Answer:
To calculate the future value of your monthly investments after saving your money, i can use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value
P = Monthly investment amount
r = Monthly interest rate
n = Number of months
Given:
Monthly investment amount (P) = 49,000 VNĐ
Monthly interest rate (r) = 6.3% / 12 = 0.00525
Number of months (n) = 10 years * 12 months/year = 120 months
Plugging in these values, i can calculate the future value:
FV = 49,000 * ((1 + 0.00525)^120 - 1) / 0.00525
Calculating this expression, the future value is approximately 7,565,000 VNĐ.
Therefore, after 10 years of investing 49,000 VNĐ per month and earning an interest rate of 6.3% per year, you would have approximately 7,565,000 VNĐ.
which must be true in order for the relationship zyx~wvu to be correct
In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:
Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.
Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.
These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).
Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.
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Who is correct and why?
Selena is incorrect because she should have substituted the values for the variables first, and then simplifed.
Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables.
Drake is incorrect because he should have simplified first, before substituting the values for the variables.
Drake is correct because he substituted the values for the variables first, and simplified correctly.
Selena and Drake both are correct.
Selena: According to the statement, Selena is said to have not substituted the values for the variables first and then simplified.If she did not follow the correct order of operations, it's possible that she made an error.Drake: According to the statement, Drake is said to have substituted the values for the variables first and then simplified. This order seems to align with the correct order of operations, but without further details, it is not possible to determine if he made any mistakes during the process.For such more questions on
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URGENT
in the first month that moiras marmalade stand was open, moira sold 145 jars of marmalade. In the second month, Moira sold 203 jars of marmalade. write the number she sold in the second month as a percentage of the number sold in the first month
Therefore, Moira sold approximately 140% as many jars in the second month compared to the first month. This means the number of jars sold in the second month was 140% of the number sold in the first month.
To find the second month's sales as a percentage of the first month's sales, we need to divide the number of jars sold in the second month by the number sold in the first month and then multiply by 100 to get the percentage.
Number of jars sold in the second month: 203
Number of jars sold in the first month: 145
Percentage of second month's sales = (203 / 145) * 100 ≈ 140%
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What is the perimeter of a rectangle with a length of 8 meters and a width of 6 meters?
16 meters
22 meters
28 meters
48 meters
The perimeter of a rectangle with a length of 8 meters and a width of 6 meters is 28 meters.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter of a rectangle is a linear measure and is expressed in linear units of meters, feet, inches, or yards.
The formula used to calculate the perimeter of a rectangle is, perimeter of a rectangle is given by:
[tex]2(\text{l} + \text{w})[/tex]
Where 'l' is the length.And 'w' is the width of the rectangle.Given the problem, we need to fin the perimeter of the rectangle with a length of 8 meters and a width of 6 meters.
So,
[tex]\text{P}=2(8+6)[/tex]
[tex]\text{P}=2\times14[/tex]
[tex]\text{P}=\bold{28 \ meters}[/tex]
Therefore, The perimeter of the rectangle is 28 meters.
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The foci of an ellipse are at $F_1 = (0,2)$ and $F_2 = (2,0).$ The ellipse passes through the origin, and intersects the $x$-axis at one other point. What is this point of intersection?
The point of intersection of the ellipse with the x-axis is $(\pm \sqrt{2}, 0)$.
To find the point of intersection of the ellipse with the x-axis, we can start by considering the distance between the foci $F_1$ and $F_2$. Using the distance formula, we find that the distance between $F_1$ and $F_2$ is $\sqrt{(2-0)^2 + (0-2)^2} = \sqrt{8} = 2\sqrt{2}$.
Since the ellipse passes through the origin, the sum of the distances from any point on the ellipse to the foci will be equal to the length of the major axis. In this case, the sum of the distances is $2a$, where $a$ represents the semi-major axis.
Since the foci are located at $(0,2)$ and $(2,0)$, we can see that $2a = 2\sqrt{2}$. Solving for $a$, we find $a = \sqrt{2}$.
Now, we can write the equation of the ellipse centered at the origin as $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Since the ellipse passes through the origin, we know that the y-coordinate of the point of intersection on the x-axis is 0.
Substituting $y = 0$ into the equation, we have $\frac{x^2}{(\sqrt{2})^2} + \frac{0^2}{b^2} = 1$, which simplifies to $\frac{x^2}{2} = 1$.
Solving for $x$, we find $x = \pm \sqrt{2}$.
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PLEASE HELP QUICKKKKKKKKKKKKK
need help with this ASAP
Answer:
The answer is,
[tex]\sqrt{3}/2[/tex]
Step-by-step explanation:
Since we have cos10cos20 - sin10sin20,
We can use the formula,
cos(a+b) = (cosa)(cosb) - (sina)(sinb)
So, we have,
cos10cos20 - sin10sin20 = cos(10 + 20)
= cos(30)
cos(30) = sqrt(3)/2
[tex]cos(30) = \sqrt{3}/2[/tex]
A car is traveling at a rate of 108 kilometers per hour. What is the cars rate in meters per second? How many meters will the car travel in 20 seconds?
Answer:
30 m/s; 600 m----------------------
Convert the speed considering that:
1 km = 1000 meters and1 hr = 3600 secondsCalculate the speed:
108 km/h = 108 * 1000/3600 m/s = 1080/36 m/s = 30 m/sThe distance in 20 seconds:
30 * 20 = 600 mStep-by-step explanation:
A car is traveling at a rate of 108 kilometers per hour
Speed of car = 108 km/hr
Converting into m/s,
1 km = 1000 metres 1 hr = 3600 seconds .[tex] \longrightarrow\tt 108 \times \dfrac{10{ \cancel{00}}}{36{ \cancel{00} }}[/tex]
[tex] \longrightarrow\tt 108 \times \dfrac{5}{18} [/tex]
[tex] \longrightarrow\tt \dfrac{540}{18} [/tex]
[tex]\longrightarrow \tt 30 \: m/s[/tex]
So the speed of car is 30 m/s
Time is 20 seconds.
Distance = speed × time
30m/s × 20 seconds 600 mHence the distance covered by the car is 600 meters
A car enters a turnpike 22 miles north of a town. The car travels north at an average speed of 64 miles per hour. How far is the car from the town after 4 hours on the turnpike?
Explain how you can use a linear function to solve this problem. Then, solve the problem.
After 4 hours on the turnpike, the car is approximately 278 miles from the town.
To solve this problem using a linear function, we can use the formula for distance: distance = speed × time. In this case, the speed is given as 64 miles per hour, and the time is given as 4 hours.
Let's define the distance from the town as a variable, say "d." Since the car travels north, the distance from the town will increase as time passes. At the start, the car is 22 miles north of the town.
Now, we can set up a linear function to represent the distance from the town as a function of time:
d = 22 + (64 × t)
In this function, "t" represents time in hours. The initial distance of 22 miles is added to the product of the speed (64 mph) and time (t).
To find the distance from the town after 4 hours, we substitute t = 4 into the function:
d = 22 + (64 × 4)
d = 22 + 256
d = 278 miles
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Given that ABCD is a rhombus, what is the value of x?
B
(4x-25)
A
OA. 29
B. 23
C. 46
D. 38
OE. 45
O F. Cannot be determined
The value of x in the rhombus ABCD is determined as 23.
option B.
What is the value of x?The value of x is calculated by applying the following formula as shown below.
the diagonals of a rhombus intersects at 90 degrees;
the complementary angle of (4x - 25) = 90 - (4x - 25)
90 - (4x - 25) = x (alternate angles are equal)
90 - 4x + 25 = x
115 = 4x + x
115 = 5x
divide both sides of the equation by 5 to obtain the value of x;
5x = 115
x = 115 / 5
x = 23
Thus, the value of x in the rhombus ABCD is determined as 23.
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What number must you add to complete the square x2+4x=15
Answer: 19
Step-by-step explanation:
x^2+4x-15=0. To complete the square, it needs to be (x+2)^2, which is x^2+4x+4. Thus, you need to add 19.
Using the following image, solve the problems below given that G is the midpoint of FH. How would you set this problem up to find x? (Hint: Enter in the equation to find x)
Using your setup, what are the values of x, FG, GH, and FH?
1. The value of x in the diagram is 1
2. The value of FG in the diagram is 20
3. The value of GH in the diagram is 20
4. The value of FH in the diagram is 40
How do i determine the value of xThe value of x can be obtained as follow:
FG = 33x - 13GH = 13x + 7Value of xFG = GH (Since G is the mid point)
33x - 13 = 13x + 7
Collect like terms
33x - 13x = 7 + 13
20x = 20
Divide both side 20
x = 20 / 20
= 1
Thus the value of x is 1
How do i determine the value of FG, GH, and FH?The value of FG can be obtained as follow:
FG = 33x - 13x = 1Value of FG =?FG = 33x - 13
= 33(1) - 13
= 33 - 13
= 20
The value of GH can be obtained as follow:
GH = 13x + 7x = 1Value of GH =?GH = 13x + 7
= 13(1) + 7
= 13 + 7
= 20
The value of FH can be obtained as follow:
FG = 20GH = 20Value of FH =?FH = FG + GH
= 20 + 20
= 40
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The measure of one of the small angles of a right triangle is 45 more than 4 times the measure of the other small angle. Find the measure of both angles.
Answer:
Step-by-step explanation
You start by knowing that a triangle has 180 degrees in total and this is a right triangle so your total needs to add up to 90. Using the formula 90 subtract 45 then divided by 4+1 and there is your smaller angle.
A photo has a side length 4 inches and 6 inches in length .After the enlargement the length becomes 5 more inches what is the length of the photo
Therefore, the length of the photo after the enlargement is 9 inches.
The initial length of the photo is given as 4 inches. After the enlargement, the length becomes 5 more inches. To find the final length, we can add 5 inches to the initial length.
Initial length of the photo: 4 inches
Additional length after enlargement: 5 inches
Final length = Initial length + Additional length
Final length = 4 inches + 5 inches
Final length = 9 inches
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What is the value of y?
150%
O A. 85
O B. 65
O C. 75
OD. 55
95°
Hello!
angle1 = (360° - 2 * 150°)/2 = 30°
angle2 = (360° - 2 * 95°)/2 = 85°
y° = 180° - (30° + 85°) = 65°
The correct answer is 65°Evaluate the following expression when x = -4 and y = 4.
x^6-x/4y
A. 1,023/4
B. 1,025/4
C. 16,385/4
D. -1,023/4
Answer: The correct answer is option C. 16,385/4.
Step-by-step explanation: First of all, we evaluate the expression x^6. Putting x= -4 gives (-4^6) which is equal to 4096. The next part (-x/4y) on substituting x = -4 and y =4 gives us the positive expression (1/4).
Adding both these parts, we get (4*4096+1)/4. This is finally evaluated as (16,384+1)/4, which is equal to the required answer of 16,385/4.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
19. A. 108 mm²
B. 404.5 in²
Step-by-step explanation:
19:
Area of Big triangle: ½*base*height
=½*(18mm+10mm)+12mm
=168mm²
Area of Small triangle=½*base*height
=½*10mm*12mm
=60mm²
Now
Area of shaded region=Area of Big triangle - Area of Small triangle
=168-60
=108 mm²
Therefore Area is 108mm².
20.
We know that:
Area of Parallelogram=Base*Height
here
Base=26 in
let's find height
Sin 45°=Opposite/Hypotenuse
Sin 45°=Height/22
Height=Sin 45°*22
Height=[tex]\frac{1}{\sqrt{2}}*22=11\sqrt{2}[/tex]=15.56
Now,
Area of parallelogram= base*height=26*15.56=404.5 in²
Therefore, Area of Parallelogram=404.5 in²
If £2000 is placed into a bank account that pays 3% compound interest per year, how much will be in the account after 2 years?
the answer
if that money increases by 3 per cent each year so 3÷100=0.03+1=1.03
1.03×1.03×2000=2121.80
If £2000 is placed into a bank account that pays 3% compound interest per year. The amount in the bank account after 2 years will be £2,121.80.
To calculate the amount in the bank account after 2 years with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = final amount in the account
P = initial principal amount
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Given:
P = £2,000
r = 3% = 0.03 (converted to decimal)
n = 1 (compounded annually)
t = 2 years
Substituting the values into the formula, we have:
A = 2000(1 + 0.03/1)^(1*2)
A = 2000(1 + 0.03)^2
A = 2000(1.03)^2
A ≈ 2000(1.0609)
A ≈ £2,121.80
Therefore, the amount in the bank account after 2 years will be approximately £2,121.80.
The calculation involves using the compound interest formula, where we add 1 to the interest rate (in decimal form) and raise it to the power of the number of compounding periods (in this case, 2 years). Multiplying this result by the initial principal of £2,000 gives us the final amount of £2,121.80.
Hence, the amount in the account after 2 years will be £2,121.80.
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Consider the diagram.
Line l is a perpendicular bisector of line segment R Q. It intersects line segment R Q at point T. Line l also contains point S. Line segment R S is 3 x + 2. Line segment S Q is 5 x minus 8.
What is QS?
The length of line segment QS is 17.
To find the length of line segment QS, we need to determine the values of x and then substitute them into the given equations.
Given:
Line segment RS = [tex]3x + 2[/tex]
Line segment SQ = [tex]5x - 8[/tex]
Since line l is the perpendicular bisector of line segment RQ, it means that line segments RS and SQ are equal in length.
Therefore, we can set up an equation:
[tex]3x + 2 = 5x - 8[/tex]
To solve for x, we can start by isolating the variable terms on one side:
[tex]2 + 8 = 5x - 3x[/tex]
[tex]10 = 2x[/tex]
Dividing both sides by 2:
[tex]x = \frac{10}{2}[/tex]
[tex]x = 5[/tex]
Now that we have found the value of x, we can substitute it into the equation for line segment SQ:
[tex]SQ = 5x - 8[/tex]
[tex]SQ = 5(5) - 8[/tex]
[tex]SQ = 25 - 8[/tex]
[tex]SQ = 17[/tex]
Therefore, the length of line segment QS is 17.
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A round wading pool has a diameter of 115cm and is 25cm deep. A hose is filling the pool at a rate of 34,000cm^3 per minute.
Therefore, it will take approximately 7.67 minutes to fill the wading pool completely.
The round wading pool has a diameter of 115 cm and a depth of 25 cm. To find the volume of the pool, we can use the formula for the volume of a cylinder, which is
V = πr^2h.
Since the pool is round, the radius (r) is half the diameter, which is
115 cm / 2 = 57.5 cm.
Plugging in the values, we have
V = π(57.5 cm)^2 * 25 cm ≈ 260,979 cm^3.
The hose is filling the pool at a rate of 34,000 cm^3 per minute.
To determine how long it will take to fill the pool, we divide the volume of the pool by the rate of filling:
260,979 cm^3 / 34,000 cm^3/min ≈ 7.67 minutes.
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A salesman earns 3% commission on all the merchandise that he sells. Last month he sold $5000 worth of merchandise. How much commission (in dollars) did he earn last month?
Hence, the salesman earned $150 in commission last month.
Commission is the sum of money that an employee earns based on a percentage of the total sales that they made. It is usually a part of an employee's income.A salesman earns a commission on all the merchandise that they sell.
The commission rate that a salesman earns is usually a percentage of the total value of the merchandise that they have sold.
A salesperson is typically paid a percentage of the price of the items that they sell.
The percentage of the commission that they earn can vary from company to company or from sales job to sales job. In this question, we have to calculate how much commission the salesman earned last month.
We know that the salesman earns a 3% commission on all the merchandise that he sells.
And last month he sold $5000 worth of merchandise.
So, we can use the following formula to calculate his commission.
Commission = (Commission Rate/100) × Total Sales
Therefore, Commission = (3/100) × $5000 = $150
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Othniel used 2/5 of a full tank of petrol to travel to Kumasi and 2/6 of the full tank of petrol to travel to Accra. Which journey required more petrol?
Othniel used 2/5 of a full tank of petrol to travel to Kumasi and 2/6 of the full tank of petrol to travel to Accra. Therefore, the journey to Kumasi required more petrol by simplifying the fractions.
To compare the amount of petrol used for the journeys to Kumasi and Accra, we'll calculate the fractions of the full tank of petrol used for each journey.
Let's assume that the full tank of petrol has a capacity of 1 unit.
Othniel used 2/5 of the full tank of petrol to travel to Kumasi.
The fraction of the full tank of petrol used for the journey to Kumasi is 2/5, which is equivalent to 0.4.
Othniel used 2/6 of the full tank of petrol to travel to Accra.
To compare the fractions accurately, we need to make the denominators equal. Since the least common multiple (LCM) of 5 and 6 is 30, we'll convert the fractions to have a denominator of 30.
Converting the fraction 2/5 to have a denominator of 30:
(2/5) * (6/6) = 12/30
Converting the fraction 2/6 to have a denominator of 30:
(2/6) * (5/5) = 10/30.
Comparing the fractions, we find that Othniel used 12/30 of the full tank of petrol to travel to Kumasi and 10/30 of the full tank of petrol to travel to Accra.
Since 12/30 is greater than 10/30, the journey to Kumasi required more petrol.
Simplifying the fractions, we have:
Journey to Kumasi: 12/30 = 2/5.
Journey to Accra: 10/30 = 1/3.
Therefore, the journey to Kumasi required more petrol than the journey to Accra.
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Read the problem and decide whether it has too much or too little
information.
On Saturday at the Boxerville Carnival, 800 people attended. On Sunday, 650
people attended. On Monday, 250 people attended. On Tuesday, 350 people
attended. How many people attended the Boxerville Carnival on the
weekend?
The problem provides the attendance numbers for four specific days of the Boxerville Carnival: Saturday (800 people), Sunday (650 people), Monday (250 people), and Tuesday (350 people). The question asks for the total number of people who attended the carnival on the weekend.
Given that the information about Saturday and Sunday attendance is provided, we have enough information to determine the total number of people who attended the carnival on the weekend. We can simply add the attendance numbers for Saturday and Sunday:
800 + 650 = 1450 people.
Therefore, the problem has sufficient information to calculate the total attendance on the weekend. It is not excessive or lacking in detail, allowing us to accurately find the desired answer.
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PLEASE HELP TODAY I WILL GIVE BRAINLIST
Answer: Triangle C only
Step-by-step explanation: using the formula to find out if the triangle are right angle (a^2+b^2=c^2) the legs are supposed to equal to the hypotenuse. A and B arentaren't equal to the hypotenuse
find the front and side elevation
The sketch of the front elevation and the side elevation of the prism are added as an attachment
How to draw the front elevation and the side elevation of the prismFrom the question, we have the following parameters that can be used in our computation:
The prism
Using the figure as a guide, we understand that:
The front elevation is a rectangle of 2m by 0.5m
While the side elevation is a rectangle merged with a trapezoid
Next, we draw the elevations (see attachment)
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The linear function f(x) = 0.5x + 80 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents the average test score in your science class, where x is the number of the test taken.
x g(x)
1 81
2 83
3 85
Part A: Determine the test average for your math class after completing test 2. (2 points)
Part B: Determine the test average for your science class after completing test 2. (2 points)
Part C: Which class had a higher average after completing test 4? Show work to support your answer. (6 points)
I really only need the math average (the first question) please thank you ill give brainliest + 100 points
Answer:
a) 81
b) 83
c) science
Step-by-step explanation:
a)
f(x) = 0.5x + 80
gn x = 2 tests
⇒ f(2) = 0.5(2) + 80
= 1 + 80
= 81
b)
gn x = 2
g(2) = 83
c)
we have g(x) = mx + b
m = (y₂-y₁)/(x₂-x₁)
= (83 - 81)/(2 - 1)
m = 2
for g(1),
g(1) = m(1) + b
81 = 2(1) + b
b = 81 -2
b = 79
⇒ g(x) = 2x + 79
and f(x) = 0.5x + 80
for 4 tests, we have x = 4
g(4) = 2(4) + 79
= 8 + 79
g(4) = 87
f(4) = 0.5(4) + 80
= 2 + 80
f(4) = 82
g(4) = 87 > f(4) = 82
∴Science class has a higher average
Why are the lines y = 5x − 1 and 10x + 2y = 0 perpendicular
Answer:
The lines are not perpendicular because the product of their slopes is not -1.
Step-by-step explanation:
y = 5x - 1
slope = 5
10x + 2y = 0
2y = -10x
y = -5x
slope = -5
The slopes are 5 and -5.
5 × (-5) = -25
The product of the slopes is -25, not -1, so the lines are not peropendicular.
Answer:
The line are not perpendicular. Perpendicular lines after opposite reciprocals.
Step-by-step explanation:
Change 10x + 2y = 0 into the slope intercept form of a line.
Subtract 10x from both sides
10x - 10x + 2y = 0 - 10 x
2y = -10x Divide both sides by 2
y = -10x/2
y = -5x.
The slope of the first equation is 5 ( y = 5x -1 ).
The slope of the second equation is -5 ( y = -5x )
The opposite reciprocal of 5 would be -1/5 not -5.
So these lines are not perpendicular.
Helping in the name of Jesus.
The base of the mountain is 6,500 feet above sea level and AB measures 230 feet across. Given that the measurements for QAP is 20° and QBP is 35°, how far above sea level is peak P ? Express your answer to the nearest foot.
Height above sea level:
Answer:
6610
Step-by-step explanation:
We have tan(X) = opposite/ adjacent
tan(QBP) = PQ/BQ
tan(35) = PQ/BQ ---eq(1)
tan(QAP) = PQ/AQ
tan(20) = [tex]\frac{PQ}{AB +BQ}[/tex]
[tex]=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}[/tex]
230*tan(20) + PQ*tan(20)*tan(35) = PQ
⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)
⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]
[tex]PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}[/tex]
[tex]= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4[/tex]
PQ = 110.4
≈110
Height above sea level = 6500 + PQ
6500 + 110
= 6610
Help me ASAP,
I will give Brainliest!
Answer:
1 Part A: volume of sand = 21195 cm³
1 Part B: vol of rectangle prism = 20400cm³
1 Part C: over-fill
2 Part A: area ≈ 427
2 Part B: h ≈ 11.7
Step-by-step explanation:
1)
Part A:
r = 15
h = 30
Vol of cylinder = πr²h
= (3.14)(15²)(30)
= 21195
volume of sand = 21195 cm³
Part B:
l = 60
w = 20
h = 17
vol of rectangle prism = lbh
= 60*20*17
= 20400
vol of rectangle prism = 20400cm³
Part C:
volume of sand = 21195 cm³
vol of rectangle prism = 20400cm³
Since volume of sand (= 21195 cm³) > vol of rectangle prism (= 20400cm³)
The sand wont fit into the rectangular prism and will over-fill the conatiner
2)
Part A:
d = 8 ⇒ r = d/2 = 8/2 = 4
h = 13
area of cylinder = 2πr(h + r)
= 2(3.14)(4)(13 + 4)
= 427.04
area ≈ 427
Part B:
l = w = 7 cm
area of prism = 2(wl + hl + hw)
also given :
area of prism = area of cylinder
⇒ 2(wl + hl + hw) = 427
⇒ 2(7*7 + h*7 + h*7) = 427
⇒ 2(49 + 2*7h) = 427
⇒ 2(49 + 14h) = 427
⇒ 49 + 14h = 427/2
⇒ 49 + 14h = 213.5
⇒ 14h = 213.5 - 49
⇒ 14h = 164.5
⇒ h = 164.5/14
h = 11.75
h ≈ 11.7
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
20. A. 357.8 in³
B. 1231.5 yd³
Step-by-step explanation:
20.
A.
Volume of Pyramid : ⅓*base area * height
here,
Base area = area of rectangle=length*breadth =10*8=80in²
Now
Height can be calculated by using Pythagorous theorem
height =[tex]\sqrt{(slant\: height)^2-(\frac{breadth}{2})^2}[/tex]
height =[tex]\sqrt{14^2-(\frac{8}{2})^2}=\sqrt{196-16}=\sqrt{180}=13.42 in[/tex]
height =13.4 in
Now
Volume of pyramid = ⅓*base area *height
Volume of Pyramid=⅓*80*13.42
Volume of Pyramid=357.8 in³
B.
Volume of cone = ⅓*area of base* height
Here
slant height=24 yd
height =?
diameter=14yd
radius =14/2=7 yd
Let's find the height:
By using the Pythagorous theorem,
slight height²=radius²+height²
substituting value
25²=7²+height²
height²=25²-7²
height =[tex]\sqrt{576}[/tex]=24 yd
Now
Area of Base= πr²=π*7²=153.94 yd²
Now
Volume = ⅓*area of base*height =⅓*153.94*24=1231.5 yd³
So,
Volume of cone is 1231.52 yd³.
