[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr}[/tex]
Step-by-step explanation:
Let y = height of the pole = 35 m (constant)
x = length of the shadow
They are related as
[tex] \tan \theta = \frac{y}{x} [/tex]
or
[tex]x = \frac{y}{ \tan\theta } = y \cot \theta[/tex]
Taking the time derivative of the above expression and keeping in mind that y is constant, we get
[tex] \frac{dx}{dt} = y( - \csc^{2} \theta) \frac{d \theta}{dt} [/tex]
Before we plug in the numbers, let's convert the degree unit into radians:
[tex]40° \times ( \frac{\pi \: rad}{180°}) = \frac{2\pi}{9} \: radians[/tex]
Since the angle is decreasing, then d(theta)/dt is negative. Therefore, the rate at which the shadow is lengthening is
[tex] \frac{dx}{dt} = (35 \: m)( - \csc^{2} \frac{2\pi}{9} )( - \frac{1}{3} \frac{rad}{hr} )[/tex]
or
[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr} [/tex]
The basketball team did not record how many baskets each player made during the last game. Zulie remembers that she made three
times as many baskets as Aileen. Melody knows that she made four more baskets than Aileen. Zoe thinks that she made 3 fewer baskets than Aileen.
Abigail is sure that she made the same number of baskets as Zoe. Altogether the five players made 82 baskets. How many baskets did each player
make?
Answer:
There is a mistake in the question. x results in a decimal answer, which is not possible for number of hoops.
Step-by-step explanation:
Aileen: x
Zulie: 3x
Melody: 4 + x
Zoe: x - 3
Abigail: x - 3
82 = (x) + (3x) + (4+x) + (x-3) + (x-3)
Combine Like Terms
x + 3x + x + x + x = 7x
4 - 3 - 3 = -2
7x - 2 = 82
7x = 80
x results in a decimal answer, which is not possible for number of hoops.
Write the equation of the line that passes through the points (-6,5) and (3,−5). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
[tex]\displaystyle y-5=-\frac{10}{9}(x+6)[/tex]
Or:
[tex]\displaystyle y+5=-\frac{10}{9}(x-3)[/tex]
Step-by-step explanation:
We want to write the equation of a line that passes through the points (-6, 5) and (3, -5) in point-slope form.
Point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Thus, first, we need to find the slope. We can use the slope formula:
[tex]\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{(-5)-(5)}{(3)-(-6)}=\frac{-10}{9}=-\frac{10}{9}[/tex]
Next, we can use either of the two given points. I'll use (-6, 5). So, let (-6, 5) be (x₁, y₁). Substitute:
[tex]\displaystyle y-(5)=-\frac{10}{9}(x-(-6))[/tex]
Or, fully simplified:
[tex]\displaystyle y-5=\frac{-10}{9}(x+6)[/tex]
Using the other point, we will acquire:
[tex]\displaystyle y-(-5)=-\frac{10}{9}(x-(3))[/tex]
Or, simplified:
[tex]\displaystyle y+5=-\frac{10}{9}(x-3)[/tex]
Share $150 among John, Mary, and Sarah so that each of the two girls receives twice as much as John. Calculate the amount of money Jon received.
In a bag there are blue sweets and red sweets. The ratio of blue sweets to red sweets is 5:3 What fraction of the sweets are blue?
Answer:
5/8
Step-by-step explanation:
SUM OF RATIOS = 5 + 3 = 8
fraction of blue sweet = blue sweet ratio / sum of ratios = 5/8
What is the y-intercept for y = 5x^2 + 2x -2?
Answer: (0, -2) or -2
Step-by-step explanation:
Sub in 0 for x since at the y intercept x is 0
[tex]y=5(0)^2+2(0)-2\\y=5(0)+0-2\\y=0+0-2\\y=-2[/tex]
Given the following system of equations, what value of x makes the equations true?
x+y= 3.25
x-y= 1.75
An icicle is 12 inches long and melts at a rate of 1/4 inch per hour
Answer:
It will take 48 hours for the entire icicle to melt.
Step-by-step explanation:
12 divided by 1/4 = 48
The linear equation to model the situation is f(x) = -1/4x + 12
Complete questionWrite a linear equation in slope-intercept form to model the situation. An icicle is 12 inches long and melts at a rate of 1/4 inch per hour.
How to determine the linear equation?The given parameters are:
Length = 12 inchesRate = 1/4 inch per hourThe above means that:
Y-intercept (c) = 12Slope (m) = -1/4A linear equation is represented as:
f(x) = mx + c
Where f(x) represents the function and x represents the number of hours.
So, we have:
f(x) = -1/4x + 12
Hence, the linear equation to model the scenario is f(x) = -1/4x + 12
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what is the area of parallelogram if base is 13 and the height 14
Answer:
A = 182
Step-by-step explanation:
14 x 13 = 182
So, 182 would be your answer.
Simplify the expression ( a^3/2)^3
Answer:
(a^9/8)
Step-by-step explanation:
(a/b)^n = (a^n/b^n)
44
Match each ratio with its simplest form.
12:15
20:36
18:24
Pls answer ASAP I need to finish this today and I’m stuck
I need help asap pls pls pls...
Answer:
c)
Step-by-step explanation:
please don't trust ;-;
two rectangles have a scale factor of 4:1. If the area of the larger rectangle is 156cm^2, what is the area of the smaller rectangle?
A. 26.75 cm^2
B. 31 cm^2
C. 9.75 cm^2
D. 39 cm^2
Answer:
c=9.75cm^2
Step-by-step explanation:
156/16 because you are deivding each side by 4 and 4x4=16 and the area is 156
I will give BRAINLIEST to the correct answer
Find the measure of angle 3
Answer:
2X+100 =8X+208
8X-2X=100-208
6X=-108
X=-18
8X+208=(8×-18)+208
=-144+208
=64
ANGLE 3=180-64
=116
Answer: The measurement of angle #3 on the photo you provided it would be a 300 Degree angle if that is what you're asking
Step-by-step explanation: If you're asking what measure of an angle #3 is the correct measurement is 300 Degrees
Suppose you have a bag with 50 letter tiles in it and 23 of the tiles are the letter Y. If
23
you pick a letter tile at random from the bag, the probability that it is the letter Y is Suppose
50
another bag has 200 letter tiles in it and 172 of the tiles are the letter Y. Write the probability of
picking a tile that is the letter Y as a fraction and as a percent. From which bag are you more likely
to pick a tile that is the letter Y?
Answer:
23
Step-by-step explanation:
234Suppose you have a bag with 50 letter tiles in it and 23 of the tiles are the letter Y. If
23
you pick a letter tile at random from the bag, the probability that it is the letter Y is Suppose
50
another bag has 200 letter tiles in it and 172 of the tiles are the letter Y. Write the probability of
picking a tile that is the letter Y as a fraction and as a percent. From which bag are you more likely
to pick a tile that is the letter Y?
The probability of picking the letter Y from bag of 50 letters is 23/50 or 0.46 or 46% and probability of picking the letter Y form bag of 200 letters is 172/200 or 0.86 or 86%. as the probability of getting the letter Y is more in second bag this it is better to pick the bag containing 200 letters.
What is a probability?The probability explains the chances of happening a event. The probability of an event is a number between 0 and 1, where, 0 indicates impossibility of the event to happen and 1 indicates certainty of the event to happen.
From the question it is said that a bag of 50 letter contain 23 Y letters. Thus the probability of the letter Y picking is 23/50 i.e, number of times the letter Y can come out if we pick the letters 50 times. So, it is certain that 23 Y letters can come out.
23/50= 0.46 or 46%
And if the bag contain 200 letters in which 172 are Y letters then the probability to pick Y is 172/200
172/100 =0.86 or 86%
As the chance to get Y letter is mor in bag containing 200 letters thus pick this bag.
thus the 1st bag probability is 46% and for 2nd bag is 86%. Hence choose 2nd bag
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WILL MARK BRAINILIEST
are the angles corresponding, alternate interior, alternate exterior, or constructive interior
Answer:
maybe it is corresponding
A ball is dropped from a height of 5m. After each bounce it rises to 35% of its previous height. After how many bounces does the ball reach a Height of less than 50cm?
Answer:
After the third bounce the ball reaches a height of less than 50cm.
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient between consecutive terms is always the same, and it's called common ratio. The nth term of a geometric sequence is given by:
[tex]A_n = A_0(r)^{n}[/tex]
In which [tex]A_0[/tex] is the first term and r is the common ratio.
A ball is dropped from a height of 5m.
This means that [tex]A_0 = 5[/tex]
After each bounce it rises to 35% of its previous height.
This means that [tex]r = 0.35[/tex]
Thus
[tex]A_n = A_0(r)^{n}[/tex]
[tex]A_n = 5(0.35)^{n}[/tex]
After how many bounces does the ball reach a Height of less than 50cm?
50cm = 0.5m. This is n for which [tex]A_n = 0.5[/tex]. Thus
[tex]A_n = 5(0.35)^{n}[/tex]
[tex]0.5 = 5(0.35)^{n}[/tex]
[tex](0.35)^n = \frac{0.5}{5}[/tex]
[tex](0.35)^n = 0.1[/tex]
[tex]\log{(0.35)^n} = \log{0.1}[/tex]
[tex]n\log{0.35} = \log{0.1}[/tex]
[tex]n = \frac{\log{0.1}}{\log{0.35}}[/tex]
[tex]n = 2.19[/tex]
Rounding up:
After the third bounce the ball reaches a height of less than 50cm.
Can u guys hurry up pleasee The manager of a local appliance store wants to conduct a customer satisfaction survey. Which population should the manager survey? A.Sales people in the store. B.People in charge of repairs at the store. C.People who bought a major appliance from the store. D.Prospective buyers who visit the store.
C. People who bought a major appliance from the store.
Step-by-step explanation:A customer satisfaction survey is a market survey carried out to analyze how satisfied users or customers are in using or consuming a particular product or service. Basically, it has to be carried out on the customers themselves. By costumers, we mean those that have bought and/or used the service or product.
For the local appliance store, the manager should survey people that have bought at least one major appliance from the store. Those are the right people that should make up the population to be surveyed. This is because;
i. They are the consumers of the product.
ii. They have bought and definitely used the product.
iii. They have some usable and useful experiences since they have handled the product.
If I had 3000 plums and I sold 100 how much money would I have plums would I have left.
Answer:
2,900 plums left
Step-by-step explanation:
3,000 plums - 100 sold plums = 2,900 plums left
Answer:
2900
Step-by-step explanation:
3000 (plums) - 100 (plums sold) = 2900 (plums left.)
You didn't say how much money you started out with by the plums.
Sean and sarah spend $70 a month eating out how much money would they have after 15 years if they invested the money instead at 4 percent compounded monthly round your answer to the nearest hundredth
Answer:
Future Value= $17,170.12
Step-by-step explanation:
Giving the following information:
Monthly deposit (A)= $70
Interest rate (i)= 0.04/12= 0.0033
Number of periods (n)= 15*12= 180 months
To calculate the future value (amount saved), we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= monthly deposit
FV= {70*[(1.0033^180) - 1]} / 0.0033
FV= $17,170.12
Pls help I don’t know how to do this
The right answer is a i think i don't known step by step
Step-by-step explanation:
a
a
need an answer asap will give the first answer brainliest
Answer:
The answer would be the first one.
m = -3n
Step-by-step explanation:
Answer:
m = -3n
Step-by-step explanation:
-6 = (-3)2 True
-12 = (-3)4 True
-18 = (-3)6 True
Kara and Karl love steak, fried chicken, hamburgers, mashed potatoes, and french fries. They like green beans and peas. How many different meals including a meat, potatoes and a green vegetable can they make from these choices? 8 meals 16 meals a. C. b. 12 meals d. 24 meals
Answer:
steak, chicken, and hamburger are meats. 3 meats.
The French fries and mashed potatoes are potatoes. 2 Potatoes.
And Green beans and peas are green vegetables. 2 Vegetables.
I think we just do 3 x 2 x 2 = 12 Meals.
hope that helps bby<3
Lucas and Tony were trying to solve the equation: x^2=16x+25 Lucas said, "The x^2, squared term is isolated, so I"ll take the square root of both sides and solve." Tony said, "I'll solve using the quadratic formula with a=1,b=16, an c equals 25." Whose solution strategy would work? Choose 1 answer:
Answer:
Tony's solution strategy
Step-by-step explanation:
Given the equation that Lucas and Tony trying to solve expressed as: x^2=16x+25
This can be written in standard form as x^2 - 16x - 25 = 0
This can then be factorized using the general formula
x = -b±√b²-4ac/2a where a, b and c are constants
From the given expression;
a = 1, b = -16, c = -15
Hence the best strategy that would have worked based on the explanation is Tony's
Answer: Neither
Step-by-step explanation: got it right on khan
Can someone help me with this? i’m struggling urgent help please!!!!
Answer:
Similar by SAS
Step-by-step explanation:
If you multiply the two given sides by 3/2 you will get the sides for the large triangle
3/2 * 10 = 30 / 2 = 15
3/2 * 24 = 72 / 2 = 36
Therefore they are similar by SAS postulate for similarity. Notice that the right angle is between the legs of the triangle. That is the main qualification that allows you to use SAS for similarity.
Find the other two angles of both the triangles, if they were similar then the triangles are similar
Pls help me solve pls show how you got the answer
Answer:
48 length units
Step-by-step explanation:
area of each squre = 9
side length of each square = sqrt(9) = 3
Length of each side of grid = 4*3 = 12
Perimeter of grid = 4 sides = 4*12 = 48 length units
Please help me I will give you 16 points I don’t know what that do but I will
Answer:
40
Step-by-step explanation:
The serving sizes, [tex]x[/tex], of 20, 80, and 120 have a required amount of meat in pounds, [tex]y[/tex], of [tex]y=\frac{1}{10}x[/tex] (the number of pounds of meat is equal to 1/10th the serving size)
However, for the row with a serving size of 40, the number of pounds of meat is equal to [tex]\frac{6}{40}=\frac{3}{20}[/tex] the serving size. Therefore, the serving size of 40 has a different ratio of serving size to pounds of meat than the other ratios.
Pls help math coordinates of pt P
Answer:
( 3, - 2 )
Step-by-step explanation:
p is located at below 3
Jaclyn used the slope formula to find the slope of the line through the points given in the table.
A 2-column table with 2 rows. Column 1 is labeled x with entries 0, negative 3. Column 2 is labeled y with entries 4, 0.
1. Point 1: (0, 4); Point 2: (negative 3, 0). 2. Slope = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction = StartFraction 0 minus 4 Over negative 3 minus 0 EndFraction = StartFraction negative 4 Over negative 3 EndFraction. 3. Slope = four-thirds.
In which step did Jaclyn make an error?
Answer: She didn't make an error.
Step-by-step explanation:
She just didn't I got it right.
Answer:
answer is D
Step-by-step explanation:
The tennis courts are 3 blocks west and 2 blocks south of Miguel’s house. The bike path is 5 blocks east and 2 blocks south of Miguel’s house. How many blocks are the tennis courts from the bike path?
Answer:
8
Step-by-step explanation:
If Miguel's house is (0,0), then the tennis court is (-3,-2), and the bike path is (5,-2). There fore, we can just count the squares between the tennis court and the bike path, which is 8.
Hope that this helps!
From the coordinate calculation, here tennis courts are 8 blocks far from the bike path.
Given that,
The tennis courts are 3 blocks west and 2 blocks south of Miguel’s house. The bike path is 5 blocks east and 2 blocks south of Miguel’s house. How many blocks are the tennis courts from the bike path is to be detemined.
Coordinate, is represented as the values on the x-axis and the y-axis of the graph.
Here on the graph,
Assume that Miguel's house is (0,0),
then accoding to the question the tennis court is (-3,-2), and the bike path is (5,-2).
Now, difference in the position dx = 5 - (-3)
= 8
Thus, from the coordinate calculation, here tennis courts are 8 blocks far from the bike path.
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Given the linear equation 5x+3y-9=0. Write another linear equation in two variables such that the geometrical representation of the pair so formed are parallel lines
Answer:[tex]5x+3y+1=0[/tex]
Step-by-step explanation:
Given
The linear equation is [tex]5x+3y-9=0[/tex]
The other linear equation parallel to the given line can be represented by
[tex]5x+3y+c=0[/tex]
Here, c can take any value . for example c=1, line becomes
[tex]\Rightarrow 5x+3y+1=0[/tex]
