Answer:
1. You have to shade 38/100 squares
2. You have to shade 65/100 squares
3. 3/5=15/25, 6/10, 9/15
The angle represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t
At the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.
How to describe the initial condition of this experiment?First of all, we would derive an expression for the position with respect to the angle (phase shift) under the appropriate conditions:
Asin(ωt + ø) = c₂sinωt + c₁cosωt.
At t = 0, we have:
y = c₂sin(0) + c₁cos(0).
y = 0 + c₁
y = 0 + 5
y = 5 units.
Therefore, we can logically deduce that at the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.
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Complete Question:
The angle Φ represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t = 0. If the weight is at its maximum positive position (weight is above equilibrium) at t = 0, then Φ = 0. If the weight is at its maximum negative position (spring is stretched and weight is below equilibrium) at t = 0, then Φ = π. If the weight is traveling in the negative direction and passing through equilibrium at t = 0, then Φ = π/2. In the response box, describe the initial condition of our experiment; specifically, describe the position of the weight and the direction in which it was traveling.
Can someone help me please
EXTRA POINTS HELP ASAP!
x + x/3 = 4/9
solve for x
Answer:
x=1
Step-by-step explanation:
1 + 1/3 = 4/9
1/3 also equals 3/9
hope this helped :)
Answer :
Value of x is 1 / 3Step-by-step explanation :
>> (3 × x + x / 3) = 4 / 9
>> (3x + x / 3) = 4 / 9
>> (4x / 3) = 4 / 9
>> 4x × 9 = 3 × 4
>> 36x = 12
>> x = 12 / 36
>> x = 6 / 18
>> x = 3 / 9
>> x = 1 / 3
CSN SOMEONE PLEASE HELP ASAP
If the ADA guidelines state that a
wheelchair ramps angle of elevation
must equal 4.8°. would a
ramp with the
following dimensions be up to code?
Show your work and explain. (Picture is
not drawn to scale.)
3.5 ft
e°
40 ft
The ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.
How to find the angle of elevation of the ramp?The angle of elevation of the ramp can be found using trigonometric ratios.
Therefore, the angle of elevation must be equal to 4.8 degrees to obey the ADA guidelines .
Hence,
tan ∅ = opposite / adjacent
opposite side = 3.5 ft
adjacent side = 40 ft
Therefore,
tan ∅ = 3.5 / 40
∅ = tan ⁻¹ 0.0875
∅ = 5.00064459756
∅ = 5 degrees
Therefore, the ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.
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Please help its confusing meeeeee
Answer:
p = 21.4 cm
∠P = 44°
Step-by-step explanation:
Apply the Pythagorean Theorem to solve for the length of p.
p² + 21² = 30²p² = 900 - 441p² = 459p = √459[tex]\fbox {p = 21.4 cm}[/tex]Now, take the inverse sine function to find angle P :
sin⁻¹ (opposite side / hypotenuse)sin⁻¹ (21/30)sin⁻¹ (0.7)[tex]\boxed {44^{o}}[/tex] (approximately)Answer:
a) 21.4 cm
b) 45.6°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and sides of a right triangle. Here, two relevant function are ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
b) Angle PThe hypotenuse of the triangle, and the side adjacent to angle P are given, so we have ...
cos(P) = (21 cm)/(30 cm)
The angle value can be found using the inverse cosine function:
P = arccos(21/30)
P ≈ 45.6°
a) Side pNow, we know angle P and the side adjacent to it. We want to find the measure of side p, which is opposite the angle. This can be done using either the sine function or the tangent function. Here, we choose to use the tangent function.
tan(P) = p/21
p = 21×tan(P) = 21·tan(45.573°)
p ≈ 21.4 . . . . cm
__
Additional comment
In the attached, part of the calculator keypad is shown so you can see that the inverse cosine function is the 2ND function of the Cos key. The calculator mode is set to DEG (lower left of display) so that angles are in units appropriate to this problem.
Of course, you can always use the Pythagorean theorem to find the length of side p. More calculations are involved, so we used trig functions instead. Note that the angle P must be found first using the approach here, and its value must be retained with enough significant digits to ensure accuracy in the 'p' calculation.
im new to algebra, so most of the stuff im writing here is basic stuff.
8x=24
4x=9
Answer:
x = 3, x = 9/4
Step-by-step explanation:
8x = 24
x = 3 Divide both sides by 8.
4x = 9
x = 9/4 Divide both sides by 4.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1.}[/tex]
[tex]\mathsf{8x = 24}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{8x = 24}[/tex]
[tex]\huge\textbf{Divide \boxed{8} to both sides:}[/tex]
[tex]\mathsf{\dfrac{8x}{8} = \dfrac{24}{8}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = \dfrac{24}{8}}[/tex]
[tex]\mathsf{x = 3}[/tex]
[tex]\huge\textbf{Therefore, the answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x =}\frak{\ 3}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{4x = 9}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{4x = 9}[/tex]
[tex]\huge\textbf{Divide \boxed{9} to both sides:}[/tex]
[tex]\mathsf{\dfrac{4x}{4} = \dfrac{9}{4}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = \dfrac{9}{4}}[/tex]
[tex]\mathsf{x = 2 \dfrac{1}{4}}[/tex]
[tex]\huge\textbf{Therefore, the answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = }\frak{\ \dfrac{9}{4}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The inequality |2x - 5 > 8 can be written as which two inequalities?
Answer:
2x - 5 < -8 or 2x - 5 > 8
Step-by-step explanation:
|2x - 5| > 8
2x - 5 < -8 or 2x - 5 > 8
The two inequalities that can be written from the |2x - 5| > 8 are:
2x - 5 > 8
-2x + 5 > 8
We have,
To split the inequality |2x - 5| > 8 into two separate inequalities, we consider both the positive and negative cases for the absolute value expression.
Positive case:
When 2x - 5 is positive, we have:
2x - 5 > 8 _____(1)
Negative case:
When 2x - 5 is negative, we have:
-(2x - 5) > 8
Simplifying the negative case:
-2x + 5 > 8 ______(2)
Now, we have two inequalities:
2x - 5 > 8
-2x + 5 > 8
These are the two inequalities resulting from the given inequality
|2x - 5| > 8.
Thus,
The two inequalities that can be written from the |2x - 5| > 8 are:
2x - 5 > 8
-2x + 5 > 8
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help me please please please
The area and circumference of a circle are 12.56square feet and 12.56ft respectively
Area and circumference of a circleThe formula for calculating the area and circumference of a circle is expressed as:
A = πr²
C = πd
where
r is the radius and d is the diameter
Area = 3.14 * (2)²
Area = 12.56ft²
For the circumference
C = 3.14(4)
C = 12.54ft
Hence the area and circumference of a circle are 12.56square feet and 12.56ft respectively
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A printing company charges a fixed rate to set up the printing press, plus a cost of $3.50 for every 100 copies. If 800 copies cost $64.00, how much will it cost to print 1500 copies?
Answer:
88.5
Step-by-step explanation:
3.5 * 8 = 28, this is how much was spent on copies printed. If 800 copies cost $64 and 28 of that was on the 3.5 fee per 100, then the flat rate must be:
64-28 = 36.
Now, let's do 1500. For 1500 copies, you will get charged $3.5 15 times. This amounts to 52.5, then adding the fixed fee of 36 dollars, you get
88.5
Given the function f(x) = -x - 3x², find the value of f(1/2) in simplest form.
Answer:
-5/4
Step-by-step explanation:
To evaluate the function, put the value of the argument where the variable is and do the arithmetic.
Function evaluationf(x) = -x -3x²
f(1/2) = -(1/2) -3(1/2)² = -1/2 -3(1/4) . . . . . use 1/2 in place of x
f(1/2) = -2/4 -3/4 = -5/4
The value in simplest form is ...
f(1/2) = -5/4
show the height of the pyramid is 9 cm
The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let us assume that the pyramid has a volume of 75 cm³ and square base area of 25 cm², hence:
Volume = (1/3) * area of base * height
75 = (1/3) * 25 * height
height = 9cm
The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm
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There are two numbers. One number is twice the other number. The difference of the smaller number and half the larger number is 20.
An equation created to find the smaller number will have_________
.
Step-by-step explanation:
x, y = 2 numbers
x = 2y
y - x/2 = 20
this is impossible to solve. there is no solution.
because the first equation tells us
y = x/2
and so the second equation is
x/2 - x/2 = 20
0 = 20
so, again, no solution.
Okay can someone explain this?
Answer:
see below
Step-by-step explanation:
90 degree clockwise will change x, y coordinates to y, -x
point D 1,3 becomes 3,-1
point E 4, 4 becomes 4,-4
point F 4, -2 becomes -2,-4
point G 1,-1 becomes -1, -1
The graphs of f(x) = 5x and its translation, g(x), are
shown on the graph.
30 Iv
25-
20
15
10 1.5
g(x)
f(x)
65432 15.
10:
-15-
20
-25
-30
(0,
51
(2,25)
(2, 15)
2 3 4 5
(0, -9)
(1,-5)
X
What is the equation of g(x)?
g(x) = 5x-9
g(x) = 5x-10
g(x) = 5-9
Og(x) = 5* - 10
Answer: [tex]g(x)=5^x - 10[/tex]
Step-by-step explanation:
g(x) is the graph of f(x) translated 10 units down.
Select the correct answer. What is the solution to the equation? -2√x+4=-12 A. 4 B. 8 C. 16 D. 64
Answer:
d. 64
Step-by-step explanation:
x^1/2 = 8
Square each side
(x^1/2 )^2=( 8)^2
x = 64
1. What is the value of the 4th iterate of
f(x) = 3x-1/x2 if x0 = -2? Round to three decimal places.
The value of the 4th iterate of the given function f(x) is -2.096
2nd option is correct.
A function's iterate is a function that is expressed as repetition of another (already iterated) function; this latter function may be referred to as the iterand.
Any function taken on its own is regarded as the first iteration.
A function is said to have an identity function at iteration zero.
According to the question,
f(x) = (3x-1)/[tex]x^{2}[/tex]
[tex]x_{o}[/tex] = -2
The first iterate is calculated by finding f(-2).
f(-2) = (3(-2)-1)/4
f(-2) = -1.75
Similarly, the next iterates are calculated as follows:
f(-1.75) = -2.048
f(-2.048) = -1.71
f(-1.71) = -2.096
Thus, the fourth iterate for the given function is [tex]x_{4}[/tex]= -2.096
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PLEASE HELP ASAP
Determine the number of terms in the sequence. Your work must be shown with fractions not decimals.
2/81, 4/27, 8/9,…,6912
we conclude that the sequence has 8 terms.
How to get the number of terms in the sequence?
Here we have the geometric sequence:
2/81, 4/27, 8/9, ..., 6912
Notice that each term is equal to 6 times the previous term, such that:
2/81*6 = 4/27
4/27*6 = 8/9
Then the n-th term is equal to:
[tex]a_n = a_1*r^{n-1}[/tex]
Where in this case:
[tex]a_1 = 2/81\\\\r = 6[/tex]
Now we need to find the value of n such that:
[tex](2/81)*6^{n-1} = 6912\\\\6^n = 6*6812*(81/2) = 1,679,616[/tex]
If we apply the natural logarithm to both sides, then:
[tex]n*ln(6) = ln(1,679,616)\\n = ln(1,679,616)/ln(6) = 8[/tex]
Then we conclude that the sequence has 8 terms.
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When Roberto got a puppy from the shelter, it weighed 10.5Ibs. The puppy gained 40% of its original weight in the first month that Roberto had him. How much did the puppy weight after the first month?
This spinner has 6 equal sections. In simplest form, what are the odds in favor of spinning blue or green?
A. 1:2
B. 1:3
C. 3:1
D. 2:1
OA=
What Is OA=
Help me please!!! Thanksss
The length of side OA in the given rhombus is: 5 units.
What is a Rhombus?A rhombus is a quadrilateral that has four sides that are all of the same length. Therefore, in the image given, the length of AB equals the length of OA.
Given the following:
A(3, 4)B(8, 4)Length of AB = |8 - 3}
Length of AB = 5 units.
AB = OA = 5 units.
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What effect does 'h' have on the graph of a parabola?
Vertical stretch
Vertical compression
Vertical shift
Horizontal shift
The effect that 'h' have on the graph of a parabola is Horizontal shift or translation .
What is translation?A translation is the movement of a shape up, down , this can also be movement from side to side.
Even though there is movement, its appearance remains the same in any other way, hence, h values cause left or right movement with respect to the graph.
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This question has two parts. Use the information to answer Part A and Part B.
Part A
Enter a number in the box to create an expression equivalent to 2-5.
Part B
Which expressions represent the distance between the two points on the
number line? Select all that apply.
A 2-5
B. 2+(-5)
c. 1-3-21
D. 12-(-3)
E. 1-3+(-2)|
OF. 1-3-(-2)
Taking 1 in the box it creates an expression equivalent to 2 - 5.
The expressions represent the distance between the two points on the
number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.
What is integers on number line?
Integers are represented using a number line. A straight line of numbers is shown visually as a number line. It is made up of positive integers like 1, 2, etc., negative integers like - 1, - 2, etc., and a zero that is neither positive nor negative.
Part A:
2 - 5 = -3
2 + 1 = 3
The distance on the number line between a number and 0 is its absolute value.
a. That distance is never negative.
b. The symbol for Absolute Value is “ | | ”.
Hence, by taking 1 in the box it creates an expression equivalent to 2 - 5.
Part B:
|-3 -2| = 1
This point represent distance from -3 to -2 on the number line is 1 unit.
|2-(-3)| = 5
This point represent distance from 2 to -3 on the number line is 5 units.
|-3 + (-2)| = 5
This point represent distance from -3 to -2 on the number line is 5 units.
|-3 - (-2)| = 1
This point represent distance from -3 to -2 on the number line is 1 units.
Therefore,
Taking 1 in the box it creates an expression equivalent to 2 - 5.
The expressions represent the distance between the two points on the
number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.
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There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat.
Probability that a card selected at random is purple = 7/25
Probability of random selectionNumber of red cards, N(red) = 12
Number of blue cards, N(blue) = 17
Number of purple cards, N(purple) = 14
Number of yellow cards, N(yellow) = 7
Total number of cards, N(total) = 12 + 17 + 14 + 7
N(total) = 50
Probability that a card selected at random will be purple
P(purple) = N(purple) / N(total)
P(purple) = 14/50
Reduce to the lowest fraction
P(purple) = 7/25
Therefore, probability that a card selected at random is purple = 7/25
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Complete Question
There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat. If a card is selected at random, what is the probability that the card is purple
Now simplify the y-terms to get the equation of the parabolic path. You do not need to expand the x-term. (2 points) Hint: Square both sides to get rid of the square roots
The simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
How to determine the simplified equation?The complete question is added as an attachment
The equation is given as
[tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex]
Subtract (x - 10)^2 from both sides
[tex](y- 6)^2 = 4^2 - (x - 10)^2[/tex]
Evaluate 4^2
[tex](y- 6)^2 =16 - (x - 10)^2[/tex]
Take the square root of both sides
[tex]y- 6= \sqrt{16 - (x - 10)^2}[/tex]
Add 6 to both sides
[tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
Hence, the simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
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Select the correct answer. A linear function on a coordinate plane. A line passing through (1, 4), (minus 2, minus 2), intersects the y- axis at 2 units and intersects the x-axis at (minus 1, 0) to form shaded portions on the left side of the line. Which of the following inequalities is graphed on the coordinate plane? A. y ≤ 2 x + 2 B. y ≥ 2 x + 2 C. y < 2 x + 2 D.
Considering the given linear function, the inequality graphed is:
B. [tex]y \geq 2x + 2[/tex].
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line intersects the y-axis at 2 units, hence the y-intercept is b = 2. The function also passes through (1,4), hence the slope is:
m = (4 - 2)/(2 - 1) = 2.
Thus the equation of the line is:
y = 2x + 2.
The left-side of the line is the values above the line, hence the inequality is:
B. [tex]y \geq 2x + 2[/tex].
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Please help I don’t know if I’m doing this correctly
Answers:
Exponential and increasingExponential and decreasingLinear and decreasingLinear and increasingExponential and increasing=========================================================
Explanation:
Problems 1, 2, and 5 are exponential functions of the form [tex]y = a(b)^x[/tex] where b is the base of the exponent and 'a' is the starting term (when x=0).
If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.
If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.
In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.
Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.
---------------------
Problems 3 and 4 are linear functions of the form y = mx+b
m = slope
b = y intercept
This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.
If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.
On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.
Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.
Which x value makes this equation true? Explain how you can tell
2x^2 - x + 10 = 38
a) x=2
b) x=4
c) x=-4
d) x=6
Answer:
b) x = 4
Explanation:
[tex]2x^2 - x + 10 = 38[/tex]
collect variables
[tex]2x^2 - x + 10 - 38 = 0[/tex]
simplify
[tex]2x^2 - x - 28 = 0[/tex]
breakdown
[tex]2x^2 -8x + 7x - 28 = 0[/tex]
factor out
[tex]2x(x - 4) + 7(x - 4) = 0[/tex]
collect into groups
[tex](2x + 7)(x - 4) = 0[/tex]
set to zero
[tex]2x + 7 = 0, x - 4 = 0[/tex]
relocate variable
[tex]2x = -7, x = 4[/tex]
final solutions
[tex]x = -3.5, x = 4[/tex]
The answer is b.
To find the value of x, we need to convert this into the form of a quadratic equation.
Subtract 38 from each side.
2x² - x + 10 - 38 = 38 - 382x² - x - 28 = 0Solve by splitting the middle term.
2x² + 7x - 8x - 28 = 0x (2x + 7) - 4 (2x + 7) = 0x = 4, x = -7/2What is the solution to this system of linear equations?
x − 3y = −2
x + 3y = 16
(7, 3)
(3, 7)
(−2, −3)
(−3, −2)
Answer:
(7,3)
Step-by-step explanation:
you can add the equations together to eliminate y and first solve for x
(x-3y = -2) + (x+3y=16) = (2x = 14)
x = 7
then plug x into one of the equations to solve for y
(7) - 3y = -2
9 = 3y
y = 3
the solution is (7,3)
Answer: (7, 3)
Step-by-step explanation:
x - 3y = -2
x + 3y = 16
Here we can add the two equations together to cancel out the y
2x = 14
divide by 2 on both sides to get
x = 7
Now that we have the X value, plug in x value into an equation to get the Y
x - 3y = -2
7 - 3y = -2
-3y = -9
y = 3
So the solution is (7, 3)
Find the surface area of the composite solid. Round your answer to the nearest hundredth.
A. 424.11 ft²
B. 438.00 ft²
C. 449.00 ft²
D. 549.78 ft²
The surface area of the composite solid is 579.84 square feet
How to determine the surface area of the solid?The composite solid that completes the question is added as an attachment
From the attached figure, we have the following figures:
Rectangular prismCylinderThe surface area of a rectangular prism is
A = 2(lw + lh + wh)
Using the dimensions of the prism, we have:
A = 2(6 * 11 + 6 * 8 + 8 * 11)
This gives
A = 404
The surface area of a cylinder is
A = 2πr^2 + 2πrh
Using the dimensions of the cylinder, we have:
A = 2 * 3.14 * 4^2 + 2 * 3.14 * 4 * 5
Evaluate
A = 226.08
The area of the circle between both shapes is
A = πr^2
This gives
A = 3.14 * 4^2
A = 50.24
The surface area of the composite solid is then calculated as:
Surface area = Area of rectangular prism + Area of cylinder - Area of circle
This gives
Surface area = 404 + 226.08 - 50.24
Evaluate
Surface area = 579.84
Hence, the surface area of the composite solid is 579.84 square feet
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help me to slove this
Answer:
1. pi. 2.49-12.25pi
Step-by-step explanation: