It will take approximately 7.66 years for the amount of Americium-241 remaining to reach 6 kg, assuming that the initial amount was 10 kg. We can use formula Q(t) = Pe^(rt) to calculate half-life of Americium-241.
To construct a function that will model the amount of Americium-241 remaining after t years from an initial amount of 10 kg, we can use the formula:
Q(t) = Pe^(rt)
where Q(t) is the amount of Americium-241 remaining after t years, P is the initial quantity (10 kg in this case), r is the decay rate (the negative of the half-life of Americium-241, which is -432.2 years), and e is the mathematical constant approximately equal to 2.71828.
Plugging in the values, we get:
Q(t) = 10 * e^(-432.2t)
This is the function that will model the amount of Americium-241 remaining after t years from an initial quantity of 10 kg.
To find out how long it will take for the amount of Americium-241 remaining to reach 6 kg, we can solve the equation Q(t) = 6 for t.
[tex]Q(t) = 6\\6 = 10 * e^(-432.2t)\\0.6 = e^(-432.2t)\\ln(0.6) = -432.2t\\t = ln(0.6) / -432.2\\[/tex]
t = approximately 7.66 years
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A total of $28000 is invested in 2 municipal bonds that pay 5.75% and 7.25% simple interest. The investor wants an annual interest income of $1790 from the investments. What amount should be invested in the 5.75% bond?
Answer:
$16,000
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
I = Interest accruedP = Principal amountr = Interest rate (in decimal form)t = Time (in years)Let investment 1 be the bond that pays 5.75% simple interest.
Let investment 2 be the bond that pays 7.25% simple interest.
Given:
P₁ + P₂ = $28,000r₁ = 5.75% = 0.0575r₂ = 7.25% = 0.0725t = 1 yearCreate two equations for the interest from both investments.
Interest from Investment 1
[tex]\implies \sf I_1=P_1 \cdot 0.0575 \cdot 1[/tex]
[tex]\implies \sf I_1=0.0575\:P_1[/tex]
Interest from Investment 2
[tex]\implies \sf I_2=P_2 \cdot 0.0725 \cdot 1[/tex]
[tex]\implies \sf I_2=(28000-P_1)0.0725[/tex]
[tex]\implies \sf I_2=2030-0.0725\:P_1[/tex]
Given that the sum of the interest from both investments is $1,790:
[tex]\implies \sf I_1+I_2=1790[/tex]
[tex]\implies \sf 0.0575\:P_1+2030-0.0725\:P_1=1790[/tex]
[tex]\implies \sf -0.015\:P_1=-240[/tex]
[tex]\implies \sf P_1=16000[/tex]
Therefore, $16,000 should be invested in the 5.75% bond.
Check:
[tex]\implies \sf I_1=16000 \cdot 0.0575 \cdot 1 = 920[/tex]
[tex]\implies \sf I_2=12000 \cdot 0.0725 \cdot 1 = 870[/tex]
[tex]\implies \sf I_1+I_2=920+870=1790[/tex]
When constructing a confidence interval for a population mean μ from a sample of size 12, the number of degrees of freedom for the critical value tα/2 is ___________________________.
b. Find the critical value tα/2 needed to construct a confidence interval of the given confidence level 90% with sample size 23
When constructing a confidence interval for a population mean the Degrees of freedom is 11 and critical value is 1.717
Degrees of freedom = df = n - 1 =12 - 1 = 11
At 90% confidence level the t is ,
α = 1 - 90% = 1 - 0.90 = 0.1
α / 2 = 0.1 / 2 = 0.05
tα /2, df = t0.05,22 = 1.717 ( using student t table)
The level of confidence denotes the likelihood that the position of a statistical parameter (such as an arithmetic mean) in a sample survey is also true for the population.
A critical value is the test statistic's value that establishes a confidence interval's upper and lower boundaries or a test statistic's threshold for statistical significance.
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Leila works mowing lawns and babysitting.She earns $8.20 an hour for mowing and $7.90 and hour and babysitting.How much will she earn for 7 hours of mowing and 4 hours of babysitting?
Answer: 89
Step-by-step explanation:
1 hr of mowing = 8.20 dollars
1 hr of babysitting = 7.90 dollars
7 hrs of mowing = 8.20 x 7 = 57.4 dollars earned
4 hrs of babysitting = 7.90 x 4 = 31.6 dollars earned
Total amount she has earned = 57.4 + 31.6 + = 89 dollars
Steven found that between 2012 and 2020, as a country's per capita chicken egg consumption increased, the country's divorce rate decreased. Based on this information, which of the following conclusions is valid?
O Eating chicken eggs prevents divorces.
O Divorces lead to a decrease in per capita chicken egg consumption.
O There is a positive association between per capita chicken egg consumption and divorce rate.
O There is a negative association between per capita chicken egg consumption '.' and divorce rate
There is a positive association between per capita chicken egg consumption and divorce rate is true.
Define statement.A statement in mathematics is a declarative utterance that can only be either true or false. A proposal is another name for a statement. It's important that there be no ambiguity. A sentence can only be true or untrue and not both for it to be a statement.
Give example of statement.A meaningful string of words that can be either true or incorrect makes up a mathematical statement. They are referred to simply as a statement. For instance, "ABC is an equilateral triangle" could be denoted by the letter "p." As a result, in an equilateral triangle, p = ABC.
There is a positive association between per capita chicken egg consumption and divorce rate is the correct and valid statement according to the given presented situation.
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May someone help me with this?
Step-by-step explanation:
0 hours -> $500 total cost
1 hour -> $575 total cost (500 + 1×75)
2 hours -> $650 total cost (500 + 2×75)
3 hours -> $725 total cost (500 + 3×75)
P(t) = 75t + 500
the purpose of a check sheet is to quickly understand the primary sources of a problem using the 80/20 rule, wherein 80 percent of defects often come from only about 20 percent of all the sources.
Based on the following question the primary sources of a problem using the 80/20 rule, wherein 80 percent of defects often come from only about 20 percent of all the sources is false
What is 80/20 rule?
Only 20% of causes result in 80% of all consequences, according to the 80/20 rule. It is used to pinpoint the crucial elements of success (often in a corporate context) and concentrate efforts therein to enhance outcomes.
What is the 80-20 rule in life?According to the 80-20 rule, 20% of activities produce 80% of the consequences. Or, to put it another way, just 20% of the input results in 80% of the outcome. An old proverb that promotes focus is the 80-20 rule, often known as the Pareto Principle.
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find the indefinite integral and check the result by differentiation. (use c for the constant of integration.) $$ \int \sqrt[3]{{\color{red}3} - {\color{red}4} x^2} ({\color{red}-8} x) \text{ }dx $$
The indefinite integral is - 1 / [5(6 + [tex]x^{5}[/tex])] + C.
An integral is considered to be indefinite if it has no upper or lower bounds. In mathematics, the most generic antiderivative of f(x) is known as an indefinite integral and expressed by the expression f(x) dx = F(x) + C. Without upper and lower bounds on the integrand, indefinite integrals are stated using the notation f(x), which represents the function as an antiderivative of F. Consequently, "f(x) dx=F" (x). As we observed in the same example with antiderivatives, the integral, x3 dx=14x4+C, is one example.
The area under the f(x) curve from x=a to x=b is represented by the definite integral of f(x), which is a NUMBER. Integral indefinite. An indefinite integral of a function f(x), also known as an antiderivative, is denoted by and its derivative is denoted by f. (x). The indefinite integral is not the only solution because the derivative of a constant is zero. Integration is the action of locating an indefinite integral.
Use a u-substitution with u = (6 + [tex]x^{5}[/tex])
du = 5[tex]x^{4}[/tex]dx
1/5 ∫ [tex]u^{-2}[/tex]du
= -1/5 [tex]u^{-1}[/tex] + C
= - 1 / [5(6 + [tex]x^{5}[/tex])] + C
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Correct Question:
Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.)
[tex]\int\limits^ {} \frac{x^{4} }{(6+x^{5})^{2} } dx[/tex]
pls help me with both of these questions
The number of times a large popcorn without butter is sold is, 49.
The conditional relative frequency of no.of Item2 sold given that
50% off is 0.27.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
The number of times a large popcorn without butter is sold is,
= 49.
The total no. of items that is 50% off is (12 + 20 + 32) = 74.
The no. of Item2 which is 50% off is 20.
So, The conditional relative frequency of no.of Item2 sold given that 50% off is,
= 20/74.
= 0.27.
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What is the value of sin0 given that (-3,4) is a point on the terminal side of 0?
Some values of f(x, y) are given below. Write out the terms of a Riemann Sum (using four squares) that gives an upper estimate of r 4 0 r 4 0 f dx dy.
To find a Riemann sum that gives an upper estimate of the double integral, we need to divide the region of integration into small subregions (in this case, squares) and take the maximum value of f(x, y) over each subregion.
The Riemann sum will then be the sum of the areas of the subregions times the maximum value of f(x, y) over each subregion.
For example, if we divide the region of integration into four squares, the Riemann sum would be given by:
Riemann sum = (area of first square) * (maximum value of f(x, y) in first
square) + (area of second square) * (maximum value of
f(x, y) in second square) + (area of third square) *
(maximum value of f(x, y) in third square) + (area of fourth
square) * (maximum value of f(x, y) in fourth square)
We can then fill in the specific values of the areas and maximum values of f(x, y) for each square based on the given values of f(x, y).
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Solve the following inequality.4x+6<3x+3
Answer:
x < - 3
Step-by-step explanation:
4x + 6 < 3x + 3 ( subtract 3x from both sides )
x + 6 < 3 ( subtract 6 from both sides )
x < - 3
Answer:
x < -3
Step-by-step explanation:
4x+6<3x+3
= 4x+6-3x<3
= 4x-3x<3-6
4x-3x<3-6
=x<3-6
x<-3
calculating Nominal GDP, Real GDP, and other economic indicators and can successfully use these indicators to draw conclusions because…
You can successfully use nominal GDP, real GDP, and other economic indicators to draw conclusions because they health of the country's economy.
What is GDP?GDP stands for Gross Domestic Product. This is a very common economic indicator that shows the value of the services and products produced by a country usually in a one year period.
What is the difference between real and nominal GDP?In general real GDP is considered to be more accurate as nominal GDP is influenced by factors such as inflation that can distort the general idea you can get about a country's economy and the total output of it.
What do economic indicators reveal?Both real, nominal GDP and other indicators show the health of the economy in a country, which makes it useful to draw conclusions about the economy.
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What is the exponential form of the expanded form below?
3.3.3.3.3.3.3
3•7
3^7
7^3
3^6
Answer:
Step-by-step explanation:
okay so its 3•7
that's all u need put that
Answer:
[tex]3^{7}[/tex]
Step-by-step explanation:
3×3×3×3×3×3×3= [tex]3^{1+1+1+1+1+1+1+1} =3^{7}[/tex]
3+3+3+3+3+3+3= 3×7
Anne Richards purchased two slippers at one price and three pajamas at another price. Let s = the price of each slipper and p = the price of each pajama. Each slipper
cost $12. How much did each pajama cost if the total purchase price was $120?
Each pajama cost $. (Simplify your answer.)
Answer:
[tex]E[/tex]ach pajama costs $32
Step-by-step explanation:
So, the said person bought:
2 slippers at a price, 3 pajamas at another price. (The prices are unknowns, s, and p)
Each slippers cost $12
We are to find the cost of each pajama, where the total purchase price is $120
With the given conditions, we formulate an equation: 2s + 3p = 120
Since s = 12, we replace for the value of s in the equation. s becomes 2 × 12 = 24.
The new equation is then: 24 + 3p = 120, where we are to find the value of p.
Collect like terms: 3p = 120 - 24 → 3p = 96
Divide both sides of the equation by 3 to find the value of p: 3p/3 = 96/3 → p = 32
Therefore, the price of each pajama is $32
I hope this helpsneed help with all these
Answer:
|
|
|
∆∆∆∆∆∆∆∆∆∆∆∆∆∆
Step-by-step explanation:
get better
If the opposite corners of the rectangle ABCD are A (5, 3) and C (10, 1) and the equation of side BC is x-2y=8, find the equations of the other three sides. You must show your work and explain why you are doing it. (Note: opposite side of a rectangle are parallel and consecutive sides are
perpendicular)
Answer:
Equation of side AB:
We know the coordinates of A and B, so we can use the point-slope form to create the equation of the line:
y - 3 = (3/5)(x - 5)
y - 3 = 3/5x - 15/5
5/3y - 15/3 = x - 5
5/3y - x = -15/3 + 5
5/3y - x + 15/3 = 5
5/3y - x + 15/3 = 0
Equation of side AB: 5/3y - x + 15/3 = 0
Equation of side DC:
We know the coordinates of C and D, so we can use the point-slope form to create the equation of the line:
y - 1 = (2/5)(x - 10)
y - 1 = 2/5x - 20/5
5/2y - 10 = x - 10
5/2y - x = -10
5/2y - x - 10 = 0
Equation of side DC: 5/2y - x - 10 = 0
Equation of side BD:
We know the equation of side BC (x - 2y = 8) and that consecutive sides are perpendicular, so we can use the slope-intercept form to find the equation of line BD:
Slope of BC = -2/1
Slope of BD = -1/-2 = 1/2
y = (1/2)x + b
We can use the coordinates of B to find b:
1 = (1/2)(8) + b
2 = 4 + b
b = -2
Equation of side BD: y = (1/2)x - 2
Step-by-step explanation:
I need help with the statement and the reasons
Explanation:
You can make use of the properties of parallel lines to prove ∠ACB≅∠DAC.
Statement . . . . Reason
2. ∠DAB +∠ABC = 180° . . . . definition of a right angle
3. AD║BC . . . . consecutive interior angles are supplementary
4. ∠ACB≅∠DAC . . . . alternate interior angles are congruent
Please Help! I need this by tomorrow! I will give BRAINLIEST
The number of bacteria in a sample is increasing according to an exponential model. After four hours, the sample contained 400 bacteria. After twelve hours, the sample contained 1,600 bacteria. Write an exponential growth model for the number of bacteria in the sample after x hours.
The solution is Option A.
The exponential growth model for the number of bacteria in the sample after x hours is [tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]
What is exponential growth factor?
The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the equation for the number of bacteria in the sample after x hours = P
The value of the equation P ( x ) is given by
After 4 hours , the sample contained 400 bacteria
So ,
when x = 4
[tex]P ( 4 ) = ae ^{4b }=400[/tex] be equation (1)
After 12 hours , the sample contained 1600 bacteria
And , when x = 12
[tex]P ( 12 ) = ae ^{12b }=1600[/tex] be equation (2)
Divide equation (2) by equation (1) , we get
[tex]\frac{P ( 12 )}{P ( 4 )} = \frac{ae ^{12b }}{ae ^{4b }} = \frac{1600}{400}[/tex]
On simplifying the equation , we get
e¹²ᵇ⁻⁴ᵇ = 4
e⁸ᵇ = 4
Taking logarithm on both sides of the equation , we get
8b = ln (4)
Divide by 8 on both sides , we get
b = ln (4) / 8
Substituting the value for b in equation (1) , we get
[tex]ae ^{4*ln (4) / 8 }=400[/tex]
[tex]ae ^{ln (4) / 2}=400[/tex]
On simplifying the equation , we get
a x 2 = 400
Divide by 2 on both sides of the equation , we get
a = 200
Therefore , the exponential growth equation is given by
Substitute the values of a and b in the equation , we get
[tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]
Hence , The exponential growth model for the number of bacteria in the sample after x hours is [tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]
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A researcher at the Centers for Disease Control and Prevention is studying the growth of a certain bacteria. He starts his experiment with 500 bacteria that grow at a rate of 18% per hour. He will check on the bacteria every 3 hours. How many bacteria will he find in 3 hours? Round your answer to the nearest whole number.
Answer:
The answer is approximately 770 bacteria after 3 hours.
given the function h(x)=8x-3/4x+5 as the values of x increase towards infinity, use a table to find out what happens to the values of h(x)
according to question,
given data.
h(x)=8x-3/4+5
then,
Martha has a $200 deductible and 20% co-payment on her health
insurance. Last year she had $6,500 in medical bills. What was
Martha's out-of-pocket expense?
Answer:
Step-by-step explanation:
To solve this problem, we need to calculate Martha's out-of-pocket expenses, and the total amount of money she had to pay for her medical bills.
First, we need to calculate the amount of money Martha had to pay toward her deductible. Since her deductible is $200, this is the amount she had to pay out of pocket.
Next, we need to calculate the amount of money Martha had to pay toward her co-payment. Since her co-payment is 20%, we can calculate this by multiplying her medical bills by the co-payment rate: $6,500 x 0.2 = $1,300.
To find Martha's total out-of-pocket expense, we can add the amount she paid towards her deductible ($200) and the amount she paid towards her co-payment ($1,300):
$200 + $1,300 = $1,500
Therefore, Martha's out-of-pocket expense was $1,500.
Martha's insurance required her to pay a $200 deductible and a 20% co-payment on the remaining balance of her medical bills. After paying the deductible, she pays 20% of the remaining $6,300 which is $1,260. So, Martha's total out-of-pocket expense was $1,460.
Explanation:Martha's health insurance plan includes a $200 deductible and a 20% co-payment. The deductible is the amount Martha has to pay before the insurance company starts to pay. In this case, Martha first pays a $200 deductible from her $6,500 medical bills, which leaves her with $6,300 to be covered by insurance and her co-payment. The 20% co-payment means Martha is responsible for paying 20% of the remaining $6,300. To calculate this, we multiply $6,300 by 0.20 (20%), which equals $1,260. Therefore, Martha's total out-of-pocket expense for her medical bills last year was the $200 deductible plus the $1,260 co-payment, equalling $1,460.
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(Factoring Algebraic Expressions MC)
x3y2 is the result of the expression employing the common factor (x - 6y).
What is Mathematical expression?Here,
The sentence is,
x⁴y² - 6x³y³
We must use the common factor to solve.
Mathematical expression refers to the combining of numbers and variables utilizing the operations addition, subtraction, multiplication, and division.
Now,
The sentence is,
x⁴y² - 6x³y³
The common factor is used to solve as,
6x3y3 - x4y2 equals x*x*x*y*y - 6*x*x*x*y*y.
= x³y² (x - 6y) (x - 6y)
Consequently, x3y2 is the value of the expression employing the common factor (x - 6y).
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What is the equation in slope-intercept form of the line that crosses the x-axis at 14 and is parallel to the line represented by y= -2/3x+6
The equation in slope intercept for the given line is y = -2/3x - 28/3.
What is Slope ?
The slope or gradient of a line in mathematics is a number that indicates the line's steepness and direction.
Given, the line crosses the x-axis at 14 and is parallel to the line represented by y= -2/3x+6.
We know that two parallel lines always have the same slope.
We can say that the line has coordinate as (14,0) and slope (m) as -2/3.
We know that the slope-intercept form of the line is,
y= mx + b
Now, We put x=14, y=0 and m=-2/3 in equation above,
We get, 0 = -2/3 × 14 + b
b = -28/3
So, the slope intercept form will be :
y = -2/3x - 28/3
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2. Calculate On landing, the plane touches the runway with a speed of 65 m/s. The figure shows the speed of the plane after 1 second. Calculate the acceleration of the plane during its landing.
The plane touches the runway with a speed of 65 m/s then the acceleration of the plane during its landing will be equal to 65 m/s².
What is acceleration?The rate of change in an object's velocity concerning time is known as acceleration in mechanics. The vector quantity of accelerations. The direction of the net force that is acting on an object determines its acceleration.
Since acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is a vector quantity as well. The definition of acceleration is the change in velocity vector over a time interval divided by the time interval.
As per the given information in the question,
Velocity, v = 65 m/s
Time, t = 1 sec.
Use the equation of acceleration,
a = v/t
a = 65/1
a = 65 m/s²
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30-(-2)*(-10)+(-5)-(-2)=
Answer:
Step-by-step explanation:
-2 * -10 = 20
Answer:
30×2×(-10)-5+2
=60×(-10)-3
=-60-3
=-63
Image below to be answered
a.The formula that describe the sequence or progression is a+(7-7n)
b. 2nd term = -10 , 3rd term = 10, 4th term = -10 and 5th term = 10
What is arithmetic and geometric progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio.
Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
The nth term of an arithmetic progression is given as a(n)= a + (n − 1) × d
In geometric progression the nth term is given as a(n)= ar^(n-1)
where a is the first term
therefore if a = 12 and d is - 7
the formula for the arithmetic progression =
a(n) = 12+(n-1) -7 = 12+( 7-7n)
If the first term of a GP is 10 with common ratio of -1
then the second term = 10×-1 = -10
third term = -10×-1 = 10
fourth term = 10×-1 = -10
fifth term = -10× -1 = 10
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Lines PQ and BC are parallel.
What is the value of x ?
Answer:
x = 40
Step-by-step explanation:
since lines PQ and BC are parallel , then
∠ BCQ and ∠ AQP are corresponding angle and are congruent , that is
∠ BCQ = 80°
the sum of the 3 angles in Δ ABC = 180° , then
x + 80 + 60 = 180
x + 140 = 180 ( subtract 140 from both sides )
x = 40
is it correct? i will brinlist to who answer first
I don't see the full picture but your answer should look like this:
4ab+(-12ab)+9ab+(-5ab)
= 4ab-12ab+9ab-5ab
= (4-12+9-5)ab
= -4ab
URGENT!! ILL GIVE
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POINTS!!!
The minimal set of coordinates required to represent any point inside a mathematical space is known as the dimension of the space in physics and mathematics.
What is 3D and 2D ?The terms 2D and 3D describe the precise sizes of a computer workstation. Using the horizontal and vertical (X and Y) axes, 2D is "flat," meaning that there are only two dimensions to the picture, which becomes a line when rotated to the side. The depth (Z) dimension is added in 3D.A two-dimensional form known as a "2D shape" is characterised by its horizontal and vertical axes (x-axis and y-axis)The three spatial dimensions of width, height, and depth are referred to as three dimensions, or 3D. The physical world is three dimensional, as is everything that can be seen there.The rectangle, square, circle, triangle, and any other polygon are a few examples of 2D forms. Cuboid, cube, sphere, cone, prism, cylinder, pyramid, etc. are a few examples of 3D forms.Fill in blanks :
A point has no dimension. it is an abstract idea of a location in space.
A vertex is where two edges meet at a point
A line has edge dimension - length . An edge is a line segment where two faces meet.
A flat plane figures has a 2 dimension - length and width
The 3 points of a 3D object is a plane.
Three dimensional objects have vertices, edges and faces unless they are the geometric solids like cylinders, cones and sphere.
when we talk about line we are looking at the measure of a one dimensional figure.
when we talk about area we are looking at the space inside of a two dimensional figure.
when we talk about volume we are looking at the total space enclosed by a three dimensional figure.
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Please can someone explain this question to me step-by step, i have a exam this Wednesday so pleasee help me!! Help is greatly greatly appreciated ^^
Thankyou!!
Answer:
AB = 45.688 metres
Step-by-step explanation:
* i used a scientific calculator for my working. i am not sure if calculators are permitted for your exam on Wednesday *
⭐AB = AD + DB
⭐AB = 16.5 + DB
Thus, we need to find DB in order to solve for AB.
First, I utilized the triangle sum theorem to find ∠BDC:
[tex]< BDC + < DCB + < B = 180\\ < BDC + 59 + 90 = 180\\ < BDC + 149 = 180\\ < BDC = 31[/tex]
Then, I utilized the linear pair sum to find ∠ADC:
[tex]< ADC + < BDC = 180\\ < ADC + 31 = 180\\ < ADC = 149[/tex]
Next, I utilized the triangle sum theorem to find ∠DAC:
[tex]< DAC + < ADC + < ACD = 180[/tex]
[tex]< DAC + 149 + 10 = 180[/tex]
[tex]< DAC + 159 = 180[/tex]
[tex]< DAC = 21[/tex]
After, I utilized the law of sines to find DC:
[tex]\frac{sin10}{16.5} = \frac{sin21}{DC}[/tex]
[tex]DCsin10 = 16.5sin21[/tex]
[tex]DC = \frac{16.5sin21}{sin10}[/tex]
[tex]DC = 34.052[/tex]
Then, I utilized the sine function to find DB for ΔBDC:
[tex]sin(59) = \frac{DB}{34.052}[/tex]
[tex]34.052sin(59) = DB[/tex]
[tex]29.188 = DB[/tex]
Finally, I substituted DB into our original equation for AB:
[tex]AB = AD + DB[/tex]
[tex]AB = 16.5 + 29.188[/tex]
[tex]AB = 45.688 metres[/tex]
Good luck on your exam on Wednesday! :-)
The height of the pole will be equal to 45 meters.
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
Given that the angle BCD is 59 and the angle BCA is 69. The height will be calculated as,
tan(59) = BD / BC
BC = BD / tan(59)
BC = 0.6BD
tan(69) = AB / BC
tan(69) = ( 16.5 + BD ) / BC
BC = 0.38( 16.5 + BD )
Equate the values of BC,
0.6BD = 0.38 ( 16.5 + BD )
0.6BD = 6.27 + 0.38BD
0.22BD =6.27
BD = 28.5 meters
The height of the pole is,
AB = AD + DB
AB = 16.5 + 28.5
AB = 45 meters
The height is 45 meters.
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