Given \cot A=\frac{3}{7}cotA= 7 3 and that angle AA is in Quadrant I, find the exact value of \cos AcosA in simplest radical form using a rational denominator.
Answers
Answer:
\(\cos A =\dfrac{3\sqrt{58}}{58}\)Step-by-step explanation:
To find:-
The value of cosA .Answer:-
We are here given that , the value of ,
\(\longrightarrow \cot A =\dfrac{3}{7}\\\)
And we are interested in finding out the value of cos A is A is in first quadrant. For that as we know that , cotangent is defined as the ratio of base and perpendicular . That is ,
\(\longrightarrow \cot A =\dfrac{b}{p} \\\)
According to the question,
\(\longrightarrow \cot A =\dfrac{3}{7}=\dfrac{b}{p} \\\)
Let us take the given ratio to be 3x:7x .
Now again as we know that cosine is defined as the ratio of base and hypotenuse. So that ,
\(\longrightarrow \cos A =\dfrac{b}{h} \\\)
Now we don't know the value of hypotenuse. For that we can use the Pythagoras theorem .
Pythagoras theorem:-
In a right angled triangle, the sum of squares of base and perpendicular is equal to the square of hypotenuse.Mathematically,
\(\longrightarrow p^2+b^2=h^2 \\\)
where the symbols have their usual meaning.
Now substitute the respective values to find out the value of hypotenuse as ,
\(\longrightarrow (3x)^2+(7x)^2=h^2\\\)
\(\longrightarrow 9x^2+49x^2 = h^2 \\\)
\(\longrightarrow 58x^2 = h^2\\\)
\(\longrightarrow h =\sqrt{58x^2}\\\)
\(\longrightarrow \boldsymbol{ h = \sqrt{58}x }\\\)
Now we can find the value of cosA as ,
\(\longrightarrow \cos A =\dfrac{b}{h} \\\)
\(\longrightarrow \cos A = \dfrac{3x}{\sqrt{58}x}\\\)
\(\longrightarrow \cos A =\dfrac{3}{\sqrt{58}} \\\)
Rationalize the denominator by multiplying numerator and denominator by √58 as ,
\(\longrightarrow \cos A =\dfrac{3\sqrt{58}}{\sqrt{58}\cdot\sqrt{58}}\\\)
Simplify,
\(\longrightarrow \boxed{\boldsymbol{\cos A =\dfrac{3\sqrt{58}}{58}}} \\\)
This is the required answer.
Related Questions
the graph of a certain quadratic function has no x-intercepts. Which of the following are possible values or the disriminant?
Answers
The possible values for the discriminant include the following:
A. -1
D. -18
What is the x-intercept?In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
Since the graph of this quadratic function has no x-intercepts, we can logically deduce that the zeros, roots, or x-intercepts of this quadratic function must be an imaginary number.
Discriminant, D = b² - 4ac
In conclusion, we can reasonably infer and logically deduce that negative numbers such as -1 and -18 are possible values for the discriminant.
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Complete Question:
The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.
A. -1
B. 3
C. 0
D. -18
rewrite the expression without absolute value bars
Answers
The expression without absolute value bars is 3.84.
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.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
|√10 - 7 |
= | 3.16 - 7 |
= | -3.84 |
= 3.84
Thus,
The value of the expression is 3.84.
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1) Pedro vai fazer um empréstimo de R$ 70.000,00 para uma reforma em seu estúdio de
fotografia e está analisando qual sistema de amortização vai utilizar, de acordo com as
propostas de uma agência financiadora, que trabalha com uma taxa de 0,85% ao mês. Ela
pretende saldar a dívida em 6 anos. Ela decidiu pelo Sistema Price, qual será o valor de cada
prestação? Qual será o valor amortizado na primeira prestação?
Answers
Answer:bb
Step-by-step explanation:
( 14 + 2 ) 2 0 = 5 + 4 0 what type of property is this?
Answers
The question provides the relationship as shown below:
\((\frac{1}{4}+2)20=5+40\)If we solve both sides individually, we have the left-hand side to give
\((\frac{1}{4}+2)20=45\)and the right-hand side to give
\(5+40=45\)Since both sides give the same result, we can attempt to manipulate the left-hand side of the equation with a common property we are familiar with: The Distributive Property.
The Distributive Property is written out as shown below:
\(a(b+c)=(a\cdot b)+(a\cdot c)\)Applying this rule to the left-hand side, we get:
\(\begin{gathered} (\frac{1}{4}+2)20=\frac{1}{4}\cdot20+2\cdot20 \\ =5+40 \end{gathered}\)This is the same expression present on the right-hand side of the equation.
Therefore, the property illustrated is the DISTRIBUTIVE PROPERTY.
look at the picture
Answers
The quadratic inequality (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y contains all the ordered pairs outside the parabola.
What is parabola?
A parabola could be a U-shaped plane curve wherever any purpose is at an equal distance from a hard and fast purpose (known because the focus) and from a fixed line that is understood because the directrix.
Main body:
In this problem we must determine a quadratic inequality of the form:
a · x² + b · x + c < y
Where a, b, c are the real coefficients of the inequality.
First, determine the coefficients of the quadratic inequality (parabola) by solving the system of linear equations:
25 · a - 5 · b + c = 0
4 · a + 2 · b + c = 0
a + b + c = - 18
(a, b, c) = (18 / 7, 54 / 7, - 180 / 7)
Second, write the quadratic in equation:
(18 / 7) · x² + (54 / 7) · x - 180 / 7 < y
hence , the equation is (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y
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If f(x)=1/x
and g(X) = x-2, which of the following is the graph of
(f•g)(x)?
Answers
Answer:
The correct answer would be A) on edge.
Step-by-step explanation:
Edge 2021.
Given m/B = 57°, m/C = 51°,
and AD bisects BAC, find mADC.
Answers
Answer:
Step-by-step explanation: B
znajdź wszystkie rozwiązania
x^4-16=0
Answers
Find the slope of the line. Describe how one variable changes in relation to the other. A. 2; distance increases by 2 miles per hour B. 2; distance decreases by 2 miles per hour C. 1/2; distance increases by 1 mile every 2 hours D. 1/2; distance decreases by 1 mile every 2 hours
Answers
The line's slope is \(\frac{1}{2}\) and the distance increases by 1 mile every 2 hours.
What is a good example of a line's slope?
The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.
A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.
B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.
C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.
D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.
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3/5 (r-7)=1
Please explain step by step on how I solve this problem
Answers
Answer:
r = 8 2/3
Step-by-step explanation:
3/5 (r-7)=1
3/5 * (r-7)=1
5/3 * 3/5 * (r-7)=1 * 5/3 ==> multiply both sides by 5/3 to remove the 3/5
from the left side of the equation and isolate r
1 * (r-7) = 5/3
r - 7 = 5/3 ==> simplify
r = 7 + 5/3 ==> add 7 on both sides to isolate r
r = 7 + 3/3 + 2/3 ==> simplify
r = 7 + 1 + 2/3
r = 8 + 2/3
r = 8 2/3
5x+2=7x-4 what is x and if you can how you did it
Answers
Answer:
x=3
Step-by-step explanation:
2 = 7x−4−5x
2 = 2x−4
2+4 = 2x
6 = 2x
\(\frac{6}{2}\) = x
3 = x
x = 3
I think the answer is X = 3
Are the ratios 6:3 and 4:2 equivalent
Answers
please help me please i really need help please
Answers
Answer:
Step-by-step explanation:
(3x+3y)=63x + -3y = 6
3x + -3y = 6
3x + -3y + 3y = 6 + 3y
3x + 0 = 6 + 3y
3x = 6 + 3y
x = 2 + y
x = 2 + y
Can someone please help meee
Answers
Answer:
90 degrees
Step-by-step explanation:
If two angles are supplementary they are a linear pair which means they form a straight line, and if you know a straight line equals 180 degrees which is the total degrees of a triangle.
Now if you have two supplementary angles and they are congruent that means not only are they right angles but its half of 180 so you divide these pair of 2 by 180 giving you your total of 90 degrees.
Have a nice rest of your day !
It has been observed that, during various forms of social competition, men experience an increase in testosterone levels. A 2018 study investigated whether a similar effect exists with players in e-sports competition. Researchers recruited 26 male e-sports players and asked them to play the competitive e-game, League of Legends. The study found that participants had an average testosterone increase of 1.11 pg/ml after playing League of Legends, with a standard deviation of 15.18 pg/ml. Obtain a 95% confidence interval for the corresponding population parameter.
Answers
Answer:
= ( -4.725, 6.945) pg/ml
Therefore at 95% confidence interval (a,b) = ( -4.725, 6.945) pg/ml
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean gain x = 1.11 pg/ml
Standard deviation r = 15.18 pg/ml
Number of samples n = 26
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
1.11+/-1.96(15.18/√26)
1.11+/-1.96(2.977042931397)
1.11+/-5.835004145539
1.11+/-5.835
= ( -4.725, 6.945) pg/ml
Therefore at 95% confidence interval (a,b) = ( -4.725, 6.945) pg/ml
Jhon walks at 5 km in10 min if Jhon walk's 2.5 km at the same speed, what is the best estimate of the time this will make
Answers
Answer:
5 min
Step-by-step explanation:
Finding the speed
Distance/Time5 km / 10 min0.5 km/minTime taken to walk 2.5 km
Distance/Speed2.5 km / 0.5 km/min5 minWhat is 28% of 307
Enter your answer as a decimal in the box
Answers
Answer:
the answer is 85.96
Step-by-step explanation:
Hope this helps, =)
Complete the solution of the equation. Find the value of y when x equals 2. -8x - 5y = -1 Enter the correct answer. DOA DONE ?
Answers
Answer: -3
Step-by-step explanation:
-8x - 5y = -1
-8(2) -5y = -1
-16 -5y = -1
-5y = 15
y = -3
Aman bought a computer for 24000 and its accessories pack worth for 1750. He sold it all for *26780. Find his gain and gain per cent.
Answers
Answer:
4%
Step-by-step explanation:
Gain percentage = 1030/25750 x 100 = 4%
Answer:
$1,030, 4%
Step-by-step explanation:
Aman spent $25,750 on a computer and accessory packs (totally worth it). He sold it for $26,780. So let's say Aman is at 0 before he bought this. He spent $25,750, so we subtract that from 0 to get -25,750. Then he sells it all for $26,780 (again totally worth it for the person buying). So we add 26,780 to the total.
-25,750 + 26,780 = 1,030
So Aman made a profit of $1,030 (now he can buy a REASONABLY priced MacBook Air or something)
So to find the percentage that he gained, we divide 1,030 by his original spending price, namely 25,750
1,030/25,750 = 0.04
Convert that to percentage form, you get 4%
Also, it's questions like this that make me question whether the people who write these questions into the textbooks should be talked to lol.
A realtor wanted to determine if there was a relationship between the size (in 100 square feet) of a new custom-built home and the price (in thousands of dollars) of the home.
Size, x Price, y
26 235
27 273
41 387
29 253
33 295
34 335
36 395
45 475
22 203
a) Determine the Person Correlation Coefficient.
b) Test whether there is a relation between size and price.
c) Draw the scatter diagram
d) Determine the Least Square line.
e) If a new custom-built home is of a size 3700 square feet what would be its price.
¬¬
Answers
The graphs , solutions and table are attached below and check out the calculation part just by scrolling down.
What is statistics ?In the field of applied mathematics known as statistics, gathering, describing, analyzing, and drawing conclusions from numerical data are important tasks. Probability theory, linear algebra, and differential and integral calculus are the main mathematical foundations of statistics.
Calculationsee the graphs and table attached below
a ) The cluster (points) shows upward direction and nearly to linear form. So it is positive Correlation.)
b ) calculation part for this part has been attached in pictures below since it was not possible to write here .
the regression line of y on x is =
Y = 11.5355X - 58.7667
c ) r^2 = 58313.22 / 62507.5556 = 0.9328
It is high correlation, So the regression equation is good fit to the given data. 93% of the total variation in y occurs because of the variation in their x.
d ) H0: Slope of Regression Coefficient is Zero
H1: Slope of Regression coefficient is not Zero.
calculation part in pictures attached .
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Find the surface area of this triangular promise correct unit
Answers
The surface area of the triangular prism would be =324,000cm²
How to calculate the triangular surface area of the given prism?To calculate the surface area of the triangular prism the formula that should be given would be as follows:
Surface area of triangular prism;
Surface area of triangular prism;= bh+(b1+b2+b3)l
where:
base length = 20cm
height = 15cm
length = 18cm
SA = 20×15(20+15+25)×18
= 300×60×18
= 324,000cm²
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The sector of a circle has an area of 104pi/9
square inches and a central angle with measure 65 degree
. What is the radius of the circle, in inches?
Answers
Answer:
Given:
Area of the sector (A) = 104π/9 square inches
Central angle (θ) = 65 degrees
The formula for the area of a sector of a circle is:
A = (θ/360) * π * r^2
We can rearrange this formula to solve for the radius (r):
r^2 = (A * 360) / (θ * π)
Plugging in the given values:
r^2 = (104π/9 * 360) / (65 * π)
r^2 = (104 * 40) / 9
r^2 = 4160 / 9
r^2 ≈ 462.22
Taking the square root of both sides:
r ≈ √462.22
r ≈ 21.49
Therefore, the radius of the circle is approximately 21.49 inches.
Answer: 8 inches
Step-by-step explanation:
2x-3<1 or 3x-1<17
Solve compound inequality
Answers
The union consists of all of the elements that are contained in each interval.
Inequality Form:
x<6
Interval Notation:
(−∞,6)
If a 10 ft tall adult elephant casts a 2 ft long shadow, then how tall is a statue that casts a 3 ft shadow?
Answers
Given data:
The given height of the elephant is h=10 ft.
The given shadow of the elephant is s=2 ft.
The shadow of the elephant from the height is,
\(\begin{gathered} \frac{s}{h}=\frac{2}{10} \\ =\frac{1}{5} \end{gathered}\)Mulitiply 3 on both sides on right hand side.
\(\begin{gathered} \frac{S}{H}=\frac{3}{3(5)} \\ =\frac{3}{15\text{ }} \end{gathered}\)Thus, 15 feet elephant cast 3 feet shadow.
Find the value of x.
Find the value of y.
Y
61
X
Answers
Answer:
61=x ( vertical opposite angle)
61=y (corresponding angle)
Step-by-step explanation:
y = 61°( corresponding angles)
x = y = 61°(vertically opposite angles)
a line with y-intercept (0,1) which passes for thought the point (1,1)
Answers
Answer:A unique line is defined by any two distinct (not identical) points. You have two distinct, which means you have a line. To find the equation for the line, we start with the slope-intercept equation for a line. This is only a template for a generic line, so we will have to find the specific values of m (slope) and b (y-intercept) that define your line.
The template: y = mx + b
b is the y-intercept, which, if you look at (0,–2), you will see is –2; it is where the line crosses the y-axis. Fill that value of b into our template to get:
y = mx – 2
Now, we only need the value of m, which is the slope. If you have two points on a line, you can calculate the slope of that line. The slope is the change (difference) of y over the change in x (difference) of x for two given points on the line. It's a fraction or ratio though sometimes it can be reduced to an integer.
So, taking your two points, you calculate the slope, m, in the following way:
(x1,y1) = (0,–2)
(x2,y2) = (5,1)
y2 – y1 1 – (–2) 1 + 2 3
m = ________ = ________ = ________ = ____
x2 – x1 5 — 0
Step-by-step explanation:
Two bicycle trails were developed in a new housing development. One trail is
3 1/2 miles long. The other trail is 3/4 as long. How long is the second trail?
Answers
The length of the second trial will be equal to 2(⁵/₈) miles.
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.
Given that two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.
The length of the second trial will be calculated as,
Length = 3/4 x ( 3¹/₂ )
Length = 2(⁵/₈)
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2. Jessica's dining room in her new townhouse is 11 feet wide by 12 feet deep. How many square feet is it?
Answers
Answer:
132 sq ft
Step-by-step explanation:
I need help! (show how you got the answer) -1\2x
Answers
Answer:
please explain what you mean better
Step-by-step explanation:
an element of material is subjected to the following state of stress: , , , and . determine the following:
Answers
The obtained stress which is acting from every direction is at 45 degree.
The transformation equations will be used to calculate the stresses acting on an inclined element.
(σ x+σ y )/2 =75 MPa
(σ x-σ y )/2 =35 MPa
Tor xy = 28 MPa
sin 2θ = sin 90° = 1
cos 2θ = cos 90° = 0
Substituting these values into Eqs
σ x1 =(σ x+σ y )/2+ (σ x-σ y )/2 cos2θ+ τxy sin2θ
= 130 MPa
τ x 1 y 1 = (σ x-σ y )/sin2θ + τxy cos2θ
σ y 1= (σ x+σ y )/2- (σ x-σ y )/cos2θ+ τxy sin2θ
= 47Mpa
Elements of stress
We can easily obtain the stresses acting on all sides of an element oriented at = 45° from these results.
The arrows indicate the true directions of the stresses. Take special note of the shear stress directions, which all have the same magnitude. Also, keep in mind that the sum of the normal stresses remains constant at 150 MPa.
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