Answer:
(x+3)(3x-5)(3x+5)
Step-by-step explanation:
Let's consider the possible rational zeros: factors of -75 over factors of 9
So one such possible 0 is -3
let's try it and see if it works:
-3 | 9 27 -25 -75
| -27 0 75
------------------------------------------
9 0 -25 0
So x+3 is a factor and we have another there which is 9x^2+0x-25 or 9x^2-25
So far we have this as the factored form (x+3)(9x^2-25)
The second factor is a difference of squares so we can factored this more:
(x+3)(3x-5)(3x+5)
--------You could have also done factored by grouping here:
9x^3+27x^2-25x-75
(9x^3+27x^2)+(-25x-75)
9x^2(x+3)+-25(x+3)
(x+3)(9x^2-25)
(x+3)(3x-5)(3x+5)
Answer:
Step-by-step explanation:
9n^3 + 27n^2 – 25n – 75=9n²(n+3)-25(n+3)
= (n+3)(9n²- 25)
but : 9n²- 25 = (3n)² - 5²
by identity : a²-b² =(a-b)(a+b)
now : a =3n and b = 5 you have : 9n²- 25 = (3n)² - 5² = (3n-5)(3n+5)
Factor the polynomial :
9n^3 + 27n^2 – 25n – 75=(n+3)(3n-5)(3n+5)
on a cm grid, point P has coordinates (3,-1) and point Q has coordinates (-5,6) calculate the shortest distance between P and Q Give your answer to 1 decimal place
Answer:
PD = 10.6
Step-by-step explanation:
Point P has coordinates (3,-1) and point Q has coordinates (-5,6)
(3 - (-5) ) = 8
-1 - 6 = -7
PD = √8^2 + (-7)^2
PD = √(64 + 49)
PD = √113
PD = 10.6
Find the derivative of f(x) = 12x2 + 8x at x = 9.
256
-243
288
224
I answer questions for you but no one ever answers my questions. You're all are so ungrateful. I've been trying to find the answer for several hours and nothing. Yes I did try to teach myself but I just cant understand it.
Answer:
It's 224.
Step-by-step explanation:
We use the power rule for a derivative.
If f(x) = ax^n then the derivative f'(x) = anx^(n-1).
So the derivative of 12x^2 + 8x
= 2*12 x^(2-1) + 8x^(1-1)
= 24x + 8x^0
= 24x + 8.
When x = 9 the derivative = 24(9) + 8
= 224.
The value of first order derivative with x=9 is 224. Therefore, option D is the correct answer.
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
The given function is f(x)=12x²+8x at x=9.
Here, first order derivative is
f'(x)=24x+8
= 24×9+8
= 224
Therefore, option D is the correct answer.
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Write an equation that fits this:
The new car decreased in value at a rate of 7% each year. the initial value of the car was was $8227
[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &8227\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=\textit{elapsed time}\ \end{cases} \\\\\\ A=8227(1-0.07)^t\implies A=8227(0.93)^t[/tex]
Final answer:
An exponential decay model represents the car's value decreasing each year by 7%, with the equation V = 8227 x (1 - 0.07)^t, where V is the car's value and t is the time in years.
Explanation:
The student is dealing with a depreciation problem in which a car decreases in value by a fixed percentage each year. To express this situation mathematically, we can use an exponential decay model. With an initial value of $8227 and an annual decrease rate of 7%, the equation to represent the car's value V at any time t in years can be written as:
V = 8227 times (1 - 0.07)^t
This equation models the car's value as it depreciates 7% per year from its initial value. When t is 0 (at the time of purchase), V will be $8227, indicating the initial value.
Find the constant difference for each table of values and use it to describe the data(linear, quadratic,or exponential
Answer:
6. quadratic
7. linear
Step-by-step explanation:
6. First differences are ...
5 -2 = 36 -5 = 15 -6 = -12 -5 = -3Second differences are ...
1 -3 = -2-1 -1 = -2-3 -(-1) = -2These are constant at -2, so the data are quadratic. The data can be described by y = 6-(x-3)^2.
__
7. The x-values are evenly spaced (though decreasing). For our purpose, we can still look at the first differences of the table values in the order given. First differences are ...
8 -4 = 412 -8 = 416 -12 = 420 -16 = 4These are constant at +4, so the data are linear. The data can be described by y = -4x +12.
Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50a+3.75b=2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?]
Answer:
168
Step-by-step explanation:
The first equation given as [tex]10.50a+3.75b=2071.50[/tex]
Where a is the number of adults and b is the number of students
Since, the number of students are given as 82, we can plug 82 into b and then do algebra and solve for a (shown below):
[tex]10.50a+3.75b=2071.50\\10.50a+3.75(82)=2071.50\\10.50a+307.5=2071.50\\10.50a=2071.50-307.5\\10.50a=1764\\a=\frac{1764}{10.50}\\a=168[/tex]
Thus, 168 adult tickets were sold
Solve the equation. 2(4 - 2x) - 3 = 5(2x + 3)
A. 3/5
B. 2/3
C. 3/2
D. 7/2
Answer:
x= -5/7
Step-by-step explanation:
The equation involves only one variable x.
so, we have to isolate the variable to get the solution of the equation
Given
[tex]2(4 - 2x) - 3 = 5(2x + 3)\\8-4x -3 = 10x+15\\5-4x = 10x+15\\-4x = 10x +15 -5\\-4x-10x=10\\-14x = 10\\x = \frac{10}{-14}\\ x = -\frac{x=5}{7}[/tex]
Hence the value of x or solution is
x= -5/7
HELP PLZZ will give brainliest <3
Given the measures a = 10, b = 40, and
A = 30°, how many triangles can possibly be formed?
Given the measures b = 10, c = 8.9, and
B = 63°, how many triangles can possibly be formed?
Answer:
0
1
Step-by-step explanation:
First question:
You are given a side, a, and its opposite angle, A. You are also given side b. Use that in the law of sines and solve for the other angle, B.
[tex] \dfrac{a}{\sin A} = \dfrac{b}{\sin B} [/tex]
[tex] \dfrac{10}{\sin 30^\circ} = \dfrac{40}{\sin B} [/tex]
[tex] \dfrac{1}{0.5} = \dfrac{4}{\sin B} [/tex]
[tex] \sin B = 2 [/tex]
The sine function can never equal 2, so there is no triangle in this case.
Answer: no triangle
Second question:
You are given a side, b, and its opposite angle, B. You are also given side c. Use that in the law of sines and solve for the other angle, C.
[tex] \dfrac{b}{\sin B} = \dfrac{c}{\sin C} [/tex]
[tex] \dfrac{10}{\sin 63^\circ} = \dfrac{}{\sin C} [/tex]
[tex] \sin C = \dfrac{8.9\sin 63^\circ}{10} [/tex]
[tex] C = \sin^{-1} \dfrac{8.9\sin 63^\circ}{10} [/tex]
[tex] C \approx 52.5^\circ [/tex]
One triangle exists for sure. Now we see if there is a second one.
Now we look at the supplement of angle C.
m<C = 52.5°
supplement of angle C: m<C' = 180° - 52.5° = 127.5°
We add the measures of angles B and the supplement of angle C:
m<B + m<C' = 63° + 127.5° = 190.5°
Since the sum of the measures of these two angles is already more than 180°, the supplement of angle C cannot be an angle of the triangle.
Answer: one triangle
In the first case with measures a=10, b=40, A=30°, no triangle can be formed as a is smaller than b sin(A). In the second case with measures b=10, c=8.9, B=63°, one triangle can be formed because b is greater than c.
Explanation:In the context of the Ambiguous Case of the Law of Sines, we can find the number of triangles formed given the measures. For the first case, a = 10, b = 40, and A = 30°, no triangle can be formed because a is less than b sin(A), which means the given side (a) is too short to reach the other side (b).
For the second case, b = 10, c = 8.9, and B = 63°, one triangle can be formed. Here, b is greater than c and therefore capable of forming one valid triangle as per the Ambiguous Case of the Law of Sines.
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a train has 1 first class carriage and 6 standard carriages.
the first class carriage has 64 seats, 3/8 are being used.
each standard carriage has 78 seats, 7/13 are being used.
Are more than half the seats on the train being used?
Answer:
Yes
Step-by-step explanation:
(3/8)·64 = 24 seats in the first class carriage are being used.
(7/13)·(78)·3 = 126 seats in the standard carriages are being used, for a total of ...
24 + 126 = 150 . . . occupied seats
The number of available seats is ...
64 +3·78 = 298
so half the seats on the train will be 298/2 = 149 seats.
150 > 149, so more than half the seats on the train are being used.
Drag each symbol and number to the correct location on the inequality. Not all symbols and numbers will be used. Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the number of years, x, for which the account will have less than or equal to $7,020. Determine the solution set to the inequality that represents this situation.
The inequality that represents Sam's situation is: x <= 18.67
To determine the inequality that represents Sam's situation, we can use the following formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the final amount
P is the principal amount
r is the interest rate
n is the number of compounding periods per year
t is the number of years
We know that Sam initially invested $4,500 (P = 4500) and that the interest rate is 3% (r = 0.03). We also know that Sam wants to determine the number of years, x (t = x), for which the account will have less than or equal to $7,020 (A = 7020).
Substituting these values into the formula, we get the following inequality:
7020 <= 4500(1 + 0.03/1)^(1x)
Solving for x, we get:
x <= log(7020/4500) / (0.03/1)
x <= 18.67
Therefore, the inequality that represents Sam's situation is:
x <= 18.67
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NEED HELP WITH A MATH QUESTION
Answer:
56.3 cm
Step-by-step explanation:
(sinA)/(27) = (sinC)/c
(sin28°)/(27) = (sin102°)/c
For this case we have that by definition, the sum of the internal angles of a triangle is 180 degrees.
Then we look for the measure of the third angle:
[tex]102 + 28 + x = 180\\x = 180-102-28\\x = 50[/tex]
According to the Law of sines:
[tex]\frac {sin (50)} {a} = \frac {Sin (28)} {27}\\a = \frac {27 * sin (50)} {sin (28)}\\a = \frac {0.76604444 * 27} {0.46947156}\\a = 44.06[/tex]
Answer:
[tex]a = 44.1[/tex]
Simplify: squareroot 64r^8 8r2 8r4 32r2 32r4
Answer:
8r^4
Step-by-step explanation:
√(64r^8) = √((8r^4)^2) = 8r^4
_____
You can make use of either or both of these rules of exponents:
(a^b)^c = a^(b·c) . . . . . used above
[tex]\sqrt[n]{a}=a^{\frac{1}{n}}[/tex]
Using the second rule, you can write the expression as ...
[tex]\sqrt{64r^8}=\sqrt{64}\cdot r^{8\cdot\frac{1}{2}}=8r^4[/tex]
Answer:
B
Step-by-step explanation:
edg21
#10 Please help me :)
Answer:
The third choice is the one you want.
Step-by-step explanation:
The formula for an arithmetic sequence is as follows:
[tex]a_{n}=a_{1}+d(n-1)[/tex]
Our first number is 8, so a1 = 8. If the second term is 5, then d = -3. Filling in our formula gives us this:
[tex]a_{n}=8-3(n-1)[/tex]
Now we need domain. Our choices are n ≥ 1 and n ≥ 0 so let's try both. Replace n in the formula with each one, one at a time, and see what the result is.
If n ≥ 0:
[tex]a_{0}=8-3(0-1)[/tex] so [tex]a_{0}=8-(-3)[/tex] which gives you that the first term, defined by [tex]a_{0}[/tex] is 11. That's not correct. Let's check n ≥ 1[tex]a_{1}=8-3(1-1)[/tex]
and [tex]a_{1}=8-0[/tex] which is 8, the first term.
A company increases their rates from $98 a month to $101.92 a month. What is the percent of increase??
Answer:
Step-by-step explanation:
98*x = 101.92
x = 101.92/98 = 1.04
The % increase is 1.04%
Final answer:
The percent increase of the company's rates from $98 to $101.92 is 4%. It is calculated by dividing the increase in rates by the original rate and then multiplying by 100.
Explanation:
To calculate the percent increase for a company's rate change from $98 a month to $101.92 a month, we first find the difference in rates. The increase is $101.92 - $98 = $3.92. To find the percentage, we divide the increase by the original amount and multiply by 100. Therefore, the percent increase is ($3.92/$98) imes 100.
Calculating this gives us a percent increase of approximately 4%. So, the company's rates have increased by 4 percent. The percentage change, or growth rate, indicates how significantly the rates have increased in comparison to the starting rate.
Need help with math question
Answer:
(-7,4)
Step-by-step explanation:
goal: (y-k)^2=4p(x-h)
y^2-8y=4x+12 Rearranged and added 4x and 12 on both sides
y^2-8y+(-8/2)^2=4x+12+(-8/2)^2 complete square time (add same thing on both sides)
y^2-8y+(-4)^2=4x+12+(-4)^2 (simplify inside the squares)
(y-4)^2=4x+12+16 (now write the left hand side as a square)
(y-4)^2=4x+28
(y-4)^2=4(x+7) factored...
vertex is (-7,4)
Answer:
(-7,4)
Step-by-step explanation:
Solve for x.
5(2x - 1) = 6
x = 1/10
x = 11/10
x = 1/2
The value of x is 11/10.
To solve for x in the equation 5(2x - 1) = 6, we need to follow these steps:
Distribute the 5 into the parenthesis:
5 × 2x - 5 × 1
= 10x - 5
Set up the equation:
10x - 5 = 6
Add 5 to both sides of the equation to get
10x = 11
To solve for x, which gives us
x = 11/10
What is the value of x in the figure below? In this diagram, ABD~CAD
Answer:
x = 25/4
Step-by-step explanation:
Because of the known similarity of the triangles, we know that
10 x
----- = ----
16 10
Cross-multiplying, we get 16x = 100, and thus x = 100/16 = 50/8 = 25/4
x = 25/4
For the given triangle the value of x is 25/4.
Hence the correct option is E.
The Pythagorean theorem states that,
For a right-angle triangle,
(Hypotenuse)²= (Perpendicular)² + (Base)²
Given that,
In ΔBAC
CB = 16
DB = x
AB = 10
Then CD = 16-x
Apply the Pythagorean theorem in ΔBAC,
Hypotenuse = CB
Perpendicular = AC
Base = AB
(Hypotenuse)²= (Perpendicular)² + (Base)²
(CB)²= (AC)² + (AB)²
(16)²= (AC)² + (10)²
(AC)² = 256 - 100
(AC)² = 156 ......(i)
Apply the Pythagorean theorem in ΔADB,
Hypotenuse = AB
Perpendicular = AD
Base = DB
Therefore,
(AB)²= (AD)² + (DB)²
(10)²= (AD)² + x²
(AD)²= 100 - x² ......(ii)
Again apply the Pythagorean theorem in ΔADC,
Hypotenuse = AC
Perpendicular = AD
Base = CD
Therefore,
(AC)²= (AD)² + (CD)²
(AC)²= (100 - x²) + (16-x)² [ from (ii) ]
(AC)²= 100 - x² + 256 + x² - 32x [Since (a-b)² = a² + b² -2ab ]
(AC)²= 356 - 32x ....(iii)
Equating the equation (i) and (iii)
356 - 32x = 156
32x = 200
x = 200/32
x = 25/4
Hence, the value of x is 25/4.
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A robot's height is 1 meter 20 centimeters. how tall is the robot in millimeters?
Answer: The height of the robot is 200 millimeters
Step-by-step explanation:
Answer:
It is 1,200
Step-by-step explanation:
A museum is building a scale model of Sue, the largest Tyrannosaurus rex skeleton ever found. Sue was 13 feet tall and 40 feet long, and her skull had a length of 5 feet. If the length of the museum's scale model skull is 3 feet, 1.5 inches, what is the difference between the scale model's length and its height?
A) 8 feet, 1.5 inches
B) 16 feet, 10.5 inches
C) 22 feet, 6.5 inches
D) 27 feet, 4 inches
Answer:
B) 16 ft, 10.5 in
Step-by-step explanation:
There are a few different ways you can work this. Since we want to know the difference between length and heigh of the model and we are given skull length of the model, it makes a certain amount of sense to find the corresponding measurements of the actual skeleton.
The actual skeleton's length was 40 ft and its height was 13 ft, so the difference between these dimensions is ...
40 ft - 13 ft = 27 ft
The actual skull is 5 ft long, so the difference is ...
(27 ft)/(5 ft) = 5.4
times the length of the skull.
The same ratio will apply to the model, so the difference between the model height and model length is 5.4 times the length of the model skull:
desired difference = 5.4 × 3 ft 1.5 in = 16.2 ft + 8.1 in
= 16 ft 10.5 in
Use the drawing tool(s) to form the correct answer on the provided number line.
Eric wants to make sure he keeps an average speed of 70 miles/hour while testing his car’s engine. He allows the car’s speed to vary a certain number of miles/hour which can be modeled by the inequality |x − 70| ≤ 4. Plot the range of speeds Eric would not drive at under the given conditions.
Answer:
see below
Step-by-step explanation:
Eric will drive between 70 -4 = 66 mph and 70+4 = 74 mph. He will not drive less than 66 or more than 74 mph.
Answer:
Step-by-step explanation:
In general, solutions to absolute value inequalities, as in this case, take two forms:
If | x | <a, then x<a or x> -a.
If | x |> a, then x> a or x <-a.
In this case, you have |x − 70| ≤ 4. So, you have two cases:
x − 70 ≤ 4 and x − 70 ≥ -4
Solving both equations:
x − 70 ≤ 4
x ≤ 4 + 70
x≤ 74
and
x - 70 ≥ -4
x ≥ -4+70
x ≥ 66
It is convenient to graph both solutions, as shown in the attached image .
The intersection between both conditions is the solution to the inequality (that is, in the image it is shown as the interval painted by both colors). In this case, the solution is 66≤x≤74
This indicates that Eric can drive within this speed range.
The range of speeds Eric would not drive at under the given conditions is x≤66 and x≥74, as shown in the other image.
The quadratic model f(x) = –5x2 + 200 represents the approximate height, in meters, of a ball x seconds after being dropped. The ball is 50 meters from the ground after about how many seconds? 2.45 3.16 5.48 7.07
Answer:
t = 5.48
Step-by-step explanation:
f(x) = -5x² + 200
given f(t) = 50 when x = time(t)
Hence,
50 = -5t² + 200
5t² = 200 - 50
5t² = 150
t² = 30
t = √30 = 5.48
The number of seconds are 5.48, the correct option is C.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given that;
f(x) = –5x2 + 200
Now,
To find the time when the ball is 50 meters from the ground, we need to solve the equation:
f(x) = 50
Substituting f(x) with -5x^2 + 200 and simplifying, we get:
-5x^2 + 200 = 50
-5x^2 = -150
x^2 = 30
x = ±√30
Since x represents time, we only consider the positive value of x. Therefore,
x ≈ 5.48
Therefore, by the quadratic equations the answer will be 5.48
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Need help with this math question
ANSWER
The vertex of this parabola is (-7,4)
EXPLANATION
The given parabola has equation:
[tex] {y}^{2} - 4x - 8y - 12 = 0[/tex]
[tex] {y}^{2} - 8y = 4x +12[/tex]
Complete the square for the quadratic equation in y.
[tex]{y}^{2} - 8y + {( - 4)}^{2} = 4x + 12 + {( - 4)}^{2} [/tex]
[tex]{y}^{2} - 8y + {( - 4)}^{2} = 4x + 12 + 16[/tex]
[tex]{( y- 4)}^{2} = 4x + 28[/tex]
[tex]{( y- 4)}^{2} = 4(x +7)[/tex]
The vertex of this parabola is (-7,4)
Answer:
(-7, 4)
Step-by-step explanation:
We are given the following equation for which we have to complete the square in order to find the vertex of this parabola:
[tex] y ^ 2 - 4 x - 8 y - 1 2 = 0 [/tex]
[tex]y^2-(\frac{8}{2} )^2-4x-12=(\frac{8}{2} )^2\\[/tex]
[tex] y ^ 2 - 1 6 - 4 x - 1 2 = 1 6 [/tex]
[tex] ( y - 4 ) ^ 2 - 4 x - 1 2-16=0[/tex]
[tex](y-4)^2=4x+28[/tex]
[tex](y-4)^2=4(x+7)[/tex]
[tex]x+7=0, y-4=0[/tex]
x = -7, y = 4
Therefore, the vertex of this parabola is (-7, 4).
Myron put $5000 in a 2-year CD playing 3% interest, compounded monthly. After 2 years, he withrew all his money. What was the amount of the withdrawal?
Answer:
$5308.79
Step-by-step explanation:
The future value can be computed from ...
FV = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual interest rate, n is the number of times per year it is compounded, and t is the number of years.
Filling in the given numbers, we have ...
FV = $5000(1 +.03/12)^(12·2) ≈ $5308.79
Myron's withdrawal will be in the amount of $5308.79.
TIMING TEST!!!!!!!!!!!!!!!!!!
The graph of f(x) = |x| is reflected across the x-axis and translated to the right 6 units. Which statement about the domain and range of each function is correct?
a)Both the domain and range of the transformed function are the same as those of the parent function.
b) Neither the domain nor the range of the transformed function are the same as those of the parent function.
c)The range but not the domain of the transformed function is the same as that of the parent function.
d)The domain but not the range of the transformed function is the same as that of the parent function
Answer:
Domain is 2 and range is 4
Step-by-step explanation:
16.
The circumference of a circle is 55/7.
What is the diameter of the circle?
(Hint: Circumference = xD)
*Use 22/7 for pie
Answer:
D=5/2
Step-by-step explanation:
Circumference of a circle = πD where D is the diameter of the circle.
In the question Circumference is =55/7 and π provided =22/7
55/7 = (22/7)D
We multiply both sides with the reciprocal f 22/7
D = (55/7) (7/22)
D = 5/2
9. Find the area of each figure to the nearest tenth 140,110,180,50 8,8,10
Answer:
18550 cm²88 ft²Step-by-step explanation:
1. There are several ways the area can be divided up so that formulas for common figures can be used to find the areas of the pieces. In the attached figure, we have identified an overall rectangle ABXE and a trapezoid BXDC that is subtracted from it.
The area of the rectangle is the product of length and width:
area ABXE = (180 cm)(140 cm) = 25,200 cm²
The area of a trapezoid is the product of its height (DX = 70 cm) and the average of its base lengths ((BX +DC)/2 = 95 cm).
area BXDC = (70 cm)(95 cm) = 6650 cm²
Then the area of figure ABCDE is the difference of these areas:
area ABCDE = area ABXE - area BXDC = (25,200 - 6,650) cm²
area ABCDE = 18,550 cm²
__
2. In order to find the area of the figure, we need to know the length DE. That length is one leg of right triangle DEA, so we can use the Pythagorean theorem. That theorem tells us ...
DE² + EA² = AD²
DE² + (8 ft)² = (10 ft)² . . . . . substitute the given values
DE² = 36 ft² . . . . . . . . . . . . .subtract 64 ft²
DE = 6 ft . . . . . . . . . . . . . . . take the square root
Now, we can choose to add the area of triangle DEA to that of square ABCE, or we can treat the whole figure as a trapezoid with bases AB=8 ft and DC=14 ft. In the latter case, the average base length is ...
(8 ft + 14 ft)/2 = 11 ft
and the area is the product of this and the 8 ft height:
area ABCD = (11 ft)(8 ft) = 88 ft²
The motion of a weight that hangs from a spring is represented by the equation h=8sin(2pi/3t). It models the weight’s height above or below the rest position as a function of time. Approximately when will the object be 3 inches above the rest position?
Answer:
0.18 seconds
Step-by-step explanation:
Using the given function, it is found that the object will be 3 inches above the rest position after 0.18 seconds.
What is the function?The function for an object's height after t seconds is given by:
[tex]h(t) = 8\sin{\left(\frac{2\pi}{3}t\right)}[/tex]
The height is of 3 inches when h(t) = 3, hence:
[tex]h(t) = 8\sin{\left(\frac{2\pi}{3}t\right)}[/tex]
[tex]3 = 8\sin{\left(\frac{2\pi}{3}t\right)}[/tex]
[tex]\sin{\left(\frac{2\pi}{3}t\right)} = \frac{3}{8}[/tex]
[tex]\sin^{-1}{\sin{\left(\frac{2\pi}{3}t\right)}} = \sin^{-1}{\left(\frac{3}{8}\right)}[/tex]
[tex]\frac{2\pi}{3}t = 0.3844[/tex]
[tex]t = \frac{3 \times 0.3844}{2\pi}[/tex]
[tex]t = 0.18[/tex]
The object will be 3 inches above the rest position after 0.18 seconds.
More can be learned about functions at https://brainly.com/question/25537936
Colton bought a CD for $760 that earns a 3.8% APR and is compounded monthly. The CD matures in 3 years. How much will this CD be worth at maturity
Answer:
$851.62
Step-by-step explanation:
The value multiplier wll be ...
(1 +r/n)^(nt)
where r is the annual interest rate (3.8%), n is the number of compoundings per year (12), and t is the number of years (3). Filling in these numbers, we see the ending value will be ...
A = $760(1 +.038/12)^(12·3) = $760(1.0031667^36) = $851.62
Answer:
$851.62
Step-by-step explanation:
In a geometric sequence, the common ratio is -5. The sum of the first 3 terms is 147. What is the value of the first term of the sequence?
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \begin{cases} r=-5\\ n=3\\ S_3=147 \end{cases} \implies 147=a_1\left( \cfrac{1-(-5)^3}{1-(-5)} \right)\implies 147=a_1\left( \cfrac{1-(-125)}{1+5} \right) \\\\\\ 147=a_1\cdot \cfrac{126}{6}\implies 147=21a_1\implies \cfrac{147}{21}=a_1\implies 7=a_1[/tex]
The first term of the geometric sequence with a common ratio of -5 and the sum of the first 3 terms being 147 is 7.
The first term of a geometric sequence where the common ratio is -5 and the sum of the first 3 terms is 147. A geometric sequence is denoted by a, ax, ax2, ax3, ..., where 'a' is the first term and 'x' is the common ratio.
Given the common ratio (x) is -5, we can express the first three terms of this geometric sequence as:
First term: a
Second term: a(-5) = -5a
Third term: a(-5)2 = 25a
The sum of these three terms equals 147:
a - 5a + 25a = 147
Combining like terms we get:
21a = 147
Now, dividing both sides by 21 to isolate 'a', we find:
a = 7
Therefore, the value of the first term of the sequence is 7.
At a competition with 6 runners, 6 medals are awarded for first place through
sixth place. Each medal is different. How many ways are there to award the
medals?
Decide if the situation involves a permutation or a combination, and then find
the number of ways to award the medals.
O
A. Permutation; number of ways = 720
O
B. Combination; number of ways = 720
O
c. Combination; number of ways = 1
O
D. Permutation; number of ways = 1
Answer:
A. Permutation; number of ways = 720
Step-by-step explanation:
For the first medal, we have 6 runners that can earn it.
For the second medal, we have 5 runners because there's one who won the first one.
For the third, we have 4 runners.
And so on up to the 6th medal where we have just one runner left.
As this happens all at the same time, we have to multiply them.
Ways to award the medals = 6*5*4*3*2*1 = 6! = 720
Remember that a permutation is a combination where the order matters. So, in this case, is a permutation because each medal is different.
Answer:
a) Permutation; number of ways = 720
Step-by-step explanation:
Alicia drove 265 miles in 5 hours. What is the average rate that she traveled?
a. 49 miles per hour
b. 51 miles per hour
c. 53 miles per hour
d. 55 miles per hour
Answer:
53 miles per hour
Step-by-step explanation:
This is the correct answer
I hope this helps you!