Answers
Step-by-step explanation:
Let simplify the identity
[tex] \frac{ \csc {}^{2} (x) - \sec {}^{2} (x) }{ \csc {}^{2} (x) + \sec {}^{2} (x) } [/tex]
[tex] \frac{ \frac{1}{ \sin {}^{2} (x) } - \frac{1}{ \cos {}^{2} (x) } }{ \frac{1}{ \sin {}^{2} (x) } + \frac{1}{ \cos {}^{2} (x) } } [/tex]
Combine Like Fractions
[tex] \frac{ \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } }{ \frac{ \sin {}^{2} (x) + \cos {}^{2} (x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } } [/tex]
Multiply by reciprocals.
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } \times \frac{ \cos {}^{2} (x) \sin {}^{2} (x) }{ \sin {}^{2} (x) + \cos {}^{2} (x) } [/tex]
Pythagorean Identity
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{1} [/tex]
Double Angle Identity
[tex] \frac{ \cos(2x) }{1} [/tex]
[tex] \cos(2x) [/tex]
Now, we need to find cos 2x. Given that we have tan x.
Note that
[tex] \cos {}^{2} (x) - \sin {}^{2} (x) = \cos(2x) [/tex]
So let find cos x and tan x.
We know that
[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]
We know that
[tex] \tan(x) = \frac{o}{a} [/tex]
[tex] \sin(x) = \frac{o}{h} [/tex]
[tex] \cos(x) = \frac{a}{h} [/tex]
So naturally,
[tex] \tan(x) = \frac{ \frac{o}{h} }{ \frac{a}{h} } = \frac{o}{a} [/tex]
So we need to find the hypotenuse,
remember Pythagorean theorem.
[tex]h {}^{2} = {o}^{2} + {a}^{2} [/tex]
Here o is 1
h is root of 5.
So
[tex] {h}^{2} = {1}^{2} + ( \sqrt{5} ) {}^{2} [/tex]
[tex] {h}^{2} = 1 + 5[/tex]
[tex] {h}^{2} = 6[/tex]
[tex]h = \sqrt{6} [/tex]
Now, we know h, let plug in to find sin x and cos x.
[tex] \sin(x) = \frac{1}{ \sqrt{6} } [/tex]
[tex] \cos(x) = \frac{ \sqrt{5} }{ \sqrt{6} } [/tex]
Let's find these values squared
[tex] \sin {}^{2} (x) = \frac{1}{6} [/tex]
[tex] \cos {}^{2} (x) = \frac{5}{6} [/tex]
Finally, use the trig identity
[tex] \frac{5}{6} - \frac{1}{6} = \frac{2}{3} [/tex]
So part I.= 2/3
ii. Use the definition of sine and cosine and Pythagorean theorem
Let sin x= o/h
Let cos x= a/h.
So
sin x squared is
[tex] \sin {}^{2} (x) = \frac{o {}^{2} }{h {}^{2} } [/tex]
[tex] \cos {}^{2} (x) = \frac{ {a}^{2} }{h {}^{2} } [/tex]
By definition,
[tex] \frac{ {o}^{2} }{ {h}^{2} } + \frac{ {a}^{2} }{h {}^{2} } = 1[/tex]
[tex] \frac{ {o}^{2} + a {}^{2} }{h {}^{2} } = 1[/tex]
Remember that
[tex]{ {o}^{2} + {a}^{2} } = {h}^{2} [/tex]
So
[tex] \frac{ {h}^{2} }{h {}^{2} } = 1[/tex]
[tex]1 = 1[/tex]
Related Questions
Someone help asap pls!! Ill mark you brainliest
Answers
Answer:
d.
Step-by-step explanation:
The parent graph is shifted right 2 and down 2
What are the domain and range of f(x) = 2x - 41?
O domain: x < 2; range: (-00,00)
O domain: (-00,00); range: f(x) > 0
O domain: (-0,00); range: f(x) ≤0
O domain: x ≥ 2; range: (-00,00)
Answers
Answer:
X intercepts (41/2, 0), Y intercepts (0, -41)
Step-by-step explanation:
I hope this helps, if it doesn't then just message me, and ill be more than happy to help :)
The domain and range of function f(x) = 2x - 41 is domain (-∞,∞) and range is (0,∞).
What is a function?A relation is a function if it has only One y-value for each x-value.
The domain of a function is the set of values that we are allowed to plug into our function.
This set is the x values in a function such as f(x).
The range of a function is the set of values that the function assumes.
The function f(x) = 2x - 41 is a linear function.
As a linear function, the domain is all real numbers, and the range is also all real numbers.
So the domain is (-∞,∞) and range is (0,∞)
Hence, the domain and range of function f(x) = 2x - 41 is domain (-∞,∞) and range is (0,∞).
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Identify the type of function represented by f(x) = 3(1.5)*.
OA. Exponential growth
B. Linear
C. Exponential decay
D. Quadratic
Answers
Answer:
A. Exponential growth function
The average rate of the first part of Yi’s walk on a park loop was 4 miles per hour. She then met up with a friend and the two walked the rest of the way at an average rate of 5 miles per hour. The entire 3-mile walk took Yi 42 minutes (0.7 hour). Which equation can be used to solve for x, the time in hours that Yi spent walking before meeting her friend?
A table showing Rate in mile per hour, Time in hours, and Distance in miles. The first row shows Part 1 and has 4, x, and 4 x. The second row shows Part 2, and has, 5, 0.7 minus x, and 5 left-parenthesis 0.7 minus x right-parenthesis.
x = 0.7 – x
x + (0.7 – x) = 1
4x + 5(0.7 – x) = 1
4x + 5(0.7 – x) = 3
Answers
The equation can be used to solve for x, the time in hours that Yi spent walking before meeting her friend would be D; 4x + 5(0.7 – x) = 3.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Total distance covered = 3 miles.
The first part walked at the rate of 4 miles per hour.
Let us consider x hours was walked in the first part.
Total distance covered in x hours at the rate of 4 miles per hour will be 4x.
Now, the Second walk rate with meeting with friend will be 5 miles per hour.
The Total time is taken = 0.7 hours.
Therefore, time is taken in the second walk only = (0.7 - x) hours.
Distance covered in second walk = 5 (0.7 - x).
Total distance covered = distance covered in the first part + distance covered in the second part.
4x + 5 (0.7 - x) = 3 miles.
Hence, correct option is D; 4x + 5(0.7 – x) = 3.
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Answer:
its d
Step-by-step explanation:
The water was pumped out of a backyard pond what is the domain of the graph that 70 time 6
Answers
The domain of the given graph is the set of all real numbers from 0 to 8.
How to find the domain of a Graph?The graph showing the water depth on the y-axis in inches against the time in minutes on the x-axis has been attached.
Now, domain is the set of all possible input values and from the graph we see that the set of all possible input values are between 0 and 8.
Thus, we can conclude that the domain of the given graph is the set of all real numbers from 0 to 8.
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Riley has 51/4 cups of chocolate chips, she needs ¾cup of chocolate chips to make one batch of cookies. how many batches of chocolate-chip cookies can Riley make
Answers
Answer:
17 batches
Step-by-step explanation:
51/4 ÷ 3/4 = 51/4 x 4/3
=17
The amount of money that kailyn earns varies directly with the number of hours she works. if she works for 15 hours and makes 146.25, how much will she make in 40 hours.
Answers
Answer:
$390
Step-by-step explanation:
The wage rate for Kailyn is ($146.25/15 hours) = $9.75/hour
40 hours would result in:
(40 hours)*($9.75/hour) = $390
please I need the answer :-)
Answers
Answer:
Step-by-step explanation:
What percent of patients with type-B blood are male? Round your answer to the nearest tenth of a percent.
Answers
Answer:
54%
Step-by-step explanation:
To find the probability for a male patient to have B blood, find the number of male patients who do have B blood and divide it by the number of patients with type B.
The number of male and B blood is 99.
The number of patients with B blood is 183.
The probability is 99/183 = 0.54.
The percent is found by multiplying by 100.
0.54*100 = 54%
Identify the geometric mean of 9 and 9/4.
Answers
The geometric mean of 9 and 9/4 will be 9/2 or 4 1/2.
How to calculate the mean?It should be noted that in order to find the geometric mean of the numbers given, give to find the square root and then multiply.
This will be:
= ✓9 × ✓9/4
= 3 × 3/2
= 9/2 = 4 1/2
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Find the value of $x$ that satisfies $\frac{1}{3x-1} = \frac{2}{x+1}$. Can someone please explain this in detail?
Answers
The value of x = 3/5 or 0.6 will satisfy the equation given.
What is an Equation ?An equation is a mathematical statement which is formed when two expressions are equated by an equal sign.
It is given that
[tex]\rm \dfrac{1}{3x-1} = \dfrac{2}{x+1}\\[/tex]
It has to be solved and the value of x has to be determined
(x+1) = 2 (3x-1)
x +1 = 6x -2
5x = 3
x = 3/5
Therefore the value of x = 3/5 or 0.6 will satisfy the equation given.
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what is the square root of 10,000,000
Answers
Answer:
1000√10or 3162.2776601683795
Step-by-step explanation:
what is the square root of 10,000,000?
√10000000
= √2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5
= √26 x 2 x 56 x 5
= 1000√10
or 3162.2776601683795
easy problem for you guys to solve
Answers
In the ΔIJH, the value of the cosec (I) is [tex]1\frac{9}{56}[/tex].
Given ΔIJH the length of the hypotenuse is 65, the length of the base is 33, and the length of the opposite side is 56.
We have to find the value of the cosec (I).
A function of an arc or angle that is most easily represented in terms of the ratios of pairs of sides of a right-angled triangle, such as the sine, cosine, tangent, cotangent, secant, or cosecant.
We know cosec (I) = hypotenuse / opposite side
Substitute the values
cosec (I) = 65/56
= [tex]1\frac{9}{56}[/tex]
Hence the value of cosec (I) is [tex]1\frac{9}{56}[/tex].
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What is the mean of the data
Answers
Answer:
hey diddle the medians the middle
you add and then divide for the mean
the mode is the one you see the most and the range is the difference between.
Hope this helps you with your question
Step-by-step explanation:
I need help with dis math problem (img included)
Answers
Answer:
4500 sec
Step-by-step explanation:
1hr 15min= 75 min
75 x 60=4500
The price of a pack of kitchen rolls is reduced by 1/6
The new price is £1.20
Work out the original price.
Answers
Answer: 1.44
Step-by-step explanation:
(original price) - (1/6 of the original price) = 1.20
If you let x = original price, then the equation is:
x - 1/6 x = 1.20
5/6 x = 1.20
x = 1.44
the original price is £1.44.
Credits to the person who also answered :)
I hope this helps!
Answer:
£1.44
Step-by-step explanation:
Since the original price was reduced by 1/6, that means the new price is 5/6 of the original price.
Let x = original price.
Write an equation and solve it.
5/6 x = £1.20
x = £1.20 × 6/5
x = £1.44
Linda purchased a birthday gift from Bed Bath and Beyond for her mother. After applying the
coupon below Linda received a $12.25 discount off her purchase. What was the price of the
gift before and after the discount?
PLS HELP SOLVE !!!
Answers
Answer:
Before discount = $61.25
After discount = $49.00
Step-by-step explanation:
Given information:
Discount = $12.25Coupon = 20%The price of the gift before the discount is 100%.
If the $12.25 discount was 20% of the purchase price, then:
⇒ original price (before discount) = (12.25 / 20) × 100 = $61.25
To find the price after the discount, simply subtract the discount from the found original price:
⇒ $61.25 - $12.25 = $49.00
Conclusion
Before discount price = $61.25After discount price = $49.00Determine the measure of each indicated angle.
Answers
Answer:
∠ABC = 52°
∠BCA = 48°
∠CAB = 80°
Step-by-step explanation:
Angle sum property of triangle: Sum of all the angles of a triangle is 180.
13x² + 12x² + 20x² = 180
Combine like terms,
45x² = 180
x² = 180 ÷ 45
x² = 4
x = √4
x = ± 2
x = 2 ; -2
∠ABC = 13x² = 13*4 = 52°
∠BCA = 12x² = 12 *4 = 48°
∠CAB = 20x² = 20 *4 = 80°
The value of x is +2 and -2 and the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
Given that:-
∠ABC = 13x² ∠ACB = 12x² and ∠CAB = 20x²
The angles will be calculated as follows:-
13x² + 12x² + 20x² = 180
45x² = 180
x² = 4
x = ±2
The angles will be:-
∠ABC = 13x² = 13 x ( 2² ) = 52
∠ACB = 12x² = 12 ( 2² ) = 48
∠CAB = 20x² = 20 ( 2² ) = 80
Therefore value of x is +2 and -2 the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.
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If the size of a storage box is 50 cm by 10 cm by 20 cm. What is the volume of the box?
Answers
Answer:
l×b×h
50×10×20
10000cm^3
Step-by-step explanation:
please mark me as brainlest
Answer:
10000 cm³
Step-by-step explanation:
Volume of rectangular box:
To find the volume of box, multiply the length, width and height of the box and its unit is cubic units
[tex]\sf \boxed{\bf Volume \ of rectangular \ box = l *w*h}[/tex]
= 50 * 1 0 * 20
= 10000 cm³
28. Think About a Plan Draw AABC. Construct another
triangle so that the three sides of AABC are the
midsegments of the new triangle.
. Can you visualize or sketch the final figure?
• Which segments in your final construction will be
parallel?
Answers
DE is the segment parallel to the side BC. The triangles have sides AB, BC, and CA. D, E, and F are the three sides' midpoints.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
The sides of the triangles are AB, BC, and CA.The mid points of the three sides are D, E, and F.
The new triangle sides are DE, EF, and FD. We can visualize the triangle as DEF given in the attachment.
Hence, DE is the segment parallel to side B.
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what is equivalent to y= a (x-h) +k
Answers
Answer:
See below
Step-by-step explanation:
I think you meant
y= a (x-h)^2 +k
this is the vertex form of a parabola with vertex (h,k)
The function h(x) is a transformation of the square root parent function,
f(x)=√x. What function is h(x)?
-5
5
-5-
h(x)
f(x)
K
I
5
Answers
Answer: [tex]h(x)=\sqrt{x+4}[/tex]
Step-by-step explanation:
The graph of h(x) is the graph of f(x) shifted 4 units left.
Complete the equations
Answers
Answer:
[tex]\boxed{\bf f(x)=4\cdot \left(\cfrac{7}{4}\right)^x}[/tex]
Step-by-step explanation:
In exponential form, a* b^x,
Where, "a" is value of the function when x=0 and "b" is the constant ratio of f(x) for consecutive for integer values of x.
Y-intercept : (0, 4) so, a = 4.
The graph also passes through (1,7), because 0 and 1 are consecutive integer x-values.
[tex]\bf b=\cfrac{7}{4}[/tex]
So therefore, the equation for f(x) is :-
[tex]\bf f(x)=4\cdot \left(\cfrac{7}{4}\right)^x[/tex]
_______________________In a grop of 25 student 6 study art & biology 10 study biology but not art 3 study neither subject given that a randomly selected study art what is the probability the student study art & biology
Answers
½ 0r 50% is the probability that the student studies Art and biology.
What is Probability?Probability is a branch of mathematics that deals with the occurrence of a random event . i.e. Probability means possibility.
According to the question,
Total number of students in the group;
n = 25 students
No. of students that study both art and biology;
n(P u Q) = 6
No. of students that study biology but not art;
n(Q u P') = 10
No. of students that study none of the 3 subjects;
n(P' u Q') = 3
So,
No. of students that study only arts is;
n(P n Q') = 25 - 6 - 10 - 3 = 6
Since, n(P u Q) = 6
Therefore by using formula;
n(P) = n(P u Q) + n(P n Q')
n(P) = 6 + 6
n(P) = 12
Hence,
Probability of the students who studies Art and biology is;
P(P n Q) = [tex]\frac{6}{12}[/tex]
P(P n Q) = ½ i.e. 50%
The probability the student study art & biology ½ i.e. 50%.
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share 518 in ratio 2:5
please answer fast with the steps
Answers
Answer:
148:370
Step-by-step explanation:
2+5=7 parts
518÷7=74
1 part =74
2×74=148
5×74=370
helpppp! i need to find general form and standard form, pleaseee HELP MEEE!)!#*(_
Answers
The general form and the standard form of the graph equation are 13x - 8y = 17 and 13x - 8y - 17 = 0 respectively
How to determine the equations?From the graph, we have the following points
(x,y) = (5,6) and (-3,-7)
Start by calculating the slope:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
This gives
[tex]m = \frac{-7 - 6}{-3 - 5}[/tex]
Evaluate the differences
[tex]m = \frac{-13}{-8}[/tex]
Evaluate the quotient
[tex]m = \frac{13}{8}[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
This gives
[tex]y = \frac{13}8(x - 5) + 6[/tex]
Multiply through by 8
8y = 13(x - 5) + 48
Open the bracket
8y = 13x - 65 + 48
Evaluate the like terms
8y = 13x - 17
Subtract 13x from both sides
-13x + 8y = -17
Multiply through by -1
13x - 8y = 17 ---- this represents the standard form
Subtract 17 from both sides
13x - 8y - 17 = 0 --- this represents the general form
Hence, the general form and the standard form of the graph equation are 13x - 8y = 17 and 13x - 8y - 17 = 0 respectively
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is 1 − 3x2 = -y linear
Answers
No. Because the x is raised to the 2nd power the equation is not linear.
Question 13 * A farmer can plant 45 kg of peanuts on 4,000 square metres of land. Which of the following represents the number of peanuts (x) he could plant on 8,500 square metres of land? C. 45 4000 8500 45 8500 1 4000 45 1 8500 4000 Question 13 * A farmer can plant 45 kg of peanuts on 4,000 square metres of land . Which of the following represents the number of peanuts ( x ) he could plant on 8,500 square metres of land ? C. 45 4000 8500 45 8500 1 4000 45 1 8500 4000
Answers
Explanation: your mom told me lastnight
The number of peanuts ( x ) he could plant on 8,500 square meters of land = 95.6 kg
What is unitary method?"It is a method of finding the value of a single unit, and based on that value we can find the required value."
For given question,
A farmer can plant 45 kg of peanuts on 4,000 square meters of land.
Using unitary method,
[tex]\frac{4000}{45}\\\\=88.8888 \\\\\approx 88.89[/tex]
This means, a farmer can plant 1 kg of peanuts on 88.89 square meters of land.
We need to find the number of peanuts ( x ) he could plant on 8,500 square meters of land.
Here, 1 kg = 88.89 square meters
x kg = 8500 square meters
[tex]\Rightarrow x=\frac{8500}{88.89}\\\\ \Rightarrow x = 95.6~kg[/tex]
Therefore, the number of peanuts ( x ) he could plant on 8,500 square meters of land = 95.6 kg
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The line y = 2x intersects the line y = x + 6 at the point A. Find the equation of the line that passes through A and has gradient 3
Answers
Answer:
Step-by-step explanation:
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
Does the point (1, StartRoot 7 EndRoot) lie on the circle shown?
Explain.
Yes, the distance from (–2, 4) to (1, ) is 4 units.
Yes, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units.
No, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is not 4 units.
No, the distance from (–2, 4) to (1, StartRoot 7 EndRoot) is not 4 units.
Answers
Yes, the distance from (-2, 0) to (1, √7) is 4 units.
How to Interpret the Equation of a Circle?
We know that the general form of equation of the circle is given by;
(x - h)² + (y - k)² = r²
where;
(h, k) is the coordinate of the center
r is the radius
From the attached image, the radius is equal to the distance between the center and the point (-2,4). Thus, r = 4 and so we have;
(x + 2)² + (y - 0)² = 4²
(x + 2)² + y² = 16
If the distance between the center and the point is equal to the radius of the circle , then the point lies on the circle and the formula to calculate the distance between two points is;
d = √[(y₂ - y₁)² + (x₂ - x₁)²]
At A(-2, 0) and B(1, √7), we have;
d = √[(√7 - 0)² + (1 - (-2))²]
d = 4 units
Therefore we can conclude that the distance from (-2, 0) to (1, √7) is 4 units.
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