Answer:
You did not ask anything, i guess that you want to find the equation of the height of the nail as a function of time.
Data that we have:
The nail is in a circular object.
the nail hits the ground every 2 seconds, then the weel does a full cycle every 2 seconds.
The maximum height of the nail is 48cm, and as the nail is stuck on the weel, the maximum height will be when the nail is on top of the weel.
From this, we can conclude that the diameter of the weel is 48cm.
Now, with this we could write the equation of the height of the nail as a function of time.
We know that this is a periodic function, so let's write it as:
f(t) = A*cos(c*t) + B
where A, B and c are constanst.
At t = 0, when the byke hits the nail, the nail must be in the ground, so we have that:
0 = A*cos(c*0) + B
A + B = 0
A = - B
and we also know that the function is periodic with T = 2s
cos(c*t) = cos(c*(t + 2s) = cos( c*t + 2s*c)
and we know that the period of the cosine function is 2*pi
then:
c*2s = 2*pi
c = (2pi/2s) = pi/s
then our function is:
f(t) = -B*cos(t*pi/s) + B
now, the maximum heightwill be when cos(t*pi/s) = -1, and this happens at t = 1s
f(1s) = -B*cos(pi) + B = 2B
And we know that the maximum height is 48cm
2*B = 48cm
B = 24cm
Then the function of the height of the nail is:
f(t) = -24cm*cos(t*pi/s) + 24cm
A rope that is 245 cm long is cut into three pieces. The ratio of the lengths of the first piece to the second piece is 2:3, and the ratio of the lengths of the second piece to the third piece is 4:5. What is the length of the longest of the three pieces?
Answer:
The length of longest piece is 105 cm.
Step-by-step explanation:
Given:
Rope is 245 cm long.
Ratio of lengths of first to second piece = 2:3.
Ratio of lengths of second to third piece = 4:5.
To find:
Length of longest piece = ?
Solution:
We are given the ratio of first and second pieces AND
ratio of second and third pieces.
Common link is second piece.
We need to make the ratio of second piece equal in both the ratio to find the ratio of all three pieces.
2:3
4:5
Multiply 1st ratio by 4 and 2nd ratio by 3:
Now, the ratio becomes:
8:12 and 12:15
And the ratio of three pieces can be represented as:
8: 12: 15, this ratio is the first piece: second piece: third piece
[tex]\Rightarrow 8x+12x+15x = 245\\\Rightarrow 35x = 245\\\Rightarrow x = \dfrac{245}{35}\\\Rightarrow x = 7[/tex]
So, the pieces lengths will be
First piece = [tex]8 \times 7 = 56[/tex] cm
Second piece = [tex]12 \times 7 = 84[/tex] cm
Third piece = [tex]15 \times 7 = 105[/tex] cm
So, the length of longest piece is 105 cm.
There are 110 applicants for three cosmetology positions. How many different ways can the three positions be filled? Select one: 215,820 ways 3 ways 1,294,920 ways 1,331,000 ways
Answer: 215,820 ways
Step-by-step explanation:
There are 110 applicants for three cosmetology positions. How many different ways can the three positions be filled?
Number of positions = 110
Number of applicants = 3
Number of way in which the positions can be filled ;
This is a combination problem
nCr = n! ÷ (n-r)! r!
110C3 = 110! ÷ (110 - 3)! 3!
110C3 = 110! ÷ 107! 3!
110C3 = (110 * 109 * 108) / (3 * 2 * 1)
110C3 = 1294920 / 6
= 215820 ways
Please answer this question now in two minutes
Answer:
q = 4 mi
Step-by-step explanation:
Using the sine or cosine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{q}{4\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
[tex]\sqrt{2}[/tex] × q = 4[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
q = 4
Pete grabbed 18 mixed nuts, 2/9 of which were almonds. Which equation shows how to determine the number of almonds Pete grabbed? A.18 divided by 2/9 =81
Answer:
18 multiplied by 2/9 = 4
Step-by-step explanation:
To determine the number of almonds that Pete grabbed, you have to multiply how much of the nuts were almonds by the total number of nuts that he grabbed. So,
2/9 × 18
= 0.2222 × 18
= 4
Pete grabbed 4 almonds out of the 18 mixed nuts that he grabbed.
Hope that helps.
Answer:
Amount of almonds = 18 × [2/9]
Amount of almonds = 4 almonds
Step-by-step explanation:
Given:
Number of mixed nuts = 18
Probability of almonds = 2/9
Find:
Amount of almonds
Computation:
Amount of almonds = Number of mixed nuts × Probability of almonds
Amount of almonds = 18 × [2/9]
Amount of almonds = 36 / 4
Amount of almonds = 4 almonds
If Camryan has 12 Tie fighters and Logan has 23 more than Camryan how many Tie fighters does Logan have.
Answer:
logan has 35 Tie fighters
Step-by-step explanation:
Camryan has 12
Logan has 23 more
23+12=35
hope i helped
-lvr
Given the coordinate points of the preimage, use the transformation given to provide the points of the image. E(−5,−1) D(−5,1) C(−1,0) B(−2,−3) Rotation: 180∘ about the origin
Answer:
The points of the image are;
E'(5, 1), D'(5, -1), C'(1, 0), E'(-2, -3)
Step-by-step explanation:
The coordinates of the preimage are E(-5, -1) D(-5, 1) C(-1, 0) B(-2, -3)
Rotation of a point 180° about the origin gives;
Coordinates of the point of the preimage before rotation = (x, y)
The coordinates of the image after rotation = (-x, -y)
Therefore, the coordinates of the points EDCB after 180° rotation about the origin are;
E(-5, -1) rotated 180° becomes E'(5, 1)
D(-5, 1) rotated 180° becomes D'(5, -1)
C(-1, 0) rotated 180° becomes C'(1, 0)
B(-2, -3) rotated 180° becomes E'(-2, -3).
Help me please ty ty ♀️❤️
Answer:
AHH! Geometry!
Thanks for this problem. Needed to refresh my skill for similarity and rations.
First, notice the lines that are on sides of the triangles. Lines with the same number of marks are the same measure. You may have already known this, but I'll just tell you for reference.
That means both of those pair of sides have equal length. What does this mean though?
Imagine that each of the line segments(the ones with two marks) are... 1 cookie (Their lengths, also, I really want a cookie.)
Now, this is where ratios come into play. Consider only the top triangle to the entire triangle. The Top Triangle has a side with the length of one cookie. That corresponding side on the entire large one is 2 cookies (because they are the same measure, and 1*2=2).
Thus, we can make a ratio, comparing the lengths of a corresponding sides.
(BTW, these are similar triangles, meaning that they have all the same angle measures, but different side lengths.)
[tex]\frac{1Cookie}{2Cookies}[/tex]
Now. (Refer to above) Similar triangles have ratios of similarity. Meaning that: Corresponding sides have a 1/3 ratio. This means, also, that all the other corresponding sides have a 1/3 ratio. Neat, huh?
Putting into other words, we can compare CB and RT with the same 1/2 ratio!(Just cancel out the cookies, its still the same ratio)
Now, that we have all our needed information, let's solve!(Also, remember to match it up properly, or else it won't work: Small triangle side/Small Triangle side=Large Triangle Side/Large Triangle Side, or something like that).
[tex]\frac{1}{3x-8} =\frac{2}{2x+4} \\2x+4=6x-16\\4x=20\\x=5[/tex]
^ ANSWER
So there you go! X is equal to 5. I'm sure you can solve the rest on your own!
Hope this helps!
Stay Safe! I'm going to get that cookie now...
Please help this is a new topic for me.
Answer:
last answer
Step-by-step explanation:
P' (2, -4)
Q' (-2, -5)
R' (1, -8)
Answer:
C. P'(2, -4) Q'(-2, -5) R'(1, -8)
Step-by-step explanation:
When you reflect something across the y-axis you change (x,y) to (-x,y).
For each point, change the x to a negative x.
P(-2, -4) --> P'(2, -4)
Q(2, -5) --> Q'(-2, -5)
R(-1, -8) --> R'(1, -8)
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
WILL GIVE BRAINLIEST PLZ HELP
Answer:
y = -5x - 9.
Step-by-step explanation:
(-2, 1)
(0, -9)
(1 - -9) / (-2 - 0) = (1 + 9) / (-2) = 10 / (-2) = 5 / (-1) = -5
Since -5 is the slope, and the y-intercept is at (0, -9), we have an equation of y = -5x - 9.
Hope this helps!
Answer:
y=-5x-9
Step-by-step explanation:
Change in x = +2
Change in y=-10
-10/2=-5
m=-5
plug in an point
example:
1=-5(2)+B
B=-9
To check your answer:
y=-5x-9
plug in an point for x given on the chart:
-5(0)-9=-9
you have 12 monkey but 5 were taken away how much do you have
Answer:
12-5=7
unless it's not a prank or a joke question
Answer:
7
Step-by-step explanation:
Original number of monkeys = 12
Number taken away = 5
So, number left = 12-5 = 7.
Hope this helps.
Please help me asap!!!
Answer:
HL theorem
Step-by-step explanation:
Since this is a right triangle, we can use the HL ( hypotenuse leg theorem)
We know that one of the legs are equal to each other by the lines on the legs and the hypotenuse is congruent by the reflexive property
Consider the construction of a pen to enclose an area. You have 500 ft of fencing to make a pen for hogs. If you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area
Answer:
The dimensions of the rectangular pen that maximize the area are [tex]w = 125\,ft[/tex] and [tex]l = 250\,ft[/tex].
Step-by-step explanation:
Let suppose that one side of the rectangular area to be fence coincides with the contour of the river, so that only three sides are needed to be enclosed. The equations of perimeter ([tex]p[/tex]) and area ([tex]A[/tex]), measured in feet and square feet, are introduced below:
[tex]p = 2\cdot w + l[/tex]
[tex]A = w\cdot l[/tex]
Where [tex]w[/tex] and [tex]l[/tex] are the length and width of the rectangle, measured in feet.
Besides, let suppose that perimeter is equal to the given amount of fencing, that is, [tex]p = 500\,ft[/tex]. The system of equations is:
[tex]2\cdot w + l = 500\,ft[/tex]
[tex]A = w\cdot l[/tex]
Let is clear the length of the rectangle and expand the area formula:
[tex]l = 500\,ft-2\cdot w[/tex]
[tex]A = w\cdot (500\,ft-2\cdot w)[/tex]
[tex]A = 500\cdot w -2\cdot w^{2}[/tex]
To determine the maximum area that can be enclosed, first and second derivatives to obtain the critical values that follow to an absolute maximum.
First derivative
[tex]A' = 500 - 4\cdot w[/tex]
Second derivative
[tex]A'' = -4[/tex]
Now, let equalize the first derivative to zero, the only critical value is:
[tex]500-4\cdot w = 0[/tex]
[tex]4\cdot w = 500[/tex]
[tex]w = 125\,ft[/tex]
Since the second derivative is a negative constant function, then, the previous outcome follows to an absolute maximum. The length of the rectangular area is: ([tex]w = 125\,ft[/tex])
[tex]l = 500\,ft - 2\cdot (125\,ft)[/tex]
[tex]l = 250\,ft[/tex]
The dimensions of the rectangular pen that maximize the area are [tex]w = 125\,ft[/tex] and [tex]l = 250\,ft[/tex].
Which of the following best describes the slope of the line below?
Answer:
I think positive
Step-by-step explanation:
Answer:
zero, D
Step-by-step explanation:
a horizontal line (left to right) would be zero
a verticle line (up and down) would be undifined
1 2 3 4 5 6 7 8 9 10 TIME REMAINING 57:18 Triangle A B C is shown. Angle A B C is a right angle. An altitude is drawn from point B to point D on side A C to form a right angle. The length of A D is 5 and the length of B D is 12. What is the length of Line segment B C, rounded to the nearest tenth? 13.0 units 28.8 units 31.2 units 33.8 units
Answer:
28.8 units
Step-by-step explanation:
In order to further explain the description of the right angled triangle ABC above, I have attached a hand drawn diagram for easier understanding.
The length of A D is 5 units
The length of B D is 12 units.
From the above triangle ABC, to solve for BC we have the following ratios.
BD : BC = AD : BD
Hence,
BD/ BC = AD/BD
= 12/BC = 5/12
Cross Multiply
12× 12 = BC × 5
BC = 12 × 12/ 5
BC = 144/5
BC = 28.8 units
Therefore, the length of Line segment B C, rounded to the nearest tenth is 28.8 units
Answer:
c.31.2
Step-by-step explanation:
Kaylee has $4,500 for a down payment and thinks she can afford monthly payments of $300. If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate), what is the maximum amount Kaylee can afford to spend on the car? [use the calculation in the text or the online calculators in the resource section]
Answer:
$17,028.06
Step-by-step explanation:
Given that :
Kaylee's down payment = $4500
monthly payment = $300
If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate).
the maximum amount Kaylee can afford to spend on the car is being calculated as the present value for all the payments.
= [tex]=\$4,500 +\dfrac{\$300}{(1+\frac{0.07}{12})} + \dfrac{\$300}{(1+\frac{0.07}{12})^2} +\dfrac{\$300}{(1+\frac{0.07}{12})^3} + ....+ \dfrac{\$300}{(1+\frac{0.07}{12})^{46}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{47}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{48}}[/tex]
Using the online desmos calculator to determine the maximum amount Kaylee can afford to spend on the car; we have:
= $17,028.06
h(1) = -26
h(n) = h(n − 1).(-9)
Find an explicit formula for h(n).
Answer:
H(n) = 234⁽ⁿ⁻¹⁾
Step-by-step explanation:
Hello,
The first thing to do when finding an explicit equation is to determine if the sequence is arithmetic or geometric.
In this question, the sequence is a geometric progression.
h(n) = h⁽ⁿ⁻¹⁾.(-9)
a = -26
r = common difference
a(n) =ar⁽ⁿ⁻¹⁾
h(n) = -26 × (-9)hⁿ⁻¹⁾
h(n) = 234⁽ⁿ⁻¹⁾
Answer:
−26⋅(−9) ^n-1
Step-by-step explanation:
Simplify this expression.
275(13 +2)
O 2765 + 2/10
O 25+277
O 2665 + 2/10
O 2675 +2V10
Hurrryyy
Answer:
2675 +2V10
Step-by-step explanation:
Answer:
D :)
Step-by-step explanation:
did on edge 2021
Which of the following are solutions to the quadratic equation? Check all that apply.
x2 + x-12 = 0
A. -1
B. 28
C. 2
D. 4
E. 3
F. -4
Answer:
x= -4 x= 3
Step-by-step explanation:
x2 + x-12 = 0
Factor
What 2 numbers multiply to -12 and add to 1
4 * -3 = -12
4+3 = 1
( x+4) ( x-3) =0
Using the zero product property
x= -4 x= 3
Answer:
E, F
Step-by-step explanation:
x² + x - 12 = 0
Let’s factor left side.
Find 2 numbers that multiply to get -12 and add to get 1
4 × -3 = -12
4 + 3 = 1
x² - 3x + 4x - 12 = 0
x(x - 3) + 4(x - 3) = 0
(x + 4)(x - 3) = 0
Set factors equal to 0.
x + 4 = 0
x = -4
x - 3 = 0
x = 3
Find the Equation of the Parallel Line
2
of
Instructions: Find the equation of the line through point (-7,2) and parallel to
= x - 1. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 1).
Y=
y =
Answer:
y = 2/5x + 4/5
Step-by-step explanation:
We'll begin by calculating the slope of the equation: y = 2/5x – 1/2
The slope of the above equation can be obtained as follow:
y = mx + c
Where m is the slope.
c is the y-intercept.
y and x are the coordinate.
Comparing:
y = 2/5x – 1/2 with y = mx + c
The slope of y = 2/5x – 1/2 is 2/5.
Now, let us determine the equation parallel to y = 2/5x – 1/2.
This is illustrated below:
The coordinate of the line => (–7, 2)
x1 = –7
y1 = 2
Slope (m) = 2/5 => Since the lines are parallel, their slope are equal.
y – y1 = m (x – x1)
y – 2 = 2/5(x – –7)
y – 2 = 2/5(x + 7)
Clear bracket
y – 2 = 2/5x + 14/5
Rearrange
y = 2/5x + 14/5 + 2
y = 2/5x + 4/5
Therefore, the equation is:
y = 2/5x + 4/5
work out the value of x and y in this diagram. All measurement are in centimeters
Answer:
X = 5
Y = 7
Step-by-step explanation:
First we will find x
4x + 2 = 3x + 7
x + 2 = + 7
x = 5
Next we will find y
2y + 9 = 4y - 5
-2y + 9 = -5
-2y = -14
y = 7
|x–5|=–5 plzz help me
Answer:
(0-5)=-5
-5-5 = 0
x=0
Step-by-step explanation:
Write the algebric expression of the difference of 'a' and 'b'
Step-by-step explanation:
An algebraic expression haa atleast one variable and operator sign such as (+,-,×,÷)
According to the question, an algebraic expression should be made from difference of 'a' and 'b'
so, the expression is (a - b) or a - b.
Hope it helps!!!!
se technology to solve 4x−11=3.2x+13. Enter the solutions in the boxes. Write the lesser solution first. Round to the nearest tenth if needed.
Answer: x=30
Step-by-step explanation: if you were looking for the value of x, hope this helps!
first, you have to make sure that the correct values are on the right side to allow us to find the answer faster and easier. your modified formula should look like this: 4x-3.2x=11+13
if you do the operations on each side, it will look like this: 0.8x=24, from here, all you have to do now is divide 24 by 0.8 to get the X value, which will result in 30!
A number is divided in the ratio 7:2. If the second part is 34, find the number.
Answer:
153.
Step-by-step explanation:
If the second part is 34 units, then the 2 of the ratio is equal to 34 / 2 = 17.
That means the first part will be 7 * 17 = 119.
119 + 34 = 153.
Hope this helps!
Find the length of AC round to the nearest hundred
Answer:
Option B. 9.11
Step-by-step explanation:
To find the length of line AB, we must first of all calculate the value of θ as shown in the attached photo.
The value of θ can be obtained as follow:
θ + 39° + 120° = 180° (sum of angles in a triangle)
θ + 159° = 180°
Collect like terms
θ = 180° – 159°
θ = 21°
Thus, we can obtain the length of line AB by using sine rule as illustrated below:
b/Sine B = c/Sine C
b = 16
Angle B = 39°
Sine C = 21°
c =?
b/Sine B = c/Sine C
16/Sine 39° = c/Sine 21°
Cross multiply
c × Sine 39° = 16 × Sine 21°
Divide both side by Sine 39°
c = (16 × Sine 21°) / Sine 39°
c = 9.11
Therefore, the length of line AB is 9.11
Which is the graph of linear inequality 6x + 2y > -10?
Answer:
The top left one.
Step-by-step explanation:
Fix this into y intercept form: y=mx+b
y>-3x-5
Because y is greater than 3x-5, the shaded area should be positive, so the top right and the bottom right will be eliminated. Now, looking at the y intercept which is the 'b' in the equation, it is -5. So the y intercept on the graph should be on negative 5, which means that the top left one is the correct answer!
Hope this helped, BRAINLIEST would really help me:)
Option 1 is the correct choice.
We have a linear inequality -
6x + 2y > -10
We have to determine which of the following graphs depicts the inequality given above.
What is an Inequality?An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.
According to the question, we have -
6x + 2y > -10
Add - 6x on both sides of inequality, we get -
- 6x + 6x + 2y > - 10 - 6x
2y > - 6x - 10
Dividing both sides of the inequality by 2, we get -
y > - 3x - 5
Now, in order to plot the graph for this inequality, let -
y = - 3x - 5
Plot the line for the above equation. Remember to plot the graph in the form of dashed line since the inequality is strict inequality.
Consider the point (0, 0) -
Solve the inequality for the point (0, 0), we get -
0 > - 3 x 0 - 5
0 > - 5
Which is true.
Hence, shade the complete area on that side of line where the point
(0, 0) lies.
Therefore, Option 1 is the correct choice.
(Refer the image attached, for reference)
To solve more questions on Plotting inequalities, visit the link below -
https://brainly.com/question/1782515
#SPJ6
Find the angle between the given vectors to the nearest tenth of a degree. u = , v = (2 points)
Answer:
3.6°Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the angle between the given vectors to the nearest tenth of a degree.
u = <8, 7>, v = <9, 7>
we will be using the formula below to calculate the angle between the two vectors;
[tex]u*v = |u||v| cos \theta[/tex]
[tex]\theta[/tex] is the angle between the two vectors.
u = 8i + 7j and v = 9i+7j
u*v = (8i + 7j )*(9i + 7j )
u*v = 8(9) + 7(7)
u*v = 72+49
u*v = 121
|u| = √8²+7²
|u| = √64+49
|u| = √113
|v| = √9²+7²
|v| = √81+49
|v| = √130
Substituting the values into the formula;
121= √113*√130 cos θ
cos θ = 121/121.20
cos θ = 0.998
θ = cos⁻¹0.998
θ = 3.6° (to nearest tenth)
Hence, the angle between the given vectors is 3.6°
Determine the equation of the line that is parallel to y=23x+4 and passes through the point (3,7).
Answer: y = 23x - 62
Step-by-step explanation:
Parallel lines have the same slope.
y = 23x + 4
m=23 b=4
Input x = 3, y = 7, & m = 23 into the Point-Slope formula to find the equation or the Slope-Intercept formula to find b (you already have m). I will choose the latter.
y = mx + b
7 = 23(3) + b
7 = 69 + b
-62 = b
m = 23, b = -62 --> y = 23x - 62
(ii) Atrader gets a profit of 20% by selling an item for £ 150. Find the buying in price.
(iii) A bank charges 12% per annum on loans. If a person borrowed a loan of
£ 20000 find the total amount that he has to repay after one year.
(a) Six workers can build a wall in 10 days. At the same rate how many
workers are needed to complet in 4 days.
(c) How many extra workers to be employed ?
Answer:
ii) £120
iii) £2,400
a) 10 workers
c) 4 workers more to be employed.
Step-by-step explanation:
ii) To find the buying price we deduct 20% (percent) from the selling price of £150.
= 20/100 x 150
= £30 (Next we substract this value from the selling price of £150) = €150 - £30 = £120
iii) A 12% interest per annum Implies a 12 percent of the borrowed amount of 20,000, which is calculated as
12% or 12/100 x 20,000 = £2,400
a) Put simply, we create an equation for the problem.
4 men * 10 days = 40 man days.
X men * 4 days = 40 man days.
Let's substitute the equation:
(X/ 4) * (4/ 10) = 40 / 40
(X/4) * 0.4= 1 (collect like terms)
0.4 * x = 4
0.4x/0.4= 4/0.4
x = 10 workers.
(c) 4 extra workers to would need to be employed since we have six already available (10-6=4).
HELPPPPPPPPPPPPPPPpppp
Answer:
Option (A)
Step-by-step explanation:
Two bases of the the given cylinder are circular in shape in the given picture.
When we take a cross-section of the cylinder parallel to the bases or perpendicular to the height, we get a circle exactly same as the bases (As shown on the rectangular slide).
Cross-section will have the same radius as the bases of the cylinder.
Therefore, Option (A) will be the answer.