a. The trigonometric ratio tanθ = -√(sec²θ - 1)
b. The trigonometric ratio secθ = -1/√(1 - sin²θ)
What are trigonometric ratios?Trigonometric ratios are the following mathematical expressions sinθ, cosθ, tanθ,secθ,cosecθ and cotθ.
a. How to express tanθ in terms of secθ for θ in Quadrant II?Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity
tan²θ + 1 = sec²θ
Making tanθ subject of the formula, we have that
tan²θ = sec²θ - 1
tanθ = ±√(sec²θ - 1)
Since in Quadrant II, tanθ is negative, we choose the negative answer.
So, tanθ = -√(sec²θ - 1)
b. How to express secθ in terms of sinθ for θ in Quadrant II?Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity
secθ = 1/cosθ and
sin²θ + cos²θ = 1
Making cosθ subject of the formula, we have that
cos²θ = 1 - sin²θ
cosθ = ±√(1 - sin²θ)
So, secθ = 1/cosθ
= ±1/√(1 - sin²θ)
Since in Quadrant III, secθ is positive, we choose the positive answer.
So, secθ = -1/√(1 - sin²θ)
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. A window is in the form of a rectangle surmounted by a semicir- cle. The rectangle is of clear glass, whereas the semicircle is of tinted glass that transmits only half as much light per unit area as clear glass does. The total perimeter is fixed. Find the proportions of the window that will admit the most light. Neglect the thick- ness of the frame.
The area of the window that lets in the most light will be the one that causes the window to transmit the most light overall.
To find the proportions of the window that will admit the lightest, we need to maximize the total area of the window while keeping the perimeter fixed. The total area of the window is the sum of the area of the rectangle and the area of the semicircle. The area of the rectangle is the product of its length and width, and the area of the semicircle is half the product of its radius and the area of a full circle with the same radius.
Since the perimeter is fixed, the length and width of the rectangle are also fixed. The radius of the semicircle can be found using the perimeter and the length and width of the rectangle.
Once we have the radius of the semicircle, we can find the area of the rectangle, the area of the semicircle, and the total area of the window. Since the semicircle is of tinted glass that transmits only half as much light per unit area as clear glass does, we will have to multiply the area of the semicircle by 0.5 to find the total amount of light transmitted by it.
Finally, we will have to compare the total amount of light transmitted by the window for different values of the length and width of the rectangle. The proportion of the window that admits the most light will be the one that results in the maximum total amount of light transmitted by the window.
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If the height of the triangle given below is 35 cm, what then is its area? (Round your final answer to the tenths place, if necessary).
Answer:
I need the width in order to solve it. . .
Formula - To calculate the area of a triangle, multiply the height by the width (this is also known as the 'base') then divide by 2.
Was there a width?
HELP
ASAP FOR 20 POINTS!
Answer:
15.01
Step-by-step explanation:
Habib cut out a rectangle that ha a perimeter of 60 inche and a length of 16 inche. They cut out another rectangle that i the ame length and twice a wide
The required perimeter of the new rectangle is 66 inches.
What is a rectangle?A quadrilateral with all of its angles equal, or right angles, is a rectangle.
In addition to having all equal angles, a square also has all equal sides.
Therefore, a particular case of a square is a rectangle.
To put it another way, a rectangle can also be a square (when all sides to are equal).
Because every square is a quadrilateral with all four angles at right angles, every square is also a rectangle.
To be a square, a rectangle's sides must all be the same length, hence not all rectangles are squares.
So, a perimeter equals 2(l+b).
50 is the circumference and 17 is the length here.
Suppose the breadth is x.
50 = 2(17+x)
50 = (2*17)+(2*x)
50 = 34 + 2x
50 - 34 = 2x
16 = 2x
16/2 = x
8 = x
The first triangle's width is eight inches.
We know that the length of the other rectangle is 17.
And that the width is two times that of the first triangle.
Length = 17, width = 2*8 = 16, etc.
For the border:
p = 2(l+b)
p = 2(17+16)
p = (2*17)+(2*16)
p = 34+32
p = 66
Therefore, the required perimeter of the new rectangle is 66 inches.
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Complete question:
Najib cuts out a rectangle that has a perimeter of 50 inches and a length of 17 inches. He cuts out another rectangle that is the same length and twice as wide. What is the perimeter of the new rectangle?
A sine function has an amplitude of 3, a period of π, and a phase shift of [tex]\frac{\pi }{4}\\[/tex]. What is the y-intercept of the function?
3
0
-3
[tex]\frac{\pi }{4}[/tex]
The y-intercept of the sine function is -3
We know that the standard form of the sine function is, y = a sin(bx + c) + d
where, amplitude = |a|
period = 2π/b
phase shift = -c/b
and vertical shift = d
Here, a sine function has an amplitude of 3, a period of π, and a phase shift of π/4
a = 3,
So, 2π/b = π
⇒ b = 2
And phase shift -c/b = π/4
⇒ -c/2 = π/4
⇒ -c = π/2
⇒ c = -π/2
So, a sine function would be,
y = 3 sin(2x + -π/2) + 0
y = 3 sin(2x + -π/2)
When x = 0,
y = 3 sin(0+ -π/2)
y = 3 sin(-π/2)
y = 3 × (-1)
y = -3
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please help i need help asap i have class in 2 hours pls
The value of x, given the angles next to the triangle, can be found to be 38 °
How to find the value of x ?To find the value of x, you first need to find the value of the other angles in the triangle.
Angles on a horizontal line add up to 180 degrees so the angle to the bottom left is:
= 180 - 134
= 46 °
The angle to the bottom right is:
= 180 - 84
= 96 °
The angles in a triangle add up to 180 ° so the value of x would be:
= 180 - 46 - 96
= 38 °
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Find the volume of the following figure.
(I need a answer to this very soon so if anybody can answer id really appreciate it :))
The volume of the prism is 103.32 cubic inches (optionD)
What is the volume of a prism?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.
The base area of the prism = 4.1×7.2 = 29.52 inches squared.
The height of the prism is 3.5 inches
Therefore volume = base area × height
volume = 29.52× 3.5 = 103.32 cubic inches.
Therefore the volume of the shape is 103.32 cubic inches.
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Based on the following calculator output, determine the population standard
deviation of the dataset, rounding to the nearest 100th if necessary.
1-Var-Stats
-
86.7142857143
Σæ = 607
Σχ2 = 59459
Sx= 33.72296095
o2 = 31.2213950714
n=7
minX = 52
Q₁ = 55
Med=87
Q3 = 110
maxX = 138
Therefore , the solution of the given problem of standard deviation comes out to be 67.15=σx .
Define standard deviation.It tells about how dispersed the data is is indicated by the standard deviation. It expresses the deviation of each observed variable from the mean. Any distribution will have roughly 95% of its values within two standard deviations of the mean.
Here,
We know population SD= Σ(xi-mu)2/n where mu is the population mean and n is the number of observation.
Here
we have n=7 and mu can be taken as x- =310.142
Standard deviation = SD=Σ(xi-mu)2/n
=>(Σxi2/n)-x-2
=>(704883/7)-(310.14)2=67.15=σx
Therefore , the solution of the given problem of standard deviation comes out to be 67.15=σx .
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What is the perimeter?
Help you plz....And no links!!
I repeat No links!!
Expanded and simplified form if 5 (m+2) + 9 (n+4)
Answer:
The answer expanded and simplified is
5m +9n +14
Me resuelven está 2 porfa
a) Each person would receive 1/6 of the cake
b) If there are 49 balls in total and each person is to get seven balls, How many persons can share the balls?
What is the problem?We know that we can be able to make us of the principles of algebra so as to be able to obtain the problems that we have to deal with in the question that appears in the image that is attached.
Given that we have the total amount of the cake as 2 1/2 and then we are told that there are 15 persons in the class thus the amount that everyone should receive would be x.
2 1/2 = 15 x
5/2 = 15x
5 = 2 * 15x
x = 5/2 * 15
x = 1/6
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MULTIPLE CHOICE QUESTION
What does the "rise" represent?
The change in y axis
the change in x axis
Rewatch
It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle
formed by third base, second base, and home plate. What can you conclude about the distance from first base to home plate, and from home plate to third base? Explain using your knowledge of congruent triangles.
Distance between first base to home plate and from home plate to third plate are equal.
Given : It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle formed by the third base to home plate ,and from home plate to third base.
The given situation and distance between first base to home plate and from home plate to third plate are equal.
On Converting the given situation into a geometry problem. So we name the require points.
Let A be the home plate,
B is first base,
C is the second base,
And D is the third base.
Now, we can present a geometrical proof:
Statement and their reasons
(1) BC = CD - ( Given )
(2) AC = AC - ( Reflexive Property )
(3) Δ ACD = Δ ACB - ( SAS Congruence - side angle side)
(4) AD = AB - ( CPCTC - Congruent Parts of Congruent Triangles are Congruent )
Therefore, the gap from 1st base to home plate, and from home plate to 3rd plate are equal.
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A circle with radius 12 cm has a segment with a central angle of 60. What is the area of the segment?
Answer:
Exact Area = 24pi square cm
Approximate Area = 75.36 square cm (when using pi = 3.14)
Note: "square cm" can be abbreviated to "cm^2" without quotes.
=============================================================
Explanation:
Let's find the area of the full circle with radius r = 12
A = pi*r^2
A = pi*12^2
A = 144pi
This is the exact area of the full circle in terms of pi. To get the approximate area, you would replace pi with something like 3.14 (though you could use more decimal digits in pi to get a more accurate area).
We found the area of the full circle, but we only want a pie slice of it. Each slice is 60 degrees, out of 360 total. So that means we want 60/360 = 1/6 of the full area.
In other words, there are 6 slices because 360/60 = 6, which means we'll divide the area we got by 6
(144pi)/6 = (144/6)pi = 24pi
The exact area of the pie slice is 24pi square cm
If you used the approximation pi = 3.14, then that leads to an approximate answer of 24*pi = 24*3.14 = 75.36 square cm
Alex has some marbles.
Billie has three times as many marbles are Alex.
Chris has 9 fewer marbles than Billie.
In total they have 68 marbles.
How many marbles does Alex have?
Answer:
11 marbles
Step-by-step explanation:
Let x = no. of marbles-Alex
3x = no. of marbles-Billie
3x - 9 = no. of marbles-Chris
x + 3x + 3x - 9 = 68
7x - 9 = 68
7x = 77
x = 11
Alex will have 11 marbles out of a total of 68 marbles.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Alex has some marbles. Billie has three times as many marbles are Alex.
Chris has 9 fewer marbles than Billie.
In total, they have 68 marbles.
Let x = no. of marbles-Alex
3x = no. of marbles-Billie
3x - 9 = no. of marbles-Chris
The number of marbles will be calculated as,
x + 3x + 3x - 9 = 68
7x - 9 = 68
7x = 77
x = 11
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A culture of bacteria has an initial population of 860 bacteria and doubles every 9 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after hours, P_0P 0 is the initial population, is the time in hours and is the doubling time, what is the population of bacteria in the culture after 4 hours, ?
Answer:
1170
Step-by-step explanation:P_0=860
P
0
=860
The initial population
t=4
t=4
Time elapsed
d=9
d=9
The doubling time
P_t = P_0\cdot 2^{\frac{t}{d}}
P
t
=P
0
⋅2
d
t
P_t=860\cdot 2^\frac{4}{9}
P
t
=860⋅2
9
4
Plug in
P_t=1170.2794\approx1170
P
t
=1170.2794≈1170
what is the sum of 2/3 and 4/5
Answer:
1 7/15 or 22/15
Step-by-step explanation:
2/3 = 10/15
4/5 = 12/15
Answer:
2/15
Step-by-step explanation:
In an amphitheater, eat are aranged in 50 emi-circular rowfacing a dome tate. The firt row contain 23 eat, and each row contain4more eat than the previou row. How many eat are in the amphitheater?
In an amphitheater, seat are arranged in 50 semi-circular row-facing a dome Tate. The first row contain 23 seat, and each row contain 4 more eat than the previous row. Therefore, there are 6050 seat are in the amphitheater.
Given that:
There are total 50 semi circular row.
In the first row there are 23 seats.
The given problem is AP series:
Arithmetic Series:
An arithmetic sequence is defined as an algebraic sequence in which each successive term has an equal difference. It is obtained by adding a constant to any preceding term. For the first term 'a' and the tolerance 'd' of the AP, here is a list of commonly used arithmetic progressions to solve various AP related problems:
Common Difference of AP: d = a2 - a1 = a3 - a2 = a4 - a3 = an - a(n-1) nth term of AP.AP: an = a + (n - 1)d of AP Sum of n terms: Sn = n/ 2( 2a+(n-1)d) = n/2(a + l),where l is the last term in the arithmetic progression.
Now,
Sum of n terms = n/2 [ 2a + (n-1)d]
= 50/2 [ 2× 23 + (50 -1)4]
= 25 [46 + 49×4]
= 25 × 242
= 6050
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The school store is selling shirts at cost for $5.50 and Jackets for $12. The volleyball coach spent $208 to buy a total of 26 shirts and jackets. How many shirts did they buy?
Answer:
16 shirts.
Step-by-step explanation:
You can make a system of equations
x + y = 26
5.50x + 12y = 208
You can solve this in many ways, however chose to graph using desmos. I got that x = 16, and y = 10.
You deposit $3000 into a bank account that pays 1.25% annual interest, compounded semi-annually. What is the final balance after 4 years
Answer:
$3,153.32
Step-by-step explanation:
Given that
The deposited amount is $3,000
The annual interest rate is 1.25%
So, the semi-annual interest rate is 1.25% ÷2 = 0.625%
And, the time period = 4 × 2 = 8
We need to find out the final balance
So,
As we know that
Future value = Present value × (1 + rate of interest)^number of years
= $3,000 × (1 + 0.625%)^8
= $3,153.32
1
Q4. What is the length of the base of a triangle that has an area of 15 cm
and a height of 3 cm?
O A) 12 cm
B) 10 cm
C) 45 cm
D) 3 cm
Q5
A) 12 cm ..............
Answer:
Area of a triangle= b · h/2
b) 10 is the correct answer because 10 x 3/2 = 15
How do you solve this?
Answer: 140^3
Step-by-step explanation:
The 3 is an exponent. To solve this, you basiclly have to multiply the three numbers and add a 3 exponent.
If the radius of a new larger circle is 36 mm, what is the area of the larger circle with the same scale?
Answer:
4072.032mm^2
Step-by-step explanation:
Given data
Radius= 36mm
The expression for the area of a circle is
A= πr^2
Substititute
A= 3.142*36^2
A= 3.142*1296
A= 4072.032mm^2
Hence the area is 4072.032mm^2
If BE=24, DF= 10, and A F= 13,
1. Find the perimeter of ΔABE
2. Find the perimeter of ΔCDF
The perimeter of ΔABE is 70 units.
The perimeter of ΔCDF is 35 units.
How to find the perimeter of a triangle?A triangle is a polygon with threes sides. The sum of angles in a triangle is 180 degrees.
Therefore, the perimeter of a triangle is the sum of the whole sides.
Triangle mid point theorem is used to find the perimeter of the triangles.
It states that the line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
Let's find the perimeter of triangle ABE.
Hence,
perimeter of triangle ABE = AB + BE + AE
BE = 24
AE = 13 + 13 = 26
AB = 10 + 10 = 20
perimeter of triangle ABE = 24 + 26 + 20 = 70 units
perimeter of triangle CDF = DF + CD + CF
perimeter of triangle CDF = 10 + 13 + 12
perimeter of triangle CDF = 35 units
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when processing an invoice what account is credited
a. accounts receivable
b. cash
c. accounts payable
d. the answer depends on the transaction
Answer:
accounts payable
Step-by-step explanation:
Because amount of money you owe
There is 2/3 of a pan of brownies left on the
counter. If you eat 2/3 of the brownies left in the
pan, what is the fraction of the whole pan that
you ate?
Answer:
He ate 4/9 of the pan of brownies.
Step-by-step explanation:
So the question might seem hard but when you read it, it said that there were 2/3 of brownies left and he ate 2/3 of that 2/3 in that pan so to figure 2/3 of 2/3 I divided 2/3 by 3 which is 2/9, 2/9 is 1/3 of 2/3 to figure out 2/3 of 2/3 you need to add by itself which you get 4/9.
A city has 5 cm of snow on the ground before a snow storm. During the storm, the amount of snow on the ground increases by 2 cm an hour.
which table shows a smaller rate of change than the one described?
Time Snow on Ground
(hours) (cm)
0
3
1
9
2
15
3
21
Time
(hours)
0
A
Ос.
Snow on Ground
(cm)
5
10
15
1
2
3
20
Time
(hours)
0
B.
Time Snow on Ground
(hours) (cm)
0
4
1
6
2
8
3
10
Snow on Ground
(cm)
6
7
8
9
1
2
3
Answer:
The answer is D because the snow on the ground increases 1 cm every one hour rather than 2 cm every hour.
Step-by-step explanation:
6 3/4 + 3 1/8 whats the answer?
Answer:
9 7/8
Step-by-step explanation:
Ty bought a notebook for $3 and pencils $2 if both items were on sale for 25%, what did Tyler spend?
Answer:
2.25 + 1.50 = 3.75
he spent $3.75
hope this helped
Step-by-step explanation:
someone pls help this is an emergency