Simplify each exponential expression using the properties of exponents and match it to the correct answer.
Answers
The match of solutions with the exponential expressions is
1) [tex]\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}=2[/tex]
2) [tex](3^3) (4^0)^2 (3(2))^{-3} (2^2)=1/2[/tex]
3) [tex]\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} =2[/tex]
4) [tex]\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}=1[/tex]
What are properties of exponents?The base will be multiplied by itself a certain number of times, as indicated by the exponent (also known as a power or degree).
What are the formulae/ properties for exponents?Formulae for solving exponents are referred to as exponents formulas. The exponent of a number is written as [tex]x^{n}[/tex], which means that x has been multiplied by itself n times.
[tex]x^{n}(x^{m})=x^{n+m} \\\frac{x^{n} }{x^{m} }=x^{n-m} \\(x^{n} )^{m} =x^{nm} \\((x)(y))^{n}=x^{n}(y^{n} \\x^{0}=1[/tex]
1) the solution of the first expression will be
[tex]\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}[/tex]
[tex](2^3) (3^{-6} ) (5^2) (3^4) / (3^{-2}) (10^2)= (2.2^2.5^2) (3^{-6}.3^4) / (3{^-2}) (10^2)= (2)(10^2) (3^{-2}) / (3^{-2}) (10^2)\\=2[/tex]
2)The solution of the second expression will be
[tex](3^3) (4^0)^2 (3(2))^{-3} (2^2)[/tex]
Any number with power zero is 1.
So,
[tex](3^3) (1^2) (3^{-3}) (2^{-3}) (2^2)= (2^{(-3+2)})=2^-1\\= 1/2[/tex]
3) The solution of third expression will be
[tex]\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} \\= \frac{(12^7) (2^{-3}) (5^{-3}) (5^2)}{(12^7) (5^{-1}) (2^{-4})} =\frac{(2^-3) (5^{(-3+2)})}{(5^{-1}) (2^{-4})} = \frac{(2^{-3}) (5^{-1})}{(5^{-1}) (2^{-}4)} = \frac{1}{(2^{-1})} = 2[/tex]
4) The solution to the forth expression will be
[tex]\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}\\=2^{0}\\ =1[/tex]
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Answer:
The person above litteraly gave you the answer just reread the first equations and then you will figure it out
Step-by-step explanation:
Related Questions
Lines de and ab intersect at point c. lines d e and a b intersect at point c. angle a c e is (2 x 2) degrees. angle e c b is (5 x 3) degrees. what is the value of x? 12 25 38 52
Answers
The correct option is B.
The value will be = 25
What is the Angles of the triangle?
The sum of the two interior angles that are not adjacent to it equals the exterior angles of a triangle, but the interior angles of a triangle always add up to 180°. Subtracting the angle of the desired vertex from 180° is another method for determining a triangle's exterior angle.
Suppose point C is where lines DE and AB converge.∠ACE = (2x+2)°
∠ECB = (5x+ 3)°
Angles ACE and ECB are additional angles according to the linear postulate, as seen in the attached diagram.
Therefore:
∠ACE+∠ECB = 180°
(2x+2)+(5x+3) = 180
2x+ 5x+ 2+ 3 = 180
7x + 5 = 180
7x = 175
x= 175/7
x = 25
Thus the value will be = 25
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I understand that the question you are lookin for is :
Lines de and ab intersect at point c. lines d e and a b intersect at point c. angle a c e is (2 x 2) degrees. angle e c b is (5 x 3) degrees. what is the value of x?
A.12
B. 25
C. 38
D. 52
The ratio of height to the base radius of a cone is 3:4. If the volume of the cone is 2000πcm³, find its radium, in cm.
Who can help me to answer this question? Please and thank you very much .
Answers
Answer:
20 cm
Step-by-step explanation:
The volume, V, of a cone with radius r and height h is given by the formula
V = [tex](1/3) \pi r^2 h[/tex]
Since it is given that the ratio of h to r is 3/4 we have the relationship
h/r = 3/4 ==> h = (3/4)r
Substituting for h in the volume equation gives us an expression in terms of r
[tex](1/3)\pir^2h = (1/3) \pi r^2 (3/4)r\\(1/3 ) (3/4) = 1/4\\[/tex]
So the expression simplifies to[tex](1/4)\pi r^3[/tex]
We are given that this volume is 2000π cm³
So
(1/4)πr³ = 2000π
Eliminating π on both sides and multiplying by 4 on both sides gives
r³ = 8000
r = ∛8000 = 20 cm Answer
A casino offers the following game: you draw one card from a standard 52-card deck. If you draw a jack, you win $1.25. If you draw a queen, you win $3.25. If you draw a king, you win $4.5 dollars. If you draw any ace except the ace of spades, you win $6.5. If you draw the ace of spades, you win $7.75. The entry fee to play this game is $1.75. Compute the expected value of this gamble (include the entry fee in your expected value).
Answers
Let [tex]W[/tex] be the random variable for the winnings from playing the game once.
• There are 4 jacks in the deck, so you draw a jack with probability 4/52 = 1/13. In this case you "win" $1.25 - $1.75 = -$0.50.
• There are 4 queens, with draw probability 4/52 = 1/13 and winnings $3.25 - $1.75 = $1.50.
• There are 4 kings, with draw probability 4/52 = 1/13 and winnings $4.50 - $1.75 = $2.75.
• There are 4 aces, and 3 of these are not of the spade suit, so the probability of drawing any of these is 3/52 and you win $6.50 - $1.75 = $4.75.
• There is only 1 ace of spaces, with draw probability 1/52 and winnings $7.75 - $1.75 = $6.00.
• Adding these up, it follows that the probability of drawing any other card is 1 - (1/13 + 1/13 + 3/52 + 1/52) = 10/13, in which you have the privilege of "winning" -$1.75.
So, the probability mass function for [tex]W[/tex] is
[tex]\mathrm{Pr}(W=w) = \begin{cases} \dfrac1{13} & \text{if } w \in \{-\$0.50, \$1.50, \$2.75\} \\\\ \dfrac3{52} & \text{if } w = \$4.75 \\\\ \dfrac1{52} & \text{if } w = \$6.00 \\\\ \dfrac{10}{13} & \text{if } w = -\$1.75 \\\\ 0 & \text{otherwise} \end{cases}[/tex]
The expected winnings from playing one round of this game are
[tex]\Bbb E[W] = \displaystyle \sum_w w\,\mathrm{Pr}(W=w)[/tex]
[tex]\Bbb E[W] = \dfrac{-\$0.50 + \$1.50 + \$2.75}{13} + \dfrac{3\cdot\$4.75}{52} + \dfrac{\$6.00}{52} + \dfrac{10\cdot(-\$1.75)}{13}[/tex]
[tex]\Bbb E[W] \approx \boxed{-\$0.67}[/tex]
PLEASE help me, im really struggling on this.
Answers
The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Let x represent the number of pounds of bananas sold and y represent the grapes sold, hence:
x + y = 52 (1)
Also:
x + 2.25y = 72 (2)
The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72
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The cross-sectional areas of a triangular prism and a right cylinder are congruent. the triangular prism has a height of 5 units, and the right cylinder has a height of 5 units. which conclusion can be made from the given information?
Answers
The conclusion can be made from the given information
The volume of the triangular prism is equal to the volume of the cylinder
Given that there are two figures
1. A right triangular prism
2. Right cylinder
The area of the cross-section of the prism is equal to the Area of a cross-section of the cylinder.
Let this value be A.
Also given that the Height of prism = Height of cylinder = 6
The volume of a prism is will be :
[tex]V _{prism} = cross section area \times height[/tex]
[tex]V _{prism} = A \times 6 = 6A[/tex] (1)
The Cross section of the cylinder is a circle.
hence the Area of the circle will be:
Area of cross-section, A = [tex]\pi \times r^2[/tex]
so, the Volume of the cylinder will be :
[tex]V _{cylinder} = \pi \times r^2 \times h[/tex]
[tex]V _{cylinder} = A \times h = A \times 6 = 6A[/tex] (2)
From equations (1) and (2) we can say that
The volume of the triangular prism is equal to the volume of the cylinder.
What is a triangular prism?A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry.If the sides of a right triangular prism are not rectangular, the prism is oblique. Right triangle prisms with square sides and equilateral bases are known as uniform triangle prisms.It is, in essence, a polyhedron with two parallel sides and three surface normals that are all in the same plane (which is not necessarily parallel to the base planes).There are parallelograms in these three faces. The identical triangle appears in every cross-section running parallel to the base faces.To learn more about triangular prism with the given link
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The half life of a substance is defined as the time required for the substance to decrease by half. If the weight of a substance begins at 128 grams, and the half life is 7 years, what will be the weight of the substance after 28 years?
Answers
the weight of the substance after 28 years is 8 grams.
How to determine the amountWe have that the half life of a substance is defined as the time required for the substance to decrease by half
The formula for calculating the half - life of a material is given as;
[tex]N(t) = N0 (\frac{1}{2} )^\frac{t}{t^\frac{1}{2} }[/tex]
Where
N(t) is final amountNo is the initial amount = 128 gramst1/2 is the half life = 7 yearst is the time elapsed = 28 yearsSubstitute into the formula
N(t) = 128 × (0. 5) ^28/ 7
N (t) = 128 × ( 0. 5) ^ 4
N(t) = 128 × 0. 0625
N(t) = 8 grams
Thus, the weight of the substance after 28 years is 8 grams.
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400
300
200
100
2
4
6
8
X
Is the graphed function linear?
Yes, because each input value corresponds to
exactly one output value.
O Yes, because the outputs increase as the inputs
increase.
O No, because the graph is not continuous.
O No, because the curve indicates that the rate of
change is not constant.
Answers
It exists not linear the curve indicates that the rate of change exists not constant.
What is a linear Function?
Linear functions exist as those whose graph exists as a straight line. A linear function exists that can be characterized by the equation
y = mx + c, Where m exists the slope and c exists the intercept on the
y-axis. A linear function contains one independent variable and one dependent variable.
Therefore, the correct answer is option c) No, because the curve indicates that the rate of change is not constant.
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Let the domain of discourse s be people. let a be statisticians and let b be people who bathe regularly. in set notation, what is the sentence all statisticians bathe regularly.
Answers
If set A shows the statistians and B shows the person who bath regularly then the notation which shows that all statistians bath regularly is A∩B.
Given that A shows the statistians and B shows the person who bath regularly.
We are required to show the sentence that "All statistians bath regularly"in set notation.
We know that set is a collection of things, place,anything which can be measured or denoted as something else.
"∪" shows union means when we put this sign between two sets then the resulting set will contain all the elements of both the sets.
"∩" shows intersection means when we put this sign between two sets then the resulting set will contain all the common elements of both the sets.
Since A represents statistians and B represents people who bath regularly and we require statistians who bath regularly is A∩B.
Hence if A shows the statistians and B shows the person who bath regularly then the notation which shows that all statistians bath regularly is A∩B.
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Which function is the inverse of f(x) = 2x + 3?
05²¹(x) = -1/2 x 1/2
s^²(x) = { x = 1/
2
O f¹(x) = -2x + 3
O f¹(x)=2x+3
Answers
Answer: Option 2
Step-by-step explanation:
Let f(y)=x.
[tex]x=2y+3\\\\x-3=2y\\\\y=\frac{1}{2}x-\frac{3}{2}\\\\f^{-1}(x)=\frac{1}{2}x-\frac{3}{2}[/tex]
The inverse of the function is,
⇒ f ⁻¹(x) = 1/2 (x - 3)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = 2x + 3
Now,
We can find the inverse of function as;
⇒ f (x) = 2x + 3
Put y = f (x);
⇒ y = 2x + 3
Solve for x;
⇒ y - 3 = 2x
⇒ x = 1/2 (y - 3)
⇒ f ⁻¹(x) = 1/2 (x - 3)
Thus, The inverse of the function is,
⇒ f ⁻¹(x) = 1/2 (x - 3)
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how do i get the method on how to solve this x+5(-2)-1
Answers
Answer:
I forgot the name but I can show you how to do it lol
Step-by-step explanation:
x+5(-2)-1
x-10-1 we multiplied 5 and -2
x-11
x=11
how I did the last one is there is a non-existent 0 with an equal sign like my teacher says so we added 11 to both sides.
How do I solve this question.
Answers
Hello, the solution of the geometry problem is in this photo.
AOC = 136°
BOC = 44°
a=44
AOC=3*44+4
=136
COB=44
check ple im not sure its right
Answers
Answer:
8
Step-by-step explanation:
You are correct The distance from -6 to 2 is 8.
Three divers went scuba diving in the ocean for a couple of hours. The table shows how much oxygen they had left in their oxygen tanks.
Diver Oxygen (liters)
Alexis seventy nine over eighth
Dante 9.3
Sofia nine and eight over fifteenth
Place the divers in order from least to greatest based on the number of liters left in their oxygen tank.
Sofia, Dante, Alexis
Alexis, Sofia, Dante
Dante, Alexis, Sofia
Dante, Sofia, Alexis
Answers
The divers in order from least to greatest based on the number of liters left in their oxygen tank will be Alexis, Dante, and Sofia. The correct answer is B.
What is ascending order?In mathematics, placing numbers in ascending order refers to doing so from least to largest from left to right. When numbers are arranged in ascending order, they are done so from least to largest.
Given that three divers went scuba diving in the ocean for a couple of hours. The table for the oxygen requirement is given below:-
Diver Oxygen (liters)
Alexis Seventy nine over eighth
Dante 9.3
Sofia Nine and eight over fifteenth
The Numbers are:-
Alexis ( Seventy nine over eighth) = 79 / 9 = 8.78
Dante = 9.3
Sofia ( Nine and eight over fifteenth ) = 9(9/15} = 9.6
The arrangement from least to highest will be Alexis, Dante, and Sofia.
The correct options are given below:-
Sofia, Dante, Alexis
Alexis, Dante, and Sofia.
Dante, Alexis, Sofia
Dante, Sofia, Alexis
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Answer:
Dante, Alexis and Sofia
Step-by-step explanation:
please tell me if I'm wrong but I'm positive its Dante, Alexis and Sofia
Find x. A. 11√6/2 B. 22 C. 33 D. 11√3/2
Answers
Answer:
B
Step-by-step explanation:
using the tangent ratio on the triangle on the right and the exact value
tan60° = [tex]\sqrt{3}[/tex] , then letting the altitude be h
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{11\sqrt{6} }{h}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by h )
11[tex]\sqrt{6}[/tex] = h × [tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
11[tex]\sqrt{2}[/tex] = h
using the sine ratio in the triangle on the left and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{x}[/tex] = [tex]\frac{11\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{2}[/tex] × x = 22[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
x = 22
i just need explanations on how to solve this. i have an upcoming test. please help.
[tex]\frac{3x}{6y} x\frac{7}{12y}[/tex]
Answers
The product of the given expression is 7x/24y²
Product of fractionsGiven the product of the fractions below
3x/6y * 7/12y
Simplify
x/2y * 7/12y
Multiply the numerator and denominator to have:
7x/24y²
Hence the product of the given expression is 7x/24y²
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someone help me out pleaseee
Answers
Answer:
[tex] \frac{29}{18} = 1 \frac{11}{18} [/tex]
Step-by-step explanation:
To solve this question, we definitely need to make w the subject.
[tex]w - \frac{5}{6} = \frac{7}{9} \\ w - \frac{5}{6} + \frac{5}{6} = \frac{7}{9} + \frac{5}{6} \\ w = \frac{29}{18} \\ = 1 \frac{11}{18} [/tex]
Find the surface area of the composite figure.
5 cm
6 cm
20 cm
4 cm
5 cm 4 cm
SA =
12 cm
-6 cm
[?] cm²
Answers
Answer:
[tex]644cm^2[/tex]
Step-by-step explanation:
First we'll work out the surface area of the pink figure.
That's the area of the two 5 by 6 rectangles on the top and bottom, plus the area of the two 5 by 20 and two 6 by 20 rectangles on the sides.
However, we note that the purple figure is blocking out a 6 by 12 section on the pink figure, so we'll need to subtract this.
The above works out to [tex]2\times(30+100+120)-72=428 cm^2[/tex].
Then we'll work out the surface area of the purple figure.
This will be the area of the two 4 by 6 rectangles at the top and bottom, plus the area of the two 4 by 12 and one 6 by 12 rectangles on the sides. Note that there's only one 6 by 12 rectangle because the other face is joined to the pink figure, so it's blocked out.
That's [tex]2\times(24+48)+72=216cm^2[/tex].
So the total surface area is [tex]428+216=644cm^2[/tex].
olives and pineapple pizza delivered two large pizzas cut into eight slices each. james and his sister both ate 5/8 of the pizza together. how many slices are left?
Answers
Alvin and Bala had 26 stickers. Alvin had 8 more stickers than Bala. How many
stickers did Bala have?
Answers
Answer:
Bala has 5 stickers
( please mark me as brainliest )
Step-by-step explanation:
total stickers = 26
= 26/2
=13
stickers Alvin had more = 8
=13 + 8
= 21
= 26 - 21
= 5
.. . Bala has 5 stickersPlease helppppp!!
Question #1 (Question un ) : What is the smallest positive integer k such that k/660 can be expressed as a terminating decimal?
Give BRAINLIST IF ANSWER!!!!!
Answers
Answer:
k = 33
Step-by-step explanation:
Terminating decimal numbers: Decimals that have a finite number of decimal places.
For a decimal to be terminating, the factors of the denominator must only contain 2 and/or 5. As 2 and 5 are prime numbers, use prime factorization to rewrite the denominator.
Prime factorization of 660:
⇒ 660 = 2 × 2 × 3 × 5 × 11
⇒ 660 = 2² × 3 × 5 × 11
Therefore:
[tex]\implies \sf \dfrac{k}{660}=\dfrac{k}{2^2 \cdot 3 \cdot 5 \cdot 11}[/tex]
The fraction will only be a terminating decimal if both 3 and 11 in the denominator are canceled out. To do this, their lowest common multiple must be the numerator:
⇒ LCM of 3 and 11 = 3 × 11 = 33
[tex]\implies \sf \dfrac{33}{660}[/tex]
[tex]\implies \sf k=33[/tex]
Therefore, the smallest positive integer k such that k/660 can be expressed as a terminating decimal is 33.
Answer:
33
Step-by-step explanation:
Which expression is equivalent to x^2 + 5x - 6? Explain how.
(1) (x + 3) (x - 2)
(2) (x + 2) (x - 3)
(3) (x - 6) (x + 1)
(4) (x + 6) (x - 1)
Answers
Answer:
(4) (x + 6)(x - 1)
Step-by-step explanation:
Hello!Given expression
[tex]x { }^{2} + 5x - 6[/tex]
Find numbers when they are multiplied gives 6 and when they are added which gives 5.
Thus, these numbers are -1 & 6.
[tex]x {}^{2} + 6x - x - 6 \\ x(x + 6) - 1(x + 6) \\ (x + 6) \: \: (x -1 )[/tex]
Can also check the multiplied values of these two values.
Hope it helps!
Answer:
(4)
Step-by-step explanation:
Determine two multiples which when multiplied gives - 6(the last term in the equation), when added, gives +5 (the middle term in the equation).
Multiples are: +6 and -1
input the two multiples in place of the middle term (+5x)
=x^2+6x-1x-6
Collect like terms
=x(x+6)-1((x+6)
Answer= (x+6)(x-1)
Confirm answer above:
Open bracket
x(x-1)+6(x-1)
x^2-x+6x-6
x^2+5x-6 (initial equation).
help solve math problem
Answers
Answer:
(c) x < -5.170
Step-by-step explanation:
The given function is an exponential function with a decay factor of 0.5 and a y-intercept of 0.5^2 = 0.25. It will be larger for more negative x-values.
EstimateWe know that 2^3 = 8, so (1/2)^-3 = 8. This means the exponent of 0.5 in the given inequality will be more negative than -3:
x +2 < -3
x < -5 . . . . . . . . subtract 2
The only answer choice in this range is ...
x < -5.170
Exact solutionTaking the logarithm of both sides of the inequality, we have ...
(x +2)log(0.5) > log(9)
x +2 < log(9)/log(0.5) . . . . . . log(0.5) < 0, so the inequality reverses
x < log(9)/log(0.5) -2 . . . . . . subtract 2
x < (0.95424251)/(-0.30103000) -2 = -3.1699250 -2
x < -5.1699250 ≈ -5.170
Help please I need this asap
Answers
Answer:
It is a little hard to see. I think that it is 10.
Step-by-step explanation:
They break even where the two lines intersect. If you look at the bottom of the graph and find 10 and then trace that straight up, I think that is where I see the lines crossing.
How many faces, edges and vertices does the shape below have?
Faces:
Edges:
Vertices:
Answers
the number of faces, edges and vertices the shape below has is 4, 4 and 6 respectively.
How to determine the numberIt is important to note that according to Euler’s formula for any convex polyhedron, the number of Faces (F) and vertices (V) added together is exactly two more than the number of edges (E).
It is mathematically written as;
Face + vertices = 2 + edges
F + V = 2 + E
From the figure given, we can see that it is a kite
Number of vertices = 4
Number of faces = 4
2 + edges = faces + vertices
2 + edges = 4 + 4
2 + edges = 8
Edges = 8 - 2
Edges = 6
Thus, the number of faces, edges and vertices the shape below has is 4, 4 and 6 respectively.
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A six-sided die is rolled. What is the probability of rolling a four or an odd number?
Answers
Answer:
2/3 or 66%
Step-by-step explanation:
there are 3 odd numbers on a 6 sided die
3 + 1 = 4
4/6 = 2/3
A 3D electron microscope magnifies objects 1 000 000 times. A water molecule has a diameter of
[tex]2 \times {10}^{ - 10} [/tex]
m.
How large will it appear in the microscope?
give your answer in milimetres.
Answers
The diameter of the water molecule is 2 * 10^-4 m or 0.2 mm.
What is a microscope?The term microscope refers to a device that is capable of increasing the size of an object. If the object is quite large, then it can be seen with the unaided eye.
Microscopes are very important in the sphere of scientific research as it was very instrumental in the study of cells and in the process of examination of other samples. There are several kinds of microscopes hay could be used for several purposes such as;
Electron microscopeCompound microscopeScanning electron microscope Light microscope etc.Each of these microscopes have a unique instance in which they could be utilized.
Given that the diameter of water is about 2 * 10^-10 m, a magnification by 1 000 000 times gives a diameter of 2 * 10^-4 m or 0.2 mm.
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Which values represent solutions to cosine (startfraction pi over 4 endfraction minus x) = startfraction startroot 2 endroot over 2 endfraction sine x, where x is an element of [0, 2pi)?
Answers
The given trigonometric function consists of trigonometric values of common angles.
The values that represent the solution to [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex], x ∈ [0, 2·π) are; [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].
What are trigonometric functions?Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilized in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.The given function is: [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex]
Where; x ∈ [0, 2·π).
We have; cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B).
[tex]cos(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}, sin(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}[/tex]Which gives:
[tex]cos(\frac{\pi }{4}-x )=\frac{\sqrt{2} }{2}. cosx+\frac{\sqrt{2} }{2}.sinx[/tex]So, we obtain:
[tex]\frac{\sqrt{2} }{2} .cosx=\frac{\sqrt{2} }{2}.sinx-\frac{\sqrt{2} }{2} .sinx=0\\cosx=0\\cos\frac{\pi }{2} =0[/tex]
Therefore, the possible solutions (x-values) to cos x = 0 are:
[tex]0[/tex] ≤ [tex]\frac{n.\pi }{2}[/tex] ≤ [tex]2.\pi[/tex]
Where, n = 1, 3, 5, .., x ∈ [0, 2·π)
We get: [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].
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Which table represents a function?
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Answer:
choice d
Step-by-step explanation:
I hand this question
Which situation will likely have no correlation?
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B. number of dogs owned versus number of plane tickets bought
Use a left-hand sum with 4
intervals to approximate the area
under f(x) = 4 - x² between
x = 0 and x = 2.
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I hope that this helps :)
Answer:
25 / 4
Step-by-step explanation:
To find the left sum, you need to....
1.) Find Δx
2.) Find [tex]x_{k-1}[/tex]
3.) Find ∑[tex]^n_{k=1}f(x_{k-1})[/tex]Δx
4.) Solve for the left sum