\mathsf{Keep: 4-7\ because\ it\ helps\ us\ solve\ for\ our\ n \ value}\\\bf{{\mathsf{4-7= -3}}}\\\\\mathsf{New\ question: -3n<-3}\\\\\mathsf{DIVIDE\ both\ sides\ by\ -3}\\\mathsf{\dfrac{-3n}{-3}=\dfrac{-3}{-3}}\\\mathsf{Cancel\ out: \dfrac{-3}{-3} \ because\ gives\ us\ 1}\\\mathsf{Keep: \dfrac{-3}{-3}\ because\ it\ gives\ us\ our\ n\ value}[/tex]
[tex]\mathsf{New\ equation: n < \dfrac{-3}{-3}}\\\mathsf{\dfrac{-3}{-3} = -3\div-3 \rightarrow 1}\\\\\huge\textsf{Answer}\huge\downarrow\\\\\boxed{\boxed{\mathsf{Answer: n < 1}}}\checkmark\\\\\\\\\textsf{Good luck on your assignment and enjoy your day!}\\\\\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
What’s the common factor for 72 and 84
Answers
Answer:
Step-by-step explanation:
This is the general method for doing this problem. First factor these numbers into primes.
72: 2 * 2 * 2 * 3 * 3
84: 2*2 * 3 * 7
Now each number has at least two 2s
Each number has at least one 3
The highest common factor is 2 * 2 * 3 = 12
evaluate 8 times (2-3) to the 2 power divided by 4
Answers
Answer:
Step-by-step explanation
8 x (-1)^2 /4
8 x 2 /4
16/4
4
The answer is 4
Suppose that P (A)=0.4 AND P (B)=0.2, If events A & B ARE Mutually EXCLUSIVE :
- What is the probability of either A or B occurring
- What is the probability of neither A nor B will happen
Answers
Part (a) Finding the probability of either A or B
We are told that events A and B are mutually exclusive. This means they cannot happen at the same time. We can say P(A and B) = 0
Furthermore,
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.4 + 0.2 - 0
P(A or B) = 0.6
Answer: 0.6=======================================================
Part (b) Finding the probability of neither A nor B
P(A or B) + P(neither A nor B) = 1
P(neither A nor B) = 1 - P(A or B)
P(neither A nor B) = 1 - 0.6
P(neither A nor B) = 0.4
The reason why this works is to imagine throwing a dart at the Venn diagram. You'll either...
you land in A or B (pick one but not both), OR,you'll land outside both regions A and B.One or the other must happen. Both events cannot happen simultaneously.
Answer: 0.4What is the constant rate???
Answers
Answer:
The constant rate is 4
Step-by-step explanation:
40 ÷ 10 = 4
80 ÷ 20 = 4
120 ÷ 30 = 4
160 ÷ 40 = 4
They all equal 4 so that is the constant rate.
Brainliest???
Match each equation to the situation it represents
1st one says Leilah
2nd one says Stetson
Answers
Answer:
leiah has not yet studied...... = 2400 - 40x = 600
stetson rests studios spaces...... = 40x - 600 = 2400
a kit contains.... =. (600 + 40) x = 2400
Step-by-step explanation:
that might make it a bit easier
PLEASE HELP!!!!!!!!!!!!!!!
Answers
Answer:
Blue
blue with a hint of orange
horizontal distance of 10 feet and rice 3 feet. Find the length of the ramp.
Answers
Answer:
Step-by-step explanation:
Tye length of the ramp can be gotten using Pythagoras theorem.
Horizontal distance = 10ft.
Vertical distance = 3ft
Length of the ramp² = 10²+3²
Length of the ramp² = 100+9
Length of the ramp² = 109
L² = 109
L =√109
L = 10.44ft
Hence the length of the ramp is 10.4ft to the nearest tenth
Factor the following expression using the GCF.
8dr – 24r
r(8d – 24)
4r(2d – 6)
8(dr – 3r)
8r(d – 3)
Answers
Answer:
the answer to your question is 8r(d-3)
hope this helps :-)
Alaina is making a birdseed mix with 2 1/3 lb sunflower seeds, 5/6 lb cracked corn, and 1/6 lb peanuts. How much cracked corn does Alaina need to make 5 lb of birdseed mix? Show your work.
Answers
Answer:1.25
Step-by-step explanation:
If you add everything it makes 3 and 1/3 pounds you want 5
If you divide 5 by 3 and 1/3 it's 1.5
Then you just need to multiply 5/6 by 1.5
For making 5 lb birdseed mix 1 ¹/₄ lb cracked corn will be used.
What is proportion ?
A proportion is an equation based on the equality of two ratios.
Here it is given that :
Alaina is making a birdseed mix with 2 1/3 lb sunflower seeds, 5/6 lb cracked corn, and 1/6 lb peanuts.
adding everything to make birdseed mix = 2 1/3 + 5/6 + 1/6 =10/3 lb
Now,
for making 10/3 lb birdseed mix = 5/6 lb cracked corn is used
in other words :
for making 1 lb birdseed mix = (5/6) x (3/10) lb cracked corn is used
that is , for making 5 lb birdseed mix = (5/6) x (3/10) x 5 lb cracked corn will be used.
= 15/12 = 5/4 = 1 ¹/₄ lb cracked corn will be used.
Therefore, for making 5 lb birdseed mix 1 ¹/₄ lb cracked corn will be used.
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Three friends are selling items at an arts and crafts fair. Kim makes $45.75 selling jewelry. Mark makes 100 times as much as Kim selling his custom picture frames. Carlos makes one tenth of the money Mark makes selling paintings. How much money does each friend make?
Answers
Answer:
mark is making $4,575, Carlos is makeing 457.50
-15= x/-0.5 8= what does x equal
Answers
x = -15/4
The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?
A. -4
B.-2
C.-1
D. 1
Answers
Answer:
n = -4
Step-by-step explanation:
You must write and solve a symbolic equation.
n - 6 = 5(n + 2), or
n - 6 = 5n + 10
Combining like terms, we get:
-16 = 4n,
and so n = -4
Answer:
A. -4
Step-by-step explanation:
Pls help!!! What is this expression in simplified form?
Answers
Answer:
My guess would be D
Step-by-step explanation:
what is the y intercept y=-4x-5
Answers
Answer:
The y-intercept y = 4x - 5 is (0,-5).
Step-by-step explanation:
hope this helps
have a great day
plz consider marking brainliest
Could I get help with this one?
Answers
Answer:
x3
Step-by-step explanation:
I need this for sis!:D I will give thanks!
Answers
Mrs. Healy has two dogs rocky and chino. rocky eats 2 dog treats each day and Chino eats 5 each day. How many treats do the dogs eat in 4 days?
Answers
Answer:
28 treats
Step-by-step explanation:
2x4
5x4
20+8=28
Answer:
the answer is 28 treats in 4 days for both dogs
Step-by-step explanation:
2*4=8+ 5*4=20= all together 28 treats for 2 dogs
hope this helped
1)
An ice machine uses 3 gallons of water every 9 hours. How many gallons of water does it use each hour? How many
hours does it take to use one gallon?
A)
B)
gallon per hour, 1 hour
gallon per hour, 3 hours
3 gallons per hour, 5 hour
gallon per hour,
1 hour
D
Answers
Answer:
B
Step-by-step explanation:An ice machine uses 3 gallons of water every 9 hours. How many gallons of water does it use each hour? How many
hours does it take to use one gallon?
A)
b)
gallon per hour, 1 hour
gallon per hour, 3 hours
3 gallons per hour, 5 hour
gallon per hour,
1 hour
D