[tex]sin(A)+cos(A)=\sqrt{2}\hspace{10em}tan(A)+cot(A)=2 \\\\[-0.35em] ~\dotfill\\\\ tan(A)+cot(A)=2\implies \cfrac{sin(A)}{cos(A)}+\cfrac{cos(A)}{sin(A)}=2 \\\\\\ \cfrac{sin^2(A)+cos^2(A)}{cos(A)sin(A)}=2\implies \boxed{\cfrac{1}{cos(A)sin(A)}=2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]sin(A)+cos(A)=\sqrt{2}\implies (~~sin(A)+cos(A)~~)^2=(\sqrt{2})^2 \\\\\\ sin^2(A)+2sin(A)cos(A)+cos^2(A)=2 \\\\\\ 2sin(A)cos(A)+sin^2(A)+cos^2(A)=2\implies 2sin(A)+1=2 \\\\\\ 2sin(A)cos(A)=1\implies \boxed{2=\cfrac{1}{cos(A)sin(A)}}[/tex]
now, another way to look at this identity will be as a unified system of equations
[tex]\begin{cases} (~~sin(A)+cos(A)~~)^2=2\\\\ ~~ ~tan(A)+cot(A)=2 \end{cases}\implies (~~sin(A)+cos(A)~~)^2=tan(A)+cot(A)[/tex]
and we'd end up with the same rigamarole.
help help help help help
Tara has a flower garden.In the garden 3/8 of are red and 3/6 are yellow . Copare the amount of red and yellow flowers using <>=
Answer:
Step-by-step explanation:
3/6 > 3/8
In a circle, an angle measuring 5. 5 radians intercepts an arc of length 8. 4. Find the
radius of the circle to the nearest 10th.
The circle's radius is equal to 3.659 or 3.7.
What is Radius?A circle's or a sphere's radius is the length of the line between the center and the edge.
From the center of the circle or sphere to any point on its perimeter, the radius' length is constant.
Its diameter is halved by its length.
A line segment from a circle's or sphere's center to its perimeter or boundary is known as the radius in geometry. I
t is a crucial component of spheres and circles and is frequently abbreviated as "r."
When discussing multiple radiuses at once, the plural form of radius is "radii." the longest line connecting any points on the opposite side of a circle or sphere.
Hence, The circle's radius is equal to 3.659 or 3.7.
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Lines m, n, and I are parallel. Line w intersects each line, as shown in the diagram below.
Based on the angle measures in the diagram, what is the value of x?
Answer:
120
Step-by-step explanation:
vertical angles are congruent :)
Two people stand on opposite ends of a bridge that crosses a river. Both can see an island located in the river. The angle
formed at the location of the first person is 37' and the angle formed at the second person is 55'. If the bridge is 5280 feet
long, how far is the first person from the island?
Answer:
The first person is about 4327.76 feet away from the island.
Step-by-step explanation:
We can draw a diagram to represent the situation. This is attached below.
Essentially, we want to find the value of x.
We are given that ∠A is 37° and ∠B is 55°.
The interior angles of a triangle must total 180°. Hence:
[tex]m\angle A+m\angle B+m\angle C=180[/tex]
Substitute:
[tex](37)+(55)+m\angle C=180[/tex]
Thus:
[tex]\displaystyle m\angle C=88^\circ[/tex]
We are also given that the length of the bridge is 5,280 feet. Since we want to find x, we can use the Law of Sines:
[tex]\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}[/tex]
The variables do not really matter. It is more important that we align the angles with their respective (i.e. opposite) sides.
The respective side to ∠C is AB which measures 5280.
The respective angle to x is ∠B, which is 55°.
Hence:
[tex]\displaystyle \frac{\sin(55)}{x}=\frac{\sin(88)}{5280}[/tex]
Solve for x. Cross-multiply:
[tex]x\sin(88)=5280\sin(55)[/tex]
Thus:
[tex]\displaystyle x=\frac{5280\sin(55)}{\sin(88)}[/tex]
Use a calculator:
[tex]\displaystyle x\approx 4327.76\text{ feet}[/tex]
The first person is about 4327.76 feet away from the island.
5.
4.2 cm
4.2 cm
square centimeters
The total area of triangle in square centimeters is 56.7cm squared .The three angles of the triangle add up to 180 degrees.
what is triangle ?The term "trigon" is occasionally (though not frequently) used to refer to a triangle, a 3-sided polygon. Every triangle consists of a set of three angles and three sides, some of which may be the same. The three angles of the triangle add up to 180 degrees. With three sides and three vertices, triangles are a specific type of polygon in geometry. The two-dimensional figure displayed here has three straight sides. A triangle is a type of 3-sided polygon.
here
Area of each triangles is 4.2 x 8.2 or 34.44.
There are two triangles, thus you don't need to divide by two.
In addition, 8.2 is obtained by deducting the top length from the overall length. (13.5-5.3)
rectangle: 22.26 x 5.3
56.7 square meters is the entire area.
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The correct question is
What is the area, in square centimeters, of the triangles are?
a) 5.3 cm
b) 4.2 cm
c) 13.5 cm
What is the SHAPE of the 22nd figure?
The color of the 15th figure is green.
The shape of the 40th figure star.
The shape of the 22nd figure triangle.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
We have,
The pattern of shapes we get is:
circle - Triangle - Square - Star
The pattern of color we get is:
Purple - Red - Green
Now,
The color of the 15th figure.
= 15 is a multiple of 3
= 5 x 3
So,
Green will be the color of the 15th figure
Now,
The shape of the 40th figure.
= 40 is a multiple of 4
= 10 x 4
So,
Star will be the shape of the 40th figure.
Now,
The shape of the 22nd figure.
= 22 ÷ 4
We get 2 as the remainder.
So,
Triangle will be the shape of the 22nd figure.
Thus,
The 15th figure color is green.
The 40th figure is a star.
The 22nd figure is a triangle.
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On a map, the distance from Langhorne to Tannersville measures 2 centimeters. What is the actual distance if the scale of the map shows that 1 centimeter is equal to 30 kilometers?
Answer:
I believe the answer is 60 kilometers.
Step-by-step explanation:
I forgot how to do this- we are doing a review and I dont know how to do this-
Answer:
36.373 not rounded
Step-by-step explanation:
Using pythagoras theorem
a^2 =b^2 +c^2
a always is the hypotenuse (the opposite side to the 90 angle)
b and c are the other sides obviously
So here we have a = 38
let b =11
So for c =sqrt(38^2 - 11^2)=36.373
What is 4(a)(c)? Calculate the answer.
The height of adult males on a given South Pacific Island is approximately normally distributed with mean 65 inches and standard deviation of 4 inches. a). Taller than 64 inches b.) shorter than 62 inches c.) between 64 inches and 68 inches d.) between 58 and 68 inches e.) taller than 58 inches
Answer:
a) 0.59871
b) 0.22663
e) 0.95994
Step-by-step explanation:
The height of adult males on a given South Pacific Island is approximately normally distributed with mean 65 inches and standard deviation of 4 inches.
We solve using z score
z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 65 inches
σ is the population standard deviation = 4 inches
a). Taller than 64 inches
This means x > 64
Hence,
64 - 65/4
=- 1/4 = -0.25
P-value from Z-Table:
P(x<64) = 0.40129
P(x>64) = 1 - P(x<64) = 0.59871
b.) shorter than 62 inches
Hence,
62 - 65/4
=- 3/4 =- 0.75
P-value from Z-Table:
P(x<62) = 0.22663
c.) between 64 inches and 68 inches
Hence,
for 64 inches
64 - 65/4
=- 1/4 = -0.25
P-value from Z-Table:
P(x = 64) = 0.40129
For 68 inches
Hence,
68 - 65/4
= 3/4= 0.75
P-value from Z-Table:
P(x = 68) = 0.77337
d.) between 58 and 68 inches
e.) taller than 58 inches
Hence,
58 - 65/4
= -6/4 = -1.5
P-value from Z-Table:
P(x<58) = 0.040059
P(x>58) = 1 - P(x<58) = 0.95994
Match the solution to its expression.
Answer:
1/3 + 1/3 = (1+1)/3 = 2/3
1) 2/3
5/7 - 2/7 = (5-2)/7 = 3/7
2) 3/7
so all you have to do is add or sub the fractions together.
1/3 + 1/3 = 2/3
5/7 - 2/7 = 3/7
for the first box is 2/3
Second box is 3/7
GOODLUCK
batch of hot chocolate is made with 21 teasoons of cocoa and 7 cups of milk.
How many teaspoons of cocoa are needed for every cup of milk?
On the double number line below, fill in the given values, then use
multiplication or division to find the missing value:
cups of milk
Answer:
Step-by-step explanation:
Ya
12x+105=55x+0 solve for x
12y=155 sovle for y
Answer:
Step-by-step explanation:
12x + 105 = 55x + 0
=> 12x + 105 = 55x
=> 55x - 12x = 105
=> 43x = 105
=> x = 105/43
12y = 155
=> y = 155/12
Write four different expressions for the perimeter of a square whose sides are all s 2 2 units long.
Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both.
What are expressions in maths?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You may think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.For a square whose side are 2 units long is :
= 2 + 2 x 2 + 2
= ( 2 + 2 ) x 2
= 2 x 4
= 2 x 3 + 2 = 8
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Write the standard equation of the circle.
Geometry b
The standard equation of the circle will be;
⇒ (x - 3)² + (y + 5)² = 16
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The circle is shown in figure.
Now,
Here, By the figure;
The radius of the circle = 7 - 3
= 4 units
And, The center of circle = (3, - 5)
We know that;
The standard equation of the circle is,
⇒ (x - h)² + (y - k)² = r²
Where, (h, k) = center and r is radius.
So, We get;
The standard equation of the circle is,
⇒ (x - 3)² + (y - (-5))² = 4²
⇒ (x - 3)² + (y + 5)² = 16
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Sara's mom takes the parkway to work. It takes her 30 minutes to travel from mile marker 88 where she enters to her exit at mile marker 121. What is her average speed
Sara's mom average speed is 66mph. The next step is to divide the distance by the time: 33/0.5 = 66 mph.
What is average speed ?You may estimate the average pace at which an object will go a distance by looking at its average speed. Average speed is calculated by dividing a quantity by the time required to obtain that quantity.
Finding the distance and the time is necessary to calculate speed.
In this situation, you must deduct mile marker 88 from 121 to determine the distance.
121 - 88 = 33mile
Even though the time is 30 minutes, you're probably interested in miles per hour. 30 minutes must be converted to 0.5 hours.
The next step is to divide the distance by the time: 33/0.5 = 66 mph.
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What is the relationship between the ratios of sin x° and cos y°?
The ratios are both identical (three fifths and three fifths).
b
The ratios are opposites (negative three fifths and three fifths).
c
The ratios are reciprocals (three fifths and five thirds).
d
The ratios are both negative (negative five thirds and negative three fifths).
Answer:
A. The ratios are both identical (three fifths and three fifths).
Step-by-step explanation:
ratio means fraction
ratio also means division
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"SOHCAHTOA"
sine equals opposite over hypotenuse cosine equals adjacent over hypotenuse tangent equals opposite over adjacent
mathworldwolframcom
sine equals opposite over hypotenuse
sine X equals 3 over 5
cosine equals adjacent over hypotenuse
cosine Y equals adjacent over hypotenuse
cosine Y equals 3 over 5
side thats 3 is adjacent for y but
side thats 3 is also opposite for x
both identical, aka C on their question is right
its the 1st option for flvs
Help :P Easy math =D
Answer
16
STEP BY FŔIGGIN STEP
simplify the first one into an exponent
-
2 exponent 8
then the second one
-
2 exponent 4
Now simplify the exponents
2 exponent 8 = 256
2 exponent 4 = 16
Use that knowledge to divide the two
256 ÷ 16 = 16
Hope I helped! :)
Answer: 16 =D
Step-by-step explanation:
2.2.2.2.2.2.2.2/2.2.2.2=16
hope this helped
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Twice the sum of a number and three is subtracted from six times a number
Answer: 2(x+6)=3(x-3)
Step-by-step explanation:
Student tickets cost $2.00 and everyone else
is $4.00. If $500 was made by selling 175
tickets, how many student tickets were sold?
Answer:
Student =100
Step-by-step explanation:
the sides of a triangle are 7,10,12 cm long. Classify the triangle
Answer:340 cm long
Step-by-step explanation: multiply 7 x 10 then 70 x 12
Find the flux of F across S,
F. N dS
where N is the upward unit normal vector to S.
F(x, y, z) = xi + yj + zk
S: z = 1 − x^2 − y^2, z ≥ 0
The flux of F across S will be [tex]\frac{3\Pi}{2}[/tex]
A vector of magnitude 1 that is at some point perpendicular to a two-dimensional curve is referred to as the unit normal vector. Normally, you search for a function that returns not just one vector but all potential unit normal vectors of a given curve.
A vector that is perpendicular to a surface at a certain location is known as the normal vector, also referred to as the "normal" to a surface. The inward-pointing normal (pointing toward the interior of the surface) and outward-pointing normal are often distinguished when normals are taken into consideration on closed surfaces.
[tex]$Z_x=-2 x: \quad Z_y=-2 y$[/tex]
[tex]$N=\langle 2 x, 2 y, 1\rangle \quad: f=\langle x, y, z\rangle$[/tex]
[tex]f. $N=2 x^2+2 y^2+z=2 x^2+2 y^2+1-x^2-y^2$[/tex]
=1+x^2+y^2
[tex]x^2+y^2=1\\ \Rightarrow \quad x=r \cos \theta\\ \Rightarrow \quad y=r \sin \theta \\ \Rightarrow x^2+y^2=r^2 \\ 0 < r < 1: \quad 0 < \theta < 2 \pi[/tex]
[tex]$R \cdot v=\int_0^{2 \pi} \int_0^1\left(1+r^2\right)(r) dr d \theta$[/tex]
[tex]$=2 \pi \int_0^1 r+r^3 d r$[/tex]
[tex]$2 \pi\left[\frac{r^2}{2}+\frac{r^4}{4}\right]_0^1$[/tex]
[tex]$=(2 \pi)\left(\frac{1}{2}+\frac{1}{4}\right)$[/tex]
[tex]$=\frac{(2 \pi)(3)}{42}=\frac{3 \pi}{2}$[/tex]
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Give the most precise classification for each figure
Answer:
D
Step-by-step explanation:
Answer:
A. Quadrilateral
Step-by-step explanation:
quardrilateral Shapes have 4 corners. and That is the Most Precise classification of this Shape
An's backpack weighs as much as Lin's backpack. Clare's backpack weighs as much as Lin's backpack. Whose backpack weighs the most? Whose backpack weighs the least? Explain or show your reasoning.
Answer:
All 3 backpacks are equal in weight, there is none that is heavier or lighter than the others. That is, the 3 backpacks have the same weight.
Step-by-step explanation:
Given that An's backpack weighs as much as Lin's backpack, and Clare's backpack weighs as much as Lin's backpack, to determine whose backpack weighs the most and whose backpack weighs the least the following mathematical reasoning must be considered:
A = L
C = L
Therefore, A = C.
Since all 3 backpacks are equal in weight, there is none that is heavier or lighter than the others. That is, the 3 backpacks have the same weight.
Find the distance between the following two points: (3,-6) (-1,-8)
A triangle has an angle that measures 126°. The other two angles are in a ratio of 11:16. What are the measures of those two angles?
Therefore, the measures of those two angles are 33° and 24°.
Define angles.An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which means "corner," is the source of the English term "angle."
Define geometry.Geometry is a branch of mathematics that studies the sizes, shapes, positions, angles, and dimensions of things.
We know, the sum of the angles in a triangle is always 180 degrees.
126 + x + y = 180
x + y = 54
Given that the two angles are in a ratio of 11:16, the proportion:
x/y = 11/16
Solving for x and y, we get:
x = 11y/16
We substitute this equation into the equation x + y = 54 and we get:
11y/16 + y = 54
Solving for y we get y = 24. Then we can use the proportion to find x:
x = 11 * 24 / 16 = 33.
So the two angles are 33° and 24°.
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a pair of sunglasses originally priced at $50 are now on sale for $31. What is the discount percentages?
Answer:
They are discounted for 38% off.
Shen's chocolate bar is 67% cocoa. If the weight of the chocolate bar is 59 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
Shen's chocolate bar is 67% cocoa. If the weight of the chocolate bar is 59 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.
Deshad runs a river tubing company that serves 300 customers a day during sunny, summer days. He knows that 45% of the customers rent life jackets. Suppose that Deshad calculates the daily proportion p ^ on top of customers who rent life jackets from his sample of 300. We can assume the customers each day represent a random sample
Here acccording to the question,We are examining the conditions under which the sampling distributions of the sample proportions given.
What is sampling distribution?
Sampling distribution is a statistic that determines the probability of an event based on data from a small group within a large population. Its primary purpose is to establish representative results of small samples of a comparatively larger population. Since the population is too large to analyze, you can select a smaller group and repeatedly sample or analyze them. The gathered data, or statistic, is used to calculate the likely occurrence, or probability, of an event.
Sampling distribution According to the given ScenarioWe are examining the conditions under which the sampling distributions of the sample proportions appear uniform, roughly normal, skewed to the left or skewed to the right.
When np10 and n(1p)10, where n is the sample size and p is the sample of proportions, are true, we know that the sampling proportions of the sample distributions will have a normal shape.
Aforementioned that our sample size is 300 people and that p = 0.45, we can use the given data to calculate
Successes anticipated: np= 300(0.45) = 135 10
Failures predicted: n(1p)=300 (10.45)=165 10
Since both of these statements are accurate, sample distribution sampling proportions will have a normal shape.
Because we anticipate each sample to have at least 10 successes and 10 failures, we have a normal sampling distribution.
As a result, the sample distribution has a roughly normal shape.
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