5. The distance between two buildings is 67 m. From the top of the shorter building, the angle of elevation to the top of the taller building is 27°. From the same position, the angle of depression to the base of the taller building is 39º. Calculate the height of the two buildings.
Answers
First, let's draw a scheme representing the measures in the text. Let's call the shorter building as A and the taller building as B.
Using this scheme, we can see that we have 2 right triangles. The height of the taller building(let's call it hB), is given by the following relation
\(\frac{h_B_{}}{67}=\tan 39^o\)Then, calculating the height we have
\(\begin{gathered} h_B=67\tan 39^o=67\times0.80978403319\ldots=54.2555302241 \\ h_B\approx54.3 \end{gathered}\)The difference between the height of the smaller building(let's call it hA) and the taller building, is given by
\(\frac{(h_B-h_A)}{67}=\tan 27^o\)Solving for h_A, we have
\(\begin{gathered} \frac{(h_B-h_A)}{67}=\tan 27^o \\ (h_B-h_A)=67\tan 27^o \\ h_A=h_B-67\tan 27^o \\ h_A\approx20.1 \end{gathered}\)The height of the smaller building is 20.1m and the height of the taller building is 54.3m.
Related Questions
Area of Rectangles
Best answer marks branlist!
Answers
Answer:
rectangle above = 3 x 5 = 15 cm²
rectangle below = 8 x 5 = 40 cm²
1.
(03.03 MC)
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 11(1.01)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)
Answers
Answer:
sept one
Step-by-step explanation:
Tell whether each sentence about the factors of of 12 is True or False.
A. Allthefactorsof12are2,3,4,6,12.
B. 1 and 12 are a factor pair.
C. 120isafactorbecause10x12=120.
D. An array showing the factor pair of 3 and 4 would have 3 rows of 4 objects.
☐ True ☐ True ☐ True ☐ True
☐ False ☐ False ☐ False ☐ False
Answers
Answer:
A. True, 1 is always a factor too but It wasn't included there
B. True
C. True
D. False, it makes no sense.
Step-by-step explanation:
Have a nice day
Three postal workers can sort a stack of mail in 15 minutes, 15 minutes, and 30 minutes, respectively. Find how long it takes them to sort the mail if all three work together.
min
Answers
Answer: 10 minutes
Step-by-step explanation:
x·1/20 + x·1/25 + x·1/100 = 1
Multiply each term by 100 to clear the equation of all fractions
100x/20 + 100x/25 + 100x/100 = 100
5x + 4x + 1x = 100
10x = 100
x = 10
The answer is 10 minutes
Rewrite in logarithmic form 19^2 = 361
Answers
Answer:
\(\log_{19}{361}=2\)
Step-by-step explanation:
We know that taking logarithms performs the transformation ...
\(b^e=x\\\\e\cdot\log{b}=\log{x}\quad\text{take logs}\\\\e=\dfrac{\log{x}}{\log{b}}\quad\text{divide by $\log{b}$}\\\\\log_b{x}=e\quad\text{use the change of base formula}\)
Then for b=19, e=2, x=361, we have
\(\boxed{\log_{19}{361}=2}\)
what is the simplified form of 4 log3x+6 log3y-7 log3z
Answers
Answer:
A
Step-by-step explanation:
Using the properties of logarithms, we can simplify the expression:
4 log3x + 6 log3y - 7 log3z = log3x^4 + log3y^6 - log3z^7
Now, we can use another property of logarithms, which states that:
loga (mn) = loga m + loga n
Using this property, we can combine the logarithms with addition or subtraction:
log3x^4 + log3y^6 - log3z^7 = log3(x^4 * y^6 / z^7)
Therefore, the simplified form of 4 log3x + 6 log3y - 7 log3z is log3(x^4 * y^6 / z^7).
4.
Which of the following is a demonstration of using the Distributive Property to factor expressions
2x +(-2x) + 4 = 0 + 4
6x + 4b - 2x = 6x - 2x + 4b
2x + (6x + 4) = (2x + 6x) + 4
3x - 24 = 3(x - 8)
Answers
please helppppppppppppppppppppppp
Answers
Answer:
1. It is true because if you take off the n's and then do it you get 7 and when you add the n's back on that is your answer 2. It is true because even if you put parentheses you still get the same answer 3.What is in the parentheses equals 0 and 5 - 0 is 5 4. You get the same answer even though the 6n and 2 are flipped flopped.
Step-by-step explanation:
Anna bought $4000of company stock, she sold 75% if it when the value doubled and the remainder at four times the purchase price, what is here total profit
Answers
Anna's total profit was $6000 + $16000 - $4000 = $14000.
How did Anna earn profit
Anna bought $4000 of company stock. The value of the stock doubled when she sold 75% of it, which means she sold 0.75 * $4000 = $3000 worth of stock when its value doubled.
Since the value of the stock doubled, Anna sold the $3000 worth of stock for 2 * $3000 = $6000.
Anna then sold the remainder of the stock (25% of the original amount) for four times the purchase price. Since she originally bought the stock for $4000, the remainder was worth 0.25 * $4000 = $1000.
Selling this remainder for four times the purchase price means that Anna sold it for 4 * $4000 = $16000.
Work out an expression for the nth term of this sequence. 3, 11, 19, 27, …
Answers
Answer:
8n-5
Step-by-step explanation:
Find the difference between the numbers, +8 so 8n then subtract the diffference from the first number so 3 - 8= -5
The expression will be 8n - 5
The radius of a circle is 20 in. Find its circumference in terms of π
Answers
Answer:
40π inches
Step-by-step explanation:
What is the formula for the circumference of a circle?
The formula for the circumference of a circle is:
C = 2πr(where C is the circumference and r is the radius)
If the radius of the circle is 20 inches, then its circumference in terms of π would be:
C = 2π × 20 = 40π inchesTherefore, the circumference of a circle when the radius is 20in is 40π inches.
Answer:
C = 40π
Step-by-step explanation:
To calculate the circumference of a circle, we will use the formula
C = 2πr
And we're asked to find C in terms of pi.
So all I need to do is plug in 20 for the radius, and then multiply.
I plug in 20 for the radius, r: C = 2π × 20
Multiply: C = 40π
Therefore, C = 40π.
find the mean and median of each of the following sets of data. determine the deviation from the mean for each data point within the sets and find the mean deviation for each set. 24.49 24.68 24.77 24.83 24.73
Answers
The average distance from the mean is 0.09.
The mean is also known as the average and is calculated by adding up all the values in the set and then dividing the sum by the total number of values.
So, for the given set of data: 24.49, 24.68, 24.77, 24.83, 24.73, the mean would be calculated as follows:
Mean = (24.49 + 24.68 + 24.77 + 24.83 + 24.73) / 5
= 24.70
It tells us what the typical value is within the data set. In this case, the mean value of the data set is 24.70.
Next, let's find the median of the set of data. The median is the middle value of a data set when it is arranged in numerical order. In this case, the data set is already arranged in numerical order, so we can easily find the median.
The median value of the data set is the middle value, which is 24.77.
Now, we will calculate the deviation from the mean for each data point within the set. The deviation from the mean tells us how far each value is from the mean value. This is calculated by subtracting the mean from each value in the set.
Deviation from the mean for each data point:
-0.21, -0.02, 0.07, 0.13, 0.03
As you can see, some values are above the mean, and some are below the mean. The deviation from the mean can be used to determine how spread out the data is from the mean value.
Finally, we will calculate the mean deviation for the set. The mean deviation is the average of the absolute values of the deviation from the mean.
Mean deviation = (|(-0.21)| + |(-0.02)| + |0.07| + |0.13| + |0.03|) / 5
= 0.09
The mean deviation tells us the average distance from the mean value.
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the graph of the quadratic parent
function 9(x)
X2 is translated 3 units to
the right and 2 units down, which of the
following equations describes the
translated graph?
A y = (x - 3)2 + 2
B y = (x - 3)2 - 2
C y = (x + 3)2 - 2
В
D y = (x + 2)2 + 3
Answers
Answer:
y = (x - 3)²-2 is the correct answer
You may want to create a table to help you with this problem.A rare birth defect occurs in approximately 0.5% of all cases in males. If we sample all themales born in 2016 in a specific region (200,000), fill out your table and answer the followingquestions. A test can be done with 96% accuracy to determine if a child has the birth defect.Out of all people, what are the chances that males get a positive test result?(Write your answer as a percentage to 2 decimals.)I
Answers
The total amound of samples is 200,000 so now we can use a rule of 3 to calculate how many males has the defect so:
\(\begin{gathered} 200000\to100 \\ x\to0.5 \end{gathered}\)so the equation is:
\(\begin{gathered} x=\frac{200000\cdot0.5}{100} \\ x=1000 \end{gathered}\)So now the probability to have a positive sample will be:
\(\begin{gathered} p=\frac{1000}{200000}\cdot100 \\ p=0.005\cdot100 \\ p=0.50 \end{gathered}\)there is a 0.50%
A playground 88 ft long and 58 ft wide is to be resurfaced at a cost of $2.75 per sq ft. What will the resurfacing cost?
The resurfacing will cost $.
(Simplify your answer. Type an integer or a decimal.)
Answers
Answer: $1856
Step-by-step explanation: 88 x 58 = 5104. 5104/2.75= 1856
I
I need to know this
Answers
The measures of the angles and arcs of the circle are;
11320317597824260853224The sum of the digits in the shaded = 1 + 3 + 7 + 2 + 3 + 4 + 6 = 26
26 - 14 = 12
Using the decoder wheel, we get; FVMMO
What is an arc of a circle?An arc is a portion or part of the circumference of the circle.
The arc angles from the diagrams indicates;
1. mPR = 90 + (90 - 67) = 113
2. mQST = mQR + mRST
mQST = 23 + 180 = 203
3. 8·x - 15 + (3·x + 8) = 180 (Linear pair angles)
11·x - 7 = 180
11·x = 187
x = 187/11 = 17
x = 17
4. LM = 3·x + 8
Therefore; LM = 3 × 17 + 8 = 59
LM = 59
5. m∠DAC = 156/2 = 78
6. mBC = 180 - 156 = 24
7. m∠ADB = 43
mAB = 43 × 2 = 86
mABD = 180 + 86 = 266
8. 2 × (7·x -3) = 17·x - 30
14·x - 6 = 17·x - 30
17·x - 14·x = 3·x = 30 - 6 = 24
x = 24/3 = 8
x = 8
9. m∠YZX = 7·x -3
m∠YZX = 7 × 8 - 3 = 53
m∠YZX = 53
10. m∠WXZ = 62/2 = 31
The angle formed by the intersection of WY and XZ is therefore;
mWZY = 180 - (2 × 53) + 63 = 137
mWXY = 180 - (2 × 31) + (17 × 8 - 30) = 224
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can anyone help me with this? im confused
Answers
Answer:
1,2,3 and 6 are similar triangles by AA similarity
Step-by-step explanation:
1) ∠DEC ≅ ∠FEG {Vertically opposite angles}
DC // GF
∠ECD ≅ ∠EGF {Alternate interior angles}
∠EDC ≅ ∠EFG {Alternate interior angles}
ΔDEC & ΔFEG are similar triangles by AA similarity
2)MN // QP
∠LQP ≅ ∠QMN {Corresponding angles }
∠LPQ ≅ ∠PNM {Corresponding angles}
ΔLQP & ΔLMN are similar triangles by AA similarity
3) In ΔSYE ,
∠S = 180 - 90 - 39
∠S = 51°
In ΔCHW,
∠H = 180 - 51 - 90
∠H = 39
ΔSYE and ΔCHW
∠S ≅ ∠W = 51°
∠Y ≅ ∠C = 90°
∠E ≅∠H = 39°
ΔSYE & ΔWCH are similar triangles by AA similarity
6) ∠P ≅ ∠Z {Given}
∠PXQ ≅∠ZXY {Vertically opposite angles}
ΔPXQ & ΔZXY are similar triangles by AA similarity
What principal do you have to deposit in a 4.5% saving account compounded monthly in order to have a total of $10,000 after 8 years?
Answers
The principle that you have to deposit in a 4.5% saving account compounded monthly will be $6,981.46.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
The rate and time are given as,
r = 0.045 / 12
r = 0.00375
n = 8 x 12
n = 96
Then the amount of investment is given as,
$10,000 = P × (1 + 0.00375)⁹⁶
$10,000 = P × (1.00375)⁹⁶
$10,000 = P × 1.43236
P = $6,981.46
The principle that you have to deposit in a 4.5% saving account compounded monthly will be $6,981.46.
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HELP!!!
Find the length of side x in simplest radical form with a rational denominator.
Answers
Answer:
Step-by-step explanation:
Square root of 2
Use a calculator to solve for x in the equation 2e3x = 400. Round your answer to three decimals.
Question 8 options:
A)
6.397
B)
1.766
C)
5.991
D)
5.298
Answers
The value of the expression is 1.766.
What is simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given the expression,
2\(e^{3x}\) = 400
divide by 2 into both sides
\(e^{3x}\) = 400/2
\(e^{3x}\) = 200
converting the expression in form of a log,
ln(\(e^{3x}\))= ln(200)
log(aⁿ) = n log(a)
3x ln(e) = ln(200) [ln(e) = 1 and ln(200) = 5.2931]
3x = 5.2931
x = 1.766
Hence Option B is correct.
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What value of x makes the equation -0.2(3x – 25) = -0.1x + 7 true?
Answers
Answer:
x = -4
Step-by-step explanation:
Ok first let's put the equation.
-0.2(3x – 25) = -0.1x + 7 (first distribute the -.2 to 3x and -25)
-0.6x + 5 = -0.1x + 7 (subtract 5 on both sides)
-0.6x = -0.1x + 2 (add -0.1x on both sides)
-0.5x = 2 (divide by -0.5 on both sides)
x = -4
Hope this helps!!
I NEEDDDDDDD HELPPPPPPPP PLEASEEEEEEEE
Answers
Answer:
point and circle
Step-by-step explanation:
cross section is slicing through. You can make a point and circle
when slicing through a sphere
if a small cup is 10 oz and cost 2.69 what is the cost per ounces
Answers
Answer:
The cost per ounce of the small cup is $0.269
Step-by-step explanation:
To find the cost per ounce, we can divide the cost of the cup by the number of ounces it holds.
Cost per ounce = Cost of the cup ÷ Number of ounces in the cup
Cost of the cup = $2.69
Number of ounces in the cup = 10 oz
So,
Cost per ounce = $2.69 ÷ 10 oz
Cost per ounce = $0.269 per oz (rounded to the nearest thousandth)
Therefore, the cost per ounce of the small cup is $0.269.
The student council is planning the school carnival. Each ticket costs $2.50. Explain how to write an equation that represents this scenario. Let X represent the number of tickets sold, and Y represents the total amount of money raised.
Answers
Answer:
the answer is c.
Answer:
Let x represent the variety of tickets sold, and y represent the total amount of cash raised. Since each price tag is $2.50, the total amount of money raised is identical to $2.50 instances the wide variety of tickets. The equation would be y = 2.50x.
Step-by-step explanation:
The x variable represents the number of tickets sold.
The y variable represents the total amount of money raised from ticket sales.
The equation for the scenario is y = 2.50x.
What is the volume of the cone with height of 6 m and diameter of 8 m rounded to the nearest cubic meter
Answers
Answer:
101 m^3
Step-by-step explanation:
v = π * r^2 * h/3
= π * 4^2 * 6/3
v= 100.53 m^3
v= 101 m^3 to the nearest cubic meter
Which of the following can NOT be answered from a regression equation?
a
predict the value of y at a particular value of x
estimate whether the linear association is positive or negative
estimate whether the association is linear or non linear
none of the above
Answers
Answer:
estimate whether the association is linear or non linear
Step-by-step explanation:
The degree of the expression 4x5ymz is 10. What is the value of m?
Answers
Answer:
the answer is 4
Step-by-step explanation:
An amount of $27,000 is borrowed for 7 years at 6.5% interest, compounded annually. If the loan is paid in full at the end of the period, how much must be paid back? Round your answer to the nearest dollar
Answers
$41958 must be paid back
Explanation:AMount borrowed = P = $27000
time = t= 7 years
n = compounded annually
n = 1
rate = 6.5% = 0.065
Amount to be paid back at the end of the period = FV
We will be apply the compound interest formula:
\(FV\text{ = P(1 +}\frac{r}{n})^{nt}\)\(\begin{gathered} FV\text{ = 27000(1 + }\frac{0.065}{1})^{1\times7} \\ FV=27000(1.065)^7 \\ FV\text{ = }41957.6367 \end{gathered}\)To the nearest dollar, $41958 must be paid back
You model your investment account using the formula y = 20000(1.035)x where x represents the
number of years and y represents the account balance after x years. What is the growth rate of your
investment?
Answers
Answer:
Step-by-step explanation:
The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.
To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.
So, the growth rate of the investment is:
1.035 - 1 = 0.035
0.035 * 100 = 3.5%
Therefore, the growth rate of the investment is 3.5%.
The growth rate of the investment can be found by subtracting 1 from the base of the exponential function and converting the result to a percentage:
growth rate = (base - 1) x 100%
growth rate = (1.035 - 1) x 100%
growth rate = 0.035 x 100%
growth rate = 3.5%
Therefore, the growth rate of the investment is 3.5%.
Find the midpoint of the line segment joining points A and B.
A(2,- 7); B(2,3)
Answers
Answer: (2, -2)
Step-by-step explanation:
\(\left(\frac{2+2}{2}, \frac{3-7}{2} \right)=(2,-2)\)
