(1 point) A street light is at the top of a 14 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 feet from the base of the pole? The tip of the shadow is moving at ft/sec.
Answers
The tip of the shadow is moving at approximately 8.96 ft/sec
To find how fast the tip of the shadow is moving when the 6-foot-tall woman is 30 feet away from the 14-foot-tall pole, we can use similar triangles and the concept of related rates.
Let x be the distance from the woman to the tip of her shadow, and y be the distance from the base of the pole to the tip of the shadow. Since the height of the pole and the height of the woman create similar triangles, we have:
(Height of woman) / (Distance from woman to tip of shadow) = (Height of pole) / (Distance from base of pole to tip of shadow)
6 / x = 14 / y
Now, we need to find the rate at which the tip of the shadow is moving (dy/dt) when the woman is 30 feet away from the pole (y = 30). Differentiate both sides of the equation with respect to time (t):
6(-dx/dt) / x^2 = 14(dy/dt) / y^2
Since the woman is walking away from the pole at 7 ft/sec:
dx/dt = 7
When the woman is 30 feet away from the pole:
y = 30
We can find x using the similar triangles:
6 / x = 14 / 30
x = (6 * 30) / 14
x = 90 / 14
Now, plug in the values of x, y, and dx/dt into the equation and solve for dy/dt:
6(-7) / (90 / 14)^2 = 14(dy/dt) / 30^2
After solving the equation:
dy/dt ≈ 8.96
So, the tip of the shadow is moving at approximately 8.96 ft/sec when the woman is 30 feet away from the base of the pole.
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Related Questions
Multiply.
2x^4 (3x³ − x² + 4x)
Answers
Answer: A
Step-by-step explanation:
When multiplying: Numbers multiply with numbers and for the x's, add the exponents
If there is no exponent, you can assume an imaginary 1 is the exponent
2x⁴ (3x³ − x² + 4x)
= 6x⁷ -2x⁶ + 8x⁵
Answer:
A. \(6x^{7} - 2x^{6} + 8x^{5}\)
Step-by-StepLabel the parts of the expression:
Outside the parentheses = \(2x^{4}\)
Inside parentheses = \(3x^{3} -x^{2} + 4x\)
You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses
\(2x^{4}\) × \(3x^{3}\)
\(2x^{4}\) × \(-x^{2}\)
\(2x^{4}\) × \(4x\)
First, multiply the whole numbers of each value before the variables
2 x 3 = 6
2 x -1 = -2
2 x 4 = 8
Now you have:
6\(x^{4}x^{3}\)
-2\(x^{4}x^{2}\)
8\(x^{4} x\)
When you multiply exponents together, you multiply the bases as normal and add the exponents together
\(6x^{4+3}\) = \(6x^{7}\)
\(-2x^{4+2}\) = \(-2x^{6}\)
\(8x^{4+1}\) = \(8x^{5}\)
Put the numbers given above into an expression:
\(6x^{7} -2x^{6} +8x^{5}\)
Key Wordsdistribution
variable
like exponents
One day a store sold 28 sweatshirts. White ones cost $9.95 and yellow ones cost $13.50. In all, $321.20 worth of sweatshirts were sold. How many of each color were sold?
Answers
Answer:
white sold = 16
yellow sold = 12
Step-by-step explanation:
w = # of white sold
y = # of yellow sold
w + y = 28 solve this for w
w = 28 - y
9.95w + 13.5y = 321.20 substitute w = 28-y into this expression and solve for y
9.95(28-y) + 13.5y = 321.20
278.60 - 9.95y + 13.50y = 321.20
278.60 + 3.55y = 321.20
3.55y = 321.20 - 278.60 = 42.60
y = 42.60/3.55 = 12 substitute this into w = 28 - y and solve for w
w = 28 - 12 = 16
find the area of the figure with coordinates A (-6,1), B (2,1), C(-3,4), D(5,4)
Answers
Answer: The area of the figure is 24 units.
Step-by-step explanation:
After plotting, the given points on the graph, we can observe that it is a parallelogram(opposite sides are equal and parallel)
Height = 4-1 = 3 units
Base = 2-(-6) = 8 units
Area of parallelogram = Base x height
= 8 x 3 square units.
= 24 square units.
Hence, the area of the figure is 24 units.
On a coordinate plane, a triangle has points (negative 5, 1), (2, 1), (2, negative 1).
Use the drop downs to answer the following questions about the distance between the points (−5, 1) and (2, −1).
What is the distance of the horizontal leg?
What is the distance of the vertical leg?
Use the Pythagorean theorem. What is the distance between the two points?
Answers
Answer:
The answer is below
Step-by-step explanation:
The points of the triangle are (- 5, 1), (2, 1), (2, - 1). The distance between two points is given by:
\(Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
The horizontal leg is formed by points with the same y axis. Therefore the points that make up the horizontal leg is (- 5, 1), (2, 1). The Distance of the horizontal leg is:
\(Horizontal\ leg=\sqrt{(2-(-5))^2+(1-1)^2}=\sqrt{7^2+0}=7\ units\)
The vertical leg is formed by points with the same x axis. Therefore the points that make up the vertical leg is (2 1), (2, 1-). The Distance of the vertical leg is:
\(Vertical\ leg=\sqrt{(2-2)^2+(-1-1)^2}=\sqrt{0+(-2)^2}=2\ units\)
The hypotenuse is gotten using Pythagorean theorem. It is gotten by:
Hypotenuse² = (Horizontal leg)² + (Vertical leg)²
Hypotenuse² = 7² + 2²
Hypotenuse² = 49 + 4 = 53
Hypotenuse = √53
Hypotenuse = 7.28 unit
Answer:
The answer are 7, 2 and 53
Step-by-step explanation:
Sarah wants to buy new pillows for her
room. Which store offers the best buy
on pillows?
Sale Price
Store
3 pillows for $40
A
4 pillows for $50
B
C
2 pillows for $19
D
1 pillow for $11
C. Store C
D. Store D
A. Store A
Answers
3 divided by 40 = 0.075 per pillow for A
4 divided by 50 = 0.08 per pillow for b
2 divided by 19 = 0.10 per pillow for c
and obviosly d is 11
your answer is A.
If p(r)=4 r^{2}+8 , evaluate p(x)+p(4) p(x)+p(4)=
Answers
The sum of p(x) and p(4) is equal to 4x^2 + 8 + 4(4)^2 + 8, which simplifies to 4x^2 + 8 + 64 + 8 = 4x^2 + 80.
Given that p(r) = 4r^2 + 8, we need to evaluate p(x) + p(4). To do this, we substitute x and 4 into the expression p(r) = 4r^2 + 8.
For p(x), we substitute x into the polynomial expression, resulting in p(x) = 4x^2 + 8.
For p(4), we substitute 4 into the expression, yielding p(4) = 4(4^2) + 8 = 4(16) + 8 = 64 + 8 = 72.
Now, we can evaluate p(x) + p(4) by substituting the calculated values: p(x) + p(4) = (4x^2 + 8) + 72 = 4x^2 + 80.
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Refer to the article "Fire Up the Sun."
How does the text make a connection between an outside temperature of 85 degrees or more and the use of the solar-powered oven?
It suggests that cooking outside on hot days is more pleasurable than being in a hot kitchen.
It explains that the black paper is not effective on days when temperatures are below 85 degrees.
It indicates that on cooler days there are more shadows and solar energy is limited.
It explains that the hotter the air temperature, the better the food will cook in the solar oven.
Answers
Answer:cook it up son
Step-by-step explanation:
6 eggs
sepaerate the yolk from the egg white
cook da eggs
eat da eggs
Answer: the answer is D
Step-by-step explanation: i did the test and got a 80
Luca is 9 years old and 129 cm tall. Medical charts show that a boy’s height at age 9 is 3/4 of his predicted adult height. Predict Luca’s adult height.
Answers
Answer:
172cm
Step-by-step explanation:
129/3=43
129+43= 172
help!! Graph y>−5/4x+5
Answers
Answer:
it's the top right.
Step-by-step explanation:
hope this helps.
10. A box contains five and two-thirds cups of rice. If three fourths of the rice will
be used, how many cups of rice remained in the box?
14
D.
Answers
Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.
To find the number of cups of rice that remained in the box, we need to calculate three-fourths (3/4) of the total amount of rice in the box.
The total amount of rice in the box is given as five and two-thirds cups. To work with a fraction, we can convert the mixed number to an improper fraction:
5 and 2/3 = (5 * 3 + 2) / 3 = 17/3 cups
Now, we can find three-fourths (3/4) of 17/3:
(3/4) * (17/3) = (3 * 17) / (4 * 3) = 51/12 = 4 and 3/12 = 4 and 1/4 cups
Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.
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I GIVE THANKS AND MARK BRAINLIEST
What is the correct answer?
Please help.
Answers
A value of 20 would fit the best in the table's empty cell to imply that there is no proof of a link between the variable and the outcome.
Option c is accurate.
The missing number trick: how does it work?The pattern between the supplied series must be found in order to determine the missing number. Verify that the series only shows increases, decreases, or both. The difference between two numbers should then be checked; this will help you discover the pattern.
How can the missing number in a figure be located?To locate the missing numbers, the candidate must first identify the pattern or relationship between these numbers and then apply it.
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This agency preserves and promotes public confidence in the U.S. Financial system by insuring deposits in banks and thrift institutions for at least $250,000.
Answers
the diagram shows a right angled triangle .
Answers
Answer:
the image should help.
Step-by-step explanation:
image explains everything.
What is the lowest conmon multiple of 3 and 4
Answers
Answer:
12
Step-by-step explanation:
You want the least common multiple of 3 and 4.
LCM3 and 4 have no common factors, so their least common multiple (LCM) is their product:
3·4 = 12
The LCM of 3 and 4 is 12.
__
Additional comment
If the numbers have a common factor, then the LCM is their product, divided by the greatest common factor.
For example, 4 and 6 have a common factor of 2. Their LCM is 4·6/2 = 12.
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To start her old lawn mower, rita has to pull a cord and hope for some luck. On any particular pull, the mower has a 20% chance of starting. What is the probability that it takes her more than 6 pulls to start the mower?.
Answers
The probability that it takes her more than 6 pulls to start the mower is 0.262144. The result is obtained by the formula of binomial distribution.
What is the formula of binomial distribution?The formula of binomial distribution is
\(P(X = x) = C_{n,x}.p^{x}. (1 - p) ^{n-x}\)
\(C_{n,x} = \frac{n!}{x! (n-x)!}\)
Where
x = number of successesn = number of trialsp = probability of a success on a single trialRita has to pull a cord to start her old lawn mower. If the probability of success is 20%, what is the probability that it takes her more than 6 pulls to start the mower?
We have:
p = 20% = 0.2n = 6Using the formula of binomial distribution,
\(P(X = 1) = C_{6,1}.(0.2)^{1}. (0.8) ^{5} = 0.393216\)
\(P(X = 2) = C_{6,2}.(0.2)^{2}. (0.8) ^{4} = 0.24576\)
\(P(X = 3) = C_{6,3}.(0.2)^{3}. (0.8) ^{3} = 0.08192\)
\(P(X = 4) = C_{6,4}.(0.2)^{4}. (0.8) ^{2} = 0.01536\)
\(P(X = 5) = C_{6,5}.(0.2)^{5}. (0.8) ^{1} = 0.001536\)
\(P(X = 6) = C_{6,6}.(0.2)^{6}. (0.8) ^{0} = 0.000064\)
The probability that it takes more than 6 pulls,
P(X > 6) = 1 - P(X ≤ 6)
P(X > 6) = 1 - [P(X = 1)+P(X = 2)+P(X = 3)+P(X = 4)+P(X = 5)+P(X = 6)]
P(X > 6) = 1 - (0.393216 + 0.24576 + 0.08192 + 0.01536 + 0.001536 + 0.00064)
P(X > 6) = 1 - 0.737856
P(X > 6) = 0.262144
Hence, the probability to take more than 6 pulls to start the old lawn mower is 0.262144.
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The following cone has a slant height of 17
cm and a radius of 8
cm.
What is the volume of the cone?
Responses
480π
320π
544π
Answers
The formula for the volume of a cone is:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is pi.
In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:
h² = s² - r²
h² = 17² - 8²
h² = 225
h = 15
Now that we have the height, we can plug in the values for r and h into the formula for the volume:
V = (1/3)π(8²)(15)
V = (1/3)π(64)(15)
V = (1/3)(960π)
V = 320π
Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.
Kirstin knows that the initial fee for adopting a dog from the animal shelter is $75. This fee needs to be considered when calculating how much a dog will cost. Write a function, C(d), to represent the cost to adopt and feed the dog in terms on the number of days (d) that kirstin owns her dog
Answers
Answer:
The function is represented by \(C(d) = 75\,USD + r\cdot d\).
Step-by-step explanation:
In this case, we must observe that total cost of the dog (\(C(d)\)) is the sum of two components: i) Fixed cost (\(C_{f}\)) - Adoption fee, ii) Variable cost (\(C_{v}\)) - Daily cost of feeding the dog, both measured in US dollars.
In addition, we suppose that variable cost is directly proportional to the number of days that Kirstin owns her dog. That is:
\(C (d) = C_{f} + C_{v}\)
\(C(d) = C_{f} + r\cdot d\)
Where:
\(d\) - Number of days that Kirstin owns her dog, measured in days.
\(r\) - Daily feeding costs, measured in US dollars per day.
If \(C_{f} = 75\,USD\), then:
\(C(d) = 75\,USD + r\cdot d\)
The function is represented by \(C(d) = 75\,USD + r\cdot d\).
List a, b, and c for the following Quadratic: 2x2 + 5x + 3 = 0
Answers
Answer:
a = 2
b = 5
c = 3
A rectangle has an area of 7. 5m2.
One of the sides is 0. 3m in length.
Work out the perimeter of the rectangle.
Answers
The perimeter of rectangle could be 50.6 if a rectangle has an area of 7. 5 and One of the sides is 0. 3m in length.
What is Area of rectangle ?
area of rectangle could be the product of its sides that is length and breadth.
Given the area of rectangle is 7.5
one of its side, length = 0.3
let other side be x .
area = length*breadth
7.5 = 0.3 * x
x = 25
hence , other side could be 25.
perimeter of rectangle = 2 (length+breadth)
= 2 * (25+0.3)
= 2 * (25.3)
= 50.6
Hence, The perimeter of rectangle is 50.6
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the margin of error of a confidence interval is the error from biased sampling methods. True or False
Answers
An item was marked down 60% from its original price. The amount of the discount was $30. Fill in the numbers that belong in the diagram to find the original price a = b = c =
Answers
Answer:
A= 30, B= 20, C= 50
Step-by-step explanation:
Just took test
Answer:
Step-by-step explanation:
—8х +4(1+ 5x) = — 6x — 14
Solve.
Answers
Answer: x=-1
Step-by-step explanation:
"five more than the product of four and a number is
equal to the product of three and that same number
increased by six."
A. X=-1
B. X= 1
C. X= 3
D. X= 1/2
Answers
Answer:
B
Step-by-step explanation:
Let the number = x
Product: 4 * x
Add 5: 4x + 5
=
3x + 6
Now equate the two parts.
4x + 5 = 3x + 6 Subtract 5 from both sides
4x + 5 - 5 = 3x + 6 - 5 Combine
4x = 3x + 1 Subtract 3x from both sides
4x-3x=3x -3x + 1 Combine
x = 1
For the equation 2x + 7 =30, x = 3
O True
O False
Answers
Have a good day <3
Answer: False
=============================================================
Explanation:
To see if the x value is a solution or not, we plug it into the equation given
2x+7 = 30 .... original equation
2*3 + 7 = 30 .... replace every x with 3, since we claim that x = 3
6 + 7 = 30 .... multiply 2 and 3 to get 6
13 = 30 ...... add 6 and 7 to get 13
We get two different numbers on either side, so the last equation is not true. We get a contradiction or false statement. So the original equation is false when x = 3. Therefore, x = 3 is not the solution.
That's why the overall claim is false.
i need help with Rational Function
Answers
Answer:
2x + 3
Step-by-step explanation:
Vol_prism =
Base area × height
which can be rearranged to be:
h = Vol/B
So you are dividing.
2x^3+11x^2+12x ÷ (x^2+4x)
You factor both expressions, cancel what you can and whatever is left is your answer. see image.
Which of the following statement(s) about multiple regression analysis is FALSE?A. Multiple regression analysis allows you to analyze more than one dependent (Y) variable at a time.B. Multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression.C. Multicollinearity occurs when two or more of the X variables are highly correlated with one another.D. Both A and B are false statements.E. All of the statements above are false.
Answers
Multiple regression analysis analyze more than one dependent variable at a time and multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression are false. Correct option is D.
The statement (A) that "Multiple regression analysis allows you to analyze more than one dependent (Y) variable at a time" is false. In multiple regression, there is only one dependent variable (Y) that is being predicted by a combination of independent variables (X).
The statement (B) that "Multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression" is also false.
Multicollinearity occurs when two or more independent variables (X) are highly correlated with each other, which can cause problems in accurately estimating the effect of each independent variable on the dependent variable.
The statement (C) that "Multicollinearity occurs when two or more of the X variables are highly correlated with one another" is true.
Therefore, the correct answer is (D) "Both A and B are false statements."
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Two points defining a linear function are shown in the table below.
-14
-10
O
What is the slope of the function?
223
32
y
-18
-12
2
06
Answers
The slope of as per the given points will be equal to 3/2. Hence, option B is correct.
What is slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the information given in the table,
The points are (-14, -18) and (-10, -12)
Use the equation given below to find the slope,
m = (y₂ - y₁)/(x₂ - x₁)
Substitute values in above equation,
m = (-12 - (-18))/(-10 - (-14))
m = (-12 + 18)/(-10 + 14)
m = 6/4
m = 3/2
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find the explicit formula for the following sequence.
15, 29, 49, 75, 107,....
Answers
Answer:
Step-by-step explanation:
We are given the sequence
\(15, 29, 49, 75, 107\\15->29 = 14\\29 -> 49 = 20\\49->75 = 26\\75 -> 107 = 32\\14, 20, 26, 32\\14 -> 20= 6\\20 -> 26 = 6\\26 -> 32 = 6\\\\6, 6, 6\\6->6 = 0\)
Since we had to find the differences twice, it is a second degree polynomial
\(y = an^2 + bn + c\\plugging \: in \: n = 1, 2, 3...\\the \: sequence \: is \\a+b+c, 4a + 2b + c, 9a + 3b + c...\\the \: diff \: under \: is \\3a + b, 5a + b, 7a + b...\\the \: diff \: under \: is \\2a, 2a, 2a...\\so, \\2a = 6\\a = 3\\3(3) + b = 14\\b = 5\\\\a +b + c = 15\\3 + 5 + c = 15\\c = 7\\\)
so,
\(y = 3n^2 + 5n + 7\)
Find the first derivative for each of the following:
y = 3x2 + 5x + 10
y = 100200x + 7x
y = ln(9x4)
Answers
The first derivatives for the given functions are:
For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.
For \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.
For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.
To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.
For the function\(y = 3x^2 + 5x + 10:\)
Taking the derivative term by term:
\(d/dx (3x^2) = 6x\)
d/dx (5x) = 5
d/dx (10) = 0
Therefore, the first derivative is:
dy/dx = 6x + 5
For the function y = 100200x + 7x:
Taking the derivative term by term:
d/dx (100200x) = 100200
d/dx (7x) = 7
Therefore, the first derivative is:
dy/dx = 100200 + 7 = 100207
For the function \(y = ln(9x^4):\)
Using the chain rule, the derivative of ln(u) is du/dx divided by u:
dy/dx = (1/u) \(\times\) du/dx
Let's differentiate the function using the chain rule:
\(u = 9x^4\)
\(du/dx = d/dx (9x^4) = 36x^3\)
Now, substitute the values back into the derivative formula:
\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)
Therefore, the first derivative is:
dy/dx = 4/x
To summarize:
For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.
For y = 100200x + 7x, the first derivative is dy/dx = 100207.
For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.
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Help, please! I want to finish this last quarter good or I may get kicked out. Thank you!!
Answers
Purple is 43.99