Answer:
awnser is 288 seriously 15 x 12 = 180
and 9 x12 =108 add together is 288
The life spans of 10 adult mayflies have a mean of 4 hours and a MAD of 2 hours. Fill in the table below with possible values for the life spans. You can use the same values more than once. Can any one of the 10 mayflies in the group live for 1 full day? Justify your answer.
No mayfly in the group can live for a full day (24 hours), as the maximum life span is 6 hours.
How to calculate life span?We can start by calculating the lower and upper limits of the range of possible values for the life spans of the mayflies.
The lower limit can be found by subtracting the MAD from the mean, and the upper limit can be found by adding the MAD to the mean:
Lower limit = mean - MAD = 4 - 2 = 2 Upper limit = mean + MAD = 4 + 2 = 6
Since we know there are 10 mayflies in the group, we can fill in the table below with values between 2 and 6 (inclusive) that add up to 40 (the total number of hours for all 10 mayflies combined):
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please help Find the common ratio for this geometric sequence. 1 1 1 2'8'32 8, 2, O A. 1/10 O B. -12 OC. 4 OD. 2
The common ratio is the factor by which each term is multiplied to get the next term, which in this case is 4.
EquationsTo find the common ratio of a geometric sequence, you can divide any term in the sequence by the previous term.
Looking at the sequence: 1, 1, 1, 2, 8, 32, 128, ...
To get from the 1st term to the 2nd term, we multiply by 1.
To get from the 2nd term to the 3rd term, we multiply by 1.
To get from the 3rd term to the 4th term, we multiply by 2.
To get from the 4th term to the 5th term, we multiply by 4.
To get from the 5th term to the 6th term, we multiply by 4.
What is common ratio?The constant ratio between succeeding words is known as the common ratio in a geometric progression (GP). Any phrase in the progression must be divided by the term before it in order to compute it.
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83
ces
Required information
[The following information applies to the questions displayed below.]
Ramirez Company installs a computerized manufacturing machine in its factory at the beginning of the year at a cost of
$84,600. The machine's useful life is estimated at 20 years, or 393,000 units of product, with a $6,000 salvage value.
During its second year, the machine produces 33,300 units of product.
Determine the machine's second-year depreciation and year end book value under the straight-line method.
Choose Numerator: /
Year 2 Depreciation
Year end book value (Year 2)
Straight-Line Depreciation
Choose Denominator:
=
=
Annual Depreciation
Expense
Depreciation expense
The machine's second-year depreciation is $6,660 and the year-end book value under the straight-line method is $65,280.
What is depreciation?The cost of a tangible asset is spread out throughout the course of depreciation. It symbolises the asset's value dropping over time as a result of damage, obsolescence, or other circumstances. Depreciation is crucial because it enables firms to account for an asset's cost over the course of its useful life rather than just in the year it was purchased.
Depreciation can be calculated using a number of different approaches, such as the straight-line method, the decreasing balance method, and the sum-of-years' digits method.
The annual depreciation expense is:
Annual Depreciation Expense = (Cost of Asset - Salvage Value) / Useful Life in Units
Annual Depreciation Expense = ($84,600 - $6,000) / 393,000
Annual Depreciation Expense = $0.20 per unit
For second year we have:
Second-Year Depreciation = Annual Depreciation Expense x Units Produced in Second Year
Second-Year Depreciation = $0.20 x 33,300
Second-Year Depreciation = $6,660
Now, the year-end book value is:
Accumulated Depreciation = Annual Depreciation Expense x Number of Years
Accumulated Depreciation = $0.20 x 2
Accumulated Depreciation = $0.40 per unit
For:
Accumulated Depreciation = $0.40 x 33,300
Accumulated Depreciation = $13,320
Also,
Book Value = Cost of Asset - Accumulated Depreciation - Salvage Value
Book Value = $84,600 - $13,320 - $6,000
Book Value = $65,280
Hence, the machine's second-year depreciation is $6,660 and the year-end book value under the straight-line method is $65,280.
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The population of Medina, Ohio is currently 26,190 people. The population is predicted to grow at a rate of 3.7% per year. What will the population of Mediana be in 7.3 years? (round your answer to the neareat hundreth)
a.) 43210.82
b.) 87896.05
c.) 34144.47
d.) 50369.13
The population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.
What do you mean by Percentage?A number can be expressed as a fraction of 100 using a percentage. It is represented by the number %.
A decimal or fraction can be multiplied by 100 to become a percentage. For instance, multiplying 0.75 (a decimal) by 100 yields 75% when converted to a percentage. The same can be done to convert 3/4 (a fraction) to a percentage by dividing 3 by 4 to get 0.75, then multiplying that number by 100 to get 75%.
To calculate the population of Medina, Ohio in 7.3 years, we can use the formula:
Population after n years = Population before ×(1 + r/100)²
where r is the annual growth rate and n is the number of years.
Substituting the given values, we get:
Population after 7.3 years = 26,190 × (1 + 3.7/100)^7.3
Population after 7.3 years = 26,190 * 1.037^7.3
Population after 7.3 years = 26,190 * 1.301
Population after 7.3 years = 34,052.9
Rounding to the nearest hundredth, we get:
Population after 7.3 years = 34,052.90 ≈ 34,052.89
Therefore, the population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.
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Find the measure of the arc or central angle indicated.Assume that lines which appear to be diameters are actual diameters
Answer: What do you mean where is the arc?
Step-by-step explanation:
The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function
F(x)=-3.452x^4+35.129x^3-93.005x^2+41.705x+177.494
Where x is the number of years since 1996. Find the number of bald eagles in the state the winter of 1999
The number of bald eagles in the state during the winter of 1999 would be 34.
rosa has a limit to the time she may play video games each day she plays for 9 mins on monday which is 30% of the time she can play how many more minutes can rosa play on monday?
According to the calculations we can conclude that Rosa can play 21 more minutes on Monday.
If 9 minutes represents 30% of the time Rosa can play video games, we can use proportional reasoning to find the total time she can play. Let x be the total time she can play in minutes.
9 / x = 30 / 100
We might cross-multiply and simplify to find x's value:
9 * 100 = 30 * x
900 = 30x
x = 900 / 30
x = 30
So Rosa can play a total of 30 minutes each day.
To find how many more minutes she can play on Monday, we subtract the time she has already played from the total time:
30 - 9 = 21
Therefore, Rosa can play 21 more minutes on Monday.
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Luna's pet miniature pig, Fiona, weighed 50 pounds at her one-year check-up. Based on her
weight at an earlier check-up, the vet had predicted Fiona would weigh 6% more than that.
What weight had the vet predicted for Fiona?
Given the equation d over 11 equals 14, solve for d.
Step-by-step explanation:
To solve for d in the equation d/11 = 14, we can multiply both sides by 11 to isolate d on one side of the equation.
d/11 = 14 (multiply both sides by 11)
d = 11 x 14
Simplifying, we get:
d = 154
Therefore, the solution for d is 154.
Which of the following statements best explains the equation below?
17.8 – 4 x 3 = 12 ÷ 3 + 1.8
The solution is : (-2,7) is the point of intersection.
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
To solve the equations by graphing, use the form y=mx + b to find the slope and y-intercept of each equation. Graph the line and find their intersection point.
y = −2x + 3 y = −4x − 1
Slope: -2 Slope: -4
Y-int: (0,3) Y-int: (0,-1)
Start at (0,3) and go down Start at (0,-1) and go down 4 units
2 units and 1 to the right. and 1 to the right. Connect the points.
Connect the points.
Continue this pattern in either direction for both lines until they intersect each point. The point of intersection (x,y) is the solution to the system of equations.
See attached graph.
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Complete question:
A pair of linear equations is shown below: y = −2x + 3 y = −4x − 1 Which of the following statements best explains the steps to solve the pair of equations graphically?
find the ratio of 4 inches to 3 yards
every 1 unit of 4 inches, there are 27 units of 3 yards. It's important to note that ratios represent a proportional relationship between two quantities and do not necessarily represent the actual values themselves.
How to solve ratio?
To find the ratio of 4 inches to 3 yards, we need to convert both measurements to a common unit of measurement.
Firstly, let's convert the 3 yards to inches, since inches are already given. There are 36 inches in a yard (3 feet in a yard, and 12 inches in a foot), so:
3 yards = 3 x 36 inches = 108 inches
Now we can compare the two measurements:
Ratio of 4 inches to 108 inches = 4/108
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 4 in this case:
4/108 = 1/27
So, the ratio of 4 inches to 3 yards is 1:27.
This means that for every 1 unit of 4 inches, there are 27 units of 3 yards. It's important to note that ratios represent a proportional relationship between two quantities and do not necessarily represent the actual values themselves.
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PART B:
If Dr. Nandi plans to transport 3.5 x 105 energy prisms that each take up 2 x 10² cubic feet of cargo
space, how much total space will the cargo take up? Answer in Scientific Notation. Show your work.
Edit View Insert Format Tools Table
Answer:
Step-by-step explanation:
just guess if not use the internet
In the figure, m∠EDF = 42°. Which other angle must have the same measure? A diagram of the inscribed quadrilateral with the points of D, E, F, and G, in which D with an angle of 42 degrees. A. ∠DEG B. ∠EGF C. ∠GDF D. ∠EGD
Therefore, the correct option is B. ∠EGF with the angle measure of 138°.
What is quadrilateral?A quadrilateral is a four-sided polygon with four vertices and four angles. It is a closed figure with four straight sides that do not intersect. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. The sum of the interior angles of a quadrilateral is always 360 degrees.
Here,
In an inscribed quadrilateral, opposite angles are supplementary. That is, the sum of the measures of any two opposite angles is 180 degrees. Therefore, to find the angle that has the same measure as ∠EDF, we need to look for the angle that is also opposite ∠EDF in the inscribed quadrilateral.
In the inscribed quadrilateral with points D, E, F, and G, we know that ∠EDF has a measure of 42 degrees. We also know that the opposite angle to ∠EDF is ∠EGF, because they share side EF.
Since opposite angles in an inscribed quadrilateral are supplementary, we can find the measure of ∠EGF by subtracting 42 degrees from 180 degrees:
∠EGF = 180° - ∠EDF
= 180° - 42°
= 138°
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Given that cos theta equals negative 5 square root 29 over 29 and theta is in quadrant 2 what is sim theta?
If cοs θ equals negative 5 square rοοt 29 οver 29 and θ is in quadrant 2 sin(θ) = οppοsite/hypοtenuse = 2√21/29.
What is trigοnοmetry?The links between triangles' sides and angles are studied in the mathematic discipline knοwn as trigοnοmetry.
We knοw that cοsine is negative in quadrant 2, sο we can draw a triangle in quadrant 2 where the adjacent side is negative and the hypοtenuse is pοsitive. Let's call the οppοsite side οf the triangle "a", the adjacent side "b", and the hypοtenuse "c".
Using the Pythagοrean theοrem, we can find the length οf the third side οf the triangle:
c² = a² + b²
29² = a² + (-5√29)²
29² = a² + 725
a² = 29² - 725
a² = 84
a = √84 = 2√21
Nοw that we knοw the lengths οf the οppοsite and adjacent sides οf the triangle, we can use the definitiοn οf sine:
sin(θ) = οppοsite/hypοtenuse = 2√21/29
Therefοre, sin(θ) equals 2√21/29.
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Complete Question:
Given that cos(θ)=−5√29/29, and θ is in Quadrant II, what is sin(θ)? Give your answer as an exact fraction with a radical, if necessary.
answer this for me please and thank you
Answer: w = -13
Step-by-step explanation:
To solve, we will isolate the variable with inverse operations.
Given:
4 + w = -9
Subtract 4 from both sides of the equation:
w = -13
When an object is dropped vertically from a platform, its height after
seconds can be estimated with the formula shown.
ℎ=ℎ0−162
ℎ
is the height of the object in feet.
ℎ0
is the initial height of the object in feet.
is the time in seconds after the drop.
Which equation and solution tells how long it takes the object to reach a height of 84
feet if its initial height is 180
feet?
The equation is 84= h₀ -16t² and
Solving the equation we get the time taken by the object will be √6 seconds.
What is equation?
An equation is a mathematical statement which is built by two expressions connected by an equal sign ('='). There must be at least one unknown variable which is to be determined. For example, 3x – 8 = 16 is an equation. Solving this equation, we get x = 8.
When an object is dropped vertically from a platform, its height after
seconds can be estimated with the formula shown.
ℎ=ℎ₀−16t²
where ℎ is the height of the object in feet.
and ℎ₀ is the initial height of the object in feet.
t is the time in seconds after the drop.
If the object reach the height 84 feet then the equation will be,
84= h₀ -16t²
If the initial height is 180 feet then the equation will be
84 = 180- 16t²
Solving the equation we get,
⇒ 16t² = 180- 84
⇒ 16t² = 96
⇒ t² = 6
⇒ t= ±√6
As time can't be negative so t= √6
Hence solving the equation we get the time taken by the object will be √6 seconds.
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3. When Ahmad goes to work, he has to pass through two sets of traffic lights, P and Q. The
probability that he has to stop at P is
7/20 .The probability that he has to stop at Q, given that he has
to stop at P is 7/10. The probability that he does not have to stop at Q, given that he does not have to
stop at P is 2/5
* Construct a tree diagram to represent the above information.
* Find the probability that he has to stop at both P and Q.
* Find the probability that he has to stop at least once.
* If he has to stop at Q, what is the probability that he would have stopped at P.
* The probability that Ahmad has to stop at both P and Q is: 7/40
* The probability that Ahmad has to stop at least once is: 27/50
* The probability that Ahmad would have stopped at P if he stops at Q is 7/13.
What is probability ?
The study of randomness or experiments falls within the canopy of the mathematical discipline of probability. When represented as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certain event, it is the gauge of the probability or chance that an event will occur. When making predictions based on a statistical study of the data at hand, probability is employed to characterise uncertain events. To aid in decision-making and risk assessment, it is utilised in a variety of disciplines, including science, architecture, finance, finance, and social sciences. Concepts like likelihood function, random variables, and anticipated values are all part of the study of probability.
given
We multiply the chances of stopping at P and Q assuming that he has already stopped at P to determine the likelihood that he must stop at both locations:
Stop at P Equals P(Stop at P and Q) P(Stop at Q | Stop at P)=7/20*7/10
= 49/200
P(Stop at least once) = 1 - P(Not stop at P) * P(Not stop at Q | Not stop at P) = 1 - (13/20) * P(Not stop at Q | Not stop at P) (2/5)\s= 37/50
The chance that he likewise stopped at P must be determined if he had stopped at Q.
Stopping at P and Q equals P(Stop at P and Q) / P(Stop at Q) = (7/20 * 7/10) / (7/20) = 7/10.
Hence, the likelihood that he would have stopped at P is 7/10 if he must stop at Q.
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which is equivalent to (3/125)*?
125 1/3×
125 1/3X
125 3x
125 [1/3]×
The answer is (B) 125 1/3×, which is equivalent to (3/125) times approximately 18.048.
What do you mean by Equivalent fraction?Equivalent fractions are fractions that have the same value but are written in different forms. They represent the same portion of a whole or a set, but their numerators and denominators may have different values.To find equivalent fractions, you can multiply or divide both the numerator and denominator of a fraction by the same number. This does not change the value of the fraction, but it changes its form.
The expression is (3/125) times something, but the value of that something is missing.
To solve the problem, we can simplify the expression (3/125) as a fraction in its lowest terms:
(3/125) = (3/5³)
Now, let's look at each of the answer choices:
125
If we multiply (3/5³) by 125, we get:
(3/5^3) * 125 = 3/5
Therefore, 125 is not equivalent to (3/125) times something.
1/3 × 125
If we multiply (3/5³) by (1/3 × 125), we get:
(3/5^3) * (1/3 × 125) = 1/5
Therefore, 1/3 × 125 is not equivalent to (3/125) times something.
125 1/3 ×
If we interpret "125 1/3 ×" as 125 and one-third multiplied by something, then we can write it as a mixed number fraction:
125 1/3 = 376/3
If we multiply (3/5³) by 376/3, we get:
(3/5³) ×(376/3) = 2256/125 = 18.048
Therefore, 125 1/3 × is equivalent to (3/125) times approximately 18.048.
125× 3x
If we interpret "125 3x" as 125 multiplied by 3 times something, then we can write it as:
125 ×3x = 375x
Therefore, 125 3x is not equivalent to (3/125) times something.
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Which is the largest angle?
A4
OC
B
5
Cannot tell
OA
с
7
6
B
will mark brainliest its timed hurry!
Answer:
I think the answer is B?
Step-by-step explanation:
Need help factoring each expressions
Answer:
a. factors of 3x²-7x-6 =(x-3) and (3x+2)
b factors of 4x²-49=(2x-7) and (2x+7)
eight x equals two thirds
Answer:
x = [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
8x = [tex]\frac{2}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
24x = 2 ( divide both sides by 24 )
x = [tex]\frac{2}{24}[/tex] = [tex]\frac{1}{12}[/tex]
Please help with this equation I’ll give brainliest
Answer:
a. A linear equation would best represent the total cost a shopper will pay for an order.
b. y = .7x + 5 would model this situation.
The length of a rectangular flower bed is 3 ft less than twice its width. The area of the bed is 54 ft2. What are the dimensions of the flower bed.
Answer:
w = 6 ft.; l = 9 ft.
Step-by-step explanation:
We know that the formula for area of a rectangle is A = lw, where l is the length and w is the width.
Because we're told that the length of the flower bed is 3 ft less than twice its width, we have l = 2w - 3
To find the length and width, can plug in 54 into the equation and substitute our formula for length into the equation.
This gives us 54 = (2w - 3)*w
If we rewrite the equation, we'll see that its quadratic:
[tex]54=(2w-3)w\\54=2w^2-3w\\0=2w^2-3w-54[/tex]
Now, we can first solve for width using the quadratic formula, which yields a positive and negative solution.
(For the sake of the quadratic equation, 0= ax^2 + bx + c is the standard form of quadratic equation and in our equation 2 is a, -3 is b, and -54 is c)
Positive:
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)+\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3+\sqrt{441} }{4}\\ \\w=\frac{3+21}{4}\\ \\w=\frac{24}{4}\\\\w=6[/tex]
Negative:
[tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)-\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3-\sqrt{441} }{4}\\ \\w=\frac{3-21}{4}\\ \\w=\frac{-18}{4}\\\\w=-4.5[/tex]
We know that we can't have a negative measure, so the width is 6 ft.
Twice the width is 12 (6 * 2) and 3 less than this is 9 (12 - 3), so the length is 9 ft.
Find the missing side lengths. Leave your answers and radicals in the simplest form.
Answer:
x = 6;
y = 3√3
Step-by-step explanation:
Use trigonometry:
[tex] \ \cos(60°) = \frac{3}{x} [/tex]
Use the property of proportion to find x:
[tex]x = \frac{3}{ \cos(60°) } = \frac{3}{0.5} = 6[/tex]
Use the Pythagorean theorem to find y:
[tex] {y}^{2} = {x}^{2} - {3}^{2} [/tex]
[tex] {y}^{2} = {6}^{2} - {3}^{2} = 36 - 9 = 27[/tex]
[tex]y > 0[/tex]
[tex]y = \sqrt{27} = \sqrt{9 \times 3} = 3 \sqrt{3} [/tex]
I I need a quick answer
Answer:
the answer is b
Step-by-step explanation:
giving brainlist(for the right answer) ! ⚠
Solve this non linear Second Order Differential Equations,
(but don't use Ai) I know if it's from there
The general solution to the differential equation is M = (1/2)n² + Bn, where B is an arbitrary constant.
Describe Differentiation?In calculus, differentiation is a process of finding the rate at which a function changes with respect to its input variable. It is the process of finding the derivative of a function, which represents the slope of the tangent line to the graph of the function at a given point.
The derivative of a function f(x) at a point x=a is denoted as f'(a) and is defined as the limit of the difference quotient as the interval between a and a+h approaches zero, where h is a small nonzero number.
The process of differentiation involves applying differentiation rules or formulas, which are a set of rules that make it easier to find the derivative of various functions. Some of the common rules include the power rule, product rule, quotient rule, and chain rule.
To solve the given differential equation:
[tex]\frac{d^{2}M }{dn^{2} } + 2n\frac{dM}{dn} =n[/tex]
We can assume a solution of the form:
[tex]M= An^{p}[/tex]
where A and p are constants to be determined.
Taking the first derivative of M with respect to n, we get:
[tex]\frac{dM}{dn} = Apn^{p-1}[/tex]
Taking the second derivative of M with respect to n, we get:
[tex]\frac{d^{2}M }{dn^{2} }= A(p)(p-1)n^{p-2}[/tex]
Substituting these expressions into the original differential equation, we get:
[tex]A(p)(p-1)n^{p-2} + 2Apn^{p-1}= n[/tex]
Simplifying, we get:
[tex]A(p)(p-1)n^{p-2} + 2Apn^{p}=n^{p+1}[/tex]
Since this equation must hold for all values of n, we can equate the coefficients of each power of n to get two equations:
A(p)(p-1) = 0
2Ap = 1
From the first equation, we get:
p = 0 or p = 1
If p = 0, then M = A, a constant. Substituting into the differential equation, we get:
0 = n
This is not true for all values of n, so p cannot be 0.
If p = 1, then M = An. Substituting into the differential equation, we get:
2An + 2nA = n
Simplifying, we get:
A = 1/2
Therefore, the solution to the differential equation is:
M = (1/2)n² + Bn
where B is a constant of integration.
Thus, the general solution to the differential equation is:
M = (1/2)n² + Bn
where B is an arbitrary constant.
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Gretchen is a famous chef taking part in a celebrity cooking contest. Contestants earn scores between 1 - 10, with 10 being perfect. There are four categories and each category is weighted differently. The judges combined their scores and the results are shown in the table below.
Gretchen's final score, out of 10, is 8.35 based on weighted averages of scores in four categories.
How to calculate Gretchen's final score?To calculate Gretchen's final score, we need to calculate the weighted average of her scores in each category.
The weight of each category is given, so we can calculate the weighted score for each category by multiplying the weight by the score.
For Taste, the weighted score is 0.30 * 8.6 = 2.58
For Presentation, the weighted score is 0.35 * 9.8 = 3.43
For Use of Ingredients, the weighted score is 0.25 * 7.7 = 1.93
For Practicality, the weighted score is 0.10 * 4.1 = 0.41
To find the final score, we add up the weighted scores for all categories:
2.58 + 3.43 + 1.93 + 0.41 = 8.35
Therefore, Gretchen's final score is 8.35 out of 10.
The question is incomplete, below is the complete question given -
Gretchen is a celebrity chef competing in a celebrity cooking competition. Contestants receive ratings ranging from 1 to 10, with 10 being the highest. There are four categories, each with its own weighting. The judges' scores were added together, and the results are presented in the table below. What is Gretchen's final score, out of 10? Do not round.
Table -
Category Weight Score
Taste 30% 8.6
Presentation 35% 9.8
Use of Ingredients 25% 7.7
Practicality 10% 4.1
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Use a formula to find the surface area of the square pyramid.
3 ft
6 ft
3 ft
The surface area of the square pyramid is 89.4 ft² as the lateral area is 80.4 ft².
How to calculate the surface area of a square pyramid?The surface area of a square pyramid is calculated by the formula
SA = B + 4ℓ, where B is the area of the base and ℓ is the lateral area.
In this case, the base area is 9 square feet (3 ft x 3 ft). The lateral area is 4ℓ, which is calculated by multiplying the slant height by the perimeter of the base.
The slant height of a square pyramid is calculated by the formula
s = √(h² + (a/2)²), where h is the height of the pyramid and a is the length of one side of the base.
In this case, the height is 3 ft and the length of one side of the base is 3 ft. Therefore, the slant height is
s = √(3² + (3/2)²)
= √(9 + 2.25)
= √11.25
= 3.35 ft.
The perimeter of the base is 6 ft (3 ft x 2). Therefore, the lateral area is
4ℓ = 4 x 3.35 ft x 6 ft
= 80.4 ft².
The surface area of the square pyramid is then
SA = B + 4ℓ
= 9 ft² + 80.4 ft²
= 89.4 ft².
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Need help with question #7
The coordinates of the matrix A with the given base S are:
<1, 2, 0, 2>
How to find the coordinates?The coordinates will be a vector of the form:
<x, y, z, k>
Such that these four values are each of the coefficients that affect each one of the matrices in the base respectively.
Then we can write a system of equations like:
x + y + z + k = 5
x - y - z = 3
x + y = 3
x = 1
We can replace the last equation in the third one to get:
1 + y = 3
y = 3 - 1
y = 2
Now we can replace x and y in the second equation:
1 + 2 - z = 3
z = 1 + 2 - 3
z = 0
And the with the first equation:
1 + 2 + 0 + k = 5
3 + k = 5
k = 5 - 3 = 2
Then the coordinates of the matrix A are:
<1, 2, 0, 2>
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