The total approximate surface area of Luther's rocket is 219.8 square inches.
Luther is building a model rocket and needs to calculate its surface area. His rocket consists of a cylindrical body with a nose cone. The diameter of the cylinder is 4 inches, the height of the cylindrical part is 12 inches (since the total height is 19 inches and the nose cone is 7 inches), and the height of the nose cone is 7 inches.
First, we calculate the surface area of the cylindrical body. The formula for the lateral surface area of a cylinder is 2πr*h, where r is the radius and h is the height. Half the diameter gives us the radius, which is 2 inches. Thus, the lateral surface area is 2π*2*12 = 48π square inches.
Next, we find the surface area of the two bases of the cylinder. The formula for the area of a circle is π[tex]r^2[/tex]. So, the area of one base is π*[tex]2^2[/tex] = 4π square inches. There are two bases, so we double this to get 8π square inches.
For the nose cone, we'll assume it is a cone whose slant height is the same as its height (because we do not have enough information to calculate the slant height if it were to differ). The surface area of a cone is πr*l, where l is the slant/linear height. Therefore, for the nose cone, we have π*2*7 = 14π square inches.
Now, we add the surface areas of the cylindrical part and the nose cone to get the total surface area of the rocket: 48π + 8π + 14π = 70π square inches.
Finally, multiplying 70π by approximately 3.14, we get the total approximate surface area of Luther's rocket: 70 * 3.14 = 219.8 square inches.
The correct answer is:
The surface area of the rocket is approximately [tex]\(48\pi + 2\pi(2 + \sqrt{53})\)[/tex] square inches, without numerical calculation.
To find the surface area of the rocket, we need to calculate the surface area of both the cylindrical body and the nose cone separately, then add them together.
1. Surface Area of the Cylindrical Body:
The cylindrical body's surface area can be calculated using the formula for the lateral surface area of a cylinder: [tex]\( A_{\text{cylinder}} = 2\pi rh \)[/tex], where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height.
Given:
- Diameter = 4 inches (radius = 2 inches)
- Total height (including nose cone) = 19 inches
- Height of the nose cone = 7 inches
Radius r = 2 inches
Height of cylindrical body = Total height - Height of nose cone = 19 inches - 7 inches = 12 inches
[tex]\( A_{\text{cylinder}} = 2\pi \times 2 \times 12 = 48\pi \)[/tex] square inches
2. Surface Area of the Nose Cone:
The surface area of a cone can be calculated using the formula: [tex]\( A_{\text{nosecone}} = \pi r_{\text{nosecone}}(r_{\text{nosecone}} + \sqrt{h_{\text{nosecone}}^2 + r_{\text{nosecone}}^2}) \), where \( r_{\text{nosecone}} \) is the radius and \( h_{\text{nosecone}} \)[/tex] is the height.
Given:
- Height of nose cone = 7 inches
Since the diameter of the rocket is 4 inches, the radius of the nose cone is also [tex]\( \frac{4}{2} = 2 \)[/tex] inches.
[tex]\( A_{\text{nosecone}} = \pi \times 2 \times (2 + \sqrt{7^2 + 2^2}) = 2\pi(2 + \sqrt{53}) \)[/tex] square inches
3. Total Surface Area:
The total surface area of the rocket is the sum of the surface areas of the cylindrical body and the nose cone.
Total Surface Area = Surface Area of Cylindrical Body + Surface Area of Nose Cone
[tex]\( = 48\pi + 2\pi(2 + \sqrt{53}) \)[/tex] square inches
Now, you can compute the numerical value.
A proportional relationship is represented by the equation 3x = 18y. If y = kx, where k is the
constant of proportionality, then what is the value of k?
NEED HELP ASAP!
Answer: 1/6
Step-by-step explanation:
3x = 18y
y = kx
where,
k = constant of proportionality
3x = 18y
Divide both side by 18
3x/18 = 18y/18
y = 1/6x
k = 1/6
On a trip, you had to change your money from dollars to British pounds.
You got 560 pounds for 800 dollars.
Which is a unit rate that describes the exchange?
original price: $50
sale price: $40
percent discount:
Answer:
20 % of the original price
Step-by-step explanation:
1). 50 - 40 = 10 $
2). 10 / 50 = 20 %
Use a calculator to find the r-value of these data. Round the value to three
decimal places.
Answer:
The answer would be B- 0.953. I hope this helps you
Answer: b
Step-by-step explanation:
A regular octagon has side lengths of 9 units. Each side of the octagon is
increased by 27 units. What are the perimeters of the original octagon
and new octagon?
Answer:
The perimeter of the original octagon is:
72 units.The perimeter of the new octagon is:
288 units.Step-by-step explanation:
When it is mentioned that an octagon is regular, it means that all its sides are equal, therefore, each side of the original octagon has a length of 9 units, considering the formula of the octagon's perimeter:
Perimeter of an octagon = 8 * length.By replacing you get:
Perimeter of the original octagon = 8 * 9 = 72 units.For the new octagon, it is mentioned that each side increases by 27 units, therefore:
New length = 27 + 9 = 36 units.Applying the formula of perimeter of an octagon with the new values we obtain:
Perimeter of the new octagon = 8 * 36 = 288 units.Final answer:
The perimeter of the original octagon is 72 units, while the perimeter of the new octagon is 288 units.
Explanation:
An octagon is a polygon with eight sides. Since each side of the regular octagon has a length of 9 units, the perimeter of the original octagon is 8 times the length of one side, which is 8 x 9 units = 72 units.
When each side of the octagon is increased by 27 units, the new length of each side becomes 9 + 27 units = 36 units. Therefore, the perimeter of the new octagon is 8 times the length of one side, which is 8 x 36 units = 288 units.
How would you explain surface area and volume to a 6th grader who is just now learning about these concepts?
Answer:
Surface area:
The area on the surface of a shape, so the area of the faces of the square or the area of the faces of the triangle.
(how to solve: find the area of all faces(b*h) and add them up)
Volume: the amount you can fill in that specific shape? Like, filling up a bathtub, how much water can it hold? That's volume.
(how to solve: its different for each shape, but squares are (B*W*H = Volume or V))
-A friendly 8th grader :)
The statue of Liberty stands on a 150 ft. pedestal. From a point 250 ft. from the base of the
pedestal, the angle of elevation to the top of Liberty's torch is 50°. Find the height of the Statue
of Liberty
how do i do it?
Answer:
148ft
Step-by-step explanation:
To solve this question, you'll have to imagine the statue makes a right angle triangle with the base since it has an angle of elevation from the base to the top of the torch.
Assuming the height from the pedestal to the top of the torch is y
The height of the statue is x
But we know the height of the pedestal = 150ft
The distance from the observer to the base of the pedestal = 250ft
And the angle of elevation = 50°
See attached document for better illustration.
Tanθ = opposite / adjacent
θ = 50°
Adjacent = 250
Opposite = y
Tan50 = t / 250
y = 50 × tan50
y = 50 × tan50
y = 50 × 1.1917
y = 297.925ft
The height of the statue from the base of the pedestal to the top of the torch is 297.925ft
The height of the statue = x
x = (height of the statue + height of the pedestal) - height of the pedestal
x = y - 150
x = 297.925 - 150
x = 147.925ft
Approximately 148ft
The height of the statue is 148ft
Nancy exercises for 3/4 hours each day for 6 days in a row. Altogether, how many hours does she exercise during 6 days?
Answer:
4 1/2
Step-by-step explanation:
3/4 =0.75
0.75*6 =4.5
4.5=4 1/2
Answer:
4 1/2 Hours is the amount she worked out
Step-by-step explanation:
3/4 = 45 min
45 x 6 = 270 min
270 ÷ 60 = 4.5 Hours
4.5 Hrs + 4 Hours 30 Min = 4 1/2
Solve for f(5).
f(x) = 2x - 4
f(5) = [?]
Answer & Explanation Included:
f(x)= 2x - 4
f(5)= 2(5) - 4
f(5)= 10 - 4
f(5)= 6
Answer: 16
Step-by-step explanation: f(x) = 2x - 4 means that if we put an x into our function, a 2x - 4 comes out.
So if we want to find f(5), we're putting a 5 into our function which means that a 2(5) - 4 comes out which simplifies to 10 - 4 or 6.
So f(5) = 6 or the value of the function at 5 equals 6.
Jared got 90% on his assignment. There were 30 questions how many did he get right
Answer:
27
Step-by-step explanation:
easy 27 divided by 30
In order to find how many correct questions Jared answered, we'll need to find 90% of 30.
To find 90% of 30, we'll need to multiply.
90% x 30 = 27
Therefore, Jared answered 27 questions correctly.
Hope this helps! :)
Ursula's grandfather gave her $20 to spend on new songs and games for her phone. Ursula has already spent $4.50 on new songs. If each game costs $1.75, how many games can Ursula buy without spending more than her grandfather gave her? Use the following inequality to solve the problem.
20≥4.50+1.75x
A
8
B
9
C
13
D
14
Answer:
A
Step-by-step explanation:
Take 20 and subtract 4.50. That leaves you with 15.5.
15.5 divided by 1.75 equals 8.
Hopes this helps! :)
I need 3 4 and 5 ill mark you brainiest
Answer:
3) x=4 4)x = 9 5) x=5
Step-by-step explanation:
3) first you have to find the inside of the angle. A straight line = 180*
180-(19x+3) = 177-19x
Than you add all the angles up to equal 180.
(177 - 19x) + (11x-2) + (9x+1) = 180
if you simplify this x = 4. You can check your answer by subbing in for x.
4)first you have to find the inside of the angle. A straight line = 180*
180- (17x-23) = 203-17x
Than add the sides up to equal 180. keep in mind there are 2 of the same angles.
(203-17x)+(7x+2)(2) = 180
Simplify
x=9
5) 180-151=29* this is the inner angle.
(11x-1)+(20x-3)+29=180
31x+25=180
x=5
Choose three types of taxes local governments may impose.
sales tax
personal property
real property
estate tax
Three types of taxes local governments may impose are Sales Tax , Personal Property and Real Property. Correct answer: A, B and C.
A sales tax is a consumption tax imposed by the government on the sale of goods and services. Personal property tax is levied annually against tangible personal property and due upon receipt of the tax bill.
Answer:
property tax
Step-by-step explanation:
:3
A boat and trailer together weigh 2265 pounds. How much force is required to hold the boat and trailer on an 18° incline to the horizontal?
Answer:
djdmdm nendkkxdekenebrnnr
{17, 8, 25, 23, 5, 31, 28} The numbers shown above belong to which of the following sets of numbers? I. Rational Numbers II. Natural Numbers III. Whole Numbers IV. Integers A. I, III, and IV only B. I, II, III, and IV C. I, II, and III only D. I and III only
Answer:
B
Step-by-step explanation:
Rational number - a number that can be written in a fraction (-1/3, 4, 7.635)
Natural number - a number that is greater than 0 and is an integer (1, 2, 3, 4, 5)
Whole number - a number that is greater or equal to 0 and is an integer (e.g. 0, 1, 2, 3, 4, 5)
Integer - a number that can be written in a fraction and has a denominator of 1 (e.g. -364, 0, 1, 84, 2347)
HELP ME WITH THIS MATH PROBLEM !!!
Answer: C. (25,10)
Step-by-step explanation:
Answer:
I believe its A. I'm not so sure thought so if its a test don't put it unless you are sure.
Step-by-step explanation:
A triangle has angles that measure 55°, 43°, and 82°. What kind of triangle is it?
A. obtuse
B. right
C. acute
Answer:
c. acute
Step-by-step explanation:
all angles are less than 90 degrees, so it is acute
In which number is the dign1 one thourad times togethan
is in the number 1 VLT?
A)
75
192
9
4790
D)
7332
Answer:
1 kvolt = 1 volt =1kv = 1000v
so 1000x 1 volt = 1000kv
The numebr would be the 4th number from end.
Step-by-step explanation:
Joe deposits $3500 into a bank account that earns interest compounded continuously. If Joe's money
doubles in 9 years, what interest rate was used?
Answer: 8%.
Step-by-step explanation:
To find this answer, use the compounding interest rate formula, or an exponential function:
[tex]A = P(r)^t[/tex]
Where A is the amount of money after t years, using P (principal) dollars as the investment and r as the rate.
We are trying to solve for r, so substitute the correct values for the other three variables:
[tex]7000 = 3500(r)^9\\\\2 = r^9[/tex]
Solving for r, we find that r to the ninth power equals 2.
Simplifying this, r is equal to 2^(1/9), or 1.08~. The interest rate was 8 percent.
To find the interest rate, we can use the formula for compound interest compounded continuously and solve for the interest rate using logarithms. The interest rate used is approximately 7.76%.
Explanation:To find the interest rate, we can use the formula for compound interest compounded continuously: A = P * e^(rt), where A is the final amount, P is the principal amount, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years. In this case, we have A = 2P, P = $3500, and t = 9 years. Plugging in these values, we get 2P = P * e^(9r), which simplifies to 2 = e^(9r). Taking the natural logarithm of both sides, we get ln(2) = 9r.
Now, we can solve for r by dividing both sides of the equation by 9: r = ln(2) / 9. Using a calculator, we find that r is approximately 0.0776. Therefore, the interest rate used is approximately 7.76%.
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One bag of Alice's chocolate almond mix contains 40 grams of almonds and 30 grams of chocolate.
0
Almonds
(grams)
Chocolate
(grams)
+
+
0
Complete the double number line diagram to show the amounts of almonds and chocolate in 1, 2, 3, and 4
bags of Alice's chocolate almond mix.
Choose 1 answer
Answer:
are are 5 chocolate in each bag
Step-by-step explanation:
Answer:
Choice B
Almonds Grams: 0, 40, 80, 120, 160
Chocolate Grams: 0, 30, 60, 90, 120
Step-by-step explanation:
What I did was I kept multiplying by 2.
If that is too difficult just continue adding 30 or 40.
A craftsman can sell 10 jewelry sets for $500 each. He knows
for each additional set he makes, the price of each set will decrease by $25. Hoy
many jewelry sets should he make if he wants to maximize his earnings?
jewelry sets
Answer:15
Step-by-step explanation:
Given
Craftsman sell 10 Jewelry set for $500 each
For each additional set he will decrease the price by $ 25
Suppose he sells n set over 10 set
Earning[tex]=\text{Price of each set}\times \text{no of set}[/tex]
Earning [tex]=(500-25n)(10+n)[/tex]
[tex]E=5000+500n-25n^2-250n[/tex]
differentiate to get the maximum value
[tex]\frac{dE}{dn}=-50n+250[/tex]
Equate [tex]\frac{dE}{dn}[/tex] to get maximum value
[tex]-50n+250=0[/tex]
[tex]n=\frac{250}{50}[/tex]
[tex]n=5[/tex]
Thus must sell 5 extra set to maximize its earnings.
Helpppppppppppppppp !!!!!!!!!!!!!!!
Answer:
Should be $160
Step-by-step explanation:Determine which equation is belongs to the graph of the limacon curve below.
[-5,5] by [-5,5]
We have been given graph of a limacon curve. We are asked to choose the equation that represents the given Limacon.
We can see that our given equation represents a cardiod. The equation of a vertical cardiod is in form [tex]r=a\pm a\cdot \text{sin}(\theta)[/tex] and equation of a horizontal cardiod is [tex]r=a\pm a\cdot \text{cos}(\theta)[/tex].
We can see that our given graph is a vertical cardiod, so its equation will be in form [tex]r=a\pm a\cdot \text{sin}(\theta)[/tex] .
The positive sign gives an upside-down cardiod and negative sign orients the cardiod upright.
Since our given graph is upright, so we will have a negative sign between 'a'.
Therefore, the equation [tex]r=2-2\cdot \text{sin}(\theta)[/tex] represents the given graph and option 'd' is the correct choice.
Answer:
C on edge 2022
Step-by-step explanation:
2(3s+5) + 4(6-3s) will u help me plz help me
Answer:
If the question is asking you to simplify, here is the simplified equation:
-6s+34
Step-by-step explanation:
Distribute the 2 and 4:
6s+10+24-12s
Simplify:
-6s+34
A laundry basket has 24 T-shirts In it 4 are navy 12 are red and the remaining or white what is the probability of randomly selecting a red shirt
The probability of randomly selecting a red shirt from a basket of 24 T-shirts, where 12 are red, is 1/2 or 50%.
Explanation:The probability of randomly selecting a red shirt from the laundry basket can be calculated by dividing the number of red shirts by the total number of shirts in the basket. Given there are 24 T-shirts in total and 12 are red, the probability P(red) is 12 divided by 24, which can be simplified.
Here is the calculation:
Total number of T-shirts: 24Number of red T-shirts: 12Probability of selecting a red T-shirt: P(red) = Number of red T-shirts / Total number of T-shirts = 12 / 24After simplifying, P(red) = 1/2 or 50%.
Translate the given phrase into an algebraic expression and simplify if possible: the difference of 10 and -18
Answer:
28
Step-by-step explanation:
10 - (-18) = x
10+18 = x (two negatives make a positive)
28 = x
The result of the given algebraic statement is 28.
Algebraic expressionsThe statement "the difference of 10 and -18" can be translated into an algebraic expression as follows:
10 - (-18)
To simplify this expression, we can simplify the double negative to have a positive sign as shown:
10 - (-18) = 10 + 18
Adding the numbers, we get:
10 - (-18) = 28
Therefore, the algebraic expression simplifies to 28.
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You are given 6 color cards: 1 red, 2 blue, 3 green. As you draw a card, YOU WILL KEEP IT. What is the probability of drawing a green card, green card, and finaly a yellow card?
Answer:
3/6, 2/5, 0/5
Step-by-step explanation:
a dog searching for a bone walks 3.5 m southeast, then 8.2 m at an angle 30 degrees north of east. Find the magnitude of the dog's resultant vector
The dog's resultant displacement vector, representing the total distance covered in the specified direction, is approximately 9.74 meters. This was calculated by breaking down each of the dog's movements into their Cartesian components, adding these components separately, and finally applying the Pythagorean theorem to find the magnitude of the resultant vector.
Explanation:To solve this problem, we first need to calculate each displacement in the rectangular (or Cartesian) coordinate system. Let's express each move of the dog as a vector.
First, the dog walks 3.5 m southeast. In the Cartesian coordinate system, this would be represented as two components: x (horizontal) and y (vertical). The x-component is 3.5*cos(45°) = 2.475 m and the y component is -3.5*sin(45°) = -2.475 m (negative because direction is south).
Second, the dog walks 8.2 m at an angle 30 degrees north of east. That gives us an x-component of 8.2*cos(30°) = 7.1 m and a y-component of 8.2*sin(30°) = 4.1 m.
Now add up separate x- and y-components: Our cumulative x-component is 2.475 m + 7.1 m = 9.575 m. The cumulative y-component is -2.475 m + 4.1 m = 1.625 m.
The resultant vector's magnitude can be determined with the Pythagorean theorem a² + b² = c² (where 'a' and 'b' are the legs and 'c' is the resultant vector). In this case: (9.575 m)² + (1.625 m)² = c². Solve for c to get
[tex]c = \sqrt{(9.575 \, \text{m})^2 + (1.625 \, \text{m})^2} = 9.74 \, \text{m}.[/tex]
In conclusion, the magnitude of the dog's resultant vector is approximately 9.74 m.
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can anyone hknow number 2?
Answer:
n = y/(r+s)
Step-by-step explanation:
(rn+sn) / y = 1
Multiply each side by y
(rn+sn) / y *y= 1*y
rn+sn = y
Factor out n
n(r+s) = y
Divide each side by (r+s)
n(r+s) / (r+s) = y/(r+s)
n = y/(r+s)
Lance earned $27 for mowing 3 lawns.What is the rate earned per lawn mowed?
Answer:
$9
Step-by-step explanation:
Since he got $27 for moving 3 lawns, you simply divide $27 by 3 to find out how much he earned per lawn. 27 / 3 = 9.
Answer:
27/3=9 so 9 dollars per lawn
Step-by-step explanation: