Answers
Answer:
See explanation
Step-by-step explanation:
[tex]tan \: A = \frac{2 \sqrt{a} }{a - 1} ...(given) \\ \because \: {sec}^{2} \: A = 1 + {tan}^{2}\: A \\ \therefore\: {sec}^{2} \: A = 1 + \bigg(\frac{2 \sqrt{a} }{a - 1} \bigg)^{2} \\\\ \hspace{38 pt} = 1 + \frac{4a}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{(a - 1)^{2} + 4a}{ {(a - 1)}^{2} } \\ \\\hspace{38 pt} = \frac{a^{2} - 2a + 1+ 4a}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{a^{2} + 2a+ 1}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{(a + 1)^{2}}{ {(a - 1)}^{2} } \\ \\ \therefore {sec}^{2} \: A = \bigg(\frac{a + 1}{ {a - 1}} \bigg) ^{2} \\ \\ \therefore \: {sec} \: A = \pm \bigg(\frac{a + 1}{ {a - 1}} \bigg)\\ \\ [/tex]
In the question It is not mentioned that in which quadrant does angle A lie, so we will assume it to be in first quadrant.
[tex] \therefore \: {sec} \: A = \bigg(\frac{a + 1}{ {a - 1}} \bigg)\\ \\
\red{ \boxed{ \bold{\therefore \: {cos} \: A = \bigg(\frac{a - 1}{ {a + 1}} \bigg)}}} \\ \\ {sin} \: A ={cos} \: A \times {tan} \: A \\ \\ \hspace{25 pt}=\bigg(\frac{a - 1}{ {a + 1}} \bigg) \times \frac{2 \sqrt{a} }{a - 1} \\ \\ \purple {\boxed { \bold{{sin} \: A = \frac{2 \sqrt{a} }{a + 1}}}}[/tex]
Related Questions
Which expression represents the volume of a rectangular prism that is not occupied by the cylinder.
Answers
Answer:
The volume of the prism not occupied by the cylinder is (150 - 25*pi)*h.
Step-by-step explanation:
In order to calculate the volume of the rectangular prism that is not occupied by the cylinder we need to calculate the total volume of the rectangular prism and subtract it by the volume of the cylinder. We have:
Rectangular prism:
Volume prism = length*height*width
Volume prism = 15*h*10 = 150*h
Cylinder:
Volume cylinder = pi*r²*h = pi*5²*h = 25*pi*h
The volume of the prism that is not occupied by the cylinder is:
volume not occupied = volume prism - volume cylinder
volume not occupied = 150*h - 25*pi*h = (150 - 25*pi)*h
The volume of the prism not occupied by the cylinder is (150 - 25*pi)*h.
You pick one card from each set and find the sum. How many different sums are possible?
Answers
Answer:
24 possibilities
Step-by-step explanation:
2*2*6=24
24 possibilities
The number of different sums possible is 24 possibilities.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We have been given that pick one card from each set and find the sum.
Therefore, we need to find the number of different sums that are possible;
2 x 2 x 6=24
24 possibilities
Hence, the number of different sums possible is 24 possibilities.
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Melissa needs to wrap a gift box that is shaped like a rectangular prism. The length is 6 inches, the width is 6 inches and the height is 8 inches. How much wrapping paper does she need to cover the whole box
Answers
Answer:
A=264
Step-by-step explanation:
When the polynomial x^4-3x^3-7x^2+7x+2 is divided by x+2 the quotient is x^3 +Bx^2 +Cx +1. Find the value of B +C
Answers
Answer:
B=-5
C=3
Step-by-step explanation:
x^4-3x^3-7x^2+7x+2= x^4-3x^3-10x^2+3x^2+7x+2
=x^4-3x^3-10x^2+ 3x^2+7x+2
=x^2(x^2-3x-10)+ 3x^2+7x+2
=x^2(x^2+2x-5x-10)+ 3x^2+6x+x+2
=x^2(x(x+2)-5(x+2))+ 3x(x+2)+1(x+2)
=(x+2)(x^2(x-5)+(3x+1))
=(x+2)(x^3-5x^2+3x+1)
Answer:
B=-5
C=3
Step-by-step explanation:
what is -4 {2 - y} + 3y = 3 {y - 4}
Answers
7y-8=3y-12
7y-3y= -12+8
4y= -4
Y= -1
can someone help? 25 points
Answers
Answer:
8 hours
Step-by-step explanation:
HE has to pay $7 an hour.
8*7=56
He has a descount of $3, so
$56-$3=$53.
Which is the exat amount of money that Tony has.
Answer:
The answer is 46
Because he wants to spend less so you would do
7x7=49
He could only rent the boat for 7 hours because that would be less than 53$
Now you do 49-3=46
Because he had a discount
So the answer is 46
Step-by-step explanation:
Hope this helped!
Solve the following system of equations {4x−6y=105x+6y=−55
Answers
Answer:
31557778998765432
Step-by-step explanation:
is it impossible
If the zeros of a function are = 2 and = 7, what was the function? Could there be more than one answer?
Answers
Answer: [tex]f(x)=x^{2} -9x+14[/tex]
Step-by-step explanation:
[tex]x=2,7[/tex]
[tex]f(x)=(x-2)(x-7)[/tex]
[tex]f(x)=x^{2} -9x+14[/tex]
a knife is 3 times the cost of spoon
9 spoons and 12 knives cost £82.80
Answers
Answer:
5 .52
Step-by-step explanation:
do the math. aaaaaaaaaaaaaaaaaaaannnnnnnnnnnnnnnnnddddddd this is the best appppp evvvvver
Can someone help me with this
Answers
Answer:
30.5 and 46
Step-by-step explanation:
The minimum is 30.5 and the maximum is 46
DESPERATE GEOMETRY HELP!!!
Answers
Answer:
b. 3
Step-by-step explanation:
pi * r^2 * h = 162 pi
plug in 18 ft for h
pi * r^2 * (18) = 162 pi
simplifies to r^2 = 9
r=3
A town has population of 5000 and grows 3.5 percent every year. What will be the population after 15 years , to the nearest whole number?
Answers
Answer:
After 15 years the population will be 7,625
Step-by-step explanation:
3.5% of 5,000 = 175
175 x 15 = 2625
2625 + 5,000 = 7625
The population after 15 years should be 8,376
Calculation of the population:Since the population is 5,000 and it grows 3.5 years and the time period is 15 years
So, the population after 15 years is
[tex]= 5,000 \times (1 + 3.5\%)^{15}\\\\[/tex]
= 8,376
Therefore, we can conclude that The population after 15 years should be 8,376
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A copy machine makes 231 copies in 5 minutes and 15 seconds. How many copies does it make per minute?
Answers
The solution is 44 copies
The number of copies the copy machine makes in one minute is 44 copies
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The number of copies the copy machine makes = 231 copies
Time required by the to make 231 copies = 5 minutes 15 seconds
5 minutes = 5 x 60 seconds
5 minutes = 300 seconds
5 minutes 15 seconds = 300 + 15 seconds
5 minutes 15 seconds = 315 seconds
So , Time required by the to make 231 copies = 315 seconds
Now , number of copies in 1 minute = 60 x ( The number of copies the copy machine makes / Time required by the to make 231 copies )
Substituting the values in the equation , we get
Number of copies in one minute A = 60 x ( 231 / 315 )
Number of copies in one minute A = 60 x 0.733
Number of copies in one minute A = 44 copies
Therefore , the value of A is 44 copies
Hence , the number of copies is 44 copies
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how do I simplify this algebraic expression 3x+2a-4x
Answers
Start by changing the -4x to + -4x.
So we have 3x + 2a + -4x.
To simplify, we can only combine what are called our like terms and in this problem, we have a pair of like terms in our x terms.
3x + -4x simplifies to -x.
So our answer is -x + 2a.
Note that if you wrote your answer as -1x + 2a, it means the same thing. However, as we move farther into math, we usually tend to drop the -1 or 1 that is in front of a variable since it's implied
The area of a circle is 4π x 2 + 12πx + 9π.
a. What is an expression for the radius of the circle?
b. What is the least possible integer value of x for the circle to exist? Explain.
Answers
Answer:B D
Step-by-step explanation:
I just got it right
The art club had an election to select a president. 75% of the 68 members of the club voted in the election. How many members voted?
Answers
Answer:
51 members voted of the 68 members
Idk what it is plz help me
Answers
Answer:
1) Starting height is 6.25
2) after 20 years it would be 30
1.25(20)=25+5=30
3) 76 years
Answer:
a) 5 feet
b) 30 feet
c) 76 years
Step-by-step explanation:
a) 5 feet. If t is 0, it'll still be 5 feet
b) 30 feet
1.25*20+5=
25+5=
30
c) 76 years
100 = 1.25t+5
1.25t=95
t=76
The expresstion 2m +10c gives the amount of money in dollars a desert store makes from selling m muffins and c cakes. How much money does the dessert store make from selling three muffins and four cakes
Answers
Answer:
$46.
Step-by-step explanation:
We plug m = 3 and c = 4 into the given expression:
Money made = 2*3 + 10*4
= $46.
In ΔHIJ, the measure of ∠J=90°, IJ = 47 feet, and HI = 68 feet. Find the measure of ∠H to the nearest degree.
Answers
Answer:
44
Step-by-step explanation:
what is the percent change between 6 to 3?
Answers
Answer:
50% = percent chang
Step-by-step explanation:
6 ÷ 50%
6 × .50 = 3
3 ÷ .50 = 6
When I visit my brother it is a 532 mile round trip. If I visit my brother once a month how many miles would I travel in a year round the miles to the nearest hundreds to estimate the answer
Answers
Answe12800 miles
Step-by-step explanation:a year is 12 months, and mile round trip means there and back. so 532x24 for the 24 trips that equals 12768. 12768 rounded to the nearest hundreds is 12800
Timothy makes reduced copies of a photograph that has an actual length of 8 in. Each time he presses the reduce button on the copier, the copy is reduced by 12%. What formula shows the pattern for the size of each copy of the photograph as it is reduced? What is the length of the photograph’s copy if Timothy presses the reduce button 5 times? Round to the nearest tenth.
Answers
Answer:
length of the photograph will be 4.2 in. after pressing the button 5 times.
Step-by-step explanation:
By pressing the button, every time size of the photograph gets reduced by 12%.
Therefore, the sequence formed by the reduced sizes of the photo will be a geometric sequence and the formula for the size of the reduced image will be,
L = [tex]l(1-\frac{12}{100})^{n}[/tex]
Where l = Actual length of the photograph
L = length of the reduced image
n = Number of times the button has been pressed
For l = 8 in. and n = 5
L = [tex]8(1-0.12)^{5}[/tex]
= [tex]8(0.88)^{5}[/tex]
= 4.22 in
L ≈ 4.2 in.
Therefore, length of the photograph will be 4.2 in. after pressing the button 5 times.
The length of the photograph's copy when the button is pressed the 5th times is 4.2 inches
The question is an illustration of an exponential function.
An exponential function is represented as:
[tex]y = ab^x[/tex]
Where:
a represents the initial value i.e. a = 8b = 1 - r; and r represents the rate. i.e. r = 12%.So, the function becomes
[tex]y = 8 \times (1 - 12\%)^x[/tex]
Express 12% as decimal
[tex]y = 8 \times (1 - 0.12)^x[/tex]
This gives
[tex]y = 8 \times 0.88^x[/tex]
When the button is pressed the 5th times, we have:
[tex]y = 8 \times 0.88^5[/tex]
[tex]y = 4.2[/tex]
Hence, the length of the photograph's copy is 4.2 inches
Read more about exponential functions at:
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BRAINLIEST!!!!!!! ANSWER QUICKLY!!!!!!!!!!!!!!!!!!!!!!!
Hi, I need help. I have a question about the Big Bang and Evolution. I don't fully understand or believe what happened. Can someone with a great mind try to explain it. Good luck by the way, I will tell you what I think in the comments. I don't believe in the Big Bang, I doubt you can convince me, but if you are willing to try..........please do.
Answers
Answer:
The big bang is showing that there is tiny atoms. The atoms grouped up with gravity and more and more grouped making a super dense dot. The dot exploded making gases creating stars. The stars were bigger so they got new atoms to join creating planets. One planet named was suitable for life so tiny germs. The rest nobody knows.
Step-by-step explanation:
Correct answers only!
To the nearest cent, how much interest will he earn in 2 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
Answer: $8.40
Step-by-step explanation:
The problem states that Scott has deposited $40 and is earning 10% interest, annually. It asks how much interest he will earn in 2 years to the nearest cent.
First, the formula given is B=p(1+r)^t. Since Scott deposits $40, 40 would be the starting amount, p.
B=40(1+r)^t
R is the interest rate: 10%. We plug in 0.10 instead of 10% because r is the interest rate, not the percentage.
B=40(1+0.10)^t
T is time: 2 years
B=40(1+0.10)^2
Now that we have the equation filled out, we plug this into a calculator.
48.4=40(1+0.10)^2
We know that the final amount is $48.40. Unfortunately, the question is asking how much interest is earned. To find that, you would subtract the Final-Initial to get the interest.
48.4-40=8.4
0.7 bar repeater in simplest form
Answers
Answer:
the answer is 7/10
Step-by-step explanation:
cause i am in honors math 6th grade. I am EXTREMELY smart!!!
James has g amount of games. Samuel, his friend, has 4 times as many games as James. Write an algebraic expression to represent how many games James has and how many games Samuel has in terms of g.
Answers
Answer: The answer is given below
Step-by-step explanation:
From the question, we are told that James has a lot of games and his friend Samuel, has 4 times as many games as James.
So let the number of games that James has be denoted by g.
Since Samuel has 4 times as the number of games that James has, then Samuel's game will be
= 4 × g
= 4g
Therefore, the expression for James will be g and the expression for the number of games Samuel has is 4g.
Four bags of peaches weigh 5.6 pounds, 3.9 pounds, 4.9 pounds, and 6.2 pounds.
What is the median weight of the bags?
Answers
The answer is 5.25
First, you need to list all of the numbers from least to greatest. Then, you remove the sides (first 3.9 and 6.2 being the least and the greatest numbers). You then have 4.9 and 5.6 so you need to add them together (getting 10.6) and divide your answer by 2 (getting 5.25).
Hope I helped and good luck :)
plzzzzzzzzzzzzzzaaaaaaaaaa
Answers
Answer:
A
Step-by-step explanation:
[tex]3x^2+5x+2=0[/tex]
[tex]x=\dfrac{-5\pm \sqrt{5^2-4(2)(3)}}{6}=\dfrac{-5\pm 1}{6}=-\dfrac{2}{3}, -1[/tex]
Therefore, the answer is choice A. Hope this helps!
Jackson and Xavier are both solving the multiplication 0.8 x 5. Jackson gets 4 as a solution, and Xavier gets 0.4. Xavier said to Jackson, "Your answer of 4 can't be right for 0.8 x 5. You need a decimal point because a product always has the same number
Answers
Answer:
Jackson
0.8×5=4
Xavier
0.8×5=0.4
If Xavier said to Jackson that his answer of 4 can't be right.
Jackson needs a decimal point because a product always have the same answer.
Then,
Xavier is right with his sayings but wrong with the answer of 0.4
The correct answer is 4.0
The decimal point should be counted from the back not from the front as Xavier did
The city limits of Las Pythagoras form a perfect shape of an isosceles right triangle whose legs are both 25 2525 kilometers long. The population in Las Pythagoras is 100 , 000 100,000100, comma, 000 people. What is the population density of Las Pythagoras?
Answers
320
Step-by-step explanation:
