Your fixed expenses are $1,235. 78/month. You want to save 5 months' worth for an emergency
fund over a year's time. How much must you save each month?
Answer:
$514.91
Step-by-step explanation:
You want to save a total of ...
5 × $1235.78
You want to do this over a 12-month period. So, you want to save 1/12 of this total each month. The amount you're saving each month is ...
5(1235.78)/12 = 514.908333... ≈ 514.91
You must save $514.91 each month to reach the goal.
Answer: $514.91
Step-by-step explanation:
($1,235.78)(5 months)=$6,178.90
6,178.90/12 months=$514.91
(just for clarity: the other person is right, just wanted to show a simpler way to achieve the answer. gl :)
Sandra spotted the sailboat from the shore and measured the angle from the waterline to the top of the boats mast to be 7° if the top of the mask is 23 feet above the water how far is the middle of the sailboat from the shore? Estimate your answer to the nearest tenth.
Answer:
The middle of the sailboat is approximately 268.8 feet from the shore.
Step-by-step explanation:
Let the distance from shore to the middle of the boat be represented by x, the angle of elevation of Sandra from the shore to the top of the boat mast is 7°. Applying the required trigonometric function to this question, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan 7° = [tex]\frac{23}{x}[/tex]
⇒ x = [tex]\frac{23}{Tan 7^{0} }[/tex]
= [tex]\frac{23}{0.12279}[/tex]
= 268.7515
∴ x = 268.8 feet
The middle of the sailboat is approximately 268.8 feet from the shore.
For a ,a relationship to be a function, which values cannot repeat: the x-
values or the y-values? *
Answer:
The x - valuesThe y-values repeat in various functions (for example: quadratic function: y=x²; y=4 for x=2 and for x=-2)
Compute the range and interquartile range for the data collected for boys and girls. Describe their differences in detail using specific terms of spread. (4 points)
Answer:
The measure of central tendency, mean and median are approximately equal for the boys indicating that the data of the boys is more evenly spread while standard deviation of the girls data is less than those of the boys indicating that the data for the girls is less widely spread.
Step-by-step explanation:
The given data are;
, 1 2 3 4 5 6 7 8 9 10
Girls, 50 32 15 56 81 50 18 81 22 55
Boys, 75 41 25 22 7 0 43 12 45 70
Sorting the data gives;
Girls, 15, 18, 22, 32, 50, 50, 55, 56, 81, 81
Boys, 0, 7, 12, 22, 25, 41, 43, 45, 70, 75
For the even numbered sample data size, the first quartile, Q₁ is found by sharing the data into two and finding the median of the left half which gives;
10/2 = 5 on each half
The first quartile, Q₁, is the median of the left 5 data points which is the 3rd data point = 22 for girls and 12 for boys
The third quartile, Q₃, is found in similar method to be the 8th data point which is 56 for girls and 45 for boys
The median = 50 for girls and 33 for boys
Therefore, the interquartile ranges are;
IQR = 56 - 22 = 34 for girls, 45 - 12 = 33 for boys
We check for outliers.
Q₁ - 1.5×IQR = 22 - 1.5*34 = -29
Q₃ + 1.5×IQR = 56 + 1.5*34 = 107
We check the mean of both data samples as follows;
Average for the girls = 46
Average for the boys = 34
Standard deviation for girls = 23.99
Standard deviation for girls = 25.43
Therefore, the measure of central tendency is more accurate for the boys indicating that the data of the boys is more evenly spread while the data for the girls is less widely spread.
What are the solutions to the equation 3(x – 4)(x + 5) = 0? x = –4 or x = 5 x = 3, x = 4, or x = –5 x = 3, x = –4, or x = 5 x = 4 or x = –5
Answer:
x= 4 x = -5
Step-by-step explanation:
3(x – 4)(x + 5) = 0
Using the zero product property
(x – 4)=0 (x + 5) = 0
x= 4 x = -5
What are the solutions to the equation 3(x – 4)(x + 5) = 0?
x = –4 or x = 5
x = 3, x = 4, or x = –5
x = 3, x = –4, or x = 5
x = 4 or x = –5
Answer:
D. x = 4 or x = –5
Step-by-step explanation:
solution for 2x is equal to 10
Answer:
The answer is 5
Step-by-step explanation:
divide 10 by two and get 5
Answer:
[tex]x = 5[/tex]
Step-by-step explanation:
We have the equation [tex]2x = 10[/tex], we can try and isolate x by dividing both sides by 2.
[tex]2x \div 2 = 10\div2\\x = 5[/tex]
Hope this helped!
The temperature in Anchorage, Alaska at 6:00 am was 2°C. If the temperature drops 2 degrees each hour, what is the temperature in degrees celsius at 2:00 pm
Answer:
-12°C
Step-by-step explanation:
6AM = 2°C
8AM= -2°C
10AM= -6°C
12AM= -8°C
2PM= -12°C
the temperature in degrees Celsius at 2:00 pm would be -14°C.
To find the temperature in degrees Celsius at 2:00 pm, we need to determine the number of hours that have passed from 6:00 am to 2:00 pm, and then calculate the temperature decrease accordingly.
From 6:00 am to 2:00 pm, a total of 8 hours have passed (6 hours from 6:00 am to 12:00 pm, and 2 hours from 12:00 pm to 2:00 pm).
Given that the temperature drops 2 degrees Celsius each hour, we can multiply the number of hours (8) by the rate of temperature decrease (2 degrees/hour):
Temperature decrease = 8 hours × 2 degrees/hour = 16 degrees
Starting with a temperature of 2°C at 6:00 am, if the temperature drops 16 degrees Celsius over 8 hours, we can subtract 16 from the initial temperature:
Temperature at 2:00 pm = 2°C - 16°C = -14°C
Therefore, the temperature in degrees Celsius at 2:00 pm would be -14°C.
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The body paint, an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to 11/2hours.
What is the probability that the painting time will be less than or equal to an hour?
What is the probability that the painting time will be more than 50 minutes?
Determine the expected painting time and its standard deviation.
Answer:
a. [tex]\mathbf{P(Y \leq 60) = 0.3333}[/tex]
b. P(Y>50) = 0.8889
c. E(y) = 67.5 and Standard deviation [tex]\sigma[/tex] = 12.99
Step-by-step explanation:
From the information given :
an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to [tex]1\frac{1}{2}[/tex]hours.
The objective is to determine the probability that the painting time will be less than or equal to an hour?
since 60 minutes make an hour;
[tex]1\frac{1}{2}[/tex]hours = 60 +30 minutes = 90 minutes
Let Y be the painting time of the automobile; then,
the probability that the painting time will be less than or equal to an hour ca be computed as :
[tex]P(Y \leq 60) = \int ^{60}_{45} f(y) dy \\ \\ \\ P(Y \leq 60) = \int ^{60}_{45} \dfrac{1}{45} dy \\ \\ \\ P(Y \leq 60) = \dfrac{1}{45} \begin {pmatrix} x\end {pmatrix}^{60}_{45} \\ \\ \\ P(Y \leq 60) = \dfrac{60-45}{45 } \\ \\ \\ P(Y \leq 60) = \dfrac{15}{45} \\ \\ \\ P(Y \leq 60) = \dfrac{1}{3} \\ \\ \\ P(Y \leq 60) = 0.3333[/tex]
What is the probability that the painting time will be more than 50 minutes?
The probability that the painting will be more than 50 minutes is P(Y>50)
So;
[tex]P(Y>50) = \int \limits ^{90}_{50} f(y) dy[/tex]
[tex]P(Y>50) = \int \limits ^{90}_{50} \dfrac {1}{45} dy[/tex]
[tex]P(Y>50) = \dfrac{1}{45}[x]^{90}_{50}[/tex]
[tex]P(Y>50) = (\dfrac{90-50}{45})[/tex]
[tex]P(Y>50) = \dfrac{40}{45}[/tex]
P(Y>50) = 0.8889
Determine the expected painting time and its standard deviation.
Let consider E to be the expected painting time
Then :
[tex]E(y) = \int \limits ^{90}_{45} y f(y) dy \\ \\ \\ E(y) = \int \limits ^{90}_{45} y \dfrac{1}{45} dy \\ \\ \\ E(y) = \dfrac{1}{45} [\dfrac{y^2}{2}]^{90}_{45} \\ \\ \\ E(y) = \dfrac{1}{45}[\dfrac{(90^2-45^2)}{2}] \\ \\ \\ E(y) = \dfrac{1}{45} (\dfrac{6075}{2}) \\ \\ \\ E(y) = \dfrac{1}{45} \times 3037.8 \\ \\ \\ \mathbf{E(y) = 67.5}[/tex]
[tex]E(y^2) = \int \limits ^{90}_{45} y^2 f(y) dy \\ \\ \\ E(y^2) = \int \limits ^{90}_{45} y^2 \dfrac{1}{45} dy \\ \\ \\ E(y^2) = \dfrac{1}{45} [\dfrac{y^3}{3}]^{90}_{45} \\ \\ \\ E(y^2) = \dfrac{1}{45}[\dfrac{(90^3-45^3)}{3}] \\ \\ \\ E(y^2) = \dfrac{1}{45} (\dfrac{637875}{3}) \\ \\ \\ E(y^2) = \dfrac{1}{45} \times 2126.25 \\ \\ \\ \mathbf{E(y^2) = 4725}[/tex]
To determine the standard deviation, we need to first know what is the value of our variance,
So:
Variance [tex]\sigma^2[/tex] = E(x²) - [E(x)]²
Variance [tex]\sigma^2[/tex] = 4725 - (67.5)²
Variance [tex]\sigma^2[/tex] = 4725 - 4556.25
Variance [tex]\sigma^2[/tex] = 168.75
Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{variance}[/tex]
Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{168.75}[/tex]
Standard deviation [tex]\sigma[/tex] = 12.99
A certain forest covers an area of 2600 km^2. Suppose that each year this area decreases by 4.75%. What will the area be after 11 years? Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
1522km^2
Step-by-step explanation:
To solve this, first convert the percentage to a decimal. That would be .0475.
Now subtract that from 1.0 to get the factor it decreases by. This would be 1-.0475 = .9525
Multiply 2600 x (.9525)^11 = 1522.258 which rounds to 1522 km^2
Answer:
The area will be 1292.98 km² after 11 years.
Step-by-step explanation:
To find what decreases by 4.57% each year in kilometers:
2600 × 4.57/100 = 26 × 4.57
= 118.82 km²
To find the area after 11 years:
118.82 × 11 = 1307.02
2600 - 1307.02 = 1292.98 km²
1292.98 km² is the answer.
What is the LCD of 1/2 and 3/5
Answer:
10
Step-by-step explanation:
How you find LCD (lowest common denominator) is that you have to look at the denominator (the bottom number) and try to find the lowest multiple between both of the numbers that is on the bottom (in this case it is 2 and 5). Sometimes you have to multiply both denominators together to get a LCD.
Example of multiplying two denominators together to get an LCD:
1/3 and 1/13 LCD is 39 because you multiply 3 and 13.
1/5 and 1/4 LCD is 20 because you multiply 5 and 4.
A 250.0 kg rock falls off a 40.0 m cliff. What is the kinetic energy of the rock just before it hits the ground (hint: conservation of energy)?
Answer:
kinetic energy body when it hits the ground is 98000 joule
1000joule = 1 kilojoule
, kinetic energy body when it hits the ground is 98 kilo-joule
Step-by-step explanation:
conservation of energy states that total energy of a system remains constant.
Potential energy of body = mgh
m = mass
g = gravitational pull = 9/8 m/s^2
h = height
kinetic energy = 1/2 mv^2
where v is the velocity of body
________________________________________
Total energy for this at any point is sum of potential energy and kinetic energy
total energy at height h
v= 0
PE = 250*9.8*40= 98,000
KE = 1/2 m0^2 = 0
total energy at when ball hits the ground
h=0
PE = 250*9.8*0 =
KE = 1/2 mv^2
_______________________________________\
Applying conservation of energy
Total energy at height h = total energy at ground
98000 = KE
Thus, kinetic energy body when it hits the ground is 98000 joule
1000joule = 1 kilojoule
, kinetic energy body when it hits the ground is 98 kilo-joule
A model of a wedge of cheese is used in a display for a deli. All the sides of the model are covered in yellow construction paper. A rectangular prism has a rectangular base with length of 15 centimeters and height of 5 centimeters. Another rectangle has length of 15 centimeters and height of 13 centimeters. Another rectangle has length of 15 centimeters, and height of 12 centimeters. The triangular sides have a base of 5 centimeters and heights of 12 centimeters. How much construction paper is needed for the model? 45 square cm 330 square cm 510 square cm 570 square cm
Answer:
510 cm²
Step-by-step explanation:
To find how much construction paper is needed for the model, we calculate the total areas of each of its sides.
The area of the first triangular sides is A₁ = 15 cm × 5 cm = 75 cm²
The area of the second triangular sides is A₂ = 15 cm × 13 cm = 195 cm²
The area of the third triangular sides is A₃ = 15 cm × 12 cm = 180 cm²
The area of each triangular side is A₄ = 1/2 × 5 cm × 12 cm = 30 cm²
The area of the two triangular sides is A₅ = 2A₄ = 2 × 30 cm² = 60 cm²
The total surface area of a wedge of cheese is A = A₁ + A₂ + A₃ + A₅ = 75 cm² + 195 cm² + 180 cm² + 60 cm² = 510 cm²
So the amount of construction paper needed equals the total surface area of the wedge of cheese = 510 cm²
Answer:
510
Step-by-step explanation:
The axis of symmetry for a quadratic equation can be found using the formula x equals StartFraction negative b Over 2 a EndFraction, where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. What is the equation when solved for a?
Answer:
[tex]a=-\frac{b}{2x}[/tex]
Step-by-step explanation:
The equation of a quadratic function is given as:
ax² + bx + c = 0
where a, b and c are the coefficient in the quadratic equation.
The axis of symmetry of the quadratic equation is given as:
[tex]x=-\frac{b}{2a}[/tex]
To get the equation for a, we have to make a the subject of formula:
[tex]x=-\frac{b}{2a}\\\\multiply\ both\ sides\ by \ 2a:\\\\x*2a=-\frac{b}{2a}*2a\\\\2ax=-b\\\\Divide\ through\ by\ 2a\\\\2ax/2a=-b/2a\\\\a=-\frac{b}{2x}[/tex]
The value of a when solved from x = -b/2a is;
a = -b/2x
We are given the formula for axis of symmetry of a quadratic equation to be;
x = -b/2a
Where;
a and b are coefficients in the quadratic equation
x represents the values along a vertical line on the coordinate plane.
Now, we want to solve for a which means we make it the subject of the equation;
Using multiplication property of equality, we multiply both sides by 2a to get;
2ax = -b
We now use division property of equality by dividing both sides by 2x to get;
a = -b/2x
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The point-slope form of the equation of the line that passes through points (-5,-1) and (10, -7 ) is y-4=1/4 (x-8) what is the slope intercept form of the equation for this line ?
Answer:
y = [tex]\frac{1}{4}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
y - 4 = [tex]\frac{1}{4}[/tex] (x - 8) ← distribute
y - 4 = [tex]\frac{1}4}[/tex] x - 2 ( add 4 to both sides )
y = [tex]\frac{1}{4}[/tex] x + 2 ← in slope- intercept form
What are the domain and range of the real-valued function f(x)=2/(x+5)?
Answer:
Domain is all real numbers, x ≠ -5
Range is all real numbers, y ≠ 0
Step-by-step explanation:
4:3=x:6, find the value of x please help me
Answer:
x=8
Step-by-step explanation:
4:3=x:6
Multiply the first set by 2
4*2 : 3*2
8:6
That means x =8
At which times could rory phone have been plugged into the charger?select three options
Answer:
9hrs 11hrs 19hrs
Step-by-step explanation:
just took the quiz on edge 2020
Answer:
9 hours, 11 hours, 19 hours.
use the formula S = 40,000 (1.06)t to calculate your salary after 4 years. Round your answer to the nearest dollar.
a. $42,400
b. $44,944
c. $47,641
d. $50,499
Answer:
d. $50,499
Step-by-step explanation:
Given:
S = 40,000 (1.06)^t
Where,
t=4 years
S=40,000(1.06)^4
=40,000(1.26247696)
=50,499.0784
To the nearest dollar
S=$50,499
The answer is d. $50,499
The Fairy Tale Spectacular is coming to town. Admission to the fair costs $32.50 and each ride costs $0.80. You have $50 to spend at the Fairy Tale Spectacular including admission. Write and solve an inequality to determine the maximum number of rides you can enjoy at the Fairy Tale Spectacular?
Answer:21
Step-by-step explanation:
50-32.5=17.5
17.5/0.8=21.875
Select the correct answer. The velocity of a train relative to the ground is represented by the distance from A to B in the diagram. The velocity of a ball thrown inside the train at an angle of 66° relative to the train is represented by the distance from B to C. What is the distance from A to C (the velocity of the ball relative to the ground), correct to two decimal places? Assume that all the points in the diagram lie in the same plane. A. 21.14 m/s B. 18.03 m/s C. 17.20 m/s D. 15.00 m/s
Answer:
Step-by-step explanation:
we use cosine formula
2×15×10×cos(180-66)=15²+10²-AC²
-300 cos 66=225+100-AC²
AC²=325+300 cos 66
[tex]AC=\sqrt{325+300 cos 66} \approx 21.14 ~m/s[/tex]
The distance from A to C is 21.14. The correct option is A.
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angles of right-angle triangles.
Velocity is defined as the ratio of the distance moved by the object at a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.
Given that the velocity of a train relative to the ground is represented by the distance from A to B in the diagram. The velocity of a ball thrown inside the train at an angle of 66° relative to the train is represented by the distance from B to C.
The distance A to C will be calculated as,
2×15×10×cos(180-66)=15²+10²-AC²
-300 cos 66=225+100-AC²
AC=√(325+300 cos 66)
AC = 21.17 m/s
Therefore, the distance from A to C is 21.14. The correct option is A.
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In the figure below, triangle DOG, triangle ION, and triangle IDO are congruent and isosceles, each with perimeter 55. The quadrilaterals FLIN, DIES, and DRAG are all squares. The perimeter of the 11-sided polygon $DRAGONFLIES$ is 127. What is the area of DRAG?
Answer:
81 sq units.
Step-by-step explanation:
Given that Triangles DOG, ION and IDO are congruent and isosceles.
Let Sides NO = IO = DO = GO = [tex]x[/tex] units
Let the sides of squares FLIN, DIES and DRAG = [tex]a[/tex] units
So, NF = FL = LI = NI = IE = ES = SD = DI = DR = RA = AG = GD = [tex]a[/tex] units
Given that perimeter of each of Triangles DOG, ION and IDO = 55 units
Sum of sides of triangle = [tex]2x+a=55 ...... (1)[/tex]
and Perimeter of 11 sided polygon DRAGONFLIES = 127 units
The perimeter of the polygon includes the sides (only outer sides are included):
DR, RA, AG, GO, ON, NF, FL, LI, IE, ES and SD
[tex]2x+9a = 127......(2)[/tex]
Solving equations (2) and (1) by subtracting (1) from equation (2):
[tex]8a = 72\\\Rightarrow a = 9 units[/tex]
Area of a square DRAG = [tex]Side^2[/tex] = [tex]9^2 = \bold{81\ sq\ units}[/tex]
Answer:
81
Step-by-step explanation:
dont ask, i just know
Which of the following best describes the graph shown below?
16
A1
1
14
O A This is the graph of a linear function
B. This is the graph of a one-to-one function
C. This is the graph of a function, but it is not one to one
D. This is not the graph of a function
The vertical line test helps us see that we have a function. Note how it is not possible to draw a single straight line through more than one point on the curve. Any x input leads to exactly one y output. This graph passes the vertical line test. Therefore it is a function.
The function is not one-to-one because the graph fails the horizontal line test. Here it is possible to draw a single straight horizontal line through more than one point on the curve. The horizontal line through y = 2 is one example of many where the graph fails the horizontal line test, meaning the function is not one-to-one.
The term "one-to-one" means that each y value only pairs up with one x value. Here we have something like y = 2 pair up with multiple x values at the same time. This concept is useful when it comes to determining inverse functions.
Which is the simplified form of the expression ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript negative 3 Baseline times ((2 Superscript negative 3 Baseline) (3 squared)) squared?
Answer:
[tex]\dfrac{1}{6561}[/tex]
Step-by-step explanation:
Given the expression [tex][(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}[/tex], Using the laws of indices to simplify the expression. The following laws will be applicable;
[tex]a^m*a^n = a^{m+n}\\(a^m)^n = a^{mn}\\[/tex]
[tex]a^{-m} = 1/a^m[/tex]
Given [tex][(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}[/tex]
open the parenthesis
[tex]= (2^{-2})^{-3}(3^{4})^{-3}* (2^{-3})^2(3^2)^2\\\\= 2^{-2*-3}* 3^{4*-3} * 2^{-3*2} * 3^{2*2}\\\\= 2^6 * 3^{-12} * 2^{-6} * 3^4\\\\collecting \ like \ terms\\\\= 2^6 * 2^{-6} * 3^{-12} * 3^4\\\\= 2^{6-6} * 3^{-12+4}\\\\= 2^0 * 3^{-8}\\\\= 1 * \frac{1}{3^8}\\ \\= \frac{1}{6561}[/tex]
Please someone help ASAP!!!!!!
Answer:
1.7 million in Northern Ireland
Step-by-step explanation:
Simply do the difference between the number of people in the UK, minus the number of people in everywhere else except northern Ireland. That is:
60.2 M - 50.4 M - 5.1 M - 3.0 M = 1.7 M
Answer:
[tex]\boxed{1.7 million}[/tex]
Step-by-step explanation:
Hey there!
To find the amount of people who lived in Northern Ireland in 2005 we need to subtract the total 60.2 mil by the England, Scotland, and Wales people.
50.4 + 5.1 + 3
= 58.5
Now we can set up the following equation,
NI = 60.2 - 58.5
NI = 1.7 million
Hope this helps :)
Meguel does not understand which digit is in the tenths location in the number 514.196 Where would it be located at
Answer:
first number after the decimal point
Step-by-step explanation:
after the decimal point is the tenths, hundredths, and thousandths place.
0.1 - tenths
0.09 - hundredths
0.006 - thousandths
What is the 6th row of Pascal's triangle?
Answer:
1, 6, 15, 20, 15, 6, 1
What is the formula for finding mean or average?
Answer:
LOOK BELOW
Step-by-step explanation:
I would not call the explanation a formula
All you have to do to solve mean or average is add all of the numbers up and divide by the total amount of numbers
so for example
0,2,4,0,2,3,2,8,6 <-------- lets find the mean/average
0+2+4+2+3+2+8+6= 27/amount of numbers
amount of numbers=9
(count the zeros too!)
27/9=3
3 is the mean or average!!!
Archer receives a day's work of pay, p, for 5 days of mowing lawns. He spent half of his money on gas. Then he spent $5 on water. Now, he has $40 left. Which equation represents how much Archer would get paid each day of mowing lawns?
Answer:
Daily pay= $18
5 days pay = $90
Step-by-step explanation:
Archer's daily pay =p
Pay for 5 days= 5p
Gas = 1/2 of 5p
= 1/2 × 5p
= 5p/2
Water = $5
Balance = $40
5p = 5/2p + 5 + 40
5p - 5/2p = 45
10p -5p /2 = 45
5/2p = 45
p= 45÷ 5/2
= 45 × 2/5
= 90/5
P= $18
5p= 5 × $18
=$90
The equation to determine Archer's daily pay is
5p = 5/2p + 5 + 40
Divide both sides by 5
p = 5/2p + 45 ÷ 5
= (5/2p + 45) / 5
p= (5/2p + 45) / 5
Cody is a lifeguard and spots a drowning child 40 meters along the shore and 70 meters from the shore to the child. Cody runs along the shore for a while and then jumps into the water and swims from there directly to the child. Cody can run at a rate of 4 meters per second and swim at a rate of 1.1 meters per second. How far along the shore should Cody run before jumping into the water in order to save the child? Round your answer to three decimal places.
Answer:
Cody should run approximately 19.978 meters along the shore before jumping into the water in order to save the child.Thus,
Step-by-step explanation:
Consider the diagram below.
In this case we need to minimize the time it takes Cody to save the child.
Total time to save the child (T) = Time taken along the shore (A) + Time taken from the shore (B)
The formula to compute time is:
[tex]time=\frac{distance}{speed}[/tex]
Compute the time taken along the shore as follows:
[tex]A=\frac{x}{4}[/tex]
Compute the time taken from the shore as follows:
[tex]B=\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}[/tex]
Then the total time taken to save the child is:
[tex]T=\frac{x}{4}+\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}[/tex]
Differentiate T with respect to x as follows:
[tex]\frac{dT}{dx}=\frac{d}{dx}[\frac{x}{4}]+\frac{d}{dx}[\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}][/tex]
[tex]=\frac{1}{4}-\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}[/tex]
Equate the derivative to 0 to compute the value of x as follows:
[tex]\frac{dT}{dx}=0[/tex]
[tex]\frac{1}{4}-\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}=0\\\\\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}=\frac{1}{4}\\\\4\cdot (40-x)=1.1\cdot [\sqrt{70^{2}+(40-x)^{2}}]\\\\\{4\cdot (40-x)\}^{2}=\{1.1\cdot [\sqrt{70^{2}+(40-x)^{2}}]\}^{2}\\\\16\cdot (40-x)^{2}=1.21\cdot [70^{2}+(40-x)^{2}}]\\\\16\cdot (40-x)^{2}-1.21\cdot (40-x)^{2}=5929\\\\14.79\cdot (40-x)^{2}=5929\\\\(40-x)^{2}=400.88\\\\40-x\approx 20.022\\\\x\approx 40-20.022\\\\x\approx 19.978[/tex]
Thus, Cody should run approximately 19.978 meters along the shore before jumping into the water in order to save the child.
find the Perimeter Of a circle whose radius is 14cm
Answer:
88 cm
Step-by-step explanation:
Perimeter = 2πr
=2(14)(22/7)
= 88 cm
Answer:
87.97cm
Step-by-step explanation:
This question is asking to solve for the circumference.
The formula for the circumference of a circle is: [tex]\pi*diameter[/tex]
To work this out you would first need to multiply the radius of 14 by 2, this gives you 28cm. This is because the radius is half of the diameter.
The final step is to multiply pi by the diameter of 28, this gives you 87.97cm (87.9645943). This is because the formula for the circumference of a circle is [tex]\pi * diameter[/tex].
1) Multiply 14 by 2.
[tex]14*2=28[/tex]
2) Multiply pi by the diameter.
[tex]\pi*28^2=87.97 cm[/tex]
