The equation becomes of the pressure is P = 90 + 10 sin(π/36(t +4 ))
By observation the sine function should be of form P= 90 + 10 sin(ω(t − c)) as it oscillates about 90 and with a factor of 10. Let time be represented by the variable t in hours from 12.00 AM.
At 2:00 P.M. that is t= 14 hours the pressure is 100 mmHg
Substituting it in the equation we get,
100 = 90 + 10 sin(ω(t − c))
10 = 10 sin(ω(14 − c))
1 = sin(ω(14 − c))
ω(14 − c) = π/2 -1)
At 2:00 A.M. that is t= 2 hours the pressure is 80 mmHg
80 = 90 + 10 sin(ω(t − c))
-10 = 10 sin(ω(2 − c))
3π/2 = ω(2 − c) -2)
dividing 2) with 1) we get
3 = (14 − c) /(2 − c)
6 - 3c = 14 - c
2c = -8
c = - 4
Substituting the value of c in 1) we get,
ω(14 − (-4)) = π/2
ω18 = π/2
ω = π/36
Thus the equation becomes P = 90 + 10 sin(π/36(t +4 ))
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find the values of A and B
please help giving brainliest
Answer:
A=3Bz/2
B=2A/3z
Step-by-step explanation:
if you need more explanation you can ask me :)
The design of a building that has a square pyramid roof as a roof is shown. The cost of material for the outside of the building and for the roof
ranges from $25 per square foot to $50 per square foot. The budget for this material is $500,000. The rectangular front of the building has a
length twice as long as its height. The slant height of the roof is the same as the height of the rectangular front of the building.
What is the maximum possible length of the rectangular front of the building to the nearest foot?
feet
The maximum possible length of the rectangular front of the building is
A. 164
B. 41
C. 82
D. 29
The maximum possible length of the rectangular front of the building is 23 feet
How to determine the maximum possible length?The complete question is attached
Let the length of the rectangular front be x and the height be y.
So, we have:
x = 2y
The building has 4 congruent sides.
So, the area of the 4 sides is
A = 4 * (x * y)
This gives
A = 4 * (x * 2x)
Evaluate
A = 8x²
For the triangular roof, we have:
Slant height, l = y
Base, b = x
So, the area of the 4 triangular faces is
A = 0.5 * 4 * xy
This gives
A = 2xy
Recall that:
x = 2y
Make y the subject
y = 1/2x
So, we have:
A = 2x * 1/2x
A = x²
The cost of designing the buildings is
C = 25 * 8x² + 50 * x²
C = 200x² + 50x²
C = 250x²
This gives
250x² = 500000
Divide both sides by 250
x² = 2000
Square both sides
x = 45
Recall that:
y = 1/2x
This gives
y = 1/2 * 45
y = 23
Hence, the maximum possible length of the rectangular front of the building is 23 feet
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Figure TUVS is a parallelogram.
Parallelogram T U V S is shown. Angle U is (4 x + 9) degrees and angle V is (6 x minus 29) degrees.
Which angles equal 91°?
angles T and V
angles S and U
angles U and V
angles S and T
Angles T and V of the parallelogram are equal to 91°.
Calculating the Value of x
In the parallelogram TUVS, adjacent angles U and V are given as,
U = 4x+9
V = 6x-29
Since U and V are adjacent angles, and as per the properties of a parallelogram, sum of adjacent angles is equal to 180°.
4x+9 + 6x-29 = 180
10x - 20 =180
10x = 200
x = 20
Calculating the Angles of the Parallelogram
∠U = 4x + 9
∠U = 4(20) + 9
∠U = 80 + 9
∠U = 89°
∠V = 6x - 29
∠V = 6(20) - 29
∠V = 120 - 29
∠V = 91°
According to the properties of a parallelogram, opposite angles are of equal measure.
∴ ∠T = ∠V and ∠S = ∠U
⇒ ∠T = 91° and ∠S = 89°
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Answer:
angles t and v
Step-by-step explanation:
edge
Find the vertex and axis of symmetry
Answer:
Below in bold.
Step-by-step explanation:
f(x) = 2x^2 - 12x + 24
Convert to vertex form:
f(x) = 2(x^2 - 6x) + 24
= 2[(x - 3)^2 - 9] + 24
= 2(x - 3)^2 - 18 + 24
= 2(x - 3)^2 + 6
So the vertex is at (3, 6) and the axis of symmetry is x = 3.
PLEASE HEPP IM STUCK
Answer:
m = -4
Step-by-step explanation:
We are given that a line intersects the points (-2, 9) and (3, -11).
We want to write the slope of this line.
The slope (m) can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
Even though we have everything we need to calculate the slope, let's label the values of the points to avoid any confusion & mistakes.
[tex]x_1=-2\\y_1=9\\x_2=3\\y_2=-11[/tex]
Now substitute these values into the formula (remember that the formula has subtraction).
m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-11-9}{3--2}[/tex]
Simplify.
m=[tex]\frac{-11-9}{3+2}[/tex]
Subtract the values on top.
m=[tex]\frac{-20}{3+2}[/tex]
Now add the values on the bottom together.
m=[tex]\frac{-20}{5}[/tex]
Now divide -20 by 5.
m = -4
Volume=
Help me please
I appreciate it so much :)
The volume of the given solid is 6322.75 cubic units.
What is the volume of the given figure?
It is given that,
The area of the regular pentagonal base, a = 35 units
Altitude of the given pyramid, h = 9 units
The formula for the volume of a pyramid with regular pentagonal base is given by,
V = (5/12) × tan(54°)ha²
Substituting the given values of a and h, we get the volume as,
V = (5/12) × tan(54°) × 9 × (35)²
V = (5/12) × (1.376) × 9 × 1225
V = (5/4) × (1.376) × 3 × 1225
V = (5/4) × 5056.8
V ≈ 6322.75 units³
Thus, the volume of the given figure comes out to be approximately equal to 6322.75 cubic units.
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A line passes through the points (-1,-1) and (5,8) which points lie on the same line?
Answer: all points [tex](x,y)[/tex] that satisfy [tex]y=\frac{3}{2}x+\frac{1}{2}[/tex]
Step-by-step explanation:
The slope of the line is
[tex]\frac{-1-8}{-1-5}=\frac{-9}{-6}=\frac{3}{2}[/tex]
So, substituting into point-slope form, the equation is
[tex]y+1=\frac{3}{2}(x+1)\\\\y+1=\frac{3}{2}x+\frac{3}{2}\\\\y=\frac{3}{2}x+\frac{1}{2}[/tex]
Therefore, all points [tex](x,y)[/tex] that satisfy [tex]y=\frac{3}{2}x+\frac{1}{2}[/tex] will lie on the same line.
PLEASE HELP ASAP!!!!!!!
Given TU is parallel to XW
Prove XW = 8
Which step is missing?
The missing step in the proof is: D. Statement: XW/UT = XV/UV, Reason: Corresponding sides of similar triangles are proportional.
What are Similar Triangles?When two triangles are proven to be similar to each other, their corresponding angles would be congruent while their corresponding sides will be proportional to each other.
In the proof given, both triangles are proven to be similar by the AA similarity theorem, therefore their corresponding sides will be proportional. This implies that: XW/UT = XV/UV.
The answer is D.
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PLRASE HELPPP PLS IM STUCK
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
Can someone help me on this pls? It’s urgent, so ASAP (it’s geometry)
Write formal proofs using LA Theorem.
Given the parameters in the diagrams, we have;
4. ∆ABC ≈ ∆DEF by ASA
5. UW ≈ XZ by CPCTC
6. QR ≈ TR by CPCTC
How can the relationship between the triangles be proven?4. The given parameters are;
<B = <E = 90°
AB = DE Definition of congruency
<A = <D Definition of congruency
Therefore;
∆ABC ≈ ∆DEF by Angle-Side-Angle, ASA, congruency postulate5. Given;
XY is perpendicular to WZ
UV is perpendicular to WZ
VW = YZ
<Z = <W
Therefore;
∆UVW ≈ ∆XYZ by Angle-Side-Angle, ASA, congruency postulate
Which gives;
UW is congruent to XZ, UW ≈ XZ, by Corresponding Parts of Congruent Triangles are Congruent, CPCTC6. Given;
PQ is perpendicular to QT
ST is perpendicular to QT
PQ ≈ ST
From the diagram, we have;
<SRR ≈ <PRQ by vertical angles theorem;
Therefore;
∆QRP ≈ ∆TRS by Side-Angle-Angle, SAA, congruency postulate
Which gives;
QR ≈ TR by Corresponding Parts of Congruent Triangles are Congruent, CPCTCLearn more about congruency postulates here:
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For decades, hoax artists have been going out into grain fields to make crop circles like the one shown below. Though many people believed these crop circles to be the work of aliens we now know that these designs were made by people with very simple tools and some geometric knowledge. To make each circle, one person stands stationary in a field holding a rope of a specific length, while another person holds the other end of the rope. The second person circles the first and uses a wooden plank to bend the grain stalks until all the grain in that circle lies flat against the ground. Then they both move to make other circles. The result is often very beautiful, especially when seen from the air. Along with the image below, Use your knowledge of the unit circle and radian measure of angles to answer the following questions. [Note: When the questions ask you to consider circles and their angle in relation to the main circle, the question is referring to the location of the center of each circle.]
a. Consider circles 1 through 6. If these circles are equally spaced around the main circle, and circle 1 is at 0°, what is the direction (in degrees) of each of these circles in relation to the main circle?
b. Consider circles 7 through 12. If circle 7 is at 45°, what is the radian measure of each of these circles in relation to the main circle? Explain how you know these values.
c. If the center of circle 3 is 100 feet away from the main circle, what are the coordinates of the center of circle 3 (the origin is at the center of the main circle)? Use these coordinates to prove that the distance from the centers of circle 3 and the main circle are 100 feet apart.
d. After creating the design, the designers want to inspect their work. They start at 0° and walk all the way around the design almost two times and stop at circle 12. How many radians did they cover during their inspection?
e. Consider circles 5 and 6. In relation to the main circles, do the center points of circles 5 and 6 have even or odd symmetry? Why?
a. circle 2 = 60°
circle 3 = 120°
circle 4 = 180°
circle 5 = 240°
circle 6 = 300°
b. circle 8 = 15°
circle 9 = 75°
circle 10 = 155°
circle 11 = 215°
circle 12 = 265°
How to determine the valuesFrom the information given, we have that;
There are six major circles
Six minor circles
a. There are 6 circles at a point
Note that angles at a point sum up to 360 degrees
Now, let's divide their sum by the six parts
= [tex]\frac{360}{6}[/tex]
= [tex]60[/tex] degrees
Then, circle 1
= 0 × 60
= 0
Circle 2
= 1 × 60
= 60°
Circle 3
= 2 × 60
= 120°
Circle 4
= 3 × 60
= 180°
Circle 5
= 4 × 60
= 240°
Circle 6
= 5 × 60
= 300°
b. We have that each of these circles ( circle 7 - 12) radian measure is
= main circle - [tex]\frac{\pi }{12}[/tex]
The relative position or direction of circle 7 - 12 to their corresponding main circles ( 1 - 6) are all the same, we then have;
For circles 8
= 60° - 45°
= 15°
Circle 9
= 120° - 45°
= 75°
Circle 10
= 180° - 45°
= 155°
Circle 11
= 240° - 45°
= 215°
Circle 12
= 300° - 45°
= 265°
They share the relationship of radian of circle 7 - 12 corresponding to circles 6 - 12 minus π/12
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PLEASE HELP IM REALLY STUCK
Answer:
5/2
Step-by-step explanation:
Answer:
1 3/4 or 1.75
Step-by-step explanation:
Formula: y1-y2/x1-x2
Plug in the given coordinates: y1 = -3, y2 = 4, x1 = 2, x2 = 6
-3-4/2-6 = -7/-4 = 7/4 = 1 3/4 or 1.75
(-4,-2) (0,2) (-2,1) find the domain and range and can you tell me if it’s a function ?? PLS HELPPP
Answer:
domain means -4,0,-2 and range is -2,2,1
A typical decision support system (DSS) includes many components including a(n) _____ which allows decision makers to easily access and manipulate the DSS and to use common business terms and phrases.
A typical decision support system (DSS) includes many components including a(n) dialogue manager which allows decision makers to easily access and manipulate the DSS and to use common business terms and phrases.
What are the components of decision support systems DSS?Decision support systems, according to Management Study HQ, are made up of three essential parts: the database, the software system, and the user interface. DSS repository.What are the 4 parts of DSS?Data management, model management, knowledge management, and user interface management make up the majority of decision support systems.What type of decision-making does DSS support?Systems for supporting data-driven decision making are used by users to make choices about organizations, inventories, and goods.When evaluating recent and historical data to report on the state of a department or the company as a whole, managers may find data-driven decision support systems to be of the most use.Learn more about decision support system here:
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PLEASE I NEED HELP SO BADLY
Answer:
[tex]3y^{2} -3y-5[/tex]
THIS IS VERY HARD PLSSS
Answer:
[tex]y=3\sqrt{x-1}-7[/tex]
Step-by-step explanation:
We are given the function [tex]y=\sqrt{x}[/tex]. Let's apply each transformation separately and see what we get. First, let's apply the vertical shift. We are told that the graph shifts downwards by 7 units. In other words, when x is 0, y should be -7 instead of 0. We can accomplish that by changing the y-intercept of the graph and subtracting our function by 7: [tex]y=\sqrt{x} -7[/tex]. Notice that the -7 is outside the square root.
Next, we can apply the horizontal transformation. We are told that the graph shifts to the right 1 unit. This means that, for [tex]y=\sqrt{x}[/tex], if y is 0, x should be 1. We can accomplish this by doing [tex]y=\sqrt{x-1}[/tex] (if x = 1, y will be 0). Now, we can combine the two transformations we have done so far: [tex]y=\sqrt{x-1}-7[/tex].
Lastly, we need to vertically stretch the function by a factor of 3. All we have to do here is multiply sqrt(x) by 3 (this way, if x is equal to 1, y should be 3 instead of 1 (3 times x)). So, we get something like this: [tex]y=3\sqrt{x}[/tex]. Now, we can combine all of the transformations we did to get our final answer:
[tex]y=3\sqrt{x-1}-7[/tex]
(Refer to the attached image)
Answer:
D. 10
Step-by-step explanation:
To find the distance between two points, use the distance formula:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]
Define the two points:
[tex]\textsf{Let }(x_1,y_1)=(4,-3)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(-4,3)[/tex]
Substitute the two defined points into the distance formula and solve for d:
[tex]\implies d=\sqrt{(-4-4)^2+(3-(-3))^2}[/tex]
[tex]\implies d=\sqrt{(-4-4)^2+(3+3)^2}[/tex]
[tex]\implies d=\sqrt{(-8)^2+6^2}[/tex]
[tex]\implies d=\sqrt{64+36}[/tex]
[tex]\implies d=\sqrt{100}[/tex]
[tex]\implies d=\sqrt{10^2}[/tex]
[tex]\implies d=10[/tex]
Therefore, the distance between the two given points is 10 units.
Formula given by
[tex]\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{(-4-4)^2+(3+3)^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{8^2+6^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{10^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=10units[/tex]
Option D
A dindercal container close at boat and have a radius 7cm and hight 6cm find total surface area of the container what is the volume of this container
A) The total surface area of the given cylindrical container is 571.76 cm² and B) The volume of the given cylindrical container is 923.62 cm³.
What are the formulae for the total surface and volume of the cylinder?Consider a cylinder with height 'h', and radius 'r'.
The total surface area of the cylinder(TSA) = 2πr (r + h) square units
and
The volume of the cylinder V = πr²h cubic units.
Calculation:It is given that,
A cylindrical container closed on both ends has a radius r = 7 cm and a height h = 6 cm.
So,
TSA = 2πr (r + h)
= 2× π × 7 × (7 + 6)
= 14 × π × 13
= 571.76 cm²
and
Volume = πr²h
= π × 7² × 6
= π × 49 × 6
= 923.62 cm³
Therefore, the total surface area and volume of the cylindrical container are 571.76 cm² and 923.62 cm³ respectively.
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Divide quotient and remainder (image)
Answer:
Hi, I'm not for sure but I think for sure for the answer is, I haven't done this math in a while btw I like math lol, but I will try my best for this answer:
The quotient: x + 4
The remainder: - 2
Step-by-step explanation:
I hope this helps you and have a lovely day of learning!
Mateo teaches a continuing education class at the library on tuesday nights. he estimates that 75% of his students are satisfied or very satisfied with the class. last week, he asked a random sample of students to take a survey on their experience in the class. however, the results showed that only 70% indicated that they are satisfied or very satisfied with the class. he decides to randomly survey more of his students. how will mateo know whether his model is valid or not?
The computed value must closely match the real value for a model to be considered valid. If the percentage of pleased or very satisfied students remains close to 75% after Mateo surveys additional students, Mateo's model is still viable. The model is faulty if the opposite is true.
How will mateo know whether his model is valid or not?In general, a valid model is one whose estimated value is close to the real value. This kind of model is considered to be accurate. It must be somewhat near to the real value if it doesn't resemble the real value.
If the findings of the survey are sufficiently similar to one another, then the model may be considered valid.
P1 equals 75%, which is the real assessment of the number of happy pupils
P2 is 70 percent; this represents the second assessment of happy pupils
In conclusion, The estimated value of a model has to be somewhat close to the real value for the model to be considered valid. If the number of students who are either pleased or extremely satisfied remains close to 75 percent following Mateo's survey of more students, then Mateo's model is likely accurate. In any other scenario, the model cannot be trusted.
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Are the ratios 2:1 and 14:6 equivalent?
yes
no
Answer:
Step-by-step explanation:
To check this, we need to know whether
2
1
=
3
2
We have,
2
1
=
2×3
1×3
=
6
3
and
3
2
=
3×2
2×2
=
6
4
We find that
6
3
<
6
4
, which means that
2
1
<
3
2
.
Therefore, The ratio 1:2 is not equivalent to the ratio 2:3
Answer:
No, they aren't equal.
Step-by-step explanation:
(14x2 + 13x + 12) + (7x2 + 20x + 4)
Answer:
21x^2 + 33x + 16
Step-by-step explanation:
(14x^2 + 13x + 12) + (7x^2 + 20x + 4)
Combine like terms:
14x^2 + 7x^2 = 21x^2
13x + 20x = 33x
12 + 4 = 16
Thus:
21x^2 + 33x + 16
Answer:
21x^2 + 33x + 16.
Step-by-step explanation:
(14x2 + 13x + 12) + (7x2 + 20x + 4) Remove the parentheses:
= 14x2 + 13x + 12 + 7x2 + 20x + 4 Bring like terms togethher:
= 14x^2 + 7x^2 + 13x + 20x + 12 + 4
= 21x^2 + 33x + 16.
PLEASE HELP ASAP!!!!
The location of the points on Cartesian plane are listed below:
Figure 1: A(x, y) = (0, 4), B(x, y) = (5, 0)
Figure 2: A(x, y) = (8.5, 4), B(x, y) = (2.5, 1.5)
How to write coordinates in a rectangular system
A point on a Cartesian plane can be represented by rectangular system of coordinates with the form:
(x, y)
Where:
x - Distance along the x-axis respect to origin.y - Distance along the y-axis respect to origin.Now we proceed to represent each point:
Figure 1: A(x, y) = (0, 4), B(x, y) = (5, 0)
Figure 2: A(x, y) = (8.5, 4), B(x, y) = (2.5, 1.5)
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The number of people in the world was 2.5 billion in 1950. The population has grown by 1.2% each year since then. Create a equation to model this situation using P to represent population (in billions) and y to represent years.
The equation which correctly models the situation in discuss is; P = 2.5(1.012)^y.
Which equation best models the situation?If follows from the task content that the situation given is that The number of people in the world was 2.5 billion in 1950.
Afterwards, The population has grown by 1.2% each year since then. Hence it follows that the function is an exponential one whose factor is; (100+1.2)%= 1.012.
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according to the graph, what is the value of the constant in the equation below?
Answer: B
Step-by-step explanation:
The product of height and width is constant.
If we take the point (0.5,1), we get the product to be 0.5.
Given the following formula, solve for a. 8=a+b+c/2
Making "a" the subject of the formula would give us: a = 8 - b - c/2
How to Solve for the Subject of Formula?Given the formula, 8 = a+b+c/2, to make a the subject of the formula, we would isolate a in the equation.
8 = a+b+c/2
8 = (2a + 2b + c)/2
2(8) = 2a + 2b + c
16 = 2a + 2b + c
16 - 2b - c = 2a
Divide both sides by 2
16/2 - 2b/2 - c/2 = 2a/2
8 - b - c/2 = a
a = 8 - b - c/2
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What’s 1/6 to 3 dp does anyone know?
❄ Hi there,
[tex]\sf{\dfrac{1}{6}\approx0.167}[/tex], rounded to 3 DP (decimal places)
[tex]\left\vert\textsf{Decimal Places = Number of digits after the decimal point}\vert[/tex]
Why round? Because the entire number goes on for ever and ever.
So, we need to round. 1/6 rounded to 3 decimal places is 0.167. We have 3 numbers after the decimal point.
❄
Use the interactive tool to find which of the following expressions have a sum of 6. Check all that apply.
8 + 2
(–4) + (-2)
(–3) + 9
7 + (–1)
The expressions that have a sum of 6 are Options C and D
How to determine the sum
In this case, we use the following rules
(-) + (-) = -
(+) + (+) = +
(+) + (-) = -
(-) + (+) = -
From the first case
8 + 2 = 10
(-4) + (-2) = -4 + -2 = -6
(-3) + 9 = -3 + 9 = 6
7 + (-1) = 7 - 1 = 6
Thus, the expressions that have a sum of 6 are Options C and D
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Which of the following is a geometric sequence?
Answer:
A
Step-by-step explanation:
Geometric sequence is when, during each successive number, a constant is being multiplied. In answer choice A, each number is getting multiplied by 3, so it is a geometric sequence.
What is the approximate side length of the square? 3.0 units 3.5 units 4.2 units 4.9 units
Answer:
(っ◔◡◔)っ ♥ the answer is C ♥
Step-by-step explanation: