Answer: (5, -1)
Step-by-step explanation:
format: f(x)
in f(5)=-1 x=5
also sometimes f(x) is called y so y= -1
put into ordered pair format
(5, -1)
AP calc please help me
a) over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.
b) the average temperature of the water in the system is 1527.
c) over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.
a) g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt
g'(-3) = -2
b) The absolute maximum value of g on the closed interval [-5, 5]=
10 + 2√7.
c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.
What is right Riemann sum formula?
The right Riemann sum formula uses the right-most value of each interval as the value of the function over that interval.
a) g(5) = 2(5) + [tex]\int\limits^5_0[/tex] ƒ(t) dt
= 10 + 2√7
g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt
g'(-3) = 2 + [tex]\int\limits^3_0[/tex]ƒ'(t) dt
= 2 - (4 + 0)
= -2
b) The absolute maximum value of g on the closed interval [-5, 5]=
10 + 2√7.
This is because the highest value of ƒ(t) dt on the interval= 4√7, which occurs at x = 2.
The highest value of g is thus given by 10 + 2√7.
c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.
This is because ƒ'(t) dt is undefined at these points, so the second derivative of g is also undefined.
a) To evaluate the S'(t) dt, we need to calculate the area under the curve of the temperature data given in the table. To do this, we use the trapezoidal rule. This gives us the following:
[tex]\int\limits^10_0[/tex] S'(t) dt = [(142 + 210 + 254 + 280 + 274 + 268)/2] × 8
= 17,088
This means that over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.
This can be interpreted in the context of the problem as the average rate at which the temperature of the water in the solar steam power system is changing over the given time interval.
b) To approximate the average temperature of the water in the system using a right Riemann approximation, we need to calculate the area under the curve of the temperature data given in the table. We can do this using the right Riemann sum formula, which gives us the following:
Right Riemann Approximation = [(210 + 254 + 280 + 274)/4] × 6 = 1527
In this case, the right-most value of each interval is lower than the true average over that interval, so the approximation will be lower than the true average.
c) To determine the total change in the temperature of the system for the interval 10≤t≤20, we need to calculate the area under the curve of the equation S'(t)=-√2xe (√x²-100)/x.
This can be done using the definite integral of the equation, which gives us the following:
Total Change = ∫1020-√2xe (√x²-100)/x dx
= -14,351
This means that over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.
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N Heracio's Computer Time Shopping Research 10% Videos 15% Homework 20% Games 20% Social dia 25% Heracio used the computer a total of 40 hours last week. How many more hours did Heracio use the computer to do homework than shop online?
Answer: According to the problem, N Heracio used the computer for 40 hours last week. We are asked to find the difference between the time spent on shopping online and doing homework.
To do this, we first need to find the amount of time spent on each activity. We can do this by multiplying the total computer time by the percentage of time spent on each activity:
Time spent on videos = 10% of 40 hours = 4 hours
Time spent on homework = 15% of 40 hours = 6 hours
Time spent on games = 20% of 40 hours = 8 hours
Time spent on social media = 25% of 40 hours = 10 hours
Time spent on shopping online = 20% of 40 hours = 8 hours
Therefore, Heracio spent 6 hours on homework and 8 hours on shopping online.
The difference between these two amounts is:
6 hours - 8 hours = -2 hours
This means that Heracio spent 2 hours more on shopping online than on doing homework.
Step-by-step explanation:
I need the answer to this please!!
Answer: 16 pounds
Step-by-step explanation:
12/3=4 and 4x4=16
x + 5 < 7
x + 5 -? ? 7-?
x ??
<----—------————————--->
-5 - 4 - 3 - 2 - 1 0 1 2 3 4 5
Graph the solution after you get your answer
The inequality can be solved to get x < 2, the graph is on the image at the end.
How to solve and graph the inequality?Here we have the inequality.
x + 5 < 7
To solve this, we need to isolate the variable, subtracting 5 in both sides we will get.
x < 7 - 5
x < 2
The graph of this inequality will be a number line with an open circle at x = 2, and an arrow that extends to the left side (because x is smaller than 2)
Then we will get the graph that you can see in the image at the end.
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The ordered pairs model an exponential function, where w is the function name and t is the input variable.
{(1, 60), (2, 240), (3, 960), (4, 3840)}
What is the function equation in sequence notation?
ANSWER: 60(4)t−1
just took the test
Answer: w(t) = 60 * 4^(t-1).
Step-by-step explanation:
The given ordered pairs model an exponential function of the form w(t) = ab^t, where w is the function name, t is the input variable, a is the initial value, and b is the growth factor.
From the first ordered pair (1, 60), we can see that the initial value a is 60. From the second and third ordered pairs (2, 240) and (3, 960), we can see that the output value is multiplied by 4 when the input value increases by 1. This means that the growth factor b is 4.
So, the function equation in sequence notation is w(t) = 60 * 4^(t-1).
Which expression is equivalent to 3^4?
Answer: is d
Step-by-step explanation:
well it is just 3 times 3 times 3 times 3
Marcus looked up the path that he had taken on his run this morning on the map shown below.
To the nearest mile, the distance that Marcus ran is 6 miles.
How to calculate the distanceTo calculate the total distance that Marcus ran in the morning, we will sum up the distance for all the routes that he ran.
From the map, the distances that Marcus ran are as follows:
1 inches + 3 inches + 2 inches + 3 inches
= 8.3 inches
The scale then shows that 4 inches equal 3 miles. Now, we convert 8.3 inches to miles and this gives us:
8.3 inches × 3 miles/4 inches
= 6.225
To the nearest miles, this is 6 miles.
Complete Question:
Marcus looked up the path that he had taken on his run this morning on the map shown below.
To the nearest mile, what is the total distance that he ran?
6 miles
8 miles
11 miles
25 miles
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A sample of a radioactive substance has an initial mass of 45.1 mg. This substance follows a continuous exponential decay model and has a half-life of 19
minutes.
(a)let t be the time (in minutes) since the start of the experiment, and
let y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
y = ()e^()t
(b) How much will be present in 9 minutes?
Do not round any intermediate computations, and round your
answer to the nearest tenth.
a) The formula relating y to t is: y = 45.1 * e^(-0.693/19 * t) b) there will be approximately 30.1 mg of the substance present after 9 minutes.
How to Write a formula relating y to t.(a) The general formula for exponential decay is y = y0 * e^(-kt), where y is the amount at time t, y0 is the initial amount, k is the decay constant, and e is Euler's number.
To find the decay constant, we can use the fact that the half-life is 19 minutes. The formula for half-life is t1/2 = ln(2) / k, where ln(2) is the natural logarithm of 2.
Substituting t1/2 = 19 and ln(2) = 0.693 into the formula gives:
19 = 0.693 / k
k = 0.693 / 19
So the formula relating y to t is:
y = 45.1 * e^(-0.693/19 * t)
(b) To find how much will be present in 9 minutes, we can plug t = 9 into the formula we found in part (a):
y = 45.1 * e^(-0.693/19 * 9) ≈ 30.1 mg
So, there will be approximately 30.1 mg of the substance present after 9 minutes.
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Write the parametric equations.
x=5t−1,y=1−3t
as a function of x in Cartesian form.
y=
f(x)=x^3-3x^2+2x+2. find f(-x).
Answer:Therefore, f(-x) = -x^3 - 3x^2 - 2x + 2.
Step-by-step explanation:o find f(-x), we replace every instance of x in the function f(x) with -x:
f(-x) = (-x)^3 - 3(-x)^2 + 2(-x) + 2
Simplifying, we get:
f(-x) = -x^3 - 3x^2 - 2x + 2
Students are making lemonade from a powdered lemon drink mix. Zachary mixes 11 cups of water and 5 cups of powdered lemon mix. Dianelys mixes 7 cups of water and 4 cups of powdered lemon mix. Use Zachary and Dianelys’s percent of powdered lemon mix to determine whose mix will be more lemony
The percentage of the powdered lemon mix in Dianelys's mix indicates that Dianelys's mix is more lemony.
What is a percentage?A percentage is an expression of a ratio of two quantities as a fraction of 100.
The number of cups of water Zachary mixes with 5 cups of powdered lemon mix = 11 cups of water
Number of cups of water Dianelys mixes with 4 cups of powdered lemon mix = 7 cups of water
Zachary's percentage of powdered lemon mix = (5/(11 + 5)) × 100 = 31.25%
Dianelys's percentage of powdered lemon mix = (4/(7 + 4)) × 100 = 36.[tex]\overline{36}[/tex]%
The percentage of powdered lemon mix for Dianelys which is more than the percentage in Zachary's powdered lemon mix indicates that Danialys mix is more lemony.
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Helpppppppp pleaseeeeee
The value of the product of -4 row one and row 3 is [90 -9 -1]
What is the product of a matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or expression.
The given matrix is
[tex]\left[\begin{array}{ccc}1&2&1\\0&4&-2\\4&-1&6\end{array}\right] \left[\begin{array}{ccc}-5&\\3\\-8&\end{array}\right][/tex]
the product is given as
-4[1 2 1] + [4 -1 3]
= [ -4 -8 -4] + [ 4 -1 3]
= [90 -9 -1]
The sum of the product is [90 -9 -1]
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PLEASE HELP I DON'T UNDERSTAND
Ten cards are numbered from 1 to 10 and placed in a box. One card is selected at random and replaced. Another card is randomly selected. What is the probability of selecting two even numbers?
P(two even numbers) _________
Answer:
30%
Step-by-step explanation:
A right rectangular prism and its net are shown below.
Answer:
A = 5
B = 4
C = 8
D = 3
Step-by-step explanation:
This is more of a visual calculation so I can't really explain much about it other than that you match up the side in the prism with the side in the net
Answer: 108
Step-by-step explanation:
If you turn the shape, where the pointy side of the ramp is facing you and you flipped it open and laid out the sides, that's the "net" image on right
A = 5 the long side of that triangle is also the short side of that rectangle
B = 3 it's the short side of the triangle
C = 8 long part of the rectangle
D = 4 long side of triangle
To find surface area. Find the area of each of the shapes and add it all up
Top Rectangle:
A=Lw=C*A = 5*8 = 40
Middle Rectangle:
A=Lw = B*C = 3*8 = 24
Bottom Rectangle:
A=LW = 4*C = 4*8=32
Triangles are same
A=1/2 bh = 1/2 D*B = 1/2 * 4* 3 =6
But there are 2 of them so A=12
Now add all the shapes together
A(total)=40+24+32+12=108
using calculations show that the height of the barrel of oil is 96.82cm
Answer:
Step-by-step explanation:
V = πr²h
h = V/(πr²)
V = 42 gal
42 gal x 3.7854 l/gal = 158.987 l
158.987 l = 158,987 ml = 158,987 cm³
r = 18/2 = 9 in
9 in x 2.54 cm/in = 22.86 cm
h = (158987 cm³) / π(22.86 cm)² ≈ 96.82 cm
depending on how you round, the more precise answer is 96.8285 ≈ 96.83
Needdd help pleaseeeee
The value of the matrix 4G + 2F is [tex]4[G] + 2[F] = \begin{bmatrix}34 & -4 & 28 & -18 & 58 \\-42 & -8 & 16 & 30 & 8 \\24 & 34 & 4 & 34\end{bmatrix}[/tex]
Matrices are an essential tool in mathematics and can be used to solve a variety of problems. In this case, we are given two matrices G and F, and we are asked to find the value of 4G + 2F.
To understand how to calculate the value of 4G + 2F, we first need to understand what it means to multiply a matrix by a scalar. When we multiply a matrix by a scalar, we simply multiply every element in the matrix by that scalar.
Now that we understand scalar multiplication, we can use it to find the value of 4G + 2F. We simply need to multiply each matrix by its respective scalar and then add the results element-wise.
[tex]4G = 4\begin{bmatrix}8 &-5 &8 &-2 &10 \\-6& -7&1 & 9& 2\\4&6 &3 &7 &5 \\-4 & -3& 0& -10& -9\end{bmatrix}= \begin{bmatrix}32 & -20 & 32 & -8 & 40 \\-24 & -28 & 4 & 36 & 8 \\16 & 24 & 12 & 28 & 20 \\-16 & -12 & 0 & -40 & -36\end{bmatrix}[/tex]
Now we have to find the value of 2[F]. that can be calculated as follows
[tex]2F = 2\begin{bmatrix}1 &8 &-2 &-5 &9 \\-9& 10&6 &-3&0\\4&5 &-4 &3 &7 \\2 &-10&-6 & -1& -8\end{bmatrix}= \begin{bmatrix}2 & 16 & -4 & -10 & 18 \\-18 & 20 & 12 & -6 & 0 \\8 & 10 & -8 & 6 & 14 \\4 & -20 & -12 & -2 & -16\end{bmatrix}[/tex]
Now we can add the two matrices element-wise to get the final result:
[tex]4G + 2F = \begin{bmatrix}32 & -20 & 32 & -8 & 40 \\-24 & -28 & 4 & 36 & 8 \\16 & 24 & 12 & 28 & 20 \\-16 & -12 & 0 & -40 & -36\end{bmatrix} +\begin{bmatrix}2 & 16 & -4 & -10 & 18 \\-18 & 20 & 12 & -6 & 0 \\8 & 10 & -8 & 6 & 14 \\4 & -20 & -12 & -2 & -16\end{bmatrix}[/tex]
[tex]4[G] + 2[F] = \begin{bmatrix}34 & -4 & 28 & -18 & 58 \\-42 & -8 & 16 & 30 & 8 \\24 & 34 & 4 & 34\end{bmatrix}[/tex]
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Find mJKM
J= 3x
L=64
JKM=(5x+4)
The measure of angle JKM is 26°
What is exterior angle theorem?The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the opposite angles in the triangle.
Also the sum of angle in a triangle is 180°
Therefore ;
3x+64 = 5x+4
collecting like terms
5x -3x = 64-4
2x = 60
x = 60/2
x = 30
since x = 30
value of the exterior angle = 5x+4
= 5×30+4
= 150+4 = 154
therefore angle JKM = 180-( 154)
= 26°
Therefore the measure of angle JKM is 26°
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Simplify 5(x+3) -9x+4... Can somebody please help me??
Answer:
-4x+19
Step-by-step explanation:
Otherwise known as option B :D
Find the perimeter of each figure
The perimeter of the composite figure is 46 metres.
How to find the perimeter of a figure?The perimeter of a figure is the sum of the whole sides of the 2 dimensional figure. Therefore, the perimeter of the composite figure is the sum of the whole sides.
Therefore, the perimeter of the figure can be found as follows:
perimeter of the shape = 5 + 6 + 9 + 11 + 3 + 12
perimeter of the shape = 11 + 9 + 11 + 15
perimeter of the shape =20 + 11 + 15
perimeter of the shape = 31 + 15
perimeter of the shape = 46 metres
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Find each of the following probabilities for a normal distribution.
a. p(z > 1.25)
b. p(z > –0.60)
c. p(z < 0.70)
d. p(z < –1.30)
The solution is: the following probabilities for a normal distribution is:
a. 0.5434
b. 0.5746
c. 0.2957
d. 0.0902
Here, we have,
Explanation:
To find each probability we need to use the normal distribution table that is accumulated to the left, so each probability is equal to
P(-1.80 < z < 0.20) = P( z < 0.20) - P( z < -1.80)
P(-1.80 < z < 0.20) = 0.5793 - 0.0359
P(-1.80 < z < 0.20) = 0.5434
P(-0.40 < z < 1.40) = P( z < 1.40) - P( z < -0.40)
P(-0.40 < z < 1.40) = 0.9192 - 0.3446
P(-0.40 < z < 1.40) = 0.5746
P(0.25 < z < 1.25) = P(z < 1.25) - P(z < 0.25)
P(0.25 < z < 1.25) = 0.8944 - 0.5987
P(0.25 < z < 1.25) = 0.2957
P(-0.90 < z < -0.60) = P(z < -0.60) - P(z < -0.90)
P(-0.90 < z < -0.60) = 0.2743 - 0.1841
P(-0.90 < z < -0.60) = 0.0902
Therefore, the answers are, the following probabilities for a normal distribution is:
a. 0.5434
b. 0.5746
c. 0.2957
d. 0.0902
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Use the Law of Sines. Find the measure x to the nearest tenth.
Answer:
Step-by-step explanation:
Law of sines states that the lengths of the sides of a triangle are proportional to the sines of the corresponding angles.
sinM/17 = sinx/10
sin M = .94551
.94551/17 = sin x /10
cross mulitply and then divide.
.954551 · 10/17 = sin x
9.4555/17 = .5562
sin inverse is 33.793 ° or rounded to 33.8°
6. A library owner wants to purchase books for the library. He wants to purchase a maximum of 27 book
between short stories and novels. The cost of each short-story book is $6 and the cost of each novel is
$10.
If he cannot spend more than $90 on books, which system of inequalities below can be used to
determine the number of short-story books, s, and the number of novels, n, he can purchase?
Answer: 6s + 10n less than or equal to 90
What is the answer to this ?
Answer:
Triangle P has been rotated clockwise by 90° about the point (0,0).
PLEASE MARK IT THE BRAINLIEST!!!!
Algebra substitution y=-3x+5 2x+y=6
The solution to the system of equations y=-3x+5 and 2x+y=6 is (x,y) = (-1,8).
To solve the system of equations using substitution, we can substitute the expression for y in the second equation with the expression for y in the first equation:
2x + y = 6
2x + (-3x + 5) = 6 (substitute y = -3x + 5)
2x - 3x + 5 = 6
-x + 5 = 6
-x = 1
x = -1
Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y:
y = -3x + 5
y = -3(-1) + 5
y = 8
We can check our solution by verifying that it satisfies both equations:
y = -3x + 5 => 8 = -3(-1) + 5 => 8 = 8 (true)
2x + y = 6 => 2(-1) + 8 = 6 => 6 = 6 (true)
Thus, our solution is correct.
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PLSSS.the function : ℝ → ℝ, () = 2^, : (0; +∞) → ℝ, () = √4 + 1 + 1.show
that the graphs of the functions and intersect at the abscissa point x=2
[tex]f(2) = g(2) = 4[/tex], which means that the graphs of the two functions intersect at x = 2.
What is the abscissa point?To show that the graphs of the functions [tex]f(x) = 2^x[/tex] and [tex]g(x) = \sqrt(4x + 1) + 1[/tex] intersect at the abscissa point x = 2, we need to show that both functions have the same value at [tex]x = 2.[/tex]
First, we evaluate f(2):
[tex]f(2) = 2^2 = 4[/tex]
Next, we evaluate g(2):
[tex]g(2) = \sqrt(4(2) + 1) + 1 = \sqrt9 + 1 = 4[/tex]
Therefore, [tex]f(2) = g(2) = 4[/tex] , which means that the graphs of the two functions intersect at [tex]x = 2[/tex] .
To visualize this, we can plot the two functions on the same set of axes:
As we can see from the graph, the two curves intersect at the point (2, 4).
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The complete question is: How can you show that the graphs of the functions f(x) = [tex]2^x[/tex] and g(x) = √(4x + 1) + 1 intersect?
Brock earned $30.00 for a week's work. If he paid 10% of it in taxes how much did he
pay in taxes?
Which is a recursive formula for this geometric sequence?
-18
, -14
, -12
, -1, . . .
The recursive formula for the geometric sequence is given as follows:
[tex]a_1 = -\frac{1}{8}[/tex][tex]a_n = 2a_{n - 1}[/tex]What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The first term of the sequence is given as follows:
[tex]a_1 = -\frac{1}{8}[/tex]
Each term is the previous term multiplied by two, hence the common ratio is given as follows:
q = 2.
Then each term is the previous term multiplied by two, and the recursive rule is given as follows:
[tex]a_n = 2a_{n - 1}[/tex]
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AquaWorks is training new employees to assemble hot water heaters. The
number of water heaters h that a trainee can assemble per 8-hour shift is given
by h = 2.1 0.9t + 4 where t is the number of days of training the trainee
has received. How many training days are required before a trainee can
assemble 9 heaters? Round up to the nearest day.
Answer:
A trainee requires 3 days of training before they can assemble 9 heaters.
Step-by-step explanation:
We are given the formula for the number of water heaters h that a trainee can assemble per 8-hour shift as:
h = 2.1 0.9t + 4
where t is the number of days of training the trainee has received. We need to find out how many training days are required before a trainee can assemble 9 heaters. So we set h to 9 and solve for t:
9 = 2.1 0.9t + 4
Subtracting 4 from both sides, we get:
5 = 2.1 0.9t
Dividing both sides by 2.1 0.9, we get:
t = (5 / (2.1 0.9))
Using a calculator, we get:
t ≈ 2.49
Rounding up to the nearest day, we get:
t = 3
Therefore, a trainee requires 3 days of training before they can assemble 9 heaters.
What is the value of "x", when 1/3x = 9 1/3?
Answer:
x=28
Step-by-step explanation:
solve for x by simplifying both sides of the equation, then isolating the variable.
have a good day :)
Answer
x=3 1/9
Step-by-step explanation:
Very confusing help I’m not sure how break this down and what’s the step
Note that adding one pair does not make the table a function. This is why it is trickly. For the table to be a function, each value of x must be related to only one unique value of y and vice versa.
How can the table become a function?For the table to become a function, we must eliminate any repeated ordered pairs such as (3, 8) and (7, 8)
For example, we can say (3, 6) and (7, 8) then pick the last to be (5, 10)
So the table becomes a function when you have:
X Y
6 0
3 6
9 12
7 8
5 10
The word linear function in mathematics refers to two separate but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
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