Answer:
I can't understand the language but try people who can
What is the area of
the segment? Express
the answer in terms
of pi.
The area of the segment is 9( π-2) units²
What is area of segment?The area of a figure is the number of unit squares that cover the surface of a closed figure.
A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.
Area of segment = area of sector - area of triangle
area of sector = 90/360 × πr²
= 1/4 × π × 36
= 9π
area of triangle = 1/2bh
= 1/2 × 6²
= 18
area of segment = 9π -18
= 9( π -2) units²
therefore the area of the segment is 9(π-2) units²
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how to write a decimal as a mixed number
Answer:
Here's an example:
convert 2.5 into a mixed number.
Make the denominator less than the original.
The easy way for this is to do 25/10
when you put it through a calculator it ends up being 2.5
(essentially the mixed number and the decimal are the SAME numbers.)
Hope this clarified. :)
To convert a decimal to a mixed number, follow these steps:
Step 1: Identify the whole number part of the decimal. This is the part of the decimal before the decimal point.
Step 2: Identify the decimal part. This is the part of the decimal after the decimal point.
Step 3: Express the decimal part as a fraction by using the place value of the last digit.
Step 4: Simplify the fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
Step 5: Combine the whole number part, the fraction, and simplify if necessary.
Here's an example:
Let's say we have the decimal 2.75.
Step 1: The whole number part is 2.
Step 2: The decimal part is 0.75.
Step 3: To express 0.75 as a fraction, we write it as 75/100. Since 75 and 100 have a common factor of 25, we can simplify it to 3/4.
Step 4: The fraction 3/4 is already in its simplest form.
Step 5: Combining the whole number part and the fraction, we have 2 3/4.
So, the decimal 2.75 can be written as the mixed number 2 3/4.
Remember to always simplify the fraction part if possible.
Un chavo mide 3 pulgadas + un 1/4 de pulgada y otro mide 9.045 cm que diferencia de tamaño hay entre ellos
The difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.
To calculate the difference in size between two people, one measuring in inches and the other measuring in centimeters, we must first convert all measurements to a common unit.
Guy measures 3 inches + 1/4 inch. We can convert 1/4 inch to a decimal fraction by dividing 1 by 4, which gives us 0.25 inches. So your measurement in inches would be 3 + 0.25 = 3.25 inches.
The other guy measures 9.045 cm. To convert centimeters to inches, we use the following relationship: 1 cm = 0.3937 inches. Multiplying the measurement in centimeters by 0.3937, we get the measurement in inches: 9.045 cm * 0.3937 = 3.5608 inches (approximately).
Now we can calculate the size difference between them. We subtract the measurement of the second chavo (3.5608 inches) from the measurement of the first chavo (3.25 inches):
3.25 inches - 3.5608 inches = -0.3108 inches.
The resulting difference is -0.3108 inches. This means that the second chavo is smaller in size than the first. Since the difference is negative, it indicates that the first chavo is bigger than the second.
In summary, the difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.
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5
x
−
2
−
(
x
−
2
)
4
x
Answer:
Step-by-step explanation:
To simplify the expression (5x - 2) / (x - 2) - (4x), we can follow these steps:
First, let's simplify the numerator:
5x - 2
Now, let's distribute the negative sign to the term (4x):
-4x
Next, let's combine the terms in the numerator:
(5x - 2) - 4x = 5x - 2 - 4x = x - 2
Now, let's rewrite the expression:
(x - 2) / (x - 2) - 4x
Since we have (x - 2) as both the numerator and denominator, we can simplify further by canceling out the common factor:
1 - 4x
Therefore, the simplified form of the expression (5x - 2) / (x - 2) - (4x) is 1 - 4x.
Which order pair? Explain.
A function can't have more than one value for an argument. Therefore, it's either (1,1) or (1,3), but since there's not (1,3) among the possible answers, it must be (1,1).
Find a, b,c, and d, such that the cubic f(x)=ax^3+bx^2+cx+d has a relative maximum at (-7, 163); has a relative minimum at (5, -125); and has a point of inflection at (-1, 19).
The cubic function with the desired properties is:
f(x) = (-3/4)x³ - (9/4)x² - (113/4)x + 63/4
To find the values of a, b, c, and d, we can use the given information about the relative maximum, relative minimum, and point of inflection.
Relative Maximum:
The point (-7, 163) is a relative maximum. At this point, the derivative of the cubic function is equal to zero. Taking the derivative of the cubic function, we have:
f'(x) = 3ax² + 2bx + c
Setting x = -7 and f'(-7) = 0, we get:
49a - 14b + c = 0
Relative Minimum:
The point (5, -125) is a relative minimum. At this point, the derivative of the cubic function is equal to zero. Taking the derivative of the cubic function, we have:
f'(x) = 3ax² + 2bx + c
Setting x = 5 and f'(5) = 0, we get:
75a + 10b + c = 0
Point of Inflection:
The point (-1, 19) is a point of inflection. At this point, the second derivative of the cubic function changes sign. Taking the second derivative of the cubic function, we have:
f''(x) = 6ax + 2b
Setting x = -1, we get:
-6a + 2b = 0
Solving the system of equations formed by the above three equations, we can find the values of a, b, c, and d.
49a - 14b + c = 0
75a + 10b + c = 0
-6a + 2b = 0
Solving these equations, we find:
a = -3/4
b = -9/4
c = -113/4
d = 63/4
Therefore, the cubic function with the desired properties is:
f(x) = (-3/4)x³ - (9/4)x² - (113/4)x + 63/4
Write a linear equation for the following table.
x = number
y = cost
0
15
35
55
75
95
y =
4
8
12
16
X +
Answer:
[tex]m = \frac{35 - 15}{4 - 0} = \frac{20}{4} = 5[/tex]
[tex]y = 5x + 15[/tex]
13.9 m
21 m
16 m
Find surface area
The Total Surface Area of the given prism is: 1,230.4 m²
How to find the surface area of the prism?The volume of the prism is calculated as:
Volume = Base Area * Height
The total surface area is the sum of the surface area of all individual surfaces and as such we have:
Total Surface Area = (21 * 16) + (21 * 16) + (21 * 16) + 2(0.5 * 16 * 13.9)
Total Surface Area = 336 + 336 + 336 + 222.4
Total Surface Area = 1,230.4 m²
That is the final total surface area of the given rectangular based prism
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Ms. Florinda is a kindergarten teacher. She buys 100 pencils and wants to give 2 pencils to each of her students. She has 2 classes, a class with 22 students and a class with 19 students.
Part A
Write an expression for how many pencils she has left after giving them out to her students.
A.
100
−
2
×
(
22
−
19
)
B.
100
−
2
×
22
−
19
C.
100
−
2
×
22
−
2
×
19
D.
100
−
22
−
19
Part B
Does she have enough pencils to give each of her students 2?
Yes or no
, she has
15,18,37,59
More or fewer
than she needs.
Answer:
Part A:
The correct expression for how many pencils Ms. Florinda has left after giving them out to her students is:
A. 100 - 2 × (22 - 19)
Part B:
To determine whether Ms. Florinda has enough pencils to give each of her students 2, we can calculate the total number of pencils needed. The total number of students is the sum of the students in both classes, which is 22 + 19 = 41.
If each student needs 2 pencils, then the total number of pencils needed is 2 × 41 = 82.
Comparing this with the initial number of pencils Ms. Florinda bought (100), we can see that she has more than enough pencils to give each of her students 2.
Yes, she has enough pencils to give each of her students 2.
She has 18 more than she needs.
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), what are the
coordinates of B?
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).
To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.
Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).
Using the midpoint formula, we can set up the following equations:
(x1 + x2) / 2 = -4
(y1 + y2) / 2 = 2
Substituting the coordinates of point A (-7, 3), we have:
(-7 + x2) / 2 = -4
(3 + y2) / 2 = 2
Simplifying the equations:
-7 + x2 = -8
3 + y2 = 4
Solving for x2 and y2:
x2 = -8 + 7 = -1
y2 = 4 - 3 = 1
Therefore, the coordinates of point B are (-1, 1).
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Let (1=1,2,3, 4, 5, 6, 7, 8, 9, 10
The list of elements in the sets are as follows:
A. A ∩ B = {2, 9}
B. B ∩ C = {2, 3}
C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D. B ∪ C = {2, 3, 5, 7, 9, 10}
How to find the elements in a set?Set are defined as the collection of objects whose elements are fixed and can not be changed.
Therefore,
universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 7, 8, 9}
B = {2, 3, 5, 9}
C = {2, 3, 7, 10}
Therefore,
A.
A ∩ B = {2, 9}
B.
B ∩ C = {2, 3}
C.
A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D.
B ∪ C = {2, 3, 5, 7, 9, 10}
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Find the value of the combination. 10C0 0 1 10
The formula to find the value of a combination is
[tex]C(n, r) = n! / (r!(n-r)!),[/tex]
where n represents the total number of items and r represents the number of items being chosen at a time. 10C0 is 1
In the combination,
n = 10 and r = 0,
so the formula becomes:
C(10,0) = 10! / (0! (10-0)!) = 10! / (1 x 10!) = 1 / 1 = 1
This means that out of the 10 items, when choosing 0 at a time, there is only 1 way to do so. In other words, choosing 0 items from a set of 10 items will always result in a single set. This is because the empty set (which has 0 items) is the only possible set when no items are chosen from a set of items. Therefore, the value of the combination 10C0 is 1.
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Pls help me asap I’m stuck in this
Answer:
Step-by-step explanation:
[tex]\angle x=\angle y=\angle z=90\deg\ \text{(angle in a semi-circle is a right angle)}[/tex]
All 3 angles are examples of the theorem which states that any angle coming off the diameter of a circle going to the edge of the circle will form a right angle.
3. Triangle ABC has the following coordinates. A=(-6,5), B=(-4,2), C=(-6,2) What are the coordinates of triangle A'B'C' if it is created by dilating triangle ABC with the origin (0,0) as the center of dilation and with a scale factor of 4?
Answer:
You multiply each coordinate by 4
Step-by-step explanation:
Rule: (x, y) to (4x, 4y)
A: (-6,5) to A' (-24, 20)
B: (-4, 2) to B' (-16, 8)
C: (-6, 2) to C' (-24, 8)
02.05 MC)
What additional information would you need to prove that ΔABC ≅ ΔDEF by SAS?
Triangle ABC is drawn with a single hash mark between A and B and triangle DEF is marked with a single hash mark between D and
(4 points)
Group of answer choices
segment AC≅segment EF
segment BC ≅ segment FE
segment AC ≅ segment FE
segment BC ≅ segment EF
Having the information that segment AC ≅ segment EF, angle B ≅ angle E, and segment BC ≅ segment FE is sufficient to prove that triangles ΔABC and ΔDEF are congruent by the Side-Angle-Side (SAS) criterion.
To prove that triangles ΔABC and ΔDEF are congruent using the Side-Angle-Side (SAS) criterion, we need the following additional information:
The length of segment AC is equal to the length of segment EF: This establishes that one pair of corresponding sides is congruent.
The measure of angle B is equal to the measure of angle E: This provides the congruent angle between the corresponding sides.
The length of segment BC is equal to the length of segment FE: This establishes that the other pair of corresponding sides are congruent.
By having this information, we can apply the SAS congruence criterion. The SAS criterion states that if two triangles have a pair of corresponding sides that are congruent, and the included angles are congruent, then the triangles are congruent.
In this case, having segments AC ≅ EF, angle B ≅ angle E, and segment BC ≅ FE would be sufficient to prove that ΔABC ≅ ΔDEF by SAS.
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Which are the roots of the quadratic function f(b) = b² - 75? Select two options.
Ob=5√3
Ob=-5√3
Ob=3√5
Ob=-3√5
Ob=25√3
The two roots of the quadratic function f(b) = b² - 75 are:
b = 5√3 and b = -5√3What is the quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.
We have
[tex]f(b) = b^2 - 75[/tex]Remember that the root of a function is the value of x when the value of the function is equal to zero.
In this problem
The roots are the values of b when the function f(b) is equal to zero.
So,
For f(b)=0
[tex]b^2-75=0[/tex]
[tex]b^2=75[/tex]
Square root both sides
[tex]b=(+/-)\sqrt{75}[/tex]
Simplify
[tex]b=(+/-)5\sqrt{3}[/tex]
[tex]b=5\sqrt{3}[/tex] and [tex]b=-5\sqrt{3}[/tex]
Therefore
[tex]\rightarrow\bold{b = 5\sqrt{3}}[/tex]
[tex]\rightarrow\bold{b=-5\sqrt{3}}[/tex]
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Which of the following is the graph of y=-(x-2)³-5?
-5-4-3-2-1
-5-4-3
S
-2+
-3
? 4
-4
-5
997
-6
-7
-8.
-9
& co
-10
1 2 3 45 x
1
2345
X
Answer:
Step-by-step explanation:
I cannot see the graphs.
Find the measure of the indicated arc.
T
56°
S
?
U
The measure of the intercepted arc SU in the circle is 112 degrees.
What is the measure of the arc length?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
From the diagram:
Inscribed angle = 56 degrees
Intercepted arc SU= ?
Plug the given value into the above formula and solve for the intercepted arc.
Inscribed angle = 1/2 × intercepted arc
56 = 1/2 × arc SU
Multiply both sides by 2:
56 × 2 = 1/2 × 2 × arc SU
112 = arc SU
Arc SU = 112°
Therefore, the intercepted arc measure 112 degrees.
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Fine the 8th term of the geometric sequence 10,50,250
Answer:
781250
Step-by-step explanation:
The sequence is has common ratio of 5 so the equation is 10*5^x-2 or 2*5^x so 2*5^8=781250
Answer:
ar⁷= 781,250
Step-by-step explanation:
a =10
ar =50
ar² = 250
8th term = ar⁷=?
r = ar/a
= 50/10
r =5
ar⁷ = 10 × 5 ⁷
=10 × 78125
= 781,250
What is the value of the rational expression below when x is equal to 4?
x-12
X-8
O A. -2
о B. 8
о C. 2
OD. -8
The value of the rational expression when x is equal to 4 is 2. The correct answer is option C: 2.
To find the value of the rational expression (x - 12)/(x - 8) when x is equal to 4, we substitute x = 4 into the expression:
[(4) - 12]/[(4) - 8]
Simplifying the numerator and denominator:
(4 - 12)/(-4)
Further simplifying the numerator:
(-8)/(-4)
Now, we can divide -8 by -4:
(-8)/(-4) = 2
So, when x is equal to 4, the value of the rational expression is 2.
Therefore, C is the right response.
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CD is perpendicular to AB and passes through point C(5, 12).
If the coordinates of A and B are (-10, -3) and (7, 14), respectively, the x-intercept of CD is {blank A}. The point {blank B} lies on CD.
Options:
Blank A:
(12,0)
(15,0)
(17,0)
(19,0)
Blank B:
(-5,24)
(-2,19)
(7,-10)
(8,11)
Answer:
Blank A: (17, 0)
Blank B: (-2, 19)
Step-by-step explanation:
Blank A:
Step 1: Find the slope of AB:
Before we can find the equation of CD, we'll first need to find the slope of AB
We can do this using the slope formula, which is given by:
m = (y2 - y1) / (x2 - x1), where
m is the slope,(x1, y1) is one point,and (x2, y2) is another point.Thus, we can plug in (-10, -3) for (x1, y1) and (7, 14) for (x2, y2) in the slope formula to find m, the slope of AB:
m = (14 - (-3)) / (7 - (-10))
m = (14 + 3) / (7 + 10)
m = 17 / 17
m = 1
Thus, the slope of AB is 1.
Step 2: Find the slope of CD:
The slope of perpendicular lines are negative reciprocals of each other as shown by the following formula:
m2 = -1 / m1, where
m2 is the slope of the line we're trying to find, and m1 is the slope of the line we know.Thus, we can plug in 1 for m1 in the perpendicular slope formula to find m2, the slope of CD:
m2 = -1 / 1
m2 = -1
Thus, the slope of CD is -1.
Step 3: Find the y-intercept of CD:
One of the equations we can use when looking for intercepts is the slope-intercept form of a line, whose general equation is given by:
y = mx + b, where
(x, y) is any point on the line,m is the slope,and b is the y-intercept.Thus, we can plug in (5, 12) for (x, y) and -1 for m to find b, the y-intercept of the line, allowing us to have the full equation in slope-intercept of CD:
12 = -1(5) + b
12 = -5 + b
17 = b
Thus, the equation of CD is y = -x + 17
For any x-intercept, the y-coordinate will always be 0 since the line is intersecting the x-axis.
Thus, we can find the x-coordinate of the x-intercept by plugging in 0 for y in y = -x + 17 and solving for x:
0 = -x + 17
-17 = -x
17 = x
Thus, the x-coordinate of the x-intercept of CD is 17.
Thus, the coordinates of the x-intercept of CD are (17, 0)
Blank B:
We can see that (-2, 19) lies on CD when we plug in (-2, 19) for (x, y) in y = -x + 17, as we get 19 on both sides of the equation when simplifying:
19 = -(-2) + 17
19 = 2 + 17
19 = 19
Thus, (-2, 19) lies on CD.
Based on the two data sets represented below, complete the following sentences. DATA SET K DATA SET K 0 0 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 DATA SET L DATA SET L 0 0 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 The center of Data Set K is than the center of Data Set L. The spread of Data Set K is than the spread of Data Set L.
Based on the provided data sets, it can be observed that both Data Set K and Data Set L have identical values. Therefore, their centers and spreads are also identical.
The center of a data set can be measured using various statistical measures such as the mean, median, or mode. Since the data sets have the same values, all these measures will yield the same result for both sets.
In this case, the center of Data Set K is equal to the center of Data Set L.
Similarly, the spread of a data set refers to the measure of variability or dispersion within the data. Common measures of spread include the range, variance, and standard deviation.
However, since the data sets are exactly the same, all these measures will yield identical results for both sets. Thus, the spread of Data Set K is the same as the spread of Data Set L.
In summary, both the center and the spread of Data Set K are the same as those of Data Set L. Therefore, there is no difference between the two data sets in terms of their central tendency or variability.
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I need help!! f(x)=-2(x-3)
Answer:
Step-by-step explanation:
Certainly! I'm here to assist you.
The given function is f(x) = -2(x - 3).
To simplify this expression, we can distribute the -2 to the terms inside the parentheses:
f(x) = -2 * x - (-2) * 3
Simplifying further:
f(x) = -2x + 6
Therefore, the simplified form of the function f(x) = -2(x - 3) is f(x) = -2x + 6.
What is the mean and median reasoning, As the last one is incorrect
The best measure of center of the data is (a) mean; because the data are close together
How to determine the best measure of center of the dataFrom the question, we have the following parameters that can be used in our computation:
The dataset of 10 values
Where we can see that there are no outliers present in the dataset
By definition, outliers are extreme values.
Since there are no outliers, it means that the mean is the best measure of center
This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean
From the list of options, we have the mean value to be 42.536
Hence, the true statement is (a)
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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 3) and (3, 1). Everything below and to the right of the line is shaded.
Which linear inequality is represented by the graph?
y > Two-thirdsx – 2
y < Two-thirdsx + 2
y > Two-thirdsx + 1
y < Two-thirdsx – 1
Answer:
y > Two-thirds x + 1 /c
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Answer:
(-2, 2)
Step-by-step explanation:
We will start by just plugging in the numbers to see if they work.
(-3, 5)
5<-(-3)+1
5<4
This is not possible, so the answer is not (-3, 5).
(-2, 2)
2<-(-2)+1
2<3
2>-2
The point (-2, 2) works for both equations, so that is the answer.
Rebecca earned $2,996 as interest by lending a certain amount at 2.00% p.m. for 12 months. Calculate the loan principal and Calculate the loan's maturity value.
The loan principal is $12,483.33, and the loan's maturity value is $15,479.33.
To calculate the loan principal, we can use the formula for simple interest:
Interest = Principal x Rate x Time
Given that Rebecca earned $2,996 as interest, the rate is 2.00% per month (or 0.02), and the time is 12 months, we can plug in these values into the formula and solve for the principal:
$2,996 = Principal x 0.02 x 12
$2,996 = Principal x 0.24
Dividing both sides of the equation by 0.24, we get:
Principal = $2,996 / 0.24
Principal = $12,483.33
So, the loan principal is $12,483.33.
To calculate the loan's maturity value, we need to add the principal and the interest earned. Since the interest earned is $2,996 and the principal is $12,483.33, the maturity value can be calculated as:
Maturity Value = Principal + Interest
Maturity Value = $12,483.33 + $2,996
Maturity Value = $15,479.33
Therefore, the loan's maturity value is $15,479.33.
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8.4.4. Define sets. How many kinds of sets Also list the operation of sets. Give the short activites for teaching Learning Union of sets. 2+2+2+4=10)
In mathematics, a set is a well-defined collection of distinct objects, called elements or members of the set. These objects can be anything: numbers, letters, people, or even other sets.
he concept of sets is fundamental in various branches of mathematics, including set theory, algebra, and statistics.There are different kinds of sets based on their properties:
Finite set: A set with a specific number of elements, which can be counted.Infinite set: A set with an endless number of elements.Empty set: A set with no elements. It is denoted by the symbol Ø or {}.
Singleton set: A set with only one element.Subset: A set whose elements are all contained within another set.Universal set: A set that includes all the possible elements of interest in a particular context.Operations on sets involve various ways of combining or manipulating sets:
Union: The union of two sets A and B is the set that contains all the elements from both sets. It is denoted by A ∪ B.Intersection: The intersection of two sets A and B is the set of elements that are common to both sets. It is denoted by A ∩ B.
Complement: The complement of a set A, denoted by A', is the set of all elements that are not in A but are in the universal set.Difference: The difference between two sets A and B is the set of elements that are in A but not in B. It is denoted by A - B.
Cartesian Product: The Cartesian product of two sets A and B is the set of all possible ordered pairs, where the first element is from set A and the second element is from set B. It is denoted by A × B.
For teaching the concept of the union of sets, you can use the following activity:
Activity: Venn Diagrams
Draw two overlapping circles on the board or use physical cut-out circles.Label one circle as Set A and the other as Set B.
Ask the students to suggest elements for each set and write them inside the circles.Discuss the elements that are common to both sets and write them in the overlapping region.Explain that the union of sets A and B represents all the elements in both sets.
Combine the elements from sets A and B, including the elements in the overlapping region, and write them in a new circle labeled as A ∪ B.Emphasize that the union includes all the distinct elements from both sets without repetition.
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The crew from Disneyland Entertainment launches fireworks at an angle. The height of the firework can be modeled by h(t) = -2t^2+ 8t + 300 where height, h, is measured in feet and the
time, t, in seconds. What is the greatest height the fireworks reach?
Answer:
The function given here is a quadratic function of the form f(t) = at^2 + bt + c, where a is -2, b is 8, and c is 300. The maximum value of a quadratic function occurs at its vertex. For a function in the form f(t) = at^2 + bt + c, the t-coordinate of the vertex is given by -b/(2a). We can use this to find the time at which the firework reaches its maximum height.
Given a = -2 and b = 8, we can calculate t = -b/(2a):
t = -8/(2*-2) = 2
We can then substitute this value back into the height equation to find the maximum height:
h(2) = -2(2)^2 + 8*2 + 300
h(2) = -8 + 16 + 300
h(2) = 308
So, the greatest height the fireworks reach is 308 feet.
2. [3 points] In order to pay for college, the parents of a child invest $20,000 in a bond that pays 8% interest compounded semiannually. How much money will there be in 18 years?
Work (1 pt)
Replace these words with a cropped picture of your work for question 2.
Answer
Explanation
The amount of money there would be in 18 years is $82078.65.
The value of the bond increased over the 18 years period.
How to determine the future value after 18 years?In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where:
A represents the future value.n represents the number of times compounded.P represents the principal.r represents the interest rate.t represents the time measured in years.By substituting the given parameters into the formula for compound interest, we have the following;
[tex]A(18) = 20000(1 + \frac{0.08}{2})^{2 \times 18}\\\\A(18) = 20000(1.04)^{36}[/tex]
Future value, A(18) = $82078.65
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Answer:
$82078.65
Step-by-step explanation:
You want the value of a $20,000 investment that pays 8% interest compounded semiannually for 18 years.
Compound interestThe value of the investment of principal amount P at interest rate r compounded n times per year for t years is given by the formula ...
A = P(1 +r/n)^(nt)
ApplicationUsing the given values, we find the amount of money in 18 years will be ...
A = $20,000(1 + 0.08/2)^(2·18) = $20,000(1.04^36) ≈ $82,078.65
In 18 years there will be $82,078.65.
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Additional comment
Some calculators and all spreadsheets have built-in functions for evaluating financial formulas.
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