Answer: To prove the given identity:
(cosec A - sec A)(cot A - tan A) = (cosec A + sec A)(sec A cosec A - 2)
We will start by simplifying both sides of the equation.
Left-hand side (LHS):
(cosec A - sec A)(cot A - tan A)
Using trigonometric identities, we can rewrite cosec A, sec A, cot A, and tan A in terms of sin A and cos A:
cosec A = 1/sin Asec A = 1/cos Acot A = cos A / sin Atan A = sin A / cos A
Substituting these values into the LHS:
(cosec A - sec A)(cot A - tan A)
= (1/sin A - 1/cos A)(cos A / sin A - sin A / cos A)
= ((cos A - sin A) / (sin A * cos A)) * ((cos A^2 - sin A^2) / (sin A * cos A))
= (cos^2 A - sin^2 A) / (sin^2 A * cos^2 A) [Using the difference of squares identity: a^2 - b^2 = (a + b)(a - b)]
= ((cos A + sin A)(cos A - sin A)) / (sin^2 A * cos^2 A)
Right-hand side (RHS):
(cosec A + sec A)(sec A cosec A - 2)
Again, using the same trigonometric identities:
(cosec A + sec A)(sec A cosec A - 2)= (1/sin A + 1/cos A)((1/cos A)(1/sin A) - 2)= ((cos A + sin A) / (sin A * cos A)) * (1 / (sin A * cos A) - 2)= (cos A + sin A) / (sin^2 A * cos^2 A) * (1 - 2sin^2 A * cos^2 A)
Now, we need to show that the LHS is equal to the RHS:
((cos A + sin A)(cos A - sin A)) / (sin^2 A * cos^2 A) = (cos A + sin A) / (sin^2 A * cos^2 A) * (1 - 2sin^2 A * cos^2 A)
To prove this, we can cancel out the common factors in the numerator and denominator of the LHS:
(cos A - sin A) = 1 - 2sin^2 A * cos^2 A
Next, we'll simplify both sides individually:
1 - 2sin^2 A * cos^2 A= 1 - 2(sin A * cos A)^2= 1 - 2(sin A * cos A)(sin A * cos A)= 1 - 2sin A * cos A * sin A * cos A= 1 - 2sin^2 A * cos^2 A
Therefore, the LHS is equal to the RHS, and the given identity has been proven.
Help me please!!!!!!!!
Answer:
The ratios are not equal, so this is not a dilation.
Step-by-step explanation:
4/3 is the first ratio
3/4 is the second ratio
Since these ratios are not equal there is not a dilation.
Select the correct triangle. Which triangle represents a reflection of triangle Aacross line m?
Chad used the table to show the ratios of the different types of sports game cards that he owns. For every 2 offense cards, he owns 4 defense cards. Which graph represents the proportional relationship between his defense and offense cards?
Chad’s Sports Cards
Card Type
Kicking Team
Offense
Special Teams
Defense
Quantity
1
2
3
4
The equation that shows the proportional relationship between his defense and offense cards is y = 2x
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the defense cards and x represent the offense cards.
For every 2 offense cards, he owns 4 defense cards. Hence:
4 = 2m
m = 2
y = 2x
The equation that shows the proportional relationship between his defense and offense cards is y = 2x
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A party platter contains 38 cupcakes: 13 chocolate, 11 yellow, and 14 lemon. You randomly select one cupcake, eat it, then randomly select another cupcake. Find the probability of selecting from the platter a chocolate cupcake and then a yellow cupcake.
The probability of selecting from the platter a chocolate cupcake and then a yellow cupcake is 0.10.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of selecting a chocolate cupcake and then a yellow cupcake = (number of chocolate cupcake / total number of cupcakes) x (number of yellow cupcakes / total number of cupcakes - 1)
(13 / 38) x (11 / 37) = 0.10
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Find the solution(s) to the system of equations represented in the graph. (5 points)
Answer:
(0, -2) and (2, 0)
Step-by-step explanation:
The solution to a systems of equations is when the x and y values are equal for two equations. This can also been seen as when the two equations intersect. So by looking at the graph you see the line and the circle intersect at the point (2, 0) and (0, -2) which are going to be the two solutions to the systems of equations.
On average, an American hummingbird flaps its wings about 3,180 times per minute.
About how many times per second does it flap its wings?
Enter your answer in the box.
times
Answer:
53 times per second
Step-by-step explanation:
There are 60 seconds in 1 minute, so divide the 3180 flaps per minute into 60 equal parts.
3180 / 60 = 53
Which of the following lists is in order from smallest to largest? 5/8, 0.6, 6.2%, 2/3, 2/3, 5/8, 0.6, 6.2% 6.2%, 0.6, 5/8, 2/3, 0.6, 6.2%, 5/8, 2/3
Answer:
6.2%, 0.6, 5/8, 2/3
Step-by-step explanation:
For some reason, you have written the same numbers over and over. It looks like there are only really 4 numbers.
I changed each number into a decimal and then compared them.
6.2% to change a percent to a decimal, move the decimal 2 places to the left so 6.2% equals 0.062.
0.6 is already in decimal form
5/8 you divide 5 by 8. Put in your calculator 5 the division symbol and then 8 to get 0.625.
2/3 is 0.6 repeating or 0.66666 forever.
Now compare:
62% = 0.62
0.6
5/8 = 0.625
2/3 = 0.66666...
Which function below has the following domain and range?
Domain: {-9, - 5, 2, 6, 10}
Range: { -2, 0, 8}
O {(-9, 10), (-2,8)}
O ((-9, -2), ( – 5, 0), (2, 8), (6, 5), (10, 9))}
O ((-2,-5), (8, 10), (0, 6), (-2, -9), (0, 2)}
O {(2,0), (-5, -2), (10, 8), (6, 0), (-9, -2)}
{(2,0),(-5,-2),(10,8),(6,0),(-9,-2)} is the correct answer (D)
Answer:
(d) {(2, 0), (-5, -2), (10, 8), (6, 0), (-9, -2)}
Step-by-step explanation:
The domain is the list of x-values. The range is the list of y-values. You are looking for the set that matches the given lists.
ChoicesA.The list of x-values is {-9, -2}. The list is too short.
B.The list of x-values is {-9, -5, 2, 6, 10}. This matches the required domain.
The list of y-values is {-2, 0, 8, 5, 9}. The list is too long.
C.The list of x-values is {-2, 8, 0, -2, 0}. The list does not match the given domain list.
D.The list of x-values is {2, -5, 10, 6, -9}. This matches the given domain.
The list of y-values is {0, -2, 8, 0, -2}. This matches the given range.
The function of interest is ...
{(2, 0), (-5, -2), (10, 8), (6, 0), (-9, -2)}
the radius of the base is 4 inches and its height is 6 inches what is the surface area of the cylinder in terms of pi
1
10 ft
Cone 1
2.5 ft
8 ftl
2 ft
Cone 2
In 1996 an outbreak of a disease affected 10 people in a large community. By 1997, the number of those infected had grown to 40. Find an exponential growth function that fits the data.
Answer: The initial population is 18 and 1 year(t=1) later it is 38
Step-by-step explanation:
38 = 18 * e^(1*k), where k is the growth rate
e^(1*k) = 38/18
Take the natural log(ln) of both sides of the = k = ln(38/18) = 0.747
P(t) = 18 * e^(0.747*t), where P(t) is the population affected at time t(years since 1996)
Determine an approximate value for y if the coordinate (-0.5387 ,y) is on the unit circle
Answer:
y = 0.8425 or y = -0.8425
Step-by-step explanation:
All points in the Cartesian coordinate system have an x and y coordinate, defined by two perpendicular measurements.
If the point is on the unit circle, then the radius of the circle is defined to be 1 unit, and the corresponding right triangle follows the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
For a unit circle:
[tex]x^2+y^2=1^2[/tex]
Substituting the known value for x, and simplifying...
[tex](-0.5387)^2+y^2=(1)^2[/tex]
[tex]0.29019769+y^2=1[/tex]
Subtracting 0.29019769 from both sides to begin to isolate "y"...
[tex]y^2=1-0.29019769[/tex]
[tex]y^2=0.70980231[/tex]
Applying the square root property...
[tex]\sqrt{y^2}=\pm \sqrt{0.70980231}[/tex]
[tex]y=\pm 0.8424976171...[/tex]
So, (to 4 decimal places), the y coordinate could be either 0.8425 or -0.8425.
With only the given information, either result is a valid answer.
What is the midpoint of the line segment graphed below?
Answer:
(4, 7/2)
Step-by-step explanation:
midpoint = x values/2, y values/2
0.1in has 4 threads how many threads are in 1 inch?
Answer:
40
Step-by-step explanation:
Set up a proportion
Inch/ threads = inch to threads
.1/4 = 1/x Cross multiple
.1x = 4 Divide both sides by .1
x = 40
What is the slope of the line containing (-2, 5) and (4,-4)?
A. 2
OB.
mle
O C. - /3/20
D. -2
Answer:
-1.5
Step-by-step explanation:
To work out the gradient of the line, we use this equation:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Substituting in, we get:
[tex] \frac{5 - ( - 4)}{ - 2 - 4} [/tex]
Which simplifies to:
[tex] \frac{9}{ - 6} = \frac{3}{ - 2} = - \frac{3}{2} = - 1.5[/tex]
Induced pluripotent stem cells are cells from adults that have been reprogrammed to imitate embryonic stem cells. Why might induced pluripotent stem cells be a valuable tool in science and medicine?
Induced pluripotent stem cells can be a valuable tool in science and medicine because: A. induced pluripotent stem cells can become any cell type in the body, but are from adults, avoiding the controversies associated with embryonic stem cells.
What is a cell?A cell can be defined as the fundamental functional, structural and smallest unit of life, which is typically found in all living organisms.
In Science, all living organisms are broadly grouped into two (2) main categories according to cell type and these include the following;
Unicellular organismsMulticellular organismsBasically, the reason why induced pluripotent stem cells can be a valuable tool in science and medicine is simply because they can become any cell type within the body of a living organism, but are usually derived from adults that are avoiding the controversies associated with embryonic stem cells.
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Complete Question:
Induced pluripotent stem cells are cells from adults that have been reprogrammed to imitate embryonic stem cells. Why might induced pluripotent stem cells be a valuable tool in science and medicine?
A. Induced pluripotent stem cells can become any cell type in the body, but are from adults, avoiding the controversies associated with embryonic stem cells
B. Induced pluripotent stem cells are the only type of stem cell that's truly pluripotent.
C. Induced pluripotent stem cells may become any cell type in the body, but are fraught with ethical questions over their use.
D. Induced pluripotent stem cells are derived from adult cells and therefore may have DNA abnormalities, allowing scientists to understand the effects of sun exposure or toxins on DNA
Assume that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12. Compute the probability P(X < 105).
The probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.
When a random variable X is normally distributed, with the mean as μ, and standard deviation as σ, then the probability P(X < x) is calculated using the Z-score table, as the probability P(Z < z), where z is calculated using the formula, z = (x - μ)/σ.
In the question, we are asked to find the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12.
We calculate as follows:
P(X < 105)
= P(Z < (105-90)/12)
= P(Z < 1.25)
Now we check the z-score table for the value of z as 1.25.
On the left column we choose the value 1.2.
On the top row, we choose the value .05.
The intersection of these, gives us the value,
P(Z < 1.25) = 0.8944.
Thus, the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.
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the domain a function g(x) is x > 3, and the range is y> 1. What are the The domain of
domain and range of its
inverse function, g
(x)?
The domain of a function is the range of its inverse, and vice versa.
So, the domain is [tex]x > 1[/tex] and the range is [tex]y > 3[/tex].
What can you say about the y-values of the two functions f(x) = 3x² -3 and
g(x) = 2* - 3?
A. g(x) has the smallest possible y-value.
B. The minimum y-value of g(x) approaches -3.
C. f(x) and g(x) have equivalent minimum y-values.
D. f(x) has the smallest possible y-value.
The y-values of the two functions f(x) = 3x² -3 and g(x) = 2* - 3 has the minimum y-value of g(x) approaches -3 and f(x) contains the smallest possible y-value.
What is a function?It exists described as a special kind of relationship and they contain a predefined domain and range according to the function every value in the domain exists connected to just one value in the range.
Given: f(x) = 3x² -3
As we can see in the graph the first term exists 3x² and exists still positive for all x.
The range for f(x) ∈ [-3, ∞)
When x = 0 then f(x) = -3
The above value exists as the smallest possible value on the y-axis.
Given: [tex]g(x) = 2^x - 3[/tex]
[tex]2^x[/tex] exists also a positive quantity and it exists as an exponential function.
The range for the g(x) ∈ (-3, ∞)
It signifies that g(x) never touches the y-axis at -3.
We can express the minimum value of g(x) approaches -3.
Therefore, the correct answer is option B. The minimum y-value of g(x) approaches -3 and option D. f(x) has the smallest possible y-value.
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what is the sum of .74+.19+3.09+1.98=
Answer:
6
Step-by-step explanation:
no calculator at hand ?
really ? you are using us a simple calculator ?
Answer:
6
Step-by-step explanation:
what is the sum of .74+.19+3.09+1.98=
0.74+
0.19+
3.09+
1.98=
-----------------
6
Circles A circular device has a diameter of 4.5 inches. What is the radius of the device? Choose one 2 points O2.25 inches O4.5 inches O 4.5 inches O 2.25 inches 10 CO D
Answer: 2.25 inches
Step-by-step explanation:
The radius of a circle is half the diameter.
Suppose that the breaking strength of a rope (in pounds) is normally distributed, with a mean of 100 pounds and a standard deviation of 16. What is the probability that a certain rope will break before being subjected to 120 pounds? (You may need to use the standard normal distribution table. Round your answer to four decimal places.)
The probability that a certain rope will break before being subjected to 120 pounds is 89.4%.
What is the probability that a certain rope will break before being subjected to 120 pounds?The probability is calculated as follows:
Mean = 100
Standard deviation = 16
The probability is obtained from the z-score.
x = mean + z-score * standard deviation
120 = 100 + z-score * 16
z-score = 20/16
z-score = 1.25
From normal distribution table, the probability with a z-score of 1.25 is 89.4%
In conclusion, the probability is obtained from the z-score.
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Find the constant of variation when t varies directly as the square of s, and t = 64 when S = 4.
Answer:
The constant of variation is 4
Step-by-step explanation:
We are looking for the constant of variation when t varies directly as the square of s
t = k s^2 where k is the constant of variation
t = 64 and s = 4
64 = k 4^2
64 = k * 16
Divide each side by 16
64/16 = k * 16/16
4 = k
The constant of variation is 4
5. a. The area of an isosceles triangle is 60cm² and its base is 10cm. Find the length of its equal side.
Answer:
H = 12cm
b
I hope I was able to help
The temperature at 6am is -8f , at 9am the temperature is 6f . If the temperature rises at a constant rate , what will the temperature be at 3:00pm
Answer:
24 F
Step-by-step explanation:
Temp increases by 4F per hour.
-8F - 6F = 12F / 3hours
The probability that a student has a Visa card (event V) is .76. The probability that a student has a Master card (event M) is .16. The probability that a student had both is .04.
Answer:
The Probability of both happening is 0.304.
Step-by-step explanation:
P(A) × P(B)
= 0.76 × 0.4
= 0.304
In a recent survey,77 % of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the health center. Round to the nearest three decimal places.
The probability of that exactly 8 of them favor the building of the health center is 0. 399
How to determine the probabilityFrom the information given, we have that 70% of the community favors the building of the health center
Number of citizens chosen = 14
P(8) = [tex]\frac{8}{14}[/tex] × [tex]\frac{70}{100}[/tex]
P(8) = [tex]0. 57[/tex] × [tex]0. 7[/tex]
P(8) = [tex]0. 399[/tex]
Thus, the probability of that exactly 8 of them favor the building of the health center is 0. 399
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Suppose that the functions p and q are defined as follows. p(x)=x+1
q(x)=2x^2-2
The value of (p*q)(5) and (q*p)(5) is 288
How to determine the composite functions?The functions are given as:
p(x)=x+1
q(x)=2x^2-2
Calculate p(5) and q(5)
p(5)=5+1 = 6
q(5)=2(5)^2-2 = 48
The functions are then calculated as:
(p*q)(5) = p(5) * q(5)
(p*q)(5) = 6 * 48
(p*q)(5) = 288
Also, we have:
(q*p)(5) = (p*q)(5)
(q*p)(5) = 288
Hence, the value of (p*q)(5) and (q*p)(5) is 288
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Complete question
Suppose that the functions p and q are defined as follows. p(x)=-x-1 q(x)=-2x^2-2 Find the following. (p*q)(5) (q*p)(5)
A closed box has a square base with side length ll feet and height hh feet. Given that the volume of the box is 29 cubic feet, express the surface area of the box in terms of ll only.
The surface area of the closed box in terms of l only, which has the square base is,[tex]2l^2 + \frac{116}{l}[/tex]
How to determine the surface areaThe volume of cuboid or box can be given as,
Volume = l × b × h
Here, (l) is the length, (b) is the width of the box and (h) is the height of the box.
A closed box has a square base with side length l feet and height h feet. Therefore, the length and width will be the same.
Then the volume of the box is 29 cubic feet. Thus,
29 = l × l × h
29 = [tex]l^2 h[/tex]
[tex]h = \frac{l^2}{29}[/tex]
The surface area of the square base box is,
Area = [tex]2l^2 + 4lh[/tex]
Substitute the value of h
Area = [tex]2l^2 + 4l\frac{29}{l^2}[/tex]
Area = ,[tex]2l^2 + \frac{116}{l}[/tex]
Therefore, the surface area of the closed box in terms of l only, which has the square base is,[tex]2l^2 + \frac{116}{l}[/tex]
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Find the area of the shaded region.
Please anyone help me!
Thank you
Answer:
7.26
Step-by-step explanation:
Here
Diameter=2m
Length =2.6m
Breadth=4m
Now
Area of circle=(22*2*2*4)/7
=22/7
=3.14m^2
again
Area of rectangle= lb
=2.6m*4m
=10.4m^2
So
Area of the shaded region is 10.4m^2-3.14m^2
=7.26m^2
The answer is 7.26 m².
To find the shaded area, subtract the area of the circle from the area of the rectangle.
(2.6 × 4) - (3.14 × 1²)10.4 - 3.147.26 m²