The series [tex]\tan(2^{-n})[/tex] is convergent.
What is convergence of series?In mathematics, the cοnvergence οf a series refers tο the behaviοr οf the series' partial sums as mοre terms are added. A series cοnverges if its sequence οf partial sums apprοaches a finite limit, which is called the sum οf the series. If the sequence οf partial sums dοes nοt apprοach a finite limit, the series diverges.
The series [tex]\tan(2^{-n})[/tex] converges because of the following reasons:
As n increases, [tex]2^{-n}[/tex] becomes very small, which makes [tex]\tan(2^{-n})[/tex] close to its linear approximation. Therefore, we can use the linear approximation of [tex]\tan(2^{-n})[/tex] to estimate its value.
The linear approximation of [tex]\tan(2^{-n})[/tex] is [tex]2^{-n}[/tex], which means that [tex]\tan(2^{-n})[/tex] ≈ [tex]2^{-n}[/tex] when [tex]2^{-n}[/tex] is small.
Since the series [tex]2^{-n}[/tex] is convergent, by comparison test, the series [tex]\tan(2^{-n})[/tex] is also convergent.
Alternatively, we can also use the fact that the series tan(x) is convergent for x ∈ (0, π/2), and since [tex]2^{-n}[/tex] → 0 as n → ∞, we have [tex]\tan(2^{-n})[/tex] → tan(0) = 0, which implies that the series [tex]\tan(2^{-n})[/tex] is convergent.
To learn more about convergence of series, visit the link:
https://brainly.com/question/15415793
#SPJ1
1pt equal how many mL
Answer:
1 American pt equals approximately 568.261 mL
OR
1 British Imperial pt is approximately 473 mL
I recommend choosing the answer that better relates to where you are from.
Step-by-step explanation:
There seem to be TWO kinds of pint sizes. A US pint is 16 ounces and an Imperial pint is 20 ounces.
19
Find the area of the triangle.
B
14
16
units squared
Since we are given the lengths of the two legs of the triangle, 14 and 16 respectively, the area of the triangle is 152.97 square units.
What is the area of this triangle?To find the area of a triangle, we can use the formula: area = (1/2) x base x height
In this case, we are given the lengths of the two legs of the triangle, 14 and 16, so we can use the Pythagorean theorem to find the length of the base:
a^2 + b^2 = c^2
14^2 + 16^2 = c^2
196 + 256 = c^2
452 = c^2
c = √452
c ≈ 21.26
To find the height, we need to drop a perpendicular from the apex to the base, forming two right triangles. Using the Pythagorean theorem again, we have:
(1/2) x base x height = area
(1/2) x 21.26 x height = area
Let's use the right triangle with legs 14 and height h as our reference. Then we have:
h^2 + 7^2 = 16^2
h^2 + 49 = 256
h^2 = 207
h = √207
h ≈ 14.39
Therefore, the area of the triangle is:
= (1/2) x 21.26 x 14.39
= 152.9657
= 152.97².
Read more about area
brainly.com/question/27947205
#SPJ1
For the following exercises, start with the graph of f (x) = 4x. Then write a function that results from the given
transformation.
32. Shift f (x) 4 units upward
33. Shift f (x) 3 units downward
34. Shift f (x) 2 units left
35. Shift f (x) 5 units right
36. Refl ct f (x) about the x-axis
37. Refl ct f (x) about the y-axis
32. g(x) = 4x + 4
This transformation shifts the graph
of f(x) 4 units upward.
33. g(x) = 4x-3
This transformation shifts the graph
of f(x) 3 units downward.
34. g(x)=4(x+2)
This transformation shifts the graph
of f(x) 2 units left.
35. g(x) = 4(x-5)
This transformation shifts the graph
of f(x) 5 units right.
36. g(x) = -4x
This transformation reflects the graph
of f(x) about the x-axis.
37. g(x) = -4x
This transformation reflects the graph
of f(x) about the y-axis.
chatGPT
PLEASE HELP Area of Cross Sections
Thus, the area of cross section perpendicular to the base area will be in form of rectangle : Area = 130.32 cm².
Explain about the Area of Cross Section?The area of a sliced piece of a 3D object, such a pipe, is known as the cross sectional area. The cross sectional area of a pipe when cut perpendicular to it's own longest axis is determined for the circle-shaped top portion of the sliced component.
Given data:
Base area of cylinder = 12.96 π cm²
height of cylinder = 18.1 cm.
Let the radius of the cylinder be 'r'.
Base area of cylinder = π*r².
π*r² = 12.96 π
r² = 12.96
r = 3.6 cm
now, the area of cross section perpendicular to the base area will be in form of rectangle with.;
Base = 2*r = 2*3.6 = 7.2 cm
height = 18.1 cm.
Area = base * height
Area = 7.2 * 18.1
Area = 130.32 cm²
Thus, the area of cross section perpendicular to the base area will be in form of rectangle : Area = 130.32 cm².
Know more about the Area of Cross Section
https://brainly.com/question/13029309
#SPJ1
What’s 4559.886 rounded to the nearest inch
Answer:
Step-by-step explanation:
Assuming that the original measurement is in millimeters, since they are commonly used in precision applications, we know that 1 millimeter is equal to 0.03937 inches. Therefore, we can convert 4559.886 millimeters to inches by multiplying by 0.03937:
4559.886 mm * 0.03937 in/mm = 179.72467632 in (rounded to 8 decimal places)
To round this to the nearest inch, we need to look at the first decimal place after the decimal point. In this case, the digit in the first decimal place is 7, which is greater than or equal to 5. Therefore, we round up to the nearest inch, which gives us:
179.72467632 in rounded to the nearest inch is 180 in.
Therefore, 4559.886 rounded to the nearest inch is 180.
i need so help plez average weight of a male African elephant is 15,000 pounds. How many tons is this?
7 tons
8 tons
7 tons 1000 pounds
30,000,000 tons
Step-by-step explanation:
The average weight of a male African elephant is 15,000 pounds.
To convert pounds to tons, we divide the weight in pounds by 2,000 (the number of pounds in a ton):
15,000 pounds ÷ 2,000 pounds/ton = 7.5 tons
Therefore, the weight of a male African elephant is approximately 7.5 tons.
So the closest answer to this question is "7 tons".
Answer:
7 tons
Step-by-step explanation:
The average weight of a male African elephant is 15,000 pounds. To convert this weight into tons, we need to divide it by 2,000 (since there are 2,000 pounds in a ton).
So, 15,000 ÷ 2,000 = 7.5 tons.
Therefore, the answer is 7 tons (since there are no fractions of tons in the options given).
Look at the following set of four whole numbers. 4 9 10 12 Find another set of four whole numbers so that: the range has increased by 2, • the mean remains the same, • the median has decreased by 1. ● You may use some of the numbers from the orignal set, but not exactly the same four numbers. My four numbers are
The required set of numbers 5, 9, 11, and 14 satisfies all the given conditions.
What is Set?In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set.
According to question:a set of four whole numbers that satisfies the given conditions:
5, 9, 11, 14
To check that this set meets the requirements:
The range of the original set (12 - 4 = 8) increased by 2 to become 10 (14 - 4 = 10).
The mean of the original set ((4 + 9 + 10 + 12) / 4 = 8.75) remains the same in the new set ((5 + 9 + 11 + 14) / 4 = 8.75).
The median of the original set is 9.5 (the average of 9 and 10), and the median of the new set is 10 - 1 = 9.
Therefore, the set of numbers 5, 9, 11, and 14 satisfies all the given conditions.
To know more about Set visit:
brainly.com/question/28860949
#SPJ1
Jump to level 1
What are m and b in the linear equation 3 + 7x + 11 + 10x = y?
m = Ex: 50 ÷
b = Ex: 50
Answer:
The given equation is 3 + 7x + 11 + 10x = y.
Simplifying the equation, we get:
y = 17x + 14
Comparing with the standard linear equation y = mx + b, we can see that:
m = 17
b = 14
Therefore, m = 17 and b = 14.
What values of y and z make
The values of y and z which makes triangle (△) QRS exactly the same (≅) as triangle (△) WVX is
y = 11z = 11How do i determine the value of y?We must note here that the sign, ≅ means exactly the same. Thus,
Line VW = Line QR
The following were obtained from the question:
Line VW = 31Line QR = y + 20Value of y =?Line VW = Line QR
31 = y + 20
Collect like terms
y = 31 - 20
y = 11
Thus, the value of y is 11
How do i determine the value of z?We can obtain the value of z as follow:
Line QS = Line WXLine QS = y + 3z + 28Line WX = 6y + z - 5Value of y = 11Value of z =?Line QS = Line WX
y + 3z + 28 = 6y + z - 5
11 + 3z + 28 = 6(11) + z - 5
11 + 3z + 28 = 66 + z - 5
3z + 39 = z + 61
Collect like terms
3z - z = 61 - 39
2z = 22
Divide both sides by 2
z = 22 / 2
z = 11
Thus, the value of z is 11
Learn more about congruent shapes:
https://brainly.com/question/20857667
#SPJ1
The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 48 miles apart. When the satellite is on one side of the two stations, the angle of elevation at A Is 87° and the angle of elevation at B Is 84°.
How far is the satellite from station A?
How High is the satellite above the ground?
Round all answers to 3 decimal places.
The distance of the satellite from station A is approximately 47 miles
The satellite is approximately 911 miles above ground
How to find the distanceLet the distance from station A to the satellite be a and the distance from the station B to the satellite be a + 48
Using trigonometry
tan 87 degrees = height of the satellite above the ground, h / a
tan 87 degrees = h / a
h = a * tan 87
while
tan 84 degrees = h / a + 48
h = (a + 48) tan 84
substituting for h
a * tan 87 = (a + 48) tan 84
a (tan 87 - tan 84) = 48 tan 84
a (9.567) = 48 tan 84
a = 48 tan 84 / 9.567
a = 47.436
The distance of the satellite from station A is approximately 47 miles
The height above ground
h = a * tan 87
h = 47.436 * tan 87
h = 910.857 miles
Learn more about angle of elevation at:
https://brainly.com/question/88158
#SPJ1
Leo is drawing a map of the recess area at his school on a coordinate grid. If the scale of the map is 1 grid = 5 feet, what is the distance from the jungle gym to the four-square courts? Round your answer to the nearest tenth if necessary.
if Leo has provided the coordinates of the jungle gym and the four-square courts, we can use the distance formula to calculate the distance between them. the four-square courts are approximately [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).
What are the coordinates of two points?The distance formula is:
[tex]d = sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]
where [tex](x1, y1)[/tex] and [tex](x2, y2)[/tex] are the coordinates of two points, and d is the distance between them.
For example, let's say the jungle gym is located at (3, 4) on the grid, and the four-square courts are located at (9, 8). Using the distance formula, we have:
[tex]d = sqrt((9 - 3)^2 + (8 - 4)^2)[/tex]
[tex]= sqrt(6^2 + 4^2)[/tex]
[tex]= sqrt(36 + 16)[/tex]
[tex]= sqrt(52)[/tex]
[tex]\approx 7.2[/tex]
Therefore, the distance from the jungle gym to the four-square courts is approximately [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).
Learn more about coordinates here:
https://brainly.com/question/16634867
#SPJ1
Which function represents the exponential graph given that (0, 1) and (4, 81/16 ) are points that lie on the graph?
f(x)=(2/3)^x
f(x)=(4)^x
f(x)=(1)^x
f(x)=(3/2)^x
The f(x) = (3/2)ˣ is the correct function that represents the given exponential graph.
What is exponential graph?An exponential graph is a type of graph that represents an exponential function. An exponential function is a mathematical function in which a constant base is raised to a variable exponent. The general form of an exponential function is: y = a * bˣ.
What is graph?A graph is a visual representation of data or information that allows us to quickly and easily understand patterns, trends, and relationships. Graphs are used to present information in a way that is easy to interpret and understand.
In the given question,
The function that represents the exponential graph given that (0, 1) and (4, 81/16 ) are points that lie on the graph is:
f(x) = (3/2)ˣ
To verify that this is the correct function, we can substitute x=0 and x=4 into the function to see if the corresponding y-values match the given points on the graph.
When x=0, f(0) = (3/2)⁰ = 1, which matches the point (0, 1).
When x=4, f(4) = (3/2)⁴ = 81/16, which matches the point (4, 81/16).
Therefore, f(x) = (3/2)ˣ is the correct function that represents the given exponential graph.
To know more about exponential graph, visit:
https://brainly.com/question/9834848
#SPJ1
please help me. somebody solve this question
Answer:
5.5 or 5 1/2 inches
Step-by-step explanation:
The longest is 12 3/4
The two smallest combined are 3 and 4 1/4 = 7 1/4
12 3/4 - 7 1/4 = 5 1/2
mework
<
Part 1 of 3
A group consists of five Democrats and six Republicans. Three people are selected to attend a conference
a. In how many ways can three people be selected from this group of eleven?
b. In how many ways can three Republicans be selected from the six Republicans?
c. Find the probability that the selected group will consist of all Republicans
a. The number of ways to select three people from the group of eleven is
Therefore, there is a 12.12% chance that the chosen party will be made up exclusively of Republicans.
what is probability ?The likelihood or chance of an occurrence occurring is measured by probability. The occurrence is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. By dividing the number of favorable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. Numerous disciplines, including statistics, mathematics, science, finance, and engineering, heavily rely on probability to make predictions and judgments about the chance of various events happening.
given
A. The combination formula can be used to determine how many options there are to choose three individuals from a group of eleven:
C(11, 3) = 11! / (3! (11-3)!) = 165
There are 165 different methods to choose three from this group of eleven people.
b. The combination formula gives the number of options to choose three Republicans from the group of six Republicans:
C(6, 3) = 6! / (3! (6-3)!) = 20
To choose three Republicans from this set of six Republicans, there are 20 possible options.
c. The ratio of the number of ways to choose three Republicans from the group of six Republicans to the total number of ways to choose three people from the group of eleven determines the likelihood of choosing three Republicans out of the group of eleven.
P(3 Republicans) = C(6, 3) / C(11, 3), which translates to 20 / 165 = 0.1212 or roughly 12.12%.
Therefore, there is a 12.12% chance that the chosen party will be made up exclusively of Republicans.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
"^ a popular shopping Centre waiting time for an ABC Ban ATM machine is found to be uniformly distributed between 1 and 5 minutes. what is the probability of waiting between 2 and 3 minutes to use the ATM
The probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur. For example, the probability of flipping a fair coin and getting heads is 1/2 or 0.5.
Since the waiting time for the ABC Ban ATM machine is uniformly distributed between 1 and 5 minutes, the probability density function is given by:
f(x) = 1/(5-1) = 1/4 for 1 ≤ x ≤ 5
To find the probability of waiting between 2 and 3 minutes, we need to find the area under the probability density function between 2 and 3. This is given by the definite integral of the probability density function over the interval [2, 3]:
P(2 ≤ x ≤ 3) = ∫2^3 f(x) dx
= ∫2^3 (1/4) dx
= (1/4) [x]2^3
= (1/4) (3-2)
= 1/4
Therefore, the probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.
To know more about probability and given link below -
https://brainly.com/question/30034780
#SPJ1
The area of a parallelogram with base b and height h is bh. Greta is using tiles shaped like parallelograms to cover her bathroom floor. Each tile has a 4.25-inch base and is 2 inches high.
What is the area of each tile?
Write your answer as a whole number or decimal.
Answer:
Each tile would be 8.5 in
Step-by-step explanation:
Area of parallelogram is A=bh, so 4.25*2= 8.5
please please please help i’ll give brainlist
The scale factor of PQRS to JKLM is 4/5.
The scale factor of JKLM to PQRS is 5/4.
The value of w, x, and y are 20, 12.5, and 20 respectively.
The perimeter ratio is 4:5.
What is scale factor?In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor of PQRS to JKLM = 15/12
Scale factor of PQRS to JKLM = 5/4 or 1.25.
Scale factor of JKLM to PQRS = 12/15
Scale factor of JKLM to PQRS = 4/5 or 0.8.
For the value of w;
15/12 = 25/w
15w = 12 × 25
w = 20
For the value of x;
15/12 = x/10.
12x = 150
x = 12.5
For the value of y:
15/12 = y/16
12y = 15 × 16
y = 20
Perimeter ratio = 12 : 15 = 4:5
Read more on scale factor here: https://brainly.com/question/20795321
#SPJ1
Find a number between 100 and 200 which is also equal to a square number
multiplied by a prime number.
Answer:
162, 147 etc.
Step-by-step explanation:
we have to find
[tex]N = k^2 \cdot p[/tex]
we can iterate k = 1 to 10 to check all possible solutions,
[tex]N = 9^2 \cdot 2[/tex]
[tex]N = 7^2 \cdot 3[/tex]
N = 162, 147 etc.
Hopefully this answer helped you!!
Use the given dimensions to nd the areas of the vehicle and chairs. Then determine if the vehicle
could be used to haul both chairs in a single trip.
The 5 ft by 8 ft dimensions of the car and the (width) 2 ft by (height) 3 ft dimensions of the chair, indicates that the vehicle can haul both chairs in one trip.
What are the dimensions of a rectangularly shaped solid?The dimensions of rectangularly shaped solid are the height, the width and the length of the solid.
The possible dimensions of the vehicle and the chair obtained from a similar online question are;
Length of the vehicle = 8 feet
Width of the vehicle = 5 feet
The height of one chair = 3 feet
The width of one chair = 2 feet
Therefore;
The width of the vehicle of 5 feet indicates that the vehicle can contain the two chairs placed side by side with their widths of 2 feet each, to get;
Width of the two chairs = 2 feet + 2 feet = 4 feet < 5 feet
The two chairs placed horizontally, such that we get;
The total length of the horizontally placed chairs = 3 feet + 3 feet = 6 feet
The combined height of the two chaires, of 6 feet is less than the length of the car which is 8 feet, therefore;
The car can haul both chairs placed horizontally in a single trip.
The vehicle could therefore be used to haul both chairs in a single trip.
Learn more on the dimensions of regular solids here: https://brainly.com/question/29014642
#SPJ1
75909931 rounded to the nearest hundred thousand
Answer:
the answer is supposably 75900000
Pee Dimensional Figures) CARGO A = lw Area of base_____ A trailer has a volume of 2,112 cubic feet and a height of 12 feet. If the width of the trailer's base 8 feet, find the area and then the length of the trailer's base. A = bh DELIVERY V = Bh
The area of the trailer's base is 176 square feet.
What is volume?Volume is a measure of the amount of space that an object occupies. It is a three-dimensional quantity that is usually measured in cubic units, such as cubic meters, cubic feet, or cubic centimeters.
According to question:We have a cargo trailer with a volume of 2,112 cubic feet, a height of 12 feet, and a width of 8 feet. We want to find the area and length of the trailer's base.
Since the volume of the trailer is given by V = lwh, we can write:
2,112 = lw(12)
Simplifying this equation, we get:
l = 2,112 / (w x 12)
l = 2,112 / (8 x 12) [Substituting the value of w as 8 feet]
l = 22
Therefore, the length of the trailer's base is 22 feet.
To find the area of the trailer's base, we can use the formula A = lw:
A = l x w
A = 22 x 8
A = 176 square feet
Therefore, the area of the trailer's base is 176 square feet.
To know more about volume visit:
https://brainly.com/question/1578538
#SPJ1
Which function is a translation one unit right of the function
f(x) = log x?
Answer:
g(x)= log(x-1)
Step-by-step explanation:
g(x) = f(x-1)
Express the trig ratios as fractions in simplest terms.
cOS K =
sin L=
cos K and sin L
Therefore, cos(K) = √(17)/9, sin(L) = 8/9, and cos(K) and sin(L) together are (√(17)/9, 8/9) are trigonometric ratios as fractions in simplest terms.
Trigonometric Ratios of Particular Angles: What Are They?It is possible to calculate trigonometric ratios for various orientations. However, we memories the trigonometric ratios of a few particular angles, such as 0°, 30°, 45°, 60°, and 90°, to make computations easier. The numbers of the ratios at these angles can be found in the trigonometric ratios table.
The Pythagorean formula can be applied to the illustration to determine the length of the third side:
c²= a²+ b²
c²= 8² + √(17)²
c²= 64 + 17
c² = 81
c = 9
We can now calculate the trigonometry ratios of angles K and L:
cos(K) = adjacent/hypotenuse = √(17)/9
sin(L) = opposite/hypotenuse = 8/9
Using the same hypotenuse number of 9, we can calculate both cos(K) and sin(L) as follows:
cos(K) = adjacent/hypotenuse = √(17)/9
sin(L) = opposite/hypotenuse = 8/9
To know more about trigonometric ratios visit:-
https://brainly.com/question/25122825
#SPJ9
(1 − cos 0) (1 + cos 0)= 1/csc²0
Step-by-step explanation:
lol sorry for untidy work
Select the correct answer.
Consider functions p and q.
log₂ (x - 1)
p(x)
q (x) = 2* - 1
Which statement is true about these functions?
=
O A.
The x-intercept of function p is the same as the x-intercept of function q.
OB.
The x-intercept of function p is less than the x-intercept of function q.
O C.
The x-intercept of function p is greater than the x-intercept of function q.
OD. The x-intercepts cannot be compared because either p or q does not have an x-intercept
Answer: Click THANKS if you like my answer. have a good day sir/maam #keep safe
D. The x-intercepts cannot be compared because either p or q does not have an x-intercept.
The function q is a constant function and its graph is a horizontal line passing through y = -1. It does not intersect the x-axis, so it does not have an x-intercept.
The function p is a logarithmic function, and its x-intercept is the point at which the graph of p intersects the x-axis. To find the x-intercept of p, we need to set p(x) = 0 and solve for x.
log₂ (x - 1) = 0
2^0 = x - 1
1 = x - 1
x = 2
So the x-intercept of p is x = 2.
Since q does not have an x-intercept, we cannot compare the x-intercepts of p and q. Therefore, the correct answer is D.
Step-by-step explanation:
hope its help <:
The ratio of the birth weight to the adult weight of a male black bear is 3:1000. The average birth weight is 12 ounces. Find the average adult weight. Your answer is probably in ounces. If there are 16 ounces in 1 pound, how many pounds does the adult bear weigh?
A black bear's average adult weight is 4000 kilograms, or 250 pounds.
How do we figure out the average?Average By adding a collection of numbers, dividing by their count, and then summing the results, the arithmetic mean is determined. For instance, the sum for 2, 3, 3, 5, 7, & 10 is equal to 30 split by 6, which equals 5.
If a male black bear's birth weight to adult weight ratio is 3:1000, the following sentence can be written:
weight at birth to adult weight is 3 to 1 000.
Let's calculate the normal adult weight using the information provided. Given that the typical birth is 12 ounces, we can establish the following ratio:
weight at birth to adult weight is 3 to 1 000.
Weight of an adult is 12: 3: 1000.
Cross-multiplying results in:
3 x adult weight is equal to 12,000
By multiplying both halves by 3, we obtain:
4000 ounces for an adult.
Divide by 16 to convert teaspoons to pounds:
Adult weight is equal to 4000 / 16 pounds, or 250 pounds.
To know more about average visit:
https://brainly.com/question/24057012
#SPJ1
Help me please anyone ?!!!!?!!
Answer:
Its b,
Step-by-step explanation:
I had this test before i chose b and it was right
Answer:
(1, 6), (2, 12), (3, 18), (4, 24)
Help with this trig identities problems.
1) Given csc Φ = 7/3 and cot Φ = - (2√10)/(3), find sec Φ.
2) Given that sec β = 6/5 and sin β > 0, find tan β and sin β.
Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.
1. We can start by using the Pythagorean identity to find the values of sin Φ:
[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1
Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:
1/(7/3) = sin Φ
sin Φ = 3/7
Next, we can use the fact that cot Φ = cos Φ/sin Φ:
cot Φ = cos Φ/(3/7) = - (2√10)/(3)
Simplifying this expression, we get:
cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7
Finally, we can use the fact that sec Φ = 1/cos Φ:
sec Φ = 1/(- 2√10/7) = -7/(2√10)
2. We can use the fact that sec β = 1/cos β to find the value of cos β:
sec β = 6/5
cos β = 5/6
Next, we can use the Pythagorean identity to find the value of sin β:
[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1
sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6
Finally, we can use the fact that tan β = sin β/cos β:
tan β = (√11/6)/(5/6) = √11/5
To learn more about Pythagorean please click on below link
https://brainly.com/question/29069676
#SPJ1
3. There are 15 students in class 7 who need the school shirt of same size and 2 meter of
cloth is required to make a shirt.
(a) Find the total length of the cloth required to make the shirt to them.
(b) How many shirts can be made from a piece of cloth 9 meter long?
Convert the length of cloth required for a shirt in decimal.
1
If the length of a piece of cloth is 36.25 meter, how many meters of cloth is left? 1
Answer:
Step-by-step explanation:
(a) Since each student needs a shirt of the same size, and 2 meters of cloth is required to make one shirt, the total length of cloth required to make shirts for 15 students would be:
Total length of cloth = 15 x 2 = 30 meters
Therefore, 30 meters of cloth would be required to make shirts for 15 students.
(b) If 2 meters of cloth are required to make one shirt, then the number of shirts that can be made from 9 meters of cloth would be:
Number of shirts = 9 / 2 = 4.5 shirts
However, since we cannot make half a shirt, the actual number of shirts that can be made from 9 meters of cloth would be 4 shirts.
To convert the length of cloth required for a shirt into decimal form, we can simply divide the length in centimeters by 100. Therefore, 2 meters of cloth would be equivalent to 200 centimeters, which is 2.00 meters in decimal form.
(c) If the length of a piece of cloth is 36.25 meters, and we use 30 meters to make shirts for 15 students, then the remaining length of cloth would be:
Remaining length of cloth = 36.25 - 30 = 6.25 meters
Therefore, 6.25 meters of cloth would be left.
Determine the geometric mean of the numbers 8 and 6. Write your answer in simplest radical form.
I’ll give brainlist!
The geometric mean of the given numbers 8 and 6 is [tex]\sqrt{14}[/tex].
What is geometric mean?The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the collection of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers collectively and calculate their nth root, where n is the total amount of data values.
In other terms, the geometric mean is the product of n numbers divided by the nth root. As a result of the fact that in mathematical mean, the data values are added before being divided by the total number of values. However, when calculating the geometric mean, we add the provided data values before taking the root of the total number of data values using the radical index.
What is Square root?A number's square root is a value that, when multiplied by itself, yields the initial number. The opposite way to square an integer is to find its square root. Squares and square roots are therefore connected ideas.
The geometric mean of the given number is given by the formula
GM=[tex]\sqrt{\\a+b}[/tex]
=[tex]\sqrt{8+6}[/tex]
=[tex]\sqrt{14}[/tex]
To know more about geometric mean, visit
https://brainly.com/question/8934175
#SPJ1