Answer:
The answer on edge is C: 0.39 seconds.
Step-by-step explanation:
At t = 0.39 seconds the object is 4 inches below the rest position option third is correct.
What is sin function?It is defined as the function which is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a]where is a amplitude of the function.
We have:
The motion of a weight that hangs from a spring is represented by the equation:
h = -5sin[(3π/4)t]
Plug h = -4
-4 = -5sin[(3π/4)t]
Or
-4 = -5sin[135t]
135t = 53.13
t = 0.39 seconds
Thus, at t = 0.39 seconds the object is 4 inches below the rest position option third is correct.
Learn more about the sin function here:
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Which statements describe the domain and range
of g(x)? Select two options.
a. The function g(x) is defined for all real numbers x.
b. The maximum value of the range is 4.
c. The maximum value of the domain is 3.
The range of g(x) is {yl -1
d. The domain of g(x) is {x|-4
Answer:
A closed circle on the graph indicates that the point is included in domain and range. An open circle indicates that the point is not included in the domain and range.
Now based on this, we will evaluate the given options:
Option A. The function g(x) is defined for all real numbers x.
The lines on the graph contain a limited values. Hence its obvious that the domain and range is not the set of all Real numbers. Hence this option is Wrong.
Option B. The maximum value of the range is 4.
From the graph we can see that the maximum/highest value along y-axis is 4. Since there is a closed circle at (-4, 4), this value is included in the range. Hence this option is True.
Option C. The maximum value of the domain is 3
There is an open circle at the point when x is 3. Hence this point is not included in the Domain. Value of domain is numbers less than 3. Hence this option is Wrong.
Next two options are incomplete. Here are the complete options and listed correctly.
Option D. The range of g(x) is {yl -1 < y ≤ 4}
This is correct because there is an open circle at point (3, -1). Hence -1 would not be included in the range. The range will be set of all values from -1 to 4, including 4 as there is a closed circle at (-4, 4)
Option E. The domain of g(x) is {x| x ≤ -4 ≤ -1 or 0 ≤ x <3}
Since there are closed circles at points where x is -4, -1 and 0, these points would be included in the Domain. 3 wont be included in the Domain as there is an open circle.
Answer:
B and D are correct.
Solve for x: 2 over 5 (x − 2) = 4x. (1 point) 2 over 9 9 negative 2 over 9 negative 9 over 2
ANSWER
[tex]x = - \frac{2}{9} [/tex]
EXPLANATION
The given equation is :
[tex] \frac{2}{5}(x - 2) = 4x[/tex]
We multiply both sides by [tex] \frac{5}{2} [/tex]
[tex] \frac{5}{2} \cdot\frac{2}{5}(x - 2) = 4x \times \frac{5}{2} [/tex]
We simplify to obtain:
[tex]x - 2 = 10x[/tex]
Group similar terms to obtain:
[tex] - 2 = 10x - x[/tex]
Simplify the right hand side.
[tex] - 2 = 9x[/tex]
Divide both sides by 9.
[tex] \frac{ - 2}{9} = \frac{9x}{9} [/tex]
[tex] - \frac{2}{9} = x[/tex]
Or
[tex]x = - \frac{2}{9} [/tex]
The second choice is correct
The solution for [tex]x[/tex] is [tex]x = -\frac{2}{9}[/tex].
To solve the equation [tex]\frac{2}{5} (x - 2) = 4x[/tex], we need to perform the following steps:
Distribute the Fraction:
We start by distributing [tex]\frac{2}{5}[/tex] to both terms inside the parentheses:
[tex]\frac{2}{5}x - \frac{2}{5} \cdot 2 = 4x[/tex]
This simplifies to:
[tex]\frac{2}{5}x - \frac{4}{5} = 4x[/tex]
Isolate the Variable:
Next, we want to get all terms involving [tex]x[/tex] on one side. We can do this by subtracting [tex]\frac{2}{5}x[/tex] from both sides:
[tex]-\frac{4}{5} = 4x - \frac{2}{5}x[/tex]
Now, we can combine the [tex]x[/tex] terms on the right:
[tex]4x - \frac{2}{5}x = \left(4 - \frac{2}{5}\right)x = \left(\frac{20}{5} - \frac{2}{5}\right)x = \frac{18}{5}x[/tex]
Thus, we have:
[tex]-\frac{4}{5} = \frac{18}{5}x[/tex]
Solve for x:
Now, we want to solve for [tex]x[/tex] by multiplying both sides of the equation by the reciprocal of [tex]\frac{18}{5}[/tex], which is [tex]\frac{5}{18}[/tex]:
[tex]x = -\frac{4}{5} \cdot \frac{5}{18} = -\frac{4}{18} = -\frac{2}{9}[/tex]
Given the multiple-choice options of [tex]\frac{2}{9}[/tex], [tex]9[/tex], [tex]-\frac{2}{9}[/tex], and [tex]-\frac{9}{2}[/tex], the correct answer is negative 2 over 9.
How do I solve substitution with picture ??
Answer:
no solution
Step-by-step explanation:
If you divide the first equation by 2 you get:
2x+2y=4 (first equation after dividing both sides by 2)
2x+2y=-4 (second equation)
This is setup for elimination.
Subtract the equations:
2x+2y=4
2x+2y=-4
--------------Subtracting!
0+0=8
0=8
0=8 is a false equation which implies the system has no solution.
Answer:
a) No Solutions
Step-by-step explanation:
It might be helpful to first get the equations in terms of y = mx + b.
The first equation (4x + 4y = -8) can be rewritten like this:
4x + 4y = -8 (original equation)
4y = 4x - 8 (subtract 4x from both sides)
y = x - 4 (divide everything by 4 to get y on its own)
and now you have an equation in terms of y = mx = b, where m is 1 and b is -4.
The second equation can be written like this:
2x + 2y = -4 (original equation)
2y = 2x - 4 (subtract 2x from both sides)
y = x - 2 (divide everything by 2 to get y on its own)
and once again we have an equation with m being 1 and b being -2.
So hopefully you should see that the equations will never touch because they have the same slope. Because the equations never touch, they have no solutions. Have a look at the graph.
Which of the following formulas would find the lateral area of a right cylinder
where h is the height and ris the radius?
O
A. LA = 2trh
O
B. LA = 27012
O
O
c. LA = ac rh
D. LA = 2017
SUBME
Answer:
2πrh unit^2.
Step-by-step explanation:
The lateral area is the circumference of the base * the height = 2πrh.
The lateral area of a right cylinder with height equal to h and r as the radius is 2πrh. Therefore, option C is the correct answer.
What is lateral surface area?All of the sides of the object are the lateral surface of an object, except its base and top (when they exist). The lateral surface area is the lateral surface zone. This is to be distinguished from the overall surface area, which, along with the base and top areas, is the lateral surface area.
The surface area that a cylinder's curved surface alone covers is known as the curved surface area (CSA) or lateral surface area. The curved surface area of a cylinder is computed using the formula 2πrh, where height of the cylinder is h and the radius of the base is r.
Therefore, option C is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Which of the following formulas would find the lateral area of a right cylinder with height equal to h and r as the radius?
A. LA = 2πr²
B. LA = 2πr
C. LA = 2πrh
D. LA = 2πr² + 2πrh
If a polynomial function f(x) has roots 0, 4, and 3+ sqrt11 what must also be a root of f(x)?
Answer:
[tex]3-\sqrt{11}[/tex]
Step-by-step explanation:
If you want rational coefficients then you would want the conjugate of any irrational zero given.
The question is equivalent to what is the conjugate of [tex]3+\sqrt{11}[/tex].
The conjugate of [tex]3+\sqrt{11}[/tex] is [tex]3-\sqrt{11}[/tex].
In general, the conjugate of a+b is a-b
or the conjugate of a-b is a+b.
Or maybe you like this explanation more:
Let [tex]x=3+\sqrt{11}[/tex]
Subtract 3 on both sides:
[tex]x-3=\sqrt{11}[/tex]
Square both sides:
[tex](x-3)^2=11[/tex]
Subtract 11 on both sides:
[tex](x-3)^2-11=0[/tex]
Use difference of squares to factor. I apply [tex]u^2-v^2=(u-v)(u+v)[/tex].
[tex]([x-3]-\sqrt{11})([x-3]+\sqrt{11})=0[/tex]
So you have either
[tex][x-3]-\sqrt{11}=0[/tex] or [tex][x-3}+\sqrt{11}=0[/tex]
Solve both for x-3 and then x.
Add sqrt(11) on both sides for first equation and subtract sqrt(11) on both sides for second equation:
[tex]x-3=\sqrt{11}[/tex] or [tex]x-3=-\sqrt{11}[/tex]
Add 3 on both sides:
[tex]x=3+\sqrt{11}[/tex] or [tex]x=3-\sqrt{11}[/tex]
Answer:
the answer is C.
Step-by-step explanation:
The circumference of a circle is 16π inches. Show how you can use this information to calculate the same circle’s area.
Answer:
A = 64 pi inches ^2
Step-by-step explanation:
Circumference is equal to
C =2*pi*r where r is the radius
16 pi = 2 * pi *r
Divide each side by 2 pi
16pi/2pi = 2pir/2pi
8 = r
The radius is 8
To find the area, we use
A = pi r^2
=pi (8)^2
= 64 pi
The equations in the system below are parallel.
How many solutions does the system have?
no solution
one unique solution
two solutions
an infinite number of solutions
The two lines are parallel, which means they never touch, cross or meet.
Answer: No solution
Answer:
no solution
Step-by-step explanation:
The difference of two numbers is 7. If the sum of the smaller number and the square of the larger number is 125, what is the larger number?
Step-by-step explanation:
x - y = 7...eqn 1
x^2 + y = 125...eqn 2
making y the subject of the formula in eqn 1
=> y = x -7...eqn 3
subst for y from eqn 3 in eqn 2
=> x^2 + x-7 = 125
=> x^2 + x - 132 = 0
=> (x + 12) (x -11) =0
x = 11 or -12
when x = 11, y = 4
when x = -12, y = -19
Answer:
The largest numbers is either -12 or 11
Step-by-step explanation:
Let the numbers be a and b and a be the largest number.
The difference of two numbers is 7
a - b = 7 ------------------------- eqn 1
The sum of the smaller number and the square of the larger number is 125
a² + b = 125 ------------------------- eqn 2
eqn 1 + eqn 2
a² + a - 132 = 0
( a + 12 ) (a - 11) = 0
a = -12 or a = 11
So the largest numbers is either -12 or 11
A
B C
D E
F G
H
What is the midpoint of AH?
The question appears to be about finding the midpoint of segment AH, which involves dividing the segment into two equal parts, either by measurement or by averaging the coordinates of A and H if available.
Explanation:The question seems to be asking about identifying the midpoint of a line segment in a geometric construction. However, the provided text alludes to various geometric proofs and theorems, rather than directly providing information about finding midpoints.
To find the midpoint of segment AH, one would need to measure the length of AH and then divide it by 2 to find the center point. If the points A and H are on a coordinate plane, the midpoint can be found by calculating the average of the x-coordinates and the y-coordinates of the endpoints A and H. Without specific coordinates or measurements, a more detailed answer cannot be provided.
The midpoint of AH is (0, 4).
Let's assign coordinates to the points A and H to make it easier to calculate the midpoint. Suppose A is at (x1, y1) and H is at (x2, y2).
The formula for finding the midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is:
[tex]M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right)[/tex]
If we assume A is at (0, 0) and H is at (0, 8) (since H is directly 'below' A on a vertical line), the coordinates are as follows:
A = (0, 0)
H = (0, 8)
Now, applying the midpoint formula:
[tex]M = \left( \frac{0 + 0}{2}, \frac{0 + 8}{2} \right) = (0, 4)[/tex]
The number of lattes sold daily by two coffee shops is shown in the table.
Shop A Shop B
55 45
52 42
56 57
48 48
57 11
30 10
45 46
41 43
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
A: Mean for both coffee shops because the data distribution is symmetric
B: Median for both coffee shops because the data distribution is not symmetric
C:Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
B: Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric
Please help I literally could not find this answer ANY where else
Very important
Answer:
D.
Step-by-step explanation:
The data is symmetric for Shop A but not for Shop B ( note the values 10 and 11 for Shop B which are a lot lower than the other values).
Mean for Shop A and Median for Shop B.
Answer:
The correct option is B.
Step-by-step explanation:
The number of lattes sold daily by two coffee shops is shown in the table.
The data set for shop A is
55, 52, 56, 48, 57, 30, 45, 41
Arrange the data in ascending order.
30, 41, 45, 48, 52, 55, 56, 57
Mean of shop A is
[tex]Mean=\frac{\sum x}{n}=\frac{30+41+45+48+52+55+56+57}{8}=48[/tex]
[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{48+52}{2}=50[/tex]
The data set for shop B is
45, 42, 57, 48, 11, 10, 46, 43
Arrange the data in ascending order.
10, 11, 42, 43, 45, 46, 48, 57
Mean of shop A is
[tex]Mean=\frac{\sum x}{n}=\frac{10+11+42+43+45+46+48+57}{8}=37.75[/tex]
[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{43+45}{2}=44[/tex]
Both data distribution are not symmetric, so it is better to describe the centers of distribution in terms of median for both coffee shops. Therefore the correct option is B.
what is the slope of the line represented by the equation f(t) =2t-6
Answer:
The slope is 2.
Step-by-step explanation:
The given line has equation: [tex]f(t)=2t-6[/tex].
This is a linear equation in [tex]t[/tex].
The slope is the coefficient of the independent variable [tex]t[/tex].
The coefficient of [tex]t[/tex] in [tex]f(t)=2t-6[/tex] is 2.
Therefore the slope is 2.
Alternatively, [tex]f(t)=2t-6[/tex] is of the form [tex]f(t)=mt+c[/tex], where [tex]m=2[/tex] is the slope.
Answer:
Step-by-step explanation:
The slope is 2 and the y intercept is -6
What is the total volume of glass used to make the award?
Answer:
204 in^3
Step-by-step explanation:
The volume of the base square is V=lwh.
When we substitute our givens, it becomes V=6(4)(2). This equals 48 in^3.
The volume of the triangle is V=.5lwh.
When we substitute our givens, it becomes V=.5(6)(4)(15-2). This equals 156 in^3.
When we add 48 and 156, we get 204 in^3.
Hope this helps :)
which of the following describes a simple event?
Answer:
I believe the answer rqould be B since only 1 thing happened
Answer: Option B
Step-by-step explanation:
Simple event is an event where all the possible outcomes have the same probability.
Are the type of events that we can write as:
P = number of a given outcome/total posible outcomes.
Here we have 3 combined options (A, C and D) that, while in parts can be described in that way, not as whole events.
The correct option is B, where the probability of getting a given number in a dice is the number of times that the number repeats (1) divided the total number of options (6), P = 1/6 for all the numbers, so this is a simple event.
How is the graph of y = 5x2 − 4 different from the graph of y = 5x2?
Answer:first equation is 4 units shifted down from the second
Step-by-step explanation:
Answer:
The graph of y = 5x²-4 differs from the graph of y = 5x² by difference of 4 units
Step-by-step explanation:
In y = 5x²-4, when y is 0 x is not 0 and when x is 0 , y is not 0
but
In y = 5x² , when y is 0 , x is 0 and vise versa.
In y = 5x² the value of y will always increase as the value of x increase.
In the figure below, what is the value of angle Z?
Answer:
=2.83 the second option
Step-by-step explanation:
Using the trigonometric ratios we can find the sides of the triangle with the acute angles.
In the triangle provided we will use COSINE
Cos ∅=adjacent/hypotenuse
Let us substitute with the values in the question into the formula.
Tan 45 =2/x
x=2/Cos 45
=2.83 units
Answer: SECOND OPTION.
Step-by-step explanation:
You can use the following identity:
[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]
In this case:
[tex]\alpha=45\°\\adjacent=2\\hypotenuse=x[/tex]
Therefore, in order to calculate the value of "x", you need to substitute values into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] and solve for "x".
This is:
[tex]cos(45\°)=\frac{2}{x}\\\\xcos(45\°)=2\\\\x=\frac{2}{cos(45\°)}\\\\x=2\sqrt{2}[/tex]
[tex]x[/tex]≈[tex]2.83[/tex]
Use an inequality symbol (<,>,=,=/) to compare 5+(-4)____14+(-13)
Answer:
The answer is equal to. Each equation equals 1.
Which polynomial could have the following graph?
y = (x + 3)(x - 1)(x - 5)
y = (x - 3)(x + 1)(x + 5)
y = -(x + 3)(x - 1)(x - 5)
y = -(x - 3)(x + 1)(x + 5)
The graph shows the solutions:
x1 = -3 ⇒ x + 3 = 0
x2 = 1 ⇒ x - 1 = 0
x3 = 5 ⇒ x - 5 = 0
The polynomial follows: y = (x + 3)(x - 1)(x - 5)
.
Answer:
y= (x+3) (x-1) (x-5)
Step-by-step explanation:
The graph crosses the x axis at the points -3,1,5
These are also called the zeros
f(x) =k (x-a) (x-b) (x-c) .....
where a,b,c,... are the zeros of the function and k is a constant
f(x) = k * (x--3) (x-1) (x-5)
f(x) = k(x+3) (x-1) (x-5)
To help determine the value of k
Take another point at x = 0, we know the value is positive
f(0) = k(3) (-1) (-5)
f(0) = k(15)
That means k must be greater than 0 Looking at the graph, it should be around 1
f(x) = (x+3) (x-1) (x-5)
When two equal forces are inclined at an angle 2a their resultant is twice as great as
when they are inclined at an angle 2B. Show that cosa = 2 cosß.
Step-by-step answer:
Referring to the attached diagram, the resultant of two forces each with magnitude F and inclined to each other at 2a equals
Ra = 2Fcos(a) ..............................(1)
Similarly, the resultant of two forces each with magnitude F and inclined to each other at 2b equals
Rb = 2Fcos(b)..............................(2)
We are given that
Ra = 2Rb ....................................(3)
Substitute (1) & (2) in (3) gives
2Fcos(a) = 2(2Fcos(b))
Expand
2Fcos(a) = 4Fcos(b)
Simplify
cos(a) = 2 cos(b) QED
Note: Please note that you might have a faster response if you posted this question in the physics or the (new) Engineering section.
Have a nice day!
4 more than the quoitient of x squared and 3
Answer:
(x^2)/3 + 4
Step-by-step explanation:
4 more means add four and the quotient of x squared and 3 shows that x squared must be divided by three before added to 4
please mark brainliest :)
Mary, Kevin, and Ahmad served a total of 126
orders Monday at the school cafeteria. Kevin served 6
more orders than Mary. Ahmad served 4
times as many orders as Kevin. How many orders did they each serve?
Answer:
Mary: 16
Kevin: 22
Ahmed: 88
Step-by-step explanation:
This could be written as the following formula.
Mary + Kevin + Ahmad = 126
and we know that
Mary + 6 = Kevin
Kevin * 4 = Ahmed
so Ahmed = (Mary + 6) * 4
When filling this in you get
Mary + Mary + 6 + (Mary + 6) * 4 = 126
Mary + Mary + 6 + 4Mary + 24 = 126
6Mary + 30 = 126
6Mary = 96
Mary = 16
So Mary served 16 orders.
Using the earlier formulas you get
Kevin = Mary + 6 = 16 + 6 = 22
Ahmed = Kevin * 4 = 22 * 4 = 88.
Now we just need to double check it.
Mary + Kevin + Ahmad = 16 + 22 + 88 = 126. Which matches what it should be.
what is the radical expression that is equivalent.
Answer:
[tex] 27^{\frac{1}{5}} = \sqrt[5]{27} [/tex]
Step-by-step explanation:
Rule of exponents:
[tex] a^{\frac{1}{n}} = \sqrt[n]{a} [/tex]
Apply the rule to this case:
[tex] 27^{\frac{1}{5}} = \sqrt[5]{27} [/tex]
14% of 3540% of 35 equals what
Answer:
173.46Step-by-step explanation:
[tex]p\%=\dfrac{p}{100}\\\\14\%=\dfrac{14}{100}=0.14\\\\3540\%=\dfrac{3540}{100}=35.40=35.4\\\\14\%\ of\ 3540\%\ of\ 35\to(0.14)(35.4)(35)=173.46[/tex]
Ari exercises 1 5/8 hours per day. If he exercises five days a week, how many total hours does he exercise in a week?
Answer:
8 1/8 hours
Step-by-step explanation:
1 5/8 * 5 = 5 25/8
5 28/5 = 5 + 3 + 1/8
= 8 1/8 hours
I think the answer is 8 1/8
can someone help me plz
Answer:
B. & E.
Step-by-step explanation:
First, to find your slope, put your line into slope-intercept form.
[tex]y=mx+b\\[/tex]
[tex]3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4} x-\frac{7}{4}[/tex]
Your slope is [tex]\frac{3}{4}[/tex].
Now, you can find the y-intercept of your parallel line by plugging your given point and your slope into point-slope form.
[tex]y-y1=m(x-x1)\\y-(-2)=\frac{3}{4} (x-(-4))\\y+2=\frac{3}{4} (x+4)\\y+2=\frac{3}{4} x+3\\y=\frac{3}{4} x+1[/tex]
Your y-intercept is 1.
If you notice, answer choice E is equivalent to one of our steps in converting it to point-slope form. Therefore, E is one of your answers.
The equation of your parallel line is:
[tex]y=\frac{3}{4} x+1[/tex]
B is also a correct answer.
If you put B into slope-intercept form, you get the following:
[tex]3x-4y=-4\\-4y=-3x-4\\y=\frac{3}{4} x+1[/tex]
This, of course, is equivalent to the parallel line which we already found, so we know it is parallel.
What is the slope of the line with equation 6x+3y=12?
Answer:
The slope m = -2Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation in the standard form:
[tex]6x+3y=12[/tex]
Convert to the slope intercept form:
[tex]6x+3y=12[/tex] subtract 6x from both sides
[tex]3y=-6x+12[/tex] divide both sides by 3
[tex]y=-2x+4[/tex]
slope: m = -2
y-intercept: b = 4
use the quadratic formula to find the solutions to the equation x^2-3x+1=0
Answer:
[tex]x_{1}=\frac{+3+\sqrt{5} }{2}\\\\x_{2}=\frac{+3-\sqrt{5} }{2}[/tex]
Step-by-step explanation:
Using:
[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]
we will have two solutions.
x^2-3x+1=0
So, a=1 b=-3 c=1
[tex]x_{1}=\frac{+3+\sqrt{-3^{2}-4*1*1} }{2*1}\\\\x_{2}=\frac{+3-\sqrt{-3^{2}-4*1*1} }{2*1}[/tex]
We have two solutions:
[tex]x_{1}=\frac{+3+\sqrt{5} }{2}\\\\x_{2}=\frac{+3-\sqrt{5} }{2}[/tex]
The answer is in the picture below! :)
|
V
Find Sn for the given geometric series. Round answers to the nearest hundredth, if necessary.
A1= 0.28,a5 = 362.88, r = 6
Select one:
a. 435.4
b. 51.4
C. 311.08
d. 874.94
The sum of the geometric series is approximately 435.4, according to the formula for geometric series summation.
To find the sum (Sn) of a geometric series, you can use the formula:
[tex]\[ Sn = \frac{{a_1 \cdot (1 - r^n)}}{{1 - r}} \][/tex]
Where:
[tex]- \( a_1 \) is the first term\\- \( r \) is the common ratio\\- \( n \) is the number of terms[/tex]
Given:
[tex]\( a_1 = 0.28 \)\( a_5 = 362.88 \)\( r = 6 \)[/tex]
We need to find [tex]\( n \)[/tex]. Since [tex]\( a_5 \)[/tex] is the fifth term, we can use the formula for the nth term of a geometric series:
[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]
Substitute the values we have:
[tex]\[ 362.88 = 0.28 \cdot 6^{(5-1)} \]\[ 362.88 = 0.28 \cdot 6^4 \]\[ 362.88 = 0.28 \cdot 1296 \]\[ 362.88 = 363.648 \][/tex]
So, [tex]\( n = 5 \).[/tex]
Now, plug the values into the sum formula:
[tex]\[ S_5 = \frac{{0.28 \cdot (1 - 6^5)}}{{1 - 6}} \]\[ S_5 = \frac{{0.28 \cdot (1 - 7776)}}{{-5}} \]\[ S_5 = \frac{{0.28 \cdot (-7775)}}{{-5}} \]\[ S_5 = \frac{{-2177}}{{5}} \]\[ S_5 = -435.4 \][/tex]
Since the sum of a series cannot be negative, the correct answer is option:
a. 435.4
the perimeter of a 14 ft , 8 ft rectangle
The perimeter of a rectangle with sides of 14 ft and 8 ft is 44 ft.
Explanation:The perimeter of a rectangle is calculated by adding all its sides. For a rectangle with sides of 14 ft and 8 ft, the perimeter is found by adding twice the length and twice the width:
Perimeter = 2(length + width)
Perimeter = 2(14 + 8) = 2(22) = 44 ft
A student says that the measures of coterminal angles are never opposites of each other. Is the student correct?
Answer:
Wrong
Step-by-step explanation:
The student is wrong. Two angles are coterminal if and only if the difference between their measures is a multiple of 360°.
The difference between the angles 180° and –180° is 360°, and they are coterminal. Therefore the student is WRONG.
Answer:
The student is wrong. Two angles are coterminal if and only if the difference between their measures is a multiple of 360°.
The difference between the angles 180° and –180° is 360°, and they are coterminal. Therefore the student is WRONG.
Step-by-step explanation:
Let u = <-3, -5>, v = <-3, 1>. Find u + v. <-2, -8> <-8, -2> <0, -6> <-6, -4>
Answer:
<-6,-4>
Step-by-step explanation:
To find u+v, all you have to do is add the corresponding components of each.
That is for example on this problem, you would do
<-3,-5>+<-3,1>
=<-3+-3,-5+1>
=<-6,-4>.