Verify the following identity:
[tex]\dfrac{1-\sin t}{\cos^2t}+\dfrac{1}{1-\sin t}=2\sec^2t[/tex]
Answers
We will simplify the left hand side of the equation to look like the right
[tex]\displaystyle \frac{1-sin(t)}{cos^{2}(t)} + \frac{1}{1 - sin(t)}[/tex]
taking the LCM
[tex]\displaystyle \frac{[1-sin(t)]^{2} + cos^{2}(t)}{[cos^{2}(t)][1 - sin(t)]}[/tex]
expanding the binomial in the numerator
[tex]\displaystyle \frac{[1 + sin^{2}(t) - 2sin(t) + cos^{2}(t)]}{[cos^{2}(t)][1 - sin(t)]}[/tex]
Since sin²x + cos²x = 1
[tex]\displaystyle \frac{[2 - 2sin(t)]}{[cos^{2}(t)][1 - sin(t)]}[/tex]
factoring out the 2 from the numerator
[tex]\displaystyle \frac{2[1 - sin(t)]}{[cos^{2}(t)][1 - sin(t)]}[/tex]
1-sin(t) will cancel out
[tex]\displaystyle \frac{2}{cos^{2}(t)}[/tex]
since cos²(t) = 1/(sec²(t))
[tex]2 sec^{2}(t)[/tex]
which is equal to the right hand side of our given equation.
So we verified the identity!
Answer:
[tex]\rm 2 \sec {}^{2} T[/tex](Verified identity)
Step-by-step explanation:
Please refer to the attachment for calculations.
I hope this helps!
![Verify The Following Identity:[tex]\dfrac{1-\sin T}{\cos^2t}+\dfrac{1}{1-\sin T}=2\sec^2t[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/LaVnMld0rkr2K0QDPA7ffRdNEOCIClJZ.jpeg)
Related Questions
In the summer reading program, a participant earns 50 stars for reading 10 books. The library tracks the number of stars(y, vertical axis) and books ( x, horizontal axis) on a graph. Which statements are correct.
A: Point(5,1) Represents the unit rate
B: Point(1,5) Represents the unit rate
C: Point(0,50) Represents the unit rate
D: Point(100,20) Represents reading 20 books
E: Point(20,100)Represents reading 20 books
Please help, I will give you the brainliest answer
Answers
Answer:
C: Point(0,50) Represents the unit rate
Step-by-step explanation:
Plz, Help Me Quickly!!
I will mark Brainliest for the best answer.
Answers
Answer:
help you with what
Step-by-step explanation:
Richard wants to paint the top and sides of the block column. What is the surface area he needs to cover?
592 sq. ft
512 sq. ft
960 sq. ft
800 sq. ft
Answers
Hope this helps!
2. List the like terms in each of the following:
i) 6a , 13b2 , -2a , 2a2 , -b2 , bc
Answers
i m not sure about the answer ...
-
Drag the steps for drawing a graph of the function f(x) = 2(x+4)2 - 3 to
arrange them in the correct order. It might help you to draw the graph as
you arrange the steps.
Plot the vertex (-4,-3).
Draw the axis of symmetry x=-4.
Reflect the points over the axis of symmetry and plot (-5, -1), (-6,5), and (-7,15).
Apply the 2x? pattern, from the vertex go right 1 up 2 and plot (-3,-1).
Apply the 2x² pattern again, from the vertex go right 2 up 8 and plot (-2,5).
Apply the 2x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1,15)
Draw a U shaped parabola
Answers
The shape of the graph of quadratic functions is the shape of a parabola.
The steps for drawing a graph of the function f(x) = 2·(x + 4)² - 3 arranged in the correct order are;
(a) Plot the vertex (-4, -3)(b) Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)(c) Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)(d) Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)(e) Draw the axis of symmetry x = -4(f) Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)(g) Draw a U shaped parabola.Reasons:
The given function is; f(x) = 2·(x + 4)² - 3
The function is given in the vertex form; f(x) = a·(x - h)² + k
Therefore, the vertex, (h, k) = (-4, -3)
Step (a);
The vertex can be plotted on the graph
Plot the vertex (-4, -3)Step (b);
Given that the quadratic term is 2·x², the pattern that can be used for the points from the vertex is therefore, 2·x²
From the vertex (-4, -3) apply the 2·x² pattern by going to the right 1 unit and up 2 × 1² = 2 units to get the point (-4 + 1, -3 + 2) = (-3. -1)
Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)Step (c);
To get the next point, the 2·x² pattern is applied with x = 2, to the vertex to get; (-4 + 2, -3 + (2×2²)) = (-2, 5)
Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)Step (d);
A third point on the graph relative to the vertex is obtained again by applying the 2·x² pattern again to the vertex with x = 3, to get;
(-4 + 3, -3 + (2 × 3²)) = (-1, 15)
Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)Step (e);
The axis of symmetry can be drawn with a vertical line passing through the vertex, which is the line, x = -4
The line x = -4 can be drawn on the graph next
Draw the axis of symmetry x = -4Step (f);
The points obtained relative to the vertex (-3, -1), (-2, 5), (-1, 15) can reflected about the axis of symmetry x = -4, to get;
(-3, -1) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-5, -1)
(-2, 5) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-7, 5)
(-1, 15) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-7, 15)
Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)Step (g);
The parabola that is U shaped can be drawn from the points plotted in the steps above.
Draw a U shaped parabolaLearn more about drawing the graph of a quadratic function here:
https://brainly.com/question/6353430
Please help me with my math homework what is the answer!!!
Answers
Answer:
Step-by-step explanation:
The letters are easy enough.
y^3 determines that 3 ys are needed. y^2 is taken in by the cubed.
x^4 determines that 4 xs are needed. x^3 is part of x^4 and you don't need any more xs
12 and 42 are the parts that will cause the problem. Factor them both into prime factors
12: 2 * 2 * 3
42: 2 * 3 * 7
You need two 2s.
You need one 3
You need one 7
LCD = 2 *2*3 * 7 = 84
A car travels at an average rate of speed of 60 miles per hour for 72 hours. How many miles does
this car travel?
Answers
Answer:
4320 miles
Step-by-step explanation:
distance= speed× time
60 ×72= 4320
The sum and difference of two positive numbers are 15 and 5 respectively. Find the numbers.
Answers
[tex]x+ y =15~~...(i)\\\\x-y = 5~~...(ii)\\\\\text{(i) +(ii):}\\\\x+y+x-y = 15+5\\\\\implies 2x = 20\\\\\implies x = \dfrac{20} 2 = 10\\\\\text{(i)-(ii):}\\\\x+y -x +y = 15 -5\\\\\implies 2y = 10\\\\\implies y=\dfrac{10}2 = 5\\\\\text{Hence the numbers are 10 and 5}[/tex]
At the beginning of the month you have $1500 in your bank account. Each time you visit the ATM you take $60 out. What is the rate at which your balance is changing each time you visit the ATM?
Group of answer choices
$3
-$60
$60
-$63
-$1500
-$3
Answers
f (x) = 3x - 2 - g (x) = 2x + 1
Answers
Answer:
Step-by-step explanation:
The answer is easy it’s 24
HELP PLEASE!!!!!!!!!!!!
Answers
Pablo has $5,483 in a savings account. The interest rate is 5%, compounded annually.
To the nearest cent, how much will he have in 3 years?
(compound interest formu)
Answers
Answer:
$6347.26Step-by-step explanation:
Given:
Initial amount P = 5483Interest rate r = 5% or 0.05Compound number n = 1Time t = 3 yearsFind the total amount in 3 years:
[tex]A = P(1+r/n)^{nt}[/tex][tex]A = 5483*(1+0.05/1)^{1*3}=5483*(1.05)^3 = 6347.26[/tex]Here we've been given,
Principal amount (p) = $5843 Compound number (n) = 1 Rate of Interest (r) = 5% = 5 × 1/100 = 0.05 Time (t) = 3 years A = ?The standard formula for Compound interest (C.P) is given by,
[tex]:\implies\tt{A = p( { \frac{1 + r}{n} )}^{n \times t} } \\ \\ \\ :\implies\tt{A = 5483( { \frac{1 + 0.05}{1}) }^{1 \times 3} } \\ \\ \\ :\implies\tt{A = 5483 \times {1.05}^{3} } \\ \\ \\ :\implies\tt{A = 6347.26}[/tex]
Please answer with an explanation (polynomials)
Answers
Answer:
[tex]-8p^2+10p-3[/tex]
Step-by-step explanation:
[tex](-1+2p)(3-4p)[/tex]
Distribute
[tex]-1(3-4p)+2p(3-4p)[/tex]
[tex]-3+4p+6p-8p^2[/tex]
Then you will organize it into standard form and combine the like terms
[tex]-8p^2+6p+4p-3[/tex]
[tex]-8p^2+10p-3[/tex]
Hope this helps!
what are some expressions that are equivalent to
–
2(5n).
Answers
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\large\text{Gu\textbf{id}\textsf{e}}\bf\downarrow[/tex]
[tex]\large\textbf{2 negatives = positive}\\\large\textbf{2 positives = positive}\\\large\textbf{1 negative \& 1 positive = negative}\\\large\textbf{1 positive \& 1 negative = negative}\\\\\large\text{Negatives are BELOW 0}\\\large\text{Positives are ABOVE 0}\\\\\large\textsf{Negatives are on the LEFT side of zero.}\\\large\textsf{Positives are on the RIGHT side of zero.}[/tex]
[tex]\huge\textsf{-2(5n) \boxed{\rightarrow} \bf -10n}\\\\\\\\\huge\boxed{\rightarrow\text{-2n + (-2n) + (-2n) + (-2n) + (-2n)}}\\\huge\boxed{\rightarrow \text{\bf -2n - 2n - 2n - 2n - 2n}}\\\huge\boxed{\rightarrow{\text{-4n - 2n - 2n - 2n}}}\\\huge\boxed{\rightarrow \text{-6n - 2n - 2n}}\\\huge\boxed{\rightarrow \text{\bf -8n - 2n}}\\\huge\boxed{\rightarrow \boxed{\text{ -10n}}}[/tex]
[tex]\huge\text{\bf -5(2n)}\\\huge\boxed{\rightarrow \text{-10n}}[/tex]
[tex]\huge\boxed{\text{\bf Therefore, your answers \underline{\underline{could}} be: }}\\\huge\boxed{\bullet \textsf{ -2n - 2n - 2n - 2n -2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -8n - 2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -5(2n)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Trey will be splitting 2 3/4 pies with himself and 5 friends. how much pie will each person get?
Answers
hope this helps!
Answer: 11/24
Step-by-step explanation:I turned 2 and 3/4 into an improper fraction which got me 11/4.
There are 5 friends and him so that's 6 people.
So we can't do 11/4 divided by 6 so we must put 6 over 1.
So 11/4 divided by 6/1
Then we do "Keep Change Flip"
We keep 11/4
We change the division sign to multiplication
Then we flip 6/1 to 1/6
Then the problem is re wrote as:
11/4 times 1/6
And that equals 11/24 as your answer
So each person gets 11/24 of the pies.
Simplify 7 1/3t−(10 2/3t−6) pls
Answers
Answer:
[tex]-\frac{10t}{3}+6[/tex]
Step-by-step explanation:
[tex]7 \frac{1}{3}t-(10 \frac{2}{3} t-6)[/tex]
Convert [tex]7\frac{1}{3}[/tex] to a mixed number
[tex]7\frac{1}{3}=\frac{7\cdot 3+1}{3}[/tex]
[tex]=\frac{22}{3}[/tex]
[tex]\bold{\frac{22}{3}t-\left(10\frac{2}{3}t-6\right)}[/tex]
Convert [tex]10\frac{2}{3}[/tex] into a mixed number
[tex]10\frac{2}{3}=\frac{10\cdot 3+2}{3}[/tex]
[tex]=\frac{32}{3}[/tex]
[tex]\bold{\frac{22}{3}t-\left(\frac{32}{3}t-6\right)}[/tex]
[tex]=\frac{22t}{3}-\frac{32t}{3}+6[/tex]
[tex]\bold{=\frac{-10t}{3}+6}[/tex]
Terms
Follow the PEMDAS order of operation:
P = ParenthesisE = ExponentsM = MultiplicationD = DivisionA = AdditionS = SubtractionYou do these steps in the order for which the equation comes. For example, start with the exponents if there are not any parentheses.
1. Which of the following is equivalent to x5/2?
1
(1)
5x
2
(3) Vr
2x
(2)
(4) Vx?
Answers
Given that the expression in the question is [tex]\displaystyle x^{\frac{5}{2} }[/tex], the equivalent expression
can be found using the rules of indices.
[tex]\displaystyle \underline{x^{\frac{5}{2} } \ is \ equivalent \ to \ x^2 \cdot\sqrt{x}}[/tex]Reasons:
The given expression is [tex]\displaystyle x^{\frac{5}{2} }[/tex]
Required:
To find the equivalent expression
Solution:
According to the rules of indices, we have;
[tex]a^{n + m} = a^n \times a^m[/tex]
[tex]a^{\frac{n}{m} } = \sqrt[m]{a^n}[/tex]
Therefore, the above expression can be expanded as follows;
[tex]\displaystyle x^{\frac{5}{2} } = x ^{2.5} = \mathbf{x^{2 + 0.5}}[/tex]
[tex]\displaystyle x^{2 + 0.5} =\mathbf{ x^2 \times x^{0.5}}[/tex]
Which gives;
[tex]\displaystyle x^2 \times x^{0.5} = \mathbf{x^2 \times \sqrt{x}}[/tex]
Therefore;
[tex]\displaystyle x^{\frac{5}{2} } \equiv x^2 \cdot\sqrt{x}[/tex], which is the form [tex]a^{\frac{n}{m} } = \sqrt[m]{a^n}[/tex]
[tex]\underline{An \ expression \ \mathbf{equivalent} \ to \ x^\frac{5}{2} \ is \ x^2 \cdot \sqrt{x}}[/tex]
Learn more about the rules of indices here:
https://brainly.com/question/8959311
please help me asap
ty..
Answers
Answer:
Y = 10x + 20
Step-by-step explanation:
sorry if im wrong
Answer:
y = 2x - 4
Step-by-step explanation:
10x - 5y = 20
Subtract 10x both sides
-5y = 20 + (-10x)
Divide by -5
y = -4 + 2x
y = 2x + (-4)
what is 8 1/5 as a improper fraction
Answers
Answer:
41/5
Step-by-step explanation:
So the answer is that 8 1/5 as a decimal is 8.2.
We convert it to an improper fraction which, in this case, is 41/5 and then we divide the new numerator (41) by the denominator to get our answer.
Find the volume of the sphere. Use 3.14 for pi please help..
Answers
Answer and Explanation: The volume of the sphere is 1.44×10^6 cubic inches(to be specific, 1,436,755 cubic inches). The explanation, which is the formula for the volume of a sphere, is in the image.
Answer:
V≈1.44×106
Step-by-step explanation:
hope this helps
I'm bad at math helpppppp
Answers
Answer:
2x + y = 18
y = 4x - 12
x = 5, y = 8
Step-by-step explanation:
x = 1st number
y = 2nd number
We can use the substitution method as we know what 'y' equals; that value will get plugged in for 'y' in the first equation as follows:
2x + 4x - 12 = 18
6x - 12 = 18
6x = 30
x = 5
y = 4(5) - 12 which is 20-12 or 8
y = 8
the area of a triangle is 162 square meters. the height is 18 meters. what is the base
Answers
Answer:
Triangle Area = (1/2) * base * height
base = 2 * Area / height
base = (2 * 162) / 18
base = 324 / 18
base = 18 meters
Step-by-step explanation:
what is the meaning of the word treacherous mean in the sentence below
QUICK plzzzz
i-ready lvl F
Answers
Answer: Guilty of or involving betrayal or deception.
Step-by-step explanation:
Write the following numbers in order from least to greatest: -5.6, 7.95, 2.06, 0, -6.89
Please help :)
I think I know it but can someone help me double check
Answers
Answer:
-6.89, -5.6, 0, 2.06, 7.95
Step-by-step explanation:
Hope this helps!
-6.89.-5.6,0,2.06,7.95
Negatives are always lesser values than positives.
A train accelerates at an average rate of 0.33 meter per second squared, and the
train starts from a complete stop. Find how long it will take the train to reach its
maximum velocity of 48 meters per second.
Pls someone help ASAP
Answers
Answer:
I don't know
Step-by-step explanation:
please mark me as the brainlist
I'm not sure if this s corrct. Can you guys check it for me?
Answers
Answer:
YUP!
Step-by-step explanation:
Let's take the 60 degrees angle first. 180-60=120
3x+x=4x
120/4=30
So you were right!
:))
HELP PLEASEEEEEE ill give u 30 point plays brainly u dont even have to show ur work
Answers
Answer:
1) 32/7
2) 7/5
3) 13/4
4) 32/15
5) 19/2
6) 57/14
Step-by-step explanation:
Use a calculator and/or multiple the coefficients with the value of the denominator then add it to the numerator and multiply.
If (6^2]^p = 6^10, what is the value of p?
A.) 2
B.) 3
C.) 4
D.) 5
Answers
Now you have like bases, so you can set the powers equal to each other. So now, 2p=10. Now p=5
Adam works for an agency.
His normal hourly rate is £8.32
The agency asks Adam to work 6 hours for a new company.
Adam will be paid time and a third of his normal hourly rate.
How much will Adam get paid in total when working for the new company
Answers
Adam normally earns 8.32 an hour. To get your answer, please follow my steps.
1. 8.32 * 6 (how much he has to work for).
Despite the two decimal places, we can ignore them and complete the process normally.
8 3 2
6
——————-
4 9 9 2
2. Add your decimals in the correct places aka 49.92!
3. Multiply 49.92 * 1/3 (a third) and you will get your answer: 16.64.
Hope this helped!
Adam receives 13.762 euros
What is division?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
Given
Adam normally earns 8.32 an hour.
1. 832 * 6 = 10.992 for 6 hours
Adam will be payed = 8.32 *1/3 = 2.77
Total payment = 10.992 + 2.77 = 13.762
To learn more about division refer to:
https://brainly.com/question/12085148
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a swimming pool is drained at a rate of 50 gallons per hour. How many pints per minute is this?
Answers
Answer:
8
Step-by-step explanation: