A man who is 6 feet tall is walking at a rate of 4 feet/second, directly away from a light that is located 10 feet above the ground.
How long is the man's shadow t seconds after he starts walking? The answer will be in terms of t.
Answers
Answer:
2.5t
Step-by-step explanation:
Let the man be
x
feet away from the street light, and his shadow length be
y
, Let the tip of the shadow be
l
feet away from the light such that
l
=
x
+
y
and we are given that
d
x
d
t
=
2
By similar triangles:
y
6
=
x
+
y
30
∴
30
y
=
6
(
x
+
y
)
∴
30
y
=
6
x
+
6
y
∴
30
y
−
6
y
=
6
x
∴
24
y
=
6
x
∴
y
=
1
4
x
Now,
l
=
x
+
y
⇒
l
=
x
+
1
4
x
∴
l
=
5
4
x
Differentiating wrt
x
gives;
d
l
d
x
=
5
4
And by the chain rule we have:
d
l
d
t
=
d
l
d
x
d
x
d
t
∴
d
l
d
t
=
5
4
×
2
∴
d
l
d
t
=
2.5
feet/sec
Related Questions
PLS HELP I NEED TO FINISH THES IN ORDER TO PASS MY GRADE
Use the graph to answer the question.
graph of triangle ABC with vertices at negative 2 comma negative 2, 3 comma 3, 2 comma negative 5
Determine the coordinates of triangle A′B′C′ if triangle ABC is rotated 270° clockwise.
A′(−2, 2), B′(3, −3), C′(−5, −2)
A′(2, −2), B′(−3, 3), C′(5, 2)
A′(2, 2), B′(−3, −3), C′(5, −2)
A′(2, −2), B′(−3, 3), C′(2, 5)
Answers
Answer:
A′(2, −2), B′(−3, 3), C′(5, 2) (2nd choice)
Step-by-step explanation:
Rotating a point 270° clockwise about the origin is the same as rotating the point counterclockwise by 90°
In either case, the coordinates of any point (x, y) become new coordinates (-y, x)
I will summarize the original and rotated points,.
Original Rotated
Point(x, y) Point(-y, x) Remarks
-------------- -------------- -------------
A(-2, -2) A'(2, -2) eliminates 1st and 3rd choices
B( 3, 3) B'(-3, 3) no luck, both 2nd and 4th choices have this
C(2, -5) C'( 5, -2) only the 2nd choice fits all three
Answer: A′(2, −2), B′(−3, 3), C′(5, 2)
The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).
The correct answer is (A).
What are coordinates in a graph?The coordinates in a graph indicate the location of a point concerning the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
To rotate a point (x,y) 270° clockwise about the origin,
We can use the formulas:
x' = y and y' = -x.
So, to rotate triangle ABC 270° clockwise, we need to apply these formulas to each vertex:
A' = (-2, 2) rotated 270° = (2, -2)
B' = (3, 3) rotated 270° = (-3, 3)
C' = (2, -5) rotated 270° = (5, 2)
Therefore,
The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).
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Write an equation of each line in standard form with integer coefficients. y=-7 x-9
Answers
The equation of the given line y = -7x - 9 in standard form is 7x + y + 9 = 0
Equation of a line in standard form can be expressed as:
Ax + By + C = 0
Where:
A and B are coefficients.
x and y are variables of degree 1 or linear variables.
C is a constant.
All coefficients and constant term should be integers, not fractions or decimals. Furthermore, A should be a positive number.
The given equation is:
y = -7x - 9
Add both sides by 7x
7x + y = -7x +7x -9
7x + y = -9
Add both sides by 9
7x + y + 9 = -9 + 9
7x + y + 9 = 0
This is the standard form of the given line equation.
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need help please find the height of a cylinder with a volume of 500 cubic meters
Answers
Answer:
height = 20 cm
Step-by-step explanation:
the volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height )
here r = 5 and V = 500π , then
π × 5² × h = 500π
25πh = 500π ( isolate h by dividing both sides by 25π )
h = [tex]\frac{500\pi }{25\pi }[/tex] = 20 cm
Write the equation of the line in slope-intercept form
2y=-12x-16
Answers
The equation of the line in slope-intercept form is y = (-6)x + (-8) .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is 2y = -12x -16 .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
2y = -12x -16
On dividing both sides of above equation by 2, we will get
y = (-6)x + (-8) equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = -6
Intercept = c = -8
The equation of the line in slope-intercept form is y = (-6)x + (-8) .
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Evaluate each algebraic expression for x=3 and (y=-2).
2x-3y
Answers
The result of the algebraic expression 2x-3y for x=3 and y=-2 is 12
Given,
The algebraic expression = 2x-3y
x= 3
y= -2
Substitute the values in the expression
2x-3y= 2(3)-3(-2)
=6+6
=12
Hence, the result of the algebraic expression 2x-3y for x=3 and y=-2 is 12.
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The trail mix that you are making requires 4 cups of raisins for every 10 cups total of trail mix. If you use 24 cups of peanuts (the other ingredient), how many total cups will you have?
Answers
Answer:
40 cups
Step-by-step explanation:
4/10 is raisin
6/10 is peanuts
24/40 is peanuts
Kevin needs to order some new supplies for the restraunt where he works. the restraunt needs at least 492 glasses. there are currently 333 glasses. if each set on sale contains 18 glasses
Answers
Answer:
Step-by-step explanation:492 is needed right,and Kevin has 333 glass.So you need 159 glasses,but you need to find out how many sets you need to get 492 glasses.If 18 glasses comes in a set you'll need to divide 159 by 18 and get 8.83333333333. Then simplefiy the number to 8.8
Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 2,1,0.5,0.25, . . . . . .
Answers
It is a geometric sequence. The next two terms are: 0.125, 0.0625
The given sequence is:
2, 1, 0.5, 0.25, . . . .
Let a(n) be the nth term, then in the above sequence
a(1) = 2
a(2) = 1
a(3) = 0.5
a(4) = 0.25
Notice that:
a(2) = a(1) x 0.5
a(3) = a(2) x 0.5
a(4) = a(3) x 0.5
A sequence, of which its next term is obtained by multiplying the previous term by a constant is called a geometric sequence. The constant is called the ratio.
Therefore this is a geometric sequence with r = 0.5
To find the next two terms, continue the multiplication process:
a(5) = a(4) x 0.5 = 0.25 x 0.5 = 0.125
a(6) = a(5) x 0.5 = 0.125 x 0.5 = 0.0625
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Solve the following problem for x. If there is more than one solution include all solutions in your answer.
|3z-6|=9
X=
X=
Answers
Answer:
z = - 1 , z = 5
Step-by-step explanation:
| 3z - 6 | = 9
the absolute value function always gives a positive result, however, the expression inside can be positive or negative, that is
3z - 6 = 9 ( add 6 to both sides )
3z = 15 ( divide both sides by 3 )
z = 5
or
- (3z - 6) = 9
- 3z + 6 = 9 ( subtract 6 from both sides )
- 3z = 3 ( divide both sides by - 3 )
z = - 1
As a check
substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = 5
| 3(5) - 6 | = | 15 - 6 | = | 9 | = 9 = right side
x = - 1
| 3(- 1) - 6 | = | - 3 - 6 | = | - 9 | = 9 = right side
then solutions are z = - 1 , z = 5
A refrigerator that originally costs $ 1,200 it's on sale for 15% off. Tax is 8%. What would be the sale price of this refrigerator be including tax
Answers
The sale price of this refrigerator be including tax $1101.6 .
The value on the label of associate article/product is termed the marked price or asking price. this is often the worth at that product is meant to be sold-out. However, there will be some discount given on this value and therefore the actualof the merchandise could also be but the marked price. it's typically denoted by MP.When Discount is obtainable, M.P. > S.P.When Discount isn't offered, M.P. < S.P.Discount is outlined because the quantity of rebate given on the label value (marked price) of a piece. it's given by merchants/shopkeepers for attracting customers for increasing their sales.Discount = Marked value – priceIt is given that a refrigerator that originally costs $ 1,200 it's on sale for 15% off.
Discount percentage = [(Discount)/(Marked price)]× 100
15 = Discount / 1200 × 100
15 = Discount / 12
Discount = 15 × 12
= $ 180
Selling price = marked price - discount
= 1200 - 180
= $ 1020
The selling tax is given by = 8% 1020
= 8 / 100 ×1020
= $ 81.6
The total amount one has to pay to buy a refrigerator is = 1020 + 81.6
= $ 1101.6
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8=3x+6y. I need help on how to find Y?
Answers
Answer:y =20
Step-by-step explanation:8 = 3x + 6y.
subtract 3x from both sides:
8-3x = 6y,
Divide both sides by 6:
8/6 - 3x/6 = Y,
4/3 - x/2 = Y.
Determine whether the following statement is true or false. If false, give a counterexample. If true, give an argument to support your conclusion.
If the sum of tine acute angles of a triangle is greater than 90 , then the triangle is acute.
Answers
The statement given is true.
If the sum of tine acute angles of a triangle is greater than 90 , then the triangle is acute.
What is acute angle ?The acute angle can be defined as the angle less than 90°. Or we can say that the angle which is between 0° and 90° is called as an acute angle of a triangle. In the triangle all the angles gives the sum of 180 degree, that means, at least two angles in every triangle are always acute angles.
According to statement given in the question. This statement is absolutely true. If the sum of two acute angle is greater than 90 then the third angle of that polygon i.e. triangle must be less than 90 which makes the whole triangle a acute . Since, all the angles are now acute angles that means less than 90 thus this made the triangle as a acute triangle.
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a boy has a metal of density 14000kg/m3 .He intends to use it to make a rectangular pipe with external dimension of 18 cm by 10 cm and internal dimension of 15 cm by 8 cm .The length of the pipe is150 cm .Calculate the mass of the pipe in kg
Answers
Mass of the pipe= 100.8kgs
Mass is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force. The greater the mass of a body, the smaller the change produced by an applied force.
mass= density x volume
given that, the area of cross- section of the pipe is rectangular ring with area,
A=(10x10) - (15x8)
=180-120
=60 cm²=0.006 m²
length of the pipe = 150 cm=h
volume= A. h
= 0.006x150x10⁻²
= 0.720x10⁻²
= 0.0072 m³
Density =14000kg/m³
mass= density x volume
= 14000 x 0.0072
= 14 x 7.2
= 100.8 kg
we got that the mass of the pipe in kgs is = 100.8kgs
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Answer:
The pipe weighs 100.8 kg.
Step-by-step explanation:
Mass is essentially a body of matter's resistance to having its speed or position change when a force is applied. The change caused by an applied force is smaller the more mass a body has.
density x volume equals mass.
Considering that the pipe's cross-section is a rectangular ring of area,
A=(10x10) - (15x8)
=180-120
=60 cm²=0.006 m²
length of the pipe = 150 cm=h
volume= A. h
= 0.006x150x10⁻²
= 0.720x10⁻²
= 0.0072 m³
Density =14000kg/m³
mass= density x volume
= 14000 x 0.0072
= 14 x 7.2
= 100.8 kg
we got that the mass of the pipe in kgs is = 100.8kgs
me i don't now this help please
Answers
Frequency is measured in Hertz, which is one per second. If the wave vibrated 10 times in 10 seconds, it would have a frequency of 1Hz According to the graph, the frequency is increasing to 2Hz then 3Hz.
This is further explained below.
What is Frequency?Generally, The number of instances of a recurring event that takes place in a certain amount of time is referred to as its frequency.
In conclusion, Hertz is the unit of measurement for frequency, and one Hertz equals one second. If the wave vibrated once per second for a whole minute, its frequency would be one hertz (Hz).
The graph indicates that the frequency will reach 2Hz, and eventually 3Hz, in the near future.
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The path is 8,000 meters. How long
is the path in kilometers?
kilometers
Answers
Explanation:
Convert from meters to km by diving by 1000.
8000/1000 = 8km
Answer:
8 kilometers
Step-by-step explanation:
8000/1000
= 8 kilometers.
54 x 10 to the power of 4
Answers
Answer: 54*10^4=540000
Step-by-step explanation:
find the interest rate if $13400 has a final value of $17829 in 4 years give your answer to 1dp
Answers
Answer: It is $4429 (interest combined) or $1107.25 (interest annually)
Step-by-step explanation:
1. Subtract 13400 from 17829:
17829 - 13400 = 4429
2. Now, we know that 4429 is the accumulated interest in 4 years, now divide 4429 by 4:
4429/4 = 1107.25
3. Now we know that 1107.25 is the interest accumulated every year.
what is the answer to b?
Answers
Answer:35
Step-by-step explanation:because x equals 3y +2 so if x=11 then just mutlipy 11x3 thats 33 then plus 2 is 35
hope that helps :}
x = 14
Because 3(4) + 2 = 14
b)
y = 3
Because 11 = 3y + 2
11-2 = 9
9 divided by 3 = 3
43 43. The area of a circle is 100 cm². Calculate its radius.
Answers
Answer:
About 5.6 cm
Step-by-step explanation:
The formula for the radius of a circle (based on the area) is [tex]\sqrt{\frac{A}{\pi } }[/tex], where [tex]A[/tex] is the area of the circle?
can someone please help me I don’t understand and it’s a really important homework
Answers
Smaller number: 9
Answer: Large number: 36
Smaller number: 9
Step-by-step explanation:
|x+1|+|3x-2|=2
Solve each equation
Answers
Answer:
2
Step-by-step explanation:
x+1 +3x-2=2 group them in like terms
3x-x+2+1=2 then subtract the variable and add the number
2x=3-2 arrange them
2x=1 divide both side by 2
therefore x=2
Aileen sold 42 MP3 players last
month at $125 per MP3 player. If
she earns $2130 per month in
base pay and makes an 18%
commission on all MP3 sales,
how much did she earn last
month?
Answers
By adding the base salary and the commissions, we conclued that Aileen did make 3,075 dollars last month.
how much did she earn last month?
She sold 42 MP3 for $125 each, and she gets a 18% commission on this, so what she wins in commissions is:
0.18*42*$125 = $945
If we add that to the base that she earns per month, which is $2,130, it gives:
$945 + $2,130 = $3,075
In this way, we conclued that Aileen did make 3,075 dollars last month.
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Enter the rational number as a decimal. Then tell whether the decimal is a terminating or a repeating
decimal.
4/5
Answers
Sergei runs a bakery. He needs at least 175 kilograms of flour in total
to complete the holiday
orders he's received. He only has 34
kilograms of flour, SO he needs to buy more.
The flour he likes comes in bags that each contain 23 kilograms of flour. He wants to buy the
smallest number of bags as possible and get the amount of flour he needs.
Let F represent the number of bags of flour that Sergei buys.
Answers
Answer:
Step-by-step explanation: Using proportions, it is found that Sergei needs to buy 7 bags.
-----------
This question is solved by proportions, using a rule of three.
He has 34 kilograms of flour.
He needs 175 kilograms.
Thus, he needs to buy 175 - 34 = 141 kilograms.
Each bag contains 23 kilograms. How many bags are needed for 141 kilograms?
1 bag - 23 kilograms
x bags - 141 kilograms
Applying cross multiplication:
[tex]23x = 141[/tex]
[tex]x = \frac{141}{23}[/tex]
[tex]x = 6.1[/tex]
Rounding up, he needs to buy 7 bags
FIFTY POINTS
y=-16t^2+40t+2
For what interval or intervals of time will the projectile be
above 18 feet?
a.) Between 1 and 1.5 seconds
b.) Less than 1 second and greater than 1.5 seconds
c.) Between 0.5 and 2 seconds
d.) Less than 0.5 second and greater than 2 seconds
Answers
Answer:
To find when the projectile is above 18 feet, we need to find the values of time when the height of the projectile is greater than 18. The height of the projectile can be found by plugging the value of time into the equation y = -16t^2 + 40t + 2.
So, we need to find the values of t when y > 18.
y = -16t^2 + 40t + 2 > 18
-16t^2 + 40t - 16 > 0
To solve this inequality, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
where a = -16, b = 40, and c = -16.
So, t = (40 ± √(40^2 - 4(-16)(-16))) / 2(-16)
t = (40 ± √(40^2 + 256)) / -32
t = (40 ± √(1616)) / -32
t = (40 ± 40) / -32
t = (80 / -32) / 2 or (0) / 2
t = -1.25 or 0
Since t has to be positive (time cannot be negative), we can only use the positive value, t = 0.5. So, the interval of time when the projectile is above 18 feet is between 0.5 and 2 seconds, which is (c).
Determine the total number of roots of each polynomial function. f (x) = (3x4 + 1)2[
Answers
The total number of roots will be 8.
We have a function f(x) = [tex](3x^{4}+1 )^{2}[/tex].
We have to determine the total number of roots for this function f(x).
What is function ?A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.
According to the question, we have function -
[tex](3x^{4}+1 )^{2}[/tex]
We can rewrite it after expanding as follows -
[tex](3x^{4}) ^{2} + 1 + 6x^{4}[/tex]
[tex]9x^{8}+6x^{4} +1[/tex]
Now, the maximum degree of the polynomial is 8. The number of roots are equal to the maximum degree of a polynomial.
Hence, the total number of roots will be 8.
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A classroom has 48 seats. There are 6 seats in each row, which are arranged In this order:
Wall 5A 5B 5C aisle 5D 5E 5F wall
Four students are already sitting in their seats in the 5th row. Lina decides to sit by the wall, as she likes to have only one person sitting next to her and be close to the windows. Alex is sitting next to the aisle, as he needs to rush out of the classroom as soon as the lesson ends. Ken and Rue are best friends and are sitting in the adjacent seats, but Rue is not sitting by the wall. Maria and Ted enter the classroom, and there are only two available seats left in the classroom in the 5th row. Maria and Ted were hoping to sit next to each other.
What are the chances that their expectations will not be met?
Answers
Answer: 6%
Step-by-step explanation:
I just baised it off of how many students were in the equation. at the end thier is only 6 seats left
Solve each equation. (m-2)-5=8-2(m-4)
Answers
The solution of the given linear equation in one variable (m-2)-5=8-2(m-4) is at m = 23/3.
According to the given question.
We have a linear equation in one variable
(m-2)-5=8-2(m-4)
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable (m-2)-5=8-2(m-4) is given by
(m -2) -5 = 8 -2(m -4)
⇒ m -2 - 5 = 8 -2m + 8 (by distributive rule)
⇒ m -7 = 16 - 2m (adding and subtracting the line terms)
⇒ m + 2m = 16 + 7
⇒ 3m = 23
⇒ m = 23/3
Hence, the solution of the given linear equation in one variable (m-2)-5=8-2(m-4) is at m = 23/3.
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Write an equation for the line on the graph below:
Answers
Answer:
y= - 6
Step-by-step explanation:
the coordinate- y of every point on the line will be - 6
Suppose you pull a card from a standard 52-card deck. Find the probability of following event. The card is a face card.
Answers
3/13 is the probability of following event. The card is a face card.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Total no.of cards = 52
Let A be the event of taking face card.
No.of face cards = 4×3 = 12
Now n(S)= 52C1 = 52, n(A) = 12C1 = 12
So P(A) = n(A)/n(S) = 12/52 = 3/13
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