The amount of power used when Sanjay applied a force of 225N to move a wheelbarrow over the given distance at a velocity of 1.8m/s is 405 watts.
What was the amount of power used to move the wheelbarrow?Power is the quantity of energy transferred per unit time. The relationship between force, velocity and power is expressed aa;
P = F × v
Given the data in the question;
Force applied F = 225N = 225kgm/s²Distance moved s = 18mVelocity v = 1.8m/sPower = ?To find the amount of power used, plug the given values into the above formula and solve for P.
P = F × v
P = 225kgm/s² × 1.8m/s
P = 225kgm²/s³ × 1.8
P = 405kgm²/s³
Power P = 405W
Therefore, the amount of power used by Sanjay is 405 watts.
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Out of every 292 containers of juice bought in a grocery store, 160 are orange juice. What fraction of juice purchased is orange juice?
The fraction of juice that is orange juice is 40/73
How to determine the fraction of juice that is orange juice?From the question, we have the following parameters that can be used in our computation:
Juice containers = 292
Orange juice = 160
The fraction of juice that is orange juice is then calculated as
Fraction = Orange juice/Juice containers
Substitute the known values in the above equation
So, we have the following equation
Fraction = 160/292
Simplify the fraction
Fraction = 40/73
Hence, the fraction is 40/73
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A golf-course architect has 4 linden trees, 5 white birch trees, and 2 bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced?
The number of ways that the landscaper can plant the trees in a row, assuming that the trees are evenly spaced is 630 ways.
How to calculate the value?According to the data, the golf course architect needs to plant 2 bald cypress trees, 5 white birch trees, and 4 linden trees in a row along a fairway. It should be noted that the number of feasible arrangements will be shown as follows based on the information provided:
Based on the information given, it should be noted that n1 =4, n2 = 5 and n3 = 2.
Therefore, the number of ways that the lineup can be possible will be:
n! / (n − r)!
where n is the number of things to choose from and we choose r of them
This will be illustrated as:
= 10! /4!5!2!
= 630
There are 630 ways.
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Use Prime Factors to find the lcm
14. 6,15
15. 8,14
16. 28,8
17. 24,36
18 25,15
Grade 8 Math
Lcm of 14. 6,15 is 210 and 15. 8,14 is 840 and 16. 28,8 is 112 and 17. 24,36 is 1224 and 18 25,15 is 450
What is prime factorization ?When a number is represented as the sum of its prime factors, this process is known as prime factorization. In prime numbers, there are just two factors: one and the number itself. 2, 3, 5, 7, 11, 13, and other prime numbers are examples of prime numbers. A number is prime factorized when it is represented as a collection of primes.
i) List all prime factors for each number.
Prime Factorization of 6 is:
2 x 3 = [tex]2^{1}[/tex] x [tex]3^{1}[/tex]
Prime Factorization of 14 is:
2 x 7 = [tex]2^{1}[/tex] x[tex]7^{1}[/tex]
Prime Factorization of 15 is:
3 x 5 = [tex]3^{1}[/tex] x [tex]5^{1}[/tex]
Find the place in the new list where each prime factor appears as a factor the most frequently before adding it there.
The new superset list is
2, 3, 5, 7
To determine the LCM, multiply these elements collectively.
LCM = 2 x 3 x 5 x 7 = 210
In exponential form:
LCM = [tex]2^{1}[/tex] x [tex]3^{1}[/tex] x [tex]5^{1}[/tex] x[tex]7^{1}[/tex] = 210
LCM = 210
Therefore,
LCM(6, 14, 15) = 210
ii)List all prime factors for each number.
Prime Factorization of 8 is:
2 x 2 x 2 = [tex]2^{3}[/tex]
Prime Factorization of 14 is:
2 x 7 = [tex]2^{1}[/tex] x [tex]7^{1}[/tex]
Prime Factorization of 15 is:
3 x 5 = [tex]3^{1}[/tex] x[tex]5^{1}[/tex]
Find the place in the new list where each prime factor appears as a factor the most frequently before adding it there.
The new superset list is
2, 2, 2, 3, 5, 7
To determine the LCM, multiply these elements collectively.
LCM = 2 x 2 x 2 x 3 x 5 x 7 = 840
In exponential form:
LCM = [tex]2^{3}[/tex] x[tex]3^{1}[/tex] x [tex]5^{1}[/tex] x [tex]7^{1}[/tex] = 840
LCM = 840
Therefore,
LCM(8, 14, 15) = 840
iii)List all prime factors for each number.
Prime Factorization of 8 is:
2 x 2 x 2 = [tex]2^{3}[/tex]
Prime Factorization of 16 is:
2 x 2 x 2 x 2 = [tex]2^{4}[/tex]
Prime Factorization of 28 is:
2 x 2 x 7 = [tex]2^{2}[/tex] x [tex]7^{1}[/tex]
Find the place in the new list where each prime factor appears as a factor the most frequently before adding it there.
The new superset list is
2, 2, 2, 2, 7
To determine the LCM, multiply these elements collectively.
LCM = 2 x 2 x 2 x 2 x 7 = 112
In exponential form:
LCM = [tex]2^{4}[/tex] x[tex]7^{1}[/tex]
= 112
LCM = 112
Therefore,
LCM(8, 16, 28) = 112
iv) List all prime factors for each number.
Prime Factorization of 17 shows:
17 is prime = 171
Prime Factorization of 24 is:
2 x 2 x 2 x 3 = [tex]2^{3}[/tex] x [tex]3^{1}[/tex]
Prime Factorization of 36 is:
2 x 2 x 3 x 3 = [tex]2^{2}[/tex] x [tex]3^{2}[/tex]
Find the place in the new list where each prime factor appears as a factor the most frequently before adding it there.
The new superset list is
2, 2, 2, 3, 3, 17
To determine the LCM, multiply these elements collectively.
LCM = 2 x 2 x 2 x 3 x 3 x 17 = 1224
In exponential form:
LCM = [tex]2^{3}[/tex] x [tex]3^{2}[/tex] x [tex]17^{1}[/tex] = 1224
LCM = 1224
Therefore,
LCM(17, 24, 36) = 1224
v)List all prime factors for each number.
Prime Factorization of 15 is:
3 x 5 = [tex]3^{1}[/tex] x [tex]5^{1}[/tex]
Prime Factorization of 18 is:
2 x 3 x 3 = [tex]2^{1}[/tex] x [tex]3^{2}[/tex]
Prime Factorization of 25 is:
5 x 5 = [tex]5^{2}[/tex]
Find the place in the new list where each prime factor appears as a factor the most frequently before adding it there.
The new superset list is
2, 3, 3, 5, 5
To determine the LCM, multiply these elements collectively.
LCM = 2 x 3 x 3 x 5 x 5
= 450
In exponential form:
LCM = [tex]2^{1}[/tex] x [tex]3^{2}[/tex] x [tex]5^{2}[/tex]
= 450
LCM = 450
Therefore,
LCM(15, 18, 25) = 450
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Blender uses an X, Y, and Z coordinate plane called the Euclidean geometry model in its design grid. In your own words, briefly describe the Euclidean geometry model and how you can use the model to create 3D objects.
Euclidean geometry is the study of flat and solid figures based on the axioms and theorems of the Greek mathematician Euclid (c. 300 BCE). Euclidean geometry is the plane and solid geometry that is usually taught in High schools.
How can Euclidean Geometry be used to create 3D Objects?Euclidean features are ideally suited to defining man-made settings (which are usually in 3D) and are reasonably simple for the user to give.
The incorporation of scene restrictions into the model acquisition process decreases the number of unique configurations for calibration and enables model reconstruction using small sets or even single photos despite the presence of multiple occlusions.
Another obvious use for such a technology is augmented reality. After rebuilding, real-world scene models can be merged with other reconstructed or synthetic models. This is particularly beneficial in architectural applications.
Indeed, before an architectural project is approved, its influence on the existing environment is represented using hand-drawn or computer-aided design (CAD) city models.
The process of creating such models is time-consuming and needs more previous knowledge than scene reconstruction from photos.
Furthermore, when necessary, classic architectural resources such as maps and architectural drawings are simple to include in an interactive reconstruction method.
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Which of the following expressions do not have a result of zero? Why don't they? If not zero, what is their result? Express your answer in complete sentences. 0 × ( − 7 ) − 8 − ( − 8 ) 0 ( − 4 ) 6 0
The expressions that do not have a result of zero among the given expression is 6/0.
How can the expression be simplified?It should be noted that the option can be written properly as :
0 x (-7)
-8 - (-8)
0/(-4)
6/0
From the first option, 0 x (-7), the simplification will give us 0.
From the second option, -8 - (-8), the simplification will give us 0.
From the third option, 0/(-4), the simplification will give us 0.
From the forth option, 6/0, the simplification will give us ∞
Therefore, the expression that will not give zero after simplification is 6/0 because it will give us infinity.
Therefore, the last option is correct.
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Evalúe the limit. Show steps
After evaluating the limit we have came to find that the limit of [tex]\lim_{h\rightarrow 0 }\frac{(4/3 +h)^3-(4/3)^3}{h}[/tex] as h approaches 0 is Undefined
What is limit?A limit is the value that a function, sequence, or index approaches as an input or as an index approaches a particular value in mathematics. The definitions of continuity, derivatives, and integrals depend on limits, which are essential to calculus and mathematical analysis.
The concept of a limit of a sequence is further generalized to include the concept of a limit of a topological network, in addition to having a connection to the category theory concepts of limit and direct limit.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit
⇒ [tex]\lim_{h\rightarrow 0 }\frac{(4/3 +h)^3-(4/3)^3}{h}[/tex]
Evalúe 0 as h
⇒ [tex]\frac{(4/3 +0)^3-(4/3)^3}{0}[/tex]
⇒ Undefined
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17. Suppose 17 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 90% a month. If the yard can only sustain 120 plants, use a logistic growth model to estimate the number of plants after 5 months. plants
Step 1: Write out the formula for logistic growth model
[tex]P(t)=\frac{KP_0e^{rt}}{K+P_0(e^{rt}-1)}[/tex][tex]\begin{gathered} \text{ Where} \\ K=\text{ the carrying capacity} \\ r=\text{ the growth rate (in decimal form)} \\ P_0=\text{ the initial population} \\ P(t)=\text{ the population at time t} \end{gathered}[/tex]Step 2: Write out the given values and substitute them into the formula
[tex]\begin{gathered} \text{ In this case,} \\ K=120 \\ r=\frac{90}{100}=0.9 \\ P_0=17 \\ t=5 \end{gathered}[/tex]Hence,
[tex]P(5)=\frac{120\times17\times e^{(0.9\times5)}}{120+17(e^{(0.9\times5)}-1)}[/tex][tex]P(5)=112[/tex]Hence, the number of plants after 5 months is approximately 112
[tex]x( {e}^{y} + 1) {}^{2} \: {e}^{ - y} dx \: + {e}^{ {x}^{2} } dy \: = 0[/tex]
Exact differential equation
The correct differential equation for [tex]x(e^{y}+1)^{2} e^{-y}dx+ e^{x^{2} }dy =0[/tex]
is [tex](e^{y}+1)^{2}e^{-y}/ -e^{x^{2}}= dy/dx\\[/tex].
to extract the differential equation we need to express it in the form of dy/dx.
[tex]x(e^{y}+1)^{2}e^{-y}dx=-e^{x^{2}}dy\\x(e^{y}+1)^{2}e^{-y} = -e^{x^{2}}dy/dx\\x(e^{y}+1)^{2}e^{-y}/ -e^{x^{2}}= dy/dx\\[/tex]
What are differential equations?
An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a place is determined by the derivatives of the function. Physicists, engineers, biologists, and other professionals primarily use it in these domains.
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How much will the house be worth?
Given:
[tex]S=C(1+r)^t[/tex]Where:
• S is the inflated value t years from now
,• r is the rate
,• C is the present value.
Let's solve for S, when:
• r = 6% = 0.06
,• C = $73,000
,• t = 12
Input values into the equation and solve for S:
[tex]S=73000(1+0.06)^{12}[/tex]Solving further:
[tex]\begin{gathered} S=73000(1.06)^{12} \\ \\ S=73000(2.012196472) \\ \\ S=146890.34\approx146890 \end{gathered}[/tex]herefore, the house will be worth $146890
NSWER:
$146,890
Assume that when adults with smartphones are randomly selected, 48% use them in meetings or classes. If 15 adult smartphone users are randomly selected, find the probability that exactly 11 of
them use their smartphones in meetings or classes.
What is the probability?
The probability that exactly 11 of them use their smartphones in meetings or classes is 3.89%
What is probability ?Probability is the likelihood of something occurring. This branch of mathematics studies the nature of chance. It is expressed as a number between 0 and 1. Probability has been brought to mathematics in order to foresee the potential of events. Probability can be defined as the degree of likely that something will occur. The probability that the outcomes of a random experiment will be as expected can be calculated using this fundamental theory of probability, which is also applied to the probability distribution. To establish the probability that a particular event will occur, we must first determine the total number of choices.
x = 11
n= 15
P =48%
=0.48
P(x=11)=[tex]15C_{11} (0.48)^{11} (1-0.48)^{4}[/tex]
=1365(0.0003116403)(0.09150625)
=0.0389
=3.89%
The probability that exactly 11 of them use their smartphones in meetings or classes is 3.89%
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If x3 = 125, find x²
The value of [tex]x^{2}[/tex] is 25 when we have (cube of x = 125) [tex]x^{3}[/tex] = 125.
According to the question,
We have the following expression:
[tex]x^{3} = 125[/tex]
Now, we will do the cube roots on both the sides:
[tex]\sqrt[3]{x^{3} } = \sqrt[3]{125}[/tex]
(We can find the cube roots of 125 by finding the Least Common Multiple or LCM.)
So, we will have the following expression:
x = 5
Now, to find the value of [tex]x^{2}[/tex], square on both the sides:
[tex]x^{2} = 5^{2}[/tex]
[tex]x^{2}[/tex] = 25
(More to know: when we square a number we multiply a number two times and when we find cube of a number then we multiply a number three times.)
Hence, the value of [tex]x^{2}[/tex] is 25.
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Joe deposited $5000 into an account with a 5.2% annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long wi
the investment to grow to $6500?
Tickets to a football match cost €8, €15 or €20 each. The number of €15 tickets sold was
double the number of €8 tickets sold. 6000 more €20 tickets were sold than €15 tickets.
If the gate receipts totalled €783 000, how many of each type of ticket were sold?
There are three different types of tickets sold, according on the query ($8, $15, and $20).
8500 $8 tickets
17000 at $15 each
23000 $20 tickets
A linear equation example is what?Ax +By = C is the typical form for two-variable linear equations. For instance, the equation 2x+3y=5 is a standard form linear equation .Finding both intercepts is rather easy when an equation is supplied in this style (x and y).
$8 tickets for x.
$15 tickets are y.
$20 tickets = z
8x + 15y + 20z = 783000 when y = 2x z = y + 6000.
conventional form for the system of linear equations
8x + 15y + 20z = 783000 2x - y = 0 y - z = -6000
x = 8500 $8 tickets
Y = 17000 tickets at $15 each
z = 23000 at $20 each.
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Kendra finds the dimensions of a sticky note. She uses a meter stick to determine that the dimensions are 1.25×10−8 meters wide by 2.5×10−6 meters long. Use scientific notation to write the dimensions in millimeters
The length and the width of the sticky note in millimeters are 2.5 × 10⁻⁵ millimeters and 1.25 × 10⁻³ millimeters respectively.
The dimension of Kendra's sticky note using a meter stick are:
The width of the sticky note is 1.25 × 10⁻⁸ meters and the length of the sticky note is 2.5 × 10⁻⁶ meters.
Now we know,
1 meter = 1000 milimeters.
Therefore, the length of the sticky note in millimeters will be:
L = 2.5 × 10⁻⁸ meters
L = 2.5 × 10⁻⁸ × 1000 millimeters
L = 2.5 × 10⁻⁸ × 10³ millimeters
L = 2.5 × 10⁻⁸ ⁺ ³ millimeters
L = 2.5 × 10⁻⁵ millimeters
So, the width of the sticky note is:
W = 1.25 × 10⁻⁶ meters
W = 1.25 × 10⁻⁶ × 10³ millimeters
W = 1.25 × 10⁻³ millimeters
Hence, the dimension in millimeters is: the width and length of the sticky note is 1.25 × 10⁻³ millimeters and 2.5 × 10⁻⁵ millimeters respectively.
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"A line goes through the points (1, -10) and (-3, -2). Find the slope of the line and write the equation
of the line in point-slope form. Show your work algebraically for full credit."
Slope
[tex]\frac{-10-(-2)}{1-(-3)}=-2[/tex]
Equation
[tex]y+10=-2(x-1)[/tex]
Please help I have no idea how to do this ❗️❗️❗️❗️❗️
The height of the air ballon at 'm' minutes is expressed in the function and the value of h(3)=1600, h(9)=2800,h(11)=3200
We have given a function h in terms of m. Now we have to explain the contextual meaning of each and every expression it contains
1.) h = It is height at which ballon is cruising above from the ground level.
2.) m = It denotes the instance of minute at which we are talking about
3.) h(m) = The height as the function of minute, means the height of the ballon in changing with respect to the minute
4.) 1000 = It is the height at which ballon was cruising earlier and then started ascending
5.)200 = 200 feet the distance covered in a minute while ascending above
6.) 200m = distance ascended for 'm ' minutes
7.) 1000+200m = The total height that balloon covered after ascending for m minutes.
Now,
height at 3 minute = h(3) = 1000+200(3)=1000+600=1600
height at 9 minute = h(9) = 1000+200(9)=1000+1800=2800
height at x minute = h(x) = 1000+200(x)= 3200
1000 + 200x = 3200
200x = 2200
x = 11
Therefore, h(3) = 1600 , h(9)= 2800,h(11)=3200 are the different values of height 'h' at different 'm' minutes.
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Which numbers are irrational? Select all that apply.
A. √25
B. √28
C. √48
D. √169
An IRRATIONAL number is a number that can't be written as a simple fraction!
What is a simple fraction? a fraction having whole numbers for the numerator and denominator. To add on that i think it also means that it can be simplified.
So we can't have a mixed number or a fraction that can't be simplified.
A. The square root of 25=5. Can we turn five into a fraction? We sure can! It's also whole, which is a good sign too.
B. The square root of 28=5.29 We can't turn B into a simplified fraction. it will be a mixed number with 6 93/100. ✅
C. The square root of 48=6.93 We also can't turn C into a simplified fraction. It will be a mixed number as well, looking like 5 29/100. ✅
D. The square root of 169=13. This is promising, it's a whole number!
ANSWER: B AND C
------------------------------------------
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The functions f(x) = 2x and g(x) = 2–x + 3 are combined using division to get function h(x). Which represents the combined function?
The expression that represents the combined function of f(x) and g(x) is h(x) = 2x/(5 - x)
How to determine the equation of the function h(x)?From the question, we have the following parameters:
Function f(x) = 2x
Function g(x) = 2 - x + 3
Evaluate the like terms in the equation of the function g(x)
So, we have
g(x) = 5 - x
From the question, we understand that:
The function h(x) is a combination of the functions f(x) and g(x) by division
This can be represented as
h(x) = f(x)/g(x)
The above also implies that the function h(x) is a composite function
Substitute the known values in the above equation
So, we have the equation of the composite function h(x) to be
h(x) = 2x/(5 - x)
Hence, the equation of the composite function h(x) is h(x) = 2x/(5 - x)
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Need help with algebra
Solution
Option D
Hence the correct answer is Option D
5. A truck rental agency charges $66 a week and $0.65 per mile to rent a truck. How many
miles can you drive in one week for $170. answer.
Answer:
I believe it's 160. Hope this helps.
Step-by-step explanation:
170 - 66 = 104
104 / 0.65 = 160
What is the following quotient?
S6+/11
√√5+√3
30+32+√55+√√33
8
30-3√2+√55-√33
2
17
8
52
2
Quotient is [tex]\frac{\sqrt{30}-3\sqrt{2}+\sqrt{55}-\sqrt{33} }{2}[/tex]
What is rationalizing?When you rationalize an equation, you remove any surpluses from the fractions' bottom (denominator). Typically, when you are requested to rationalize or simplify an expression, it also suggests that you should do so.
To make a fraction's denominator a rational number, we rationalize any radicals or surds present. To accomplish this, we often multiply the numerator and denominator by an appropriate radical, then simplify. Divide and multiply the supplied fraction by the same square root value to rationalize the denominator. The denominator will be a rational integer in this case.
Given Data
[tex]\frac{\sqrt{6}+\sqrt{11} }{\sqrt{5} +\sqrt{3} }[/tex]
Rationalizing,
[tex]\frac{\sqrt{6} +\sqrt{11} }{\sqrt{5}+\sqrt{3} }[/tex] × [tex]\frac{\sqrt{5} -\sqrt{3} }{\sqrt{5} -\sqrt{3} }[/tex]
[tex]\frac{\sqrt{6}+\sqrt{11}(\sqrt{5}-\sqrt{3} ) }{\sqrt{5}+\sqrt{3} (\sqrt{5}-\sqrt{3} }[/tex]
[tex]\frac{\sqrt{30}-\sqrt{18}+\sqrt{55} -\sqrt{33} }{5-3}[/tex]
Quotient is [tex]\frac{\sqrt{30}-3\sqrt{2} +\sqrt{55}-\sqrt{33} }{2}[/tex]
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Use the labeled point to write a point-slope form for the line.
the point slope of the line is
1. Give the values of x for sinx=-1/2 where o' ≤ x ≤ 360°: x₁ = and x₂ =
Answer:
Sine is negative in III and IV quadrants. Now sin 30 1/2. Taking = 30, Sin (180+0) = sin (360-0): =- sin 0. So x = 210 degrees or 330 degrees
Step-by-step explanation:
james has 12510 toys he wants to share 80 toys with his friends
Answer: 156.375
Step-by-step explanation:
Consider the inequality 7 + 4x > x − 2.
Which value(s) of x are solutions? Select all that apply
x = −3
x = 0
x = 3
x = −6
The values of x that satisfies the inequality are:
x = 0 and x = 3
Given,
The inequality = 7 + 4x > x - 2
We have to find the values of x that satisfies the inequality.
Lets check:
Check for x = -37 + 4 × -3 > -3 - 2
7 - 12 > -5
-5 > -5
Here, -5 = -5
So,
The value x = -3 will not satisfy the inequality
Check for x = 07 + 4 × 0 > 0 - 2
7 > -2
The value x = 0 satisfies the inequality
Check for x = 37 + 4 × 3 > 3 - 2
7 + 12 > 1
19 > 1
The value x = 3 satisfies the inequality
Check for x = -67 + 4 × -6 > -6 - 2
7 - 24 > -8
-17 > -8
As negative values -17 is less than -8.
So, the value x = -6 will not satisfies the inequality
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Which graph is defined by the function given below?
y = (x - 5)(x-5)
Answer: The graph for this quadratic function has an x intercept of 5 and a y intercept of 25.
Step-by-step explanation: The picture of the graph is attached below.
(I don't know if this is what you're looking for but hope it helps!)
The area of a square garden is 81 m². How long is each side of the garden?
Each side is m long.
Answer:
each side would be 9m long
The length of each side of the square garden is 9 meters long.
What is the perimeter?The perimeter of any 2D figure is the sum of the lengths of all the sides except the circle which has a perimeter or circumference which is 2πr.
We know the area of a square is a product of any two sides of the square and all four sides of a square are of the same length.
Given a square has an area of 81m².
∴ We have to determine such a number which when multiplied by itself results in 81.
Such a unique number is 9.
So, the area of the square can be written as (9×9) m².
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In parts (a) and (b), identify whether the events are Mutually Exclusive, Independent, or Neither (events cannot be both disjoint and independent). which is the correct answera) You and a randomly selected student from your class both earn A's in this course.IndependentMutually ExclusiveNeitherb) You and your class partner both earn A's in this course.NeitherMutually ExclusiveIndependentc) If two events can occur at the same time, they must be independent.TrueFalse
(a) You and a randomly selected student from your class both earn A's in this course.
Answer: Here selection of one student is independent of the other.
Therefore it is independent.
(b) You and your class partner both earn A's in this course.
Answer: Here enough data is not available to comment whether the given event is mutually exclusive or independent.
Therefore it is neither.
(c) If two events can occur at the same time, they must be independent.
Answer: If both the events occur at the same time then it is not necessary they are independent.
Therefore it is False.
for positive acute angles A and B, it is known that tan A = 11/60 and cos B 5/13 Find the value of cos(A - B) in simplest form
The value of cos(A - B) in the simplest form will be 0.547.
What is geometry?It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.
It is given that,
tan A = 11/60
tan A = p/b
From Pythagoras therorm
h=√(p²+b²)
h=√(11²+60²)
h=61
Sin A = p/h = 11/60
Cos A = b/h = 60/61
If cos B = 5/13
Sin B = 12/13
cos (A - B) = cos A cos B + sin A sin B
cos (A - B) = (60/61)×(5/13) + (11/60)×(12/13)
cos (A - B) =0.547
Thus, the value of cos(A - B) in the simplest form will be 0.547.
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