To find the total surface area of a cross-section solid, it is necessary to identify all the faces or surfaces of the solid, find the area of each individual face or surface, and then add them all together.
After finding the area of each individual face or surface, the final step is to add them all together to get the total surface area of the cross-section solid. This can be expressed mathematically as:
Total Surface Area = Area of Face 1 + Area of Face 2 + ... + Area of Face n
Where n represents the total number of faces or surfaces of the solid.
Pythagoras theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed mathematically as:
c² = a² + b²
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
By using Pythagoras theorem to find the length of an unknown side, it is then possible to use the appropriate formula to find the area of the face or surface and then add it to the total surface area of the cross-section solid.
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irst, rewrite (11)/(20) and (13)/(25) so that they have a common denominator
Answer:
55/100 and 48/100, in decimal form it will be 0.55 and 0.48
Step-by-step explanation:
11/20 and 12/25
The common denominator in this question will be 100
55/100 and 48/100
Which graph is correct?
The system of inequalities is correctly graphed on Shannon's graph.
Which graph shows the system of inequalities?Here we have the following system of inequalities:
y ≥ (1/2)*x - 1
x - y > 1
We can rewrite the second inequality as:
y < x - 1
Then the system becoimes:
y ≥ (1/2)*x - 1
y < x - 1
The first line will be one with positive slope, it is solid (due to the symbol ≥) and the shaded area is above the line.
For the second we will have a dashed line, and now the shaded area is below the dashed line.
From that, we caonclude that Shannon's graph is the correct one.
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DEFGTSRQ.
G
24
24
F
Save answer
24
24
E
Q
230
R
8
8
T
8
S
D
What is the similarity ratio of DEFG to TSRQ?
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
The ratio of similarity DEFG to TSRQ is '3: 1'.
The similarity of quadrilateral:Two quadrilaterals are considered similar if they have the same shape but may have different sizes. Similar quadrilaterals have corresponding angles that are congruent, and their corresponding sides are in proportion to each other.
The ratio of similarity is a measure of how much two geometric figures are enlarged or reduced to become similar.
Here we have
Quadrilateral DEFG and Quadrilateral TSRQ.
Where DEFG similar to TSRQ
Hence, the ratio of corresponding sides will be equal
=> DE/TS = EF/SR = FG/RQ = DG/TQ
=> 24/8 = 24/8 = 24/8 = 24/8 = 3/1
Therefore,
The ratio of similarity DEFG to TSRQ is '3: 1'.
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a) An electrical wind generator has propeller blades that are 3 meter long. If the blades are rotating at 6 revolution per minute, what is the linear velocity (to the nearest meter per minute) of a point on the tip of one of the blades?
b) Find the arc length and the area of the circular sector with central angle 25and the radius of the circle is 12cm.
a) To find the linear velocity of a point on the tip of one of the blades, we need to use the formula: V = 2πr/T where V is the linear velocity, r is the radius of the circle, and T is the period of rotation. In this case, the radius of the circle is the length of the propeller blades, which is 3 meters, and the period of rotation is the inverse of the frequency of rotation, which is 1/6 minutes. Plugging in the values, we get: V = 2π(3)/(1/6) = 36π meters per minute. To the nearest meter per minute, the linear velocity is approximately 113 meters per minute.
b) To find the arc length and the area of the circular sector, we need to use the formulas: Arc length = θr and Area = (θr^2)/2 where θ is the central angle in radians, and r is the radius of the circle. In this case, the central angle is 25 degrees, which is equivalent to (25π)/180 radians, and the radius of the circle is 12 cm. Plugging in the values, we get: Arc length = ((25π)/180)(12) = (5π)/3 cm and Area = (((25π)/180)(12^2))/2 = (25π)/3 cm^2. Therefore, the arc length is approximately 5.24 cm and the area is approximately 26.18 cm^2.
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1. determine the derivative of a function by applying the appropriate derivative rules for both equations.
2. apply the derivative to determine other information about a function for both equations.
Differentiate 2 of the following Please
f(x) = (3 – 2x^3)^3 / f(t) = 100(6-t)/t+3
solve for t to get t = 4
1. To find the derivative of f(x) = (3 – 2x^3)^3 we can apply the power rule, the chain rule, and the product rule. The power rule states that the derivative of f(x) = x^n is f'(x) = nx^n-1. The chain rule states that the derivative of f(x) = g(h(x)) is f'(x) = g'(h(x))*h'(x). The product rule states that the derivative of f(x) = uv is f'(x) = u'v + uv'. In this case, we can rewrite f(x) as f(x) = (h(x))^3 where h(x) = 3 - 2x^3. We then apply the chain rule to get f'(x) = 3(3 - 2x^3)^2(-6x^2). Similarly, we can find the derivative of f(t) = 100(6-t)/t+3. We can rewrite f(t) as f(t) = u(t)v(t) where u(t) = 100 and v(t) = (6-t)/t+3. Applying the product rule, we get f'(t) = 100(-1/(t+3)^2) + (6-t)(-1/(t+3)^2).
2. To find other information about a function, we can use the derivative we just found. For example, if we want to find the maximum or minimum values of a function, we can set the derivative equal to 0 and solve for the x or t values. In the case of f(x), we can set 3(3 - 2x^3)^2(-6x^2) = 0 and solve for x to get x = (sqrt(3/2))^(1/3). Similarly, for f(t) we can set 100(-1/(t+3)^2) + (6-t)(-1/(t+3)^2) = 0 and solve for t to get t = 4. We can also use derivatives to find the equation of a tangent line to a function at any given point. In this case, we would use the derivative we found in order to calculate the slope of the tangent line at any given point and then use point-slope form to find the equation of the line.
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5(y+x)-6(x-y)=-8 asses through the point (14,3) and is perpendicular to the given
The equation of the line that passes through the point (14,3) and is perpendicular to the given equation is y = x - 11.
To solve the equation 5(y+x)-6(x-y)=-8, we need to use the distributive property and combine like terms.
5(y+x)-6(x-y)=-8
Distribute the 5 and -6:
5y + 5x - 6x + 6y = -8
Combine like terms:
11y - x = -8
Now, we need to find the slope of the line that passes through the point (14,3) and is perpendicular to the given equation.
The slope of the given equation is -1, so the slope of the perpendicular line is the negative reciprocal, which is 1.
Using the point-slope form, we can write the equation of the perpendicular line:
y - 3 = 1(x - 14)
Distribute the 1:
y - 3 = x - 14
Add 3 to both sides:
y = x - 11
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Victor used a 36-month line of
credit for $15,000 to remodel his
kitchen. If the interest rate is 2. 5%,
how much will he pay in interest?
Answer:
Step-by-step explana2 4
457
6.46
Can someone help please
Answer:
10.39; 6
Step-by-step explanation:
Horizontal component= |v| Cos theta = 12 Cos 60° = 6
Vertical component= |v| Sin theta = 12 Sin 60° = 10.39
What is the measure of arc IJ?
Check the picture below.
19. sin!/2 x cos x – sin5/2 x cos x = cos x/sin x 20. secx(sec x tan x) - sec4 x(sec x tan x) sec5 x tanx -
cosx = cos4x = cos5x.
19. Using the identity sin2x + cos2x = 1, we can rewrite the equation as:
sin2x/2 - sin2x/2 = cosx/sinx
Simplifying both sides: cosx/sinx = 0
Therefore, cosx = 0 and sinx = 0.
20. Using the identities secx = 1/cosx, tanx = sinx/cosx, and sec2x = 1 + tan2x, we can rewrite the equation as:
secx(secx tanx) - sec4x(secx tanx) = sec5x tanx
Simplifying: secx - sec4x = sec5x
Therefore, secx = sec4x = sec5x.
Simplifying further: 1/cosx = 1/cos4x = 1/cos5x
Therefore, cosx = cos4x = cos5x.
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The wait time for a new roller coaster is at least 90 minutes. State the null and alternative hypothesis for the scenario using math symbols and words.
The Null Hypothesis (H0: μ ≤ 90) and Alternative Hypothesis (Ha). of the wait time for a new roller coaster is at least 90 minutes.
What are the Null Hypothesis and Alternative Hypothesis?The null hypothesis states that a population parameter is equal to a value. The null hypothesis is often an initial claim that researchers specify using previous research or knowledge.
Null Hypothesis (H0): The wait time for a new roller coaster is equal to or less than 90 minutes (H0: μ ≤ 90).
Alternative Hypothesis (Ha): The wait time for a new roller coaster is greater than 90 minutes (Ha: μ > 90).
In words, the null hypothesis states that the average wait time for the new roller coaster is equal to or less than 90 minutes.
The alternative hypothesis states that the average wait time is greater than 90 minutes.
We use the symbol μ to represent the population means of wait times for the new roller coaster.
Therefore, the Null Hypothesis (H0: μ ≤ 90) and Alternative Hypothesis (Ha). of the wait time for a new roller coaster is at least 90 minutes.
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Find the following in slope intercept form
The equation of a horizontal line that passes through (4,2)
The equation of a horizontal line that passes through (4,2) in slope intercept form is y = 2.
A horizontal line has a slope of 0, which means that the y-value remains constant while the x-value changes. In slope intercept form, the equation of a line is written as y = mx + b, where m is the slope and b is the y-intercept.
Since the slope of a horizontal line is 0, the equation of a horizontal line can be written as y = 0x + b, or simply y = b. The y-intercept is the value of y when x = 0, which is the same as the y-value of any point on the line.
In this case, the line passes through the point (4,2), so the y-value is 2. Therefore, the equation of the line in slope intercept form is y = 2.
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For
each of the following, find the formula for an exponential function
that passes through the two points given.
a. (-1, 2/3) and (2,18)
f(x) =
b. (-1,7) and (2,4)
g(x) =
(If needed, round to 3 decim
The values of x are 0.732 and -2.732.
Given function:f(x) = g(x)We need to determine the value of x.For, f(x) = g(x), we have the following equation:f(x) = x^2 + 2x + 1 = 2x + 3g(x) = 2x + 3To solve for x, we can substitute the value of g(x) in the first equation:x^2 + 2x + 1 = g(x)Substituting g(x) = 2x + 3 in the above equation:x^2 + 2x + 1 = 2x + 3x^2 + 2x - 2 = 0x^2 + 2x - 2 = 0Applying the quadratic formula, we get:$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$Where, a = 1, b = 2, and c = -2Substituting the values in the formula, we get:$$x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-2)}}{2(1)}$$$$x = \frac{-2 \pm \sqrt{12}}{2}$$$$x = -1 \pm \sqrt{3}$$Therefore, the value of x is x = -1 + √3 or x = -1 - √3.To round off the answer to 3 decimal places, we get:x = -1 + 1.732 = 0.732 or x = -1 - 1.732 = -2.732Hence, the values of x are 0.732 and -2.732.
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two runners are racing against each other. jeri graphs a linear equation for each runner that shows the runners distance from the starting line over time. the two equations form a system that has infinitely many solutions. describe the intersection points of the lines an situations explain what solution means in this
Answer:If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. the intersection points (-3,3) Since the system is infinite it means there is 1 line on the graph-
Step-by-step explanation:
the cost of a ticket to the circus is $15 for children and $40 for adults. on a certain day ,attendance at the circus was 1,000 and the total gate revenue was $30,000. How many children and how many adults bought tickets?
400 children and 600 adults bought tickets to the circus.
Let's call the number of children who bought tickets "C" and the number of adults who bought tickets "A". We can set up two equations to represent the information given in the question:
C + A = 1000 (the total number of people who bought tickets)
15C + 40A = 30000 (the total gate revenue)
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for C in terms of A:
C = 1000 - A
Now we can substitute this equation into the second equation to solve for A:
15(1000 - A) + 40A = 30000
15000 - 15A + 40A = 30000
25A = 15000
A = 600
So 600 adults bought tickets. We can use the first equation to find the number of children who bought tickets:
C + 600 = 1000
C = 400
So 400 children bought tickets. Therefore, the answer is that 400 children and 600 adults bought tickets to the circus.
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Sheng has two credit cards. He used his credit card statements to make the summary table that follows. Sheng is also eligible for a debt consolidation loan with an APR of 10.7% that reduces his monthly payments to $179.37. This loan will take six years to pay off, and Sheng will pay a total of $3,414.39 in interest charges. How much more in interest charges will the debt consolidation loan cost Sheng?
The debt consolidation loan will cost Sheng an additional $1,997.69 in interest charges compared to his credit cards.
Calculating how much more in interest the debt consolidation loan will cost ShengFrom question, we are to calculate how much more in interest the debt consolidation loan will cost Sheng
To calculate the interest charges for Sheng's credit cards, we need to use the following formula:
Interest Charges = Balance x APR x Number of Days in Billing Cycle / 365
Using this formula, we can calculate the interest charges for each of Sheng's credit cards:
For Credit Card A:
Interest Charges = $2,500 x 0.19 x 30 / 365 = $4.94
For Credit Card B:
Interest Charges = $3,000 x 0.22 x 30 / 365 = $6.01
So, the total interest charges for Sheng's credit cards are:
Total Interest Charges = $4.94 + $6.01 = $10.95
Now, let's calculate the total cost of the debt consolidation loan:
Total Cost = Total Monthly Payments x Number of Payments - Loan Amount
Total Monthly Payments = $179.37
Number of Payments = 6 x 12 = 72
Loan Amount = ?
To find the loan amount, we need to solve for it using the interest rate and the total interest charges:
Loan Amount = Total Interest Charges / (APR x Number of Payments / 12)
Loan Amount = $3,414.39 / (0.107 x 72 / 12) = $25,000
So, the total cost of the debt consolidation loan is:
Total Cost = $179.37 x 72 - $25,000 = $2,008.64
Therefore, the additional interest charges for the debt consolidation loan compared to Sheng's credit cards are:
Additional Interest Charges = Total Cost - Total Interest Charges
Additional Interest Charges = $2,008.64 - $10.95 = $1,997.69
Hence, the debt consolidation loan will cost him an additional $1,997.69 in interest charges
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what shape has the largest area for a given perimeter?
With process
Answer: A circle
Step-by-step explanation: a circle
fast
1,500 decagrams = 150 kilograms True False
At this Sunday’s Super Bowl game, 150 out of thefirst 500 people who entered the main gate were not wearing team jerseys. Ifthis sample is representative of the 75,000 people attending the game, abouthow many of them will probably NOT be wearing team jerseys?
About 22,500 people at the Super Bowl game will not be wearing team jerseys.
Finding populations that will not wear jerseys:Here the entire population is proportional to the number of people who entered the main gate without wearing team jerseys.
Find the proportion of people not wearing team jerseys by dividing 150 by 500. Now multiply the resultant proportion by the actual population.
Here we have
150 out of the first 500 people who entered the main gate were not wearing team jerseys,
The proportion of people not wearing team jerseys
=> p = 150/500 = 0.3
Given that the sample is representative of the entire population of 75,000 people attending the game,
The population that will not be wearing team jerseys can be calculated as follows
75,000 x 0.3 = 22,500
Therefore,
About 22,500 people at the Super Bowl game will not be wearing team jerseys.
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Samuel is printing 13 posters for a campaign. The printer charges a setup fee of $14.21 plus $3.90 per poster (taxes included). Samuel estimates a reasonable total cost to print the posters to be $77.92.
Is this a reasonable estimate?
A.
No, the estimate should be greater than $77.92.
B.
Yes, the estimate is very close.
C.
No, the estimate should be less than $77.92.
The answer is (C) No, the estimate should be less than $77.92.
What is estimation?Estimation cost refers to the process of approximating or calculating the cost of a project or service before it is actually carried out or completed. This is an important step in budgeting and financial planning, as it helps individuals and organizations to anticipate and prepare for the financial impact of a particular activity or initiative.
To determine if the estimate of $77.92 is reasonable, we can calculate the actual cost of printing 13 posters using the given information:
Setup fee: $14.21
Cost per poster: $3.90
Number of posters: 13
Total cost = setup fee + (cost per poster x number of posters)
Total cost = $14.21 + ($3.90 x 13)
Total cost = $14.21 + $50.70
Total cost = $64.91
We can see that the actual cost of printing 13 posters is $64.91, which is less than the estimated cost of $77.92. Therefore, the estimate of $77.92 is not reasonable and the answer is (C) No, the estimate should be less than $77.92.
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What is the answer to this problem
Answer: y = -5/3x + 4
Step-by-step explanation:
The slope intercept form is y = mx + b
The slope (m) is rise over run, so slope = -5/3
The y-intercept (b) is 4 because that is where the line intersects the y-axis at.
Hope this helps!
PLEASE HELP ASAP!!!!!!!!!!!
A cylinder has a volume of 1 1/3 and a radius of 1/3 in. What is the height of the cylinder?
the height of the cylinder is 12/π inches. This is an exact value, but if you want an approximate decimal value, you can use a calculator and substitute 3.14 or 22/7 for π. For example, if we use π ≈ 3.14, we get:
h ≈ 12/3.14
h ≈ 3.822 inches (rounded to three decimal places)
In a group of 39 students, 14 study both Art and Biology. 5 study Biology but not Art. 6 study neither subject. How many study Art?
Answer:
11
Step-by-step explanation:
find from the first principle the derivative with respect to x of the function y equals to x square minus x + 3
Answer:
To find the derivative of the function y = x^2 - x + 3 using the first principle, we start by applying the definition of the derivative:
f'(x) = lim (h -> 0) [f(x+h) - f(x)] / h
where f(x) = x^2 - x + 3.
Now we substitute the function into the equation and simplify:
f'(x) = lim (h -> 0) [(x+h)^2 - (x+h) + 3 - (x^2 - x + 3)] / h
f'(x) = lim (h -> 0) [(x^2 + 2xh + h^2 - x - h + 3) - (x^2 - x + 3)] / h
f'(x) = lim (h -> 0) [2xh + h^2 - h] / h
Now we can cancel out the h in the numerator and denominator, leaving:
f'(x) = lim (h -> 0) [2x + h - 1]
Finally, we take the limit as h approaches 0:
f'(x) = 2x - 1
Therefore, the derivative of y = x^2 - x + 3 with respect to x is f'(x) = 2x - 1.
Step-by-step explanation:
Answer:
[tex]\dfrac{\text{d}y}{\text{d}x}=2x-1[/tex]
Step-by-step explanation:
Differentiating from First Principles is a technique to find an algebraic expression for the gradient at a particular point on the curve.
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\\\end{minipage}}[/tex]
The point (x + h, f(x + h)) is a small distance along the curve from (x, f(x)). As h gets smaller, the distance between the two points gets smaller. The closer the points, the closer the line joining them will be to the tangent line.
To differentiate y = x² - x + 3 using first principles, substitute f(x + h) and f(x) into the formula:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{(x+h)^2-(x+h)+3-(x^2-x+3)}{(x+h)-x}\right][/tex]
Simplify the numerator:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{x^2+2hx+h^2-x-h+3-x^2+x-3)}{x+h-x}\right][/tex]
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2hx+h^2-h}{h}\right][/tex]
Separate into three fractions:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2hx}{h}+\dfrac{h^2}{h}-\dfrac{h}{h}\right][/tex]
Cancel the common factor, h:
[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\:2x+h-1\:\right][/tex]
As h → 0, the second term → 0:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2x-1[/tex]
The answer I choose was wrong I need help choosing the right one
The value of the length WY is 40√3 mm. Option J
How to determine the measure of the lengthThe different types of trigonometric identities are;
cotangenttangentcosinesinesecantcosecantFrom the information given, we have that;
Opposite side = WY
Angle of elevation, θ = 60 degrees
Adjacent side = 40mm
Now, let's use the tangent identity;
tan θ = WY/40
substitute the value
tan 60 = WY/40
cross multiply
WY = 40 × √3
Multiply the values
WY = 40√3 mm
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model with a proportion
The decrease in price for notebooks was $1.60, a 40% decrease. What was al original price and what is the new price?
The new price of the notebooks is $2.40.
To find the original price and the new price of the notebooks, we can use a proportion model. Let's call the original price "x" and the new price "y".
The proportion model for this problem would be:
40/100 = 1.60/x
To solve for x, we can cross-multiply:
40x = 100(1.60)
And then divide both sides by 40:
x = 4
So the original price of the notebooks was $4.00. To find the new price, we can subtract the decrease in price from the original price:
y = x - 1.60
y = 4 - 1.60
y = 2.40
So the new price of the notebooks is $2.40.
40/100 = 1.60/4
0.4 = 0.4
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Isabella bought a new dress for the Spring Dance that was on sale for 35% off the regular price of $135. 00 The total cost included 8. 5% sales tax. What was the total cost?
The total cost of the dress including sales tax is 95.21.
The amount of discount that Isabella received on the dress is:
35% of 135.00 = 0.35 x 135.00 = 47.25
So, the price she paid for the dress after the discount is:
135.00 - 47.25 = 87.75
To find the total cost including sales tax, we need to add the sales tax to the price of the dress:
Sales tax = 8.5% of 87.75 = 0.085 x 87.75 = 7.46
Total cost = Price of dress after discount + Sales tax
= 87.75 + 7.46
= 95.21
Therefore, the total cost of the dress including sales tax is 95.21.
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A souvenir postcard is 5 1/4 inches long and 3 1/2 inches wide. What is the area of the postcard?
The paper is 147/8 square inches in size. If preferred, this can be condensed to a mixed number or decimal.
what is surface area ?A three-dimensional object's surface area is the sum of its sides. It is a measurement of the object's visible surface area. Depending on the shape of the item, different surface area formulas apply. For instance, adding the surface areas of all six sides of a rectangular prism will yield its surface area. The calculation for a rectangular prism's surface area is: Flat area equals 2lw + 2lh + 2wh where the rectangular prism's dimensions are l for length, w for breadth, and h for height.
given
The length and breadth of the postcard must be multiplied to determine its area.
The mixed integers must first be transformed into improper fractions:
5 1/4 = 21/4
3 1/2 = 7/2
We can now multiply:
Area is equal to length times breadth.
Area = (21/4) × (7/2)
Area = (21 × 7) / (4 x 2)
Area = 147/8
The paper is 147/8 square inches in size. If preferred, this can be condensed to a mixed number or decimal.
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The height, in feet, of a toy rocket that is launched from 4 feet above the ground can be modeled using the equation provided where t is the time after the rocket is launched. To the nearest foot, what is the height of the rocket 3 seconds after it is launched?
Answer:
). The rocket was launched from 73 feet above ground.
b). The rocket took [Vy / g] = 30 / 3 = 10s to reach its maximum height of [Vy^2 / (2 * g)] = 30^2 / 6 = 150 feet.
It then fell -(73 + 150) = -223 feet to the ground in a time of sqrt(2 * -223 / -3) = 12.192894s.
Total time of flight = (10 + 12.192894) = 22.192894s.
The rocket landed with a vertical velocity of -sqrt(2 * -223 * -3) = -36.578682ft/s.
Step-by-step explanation:
Answer:
Unfortunately, there is no equation provided in the question. However, I can provide a general formula for the height of a rocket launched from a certain height h0 with an initial velocity v0, under the influence of gravity:
h(t) = -1/2gt^2 + v0t + h0
where g is the acceleration due to gravity, which is approximately 32.2 feet per second squared.
Using this formula, we can calculate the height of the rocket 3 seconds after it is launched:
h(3) = -1/2(32.2)(3)^2 + 0 + 4
= -1/2(32.2)(9) + 4
= -145.35 + 4
= -141.35
To the nearest foot, the height of the rocket 3 seconds after it is launched is -141 feet. Note that the negative sign indicates that the rocket has fallen below its initial height of 4 feet due to the influence of gravity.
For each of the following polynomial find the following (3-3x^(3)-7x^(2))-(-2x^(2)-3x+7)
The result of the (3-3x^(3)-7x^(2))-(-2x^(2)-3x+7) polynomial is -3x^(3) - 5x^(2) + 3x - 4.
What is polynomial?A polynomial is a mathematical expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
To find the result of the given polynomials, we need to combine like terms. Like terms are terms that have the same variable and the same exponent.
Step 1: Distribute the negative sign to the second polynomial:
(3 - 3x^(3) - 7x^(2)) - (-2x^(2) - 3x + 7) = (3 - 3x^(3) - 7x^(2)) + (2x^(2) + 3x - 7)
Step 2: Combine like terms:
3 - 3x^(3) - 7x^(2) + 2x^(2) + 3x - 7 = -3x^(3) - 5x^(2) + 3x - 4
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