Answer:
The minimum amount of time required is 74.7 seconds.
Step-by-step explanation:
The question can be solved in two cases:
i. diagonal swimming of Brandon across the river
ii. Running of the rest distance by Brandon.
Case I: Since he would swim diagonally across the river, then the diagonal distance can be determined by applying appropriate trigonometric function.
Let the diagonal be represented by x, an included angle θ = [tex]45^{o}[/tex] is formed at his starting point (angle formed by the diagonal and the length of the width of the river).
So that:
Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
Cos [tex]45^{o}[/tex] = [tex]\frac{70}{x}[/tex]
x = [tex]\frac{70}{Cos 45^{o} }[/tex]
= 98.995
x = 99 m
The diagonal distance covered by Brandon is 99 m.
The time to cover this distance can be calculated by:
speed = [tex]\frac{distance}{time}[/tex]
time = [tex]\frac{distance}{speed}[/tex]
Given that his swimming rate is 2 m/s, then:
time = [tex]\frac{99}{2}[/tex]
= 49.5
The time taken by Brandon to swim diagonally is 49.5 seconds.
Case II: Since he want to cover a total distance of 250 m;
remaining distance to be covered = 250 - 99
= 151
time = [tex]\frac{distance}{speed}[/tex]
Given that he runs at 6 m/s, then;
time = [tex]\frac{151}{6}[/tex]
= 25.1667
The time taken by Brandon to run the remaining distance is 25.2 seconds.
The minimum amount of time required = time taken by Brandon to swim diagonally + time taken by Brandon to run the remaining distance
= 49.5 + 25.2
= 74.7
The minimum amount of time required is 74.7 seconds.
Minimum amount of time to reach the desired point is 79.5 s
Brandon is on one side of a river
The width of the river = 70 m
Brandon wants to reach a point that is 250 m downstream of opposite side as quickly as possible by swimming diagonally across the river then running the rest of the way.
The swimming speed of Brandon = 2 m/s
The speed of running of Brandon = 6 m/s
Let us consider that the included angle be 45°
[tex]\rm cos \; \theta = \dfrac{70}{x} \\\\cos \; 45 = \dfrac{70}{x} \\\x = \dfrac{70}{0.707} \approx 99[/tex]
So the distance traveled by Brandon in water is 99 m
As the swimming speed of Brandon is given 2 m/s
So the time taken by Brandon to cross the river is given as follows
[tex]\rm Time = \dfrac{Distance}{Speed}[/tex]
[tex]\rm Time \; to\; cross\; the\; river = \dfrac{99}{2} = 49.5 \; s[/tex]
Let the horizontal distance covered by Brandon by swimming is H
So from Pythagorean theorem we can write
[tex]\rm H = \sqrt{99^2 -70^2 } = 70[/tex]
The distance that is left to be traveled by running is 250 - 70 = 180 m
So Time taken in running to reach the point by running = 180/6 = 30 s
So the time to reach the desired point = 49.5 + 30 = 79.5 s
For more information please refer to the link given below
https://brainly.com/question/14930619
Sasha purchased paint that will cover 400 square feet per gallon. Sasha needs to paint a 4704-square-foot surface with 2 coats of paint.
How many gallons of paint will she need for this project?
A.11
B.12
C.23
D.24
Answer:
D. 24
Explanation:
First you would need to find how many you need for one coat.
400 times 12 = 4,800
(That will give you a little extra paint)
Then just double 12 to get two coats and you would get D.
Have a nice day!
Hope this helped.
Please give me the correct answer.
Answer:
[tex] -m + 6 = 3m + 14 [/tex]
Step-by-step explanation:
Given:
[tex] -(m - 6) = 3m + 14 [/tex]
Required:
Multiply (m - 6) by -1.
Solution:
To multiply (m - 6) by -1, we would be applying the distributive property. This means that we would multiply each term in the parentheses by -1.
Thus:
[tex] -1(m) -1(-6) = 3m + 14 [/tex]
The result would be:
[tex] -m + 6 = 3m + 14 [/tex] (negative times negative = positive)
i need help with these 9 questions they’re pretty simple
Answer:
1. n = 4
2. n = -29
3. n = -28
4. n = -48
5. n = -22
6. n = 97
7. n = 220
8. n = -18
9. n = 36
Step-by-step explanation:
1. -n = -4
Multiply both by -1 to get n = 4
2. 12 + n = -17
Subtract 12 from both sides of the equation to get n = -29
3. -n/14 = 2
Multiply by 14 on both sides of the equation to get -n = 28
Multiply -1 on both sides of the equation to get n = -28
4. -42 = n + 6
Subtract 6 from both sides of the equation to get -48 = n or n = -48
5. -4n = 88
Divide -4 on both sides of the equation to get n = -22
6. n + -3 = 94
Add 3 to both sides of the equation to get n = 97
7. 11 = -n/-20
Multiply by -20 on both sides of the equation to get -220 = -n or -n = -220
Multiply -1 on both sides of the equation to get n = 220
8. -108 = 6n
Divide by 6 on both sides of the equation to get -18 = n or n = -28
9. 67 = 31 + n
Subtract 31 from both sides of the equation to get 36 = n or n = 36
I Hope That This Helps! :)
2 1/7 divided by 1 2/5
The scores of seven people playing a card game are listed below.
Answer:
there is nothing but a black screen
Step-by-step explanation:
Answer:Even though theres no screen the answers IQR is 73
Write the next three terms in each sequence. Make sure your
answers are separated by a comma and a space; like 1, 2, 3
25, 26, 27, 28, ...
Answer:
29,30,31
this is basically like counting just add 1
Please please please help quickly!
Um th eanswer is 56-64-34-3402-30 = 19038
Ramen noodles. There are 20 ramen noodle packages in a bag. There are 10 beef flavored, and the other 10 are chicken flavored. What is the probability of getting at least one chicken and at least one beef flavor when you grab 3 packages randomly?
Answer:
0.789
Step-by-step explanation:
Number of beef flavored Ramen noodles = 10
Number of chicken flavored Ramen noodles = 10
Total number of noodles = 20
Number of ways to select 3 packages:
[tex]_{20}C_3= \dfrac{20\times 19\times 18}{3\times 2\times 1}=1140[/tex]
Number of ways to select two beef flavored Ramen noodle = [tex]_{10}C_2[/tex] = 45
Number of ways to select one chicken flavored Ramen noodle = 10
Number of ways to select two chicken flavored Ramen noodle = [tex]_{10}C_2[/tex] = 45
Number of ways to select one chicken flavored Ramen noodle = 10
Total number of ways so that one chicken and one beef Ramen selected = 450 + 450 = 900
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Required probability is:
[tex]\dfrac{900}{1140} = 0.789[/tex]
Mr Thompson wants to cut a 5-ft rope into a 1/4-ft sections how many 1/4 sections will he have
Answer:
20 pieces of rope
Step-by-step explanation:
Mr. Thompson has a 5-ft rope. If he cuts the rope into 1/4-ft pieces, that means for every foot, there are 4 pieces of rope. There are 5-ft of rope, so we multiply 5 and 4 to get the number of pieces of rope.
5 x 4 = 20 pieces of rope.
I hope that this helps! :)
I don’t understand plz help me
Answer:
C×6=D
Step-by-step explanation:
You don't know her me calculators they have or they bought so you take C for the calculators multiply by 6 and D is the product or answer.
When full, a cinema house has n people. When 280 people have taken seat the remaining seats comes to $384 if each tickets cost $1.20 find the number of seats in the cinema house?
Answer: 600 seats
Step-by-step explanation:
384/$1.20 = 320 seats
N - 280 = 320
+280. +280
N = 600
The total number of seats in the cinema house will be 600 seats.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
When full, a cinema house has n people. When 280 people have taken a seat the remaining seats come to $384 if each ticket cost $1.20.
Then the total number of seats in the cinema house will be given as,
⇒ 280 + $384 / $1.20
⇒ 280 + 320
⇒ 600 seats
The total number of seats in the cinema house will be 600 seats.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
help lol i forgot the picture
Answer:
x=12
Step-by-step explanation:
4(12)+17 equals 65
(12)+23 equals 35
180-80=100
65+35=100
What is the perimeter of an equilateral triangle which has an area of 96\sqrt{3}96
3
Answer:b
Step-by-step explanation:
Which of the following is a solution for 5 - 2xs-3?
-4
4
1
-1
Pls help me, im not understand this
Answer:
Step-by-step explanation:
Mathematics value in words?
Answer:
Wdym
Step-by-step explanation:
Mathematics value in words
which of the following would you expect to have the highest interest? a 5-year CD a 10-year CD and online savings account or savings account at a Traditional Bank
Answer:10-year CD
Step-by-step explanation:
No
hectare is equal to 2.471 acres. A land developer buys a hectare of land to build homes. Each home will be built on 0.25 acres of land. How many homes can the land developer build on the hectare of space?
Answer:
2.221
Step-by-step explanation:
Multiply the divisor and the dividend by the same power of 10 so that the divisor is a whole number. To check if your answer is reasonable, estimate the quotient by rounding the divisor and dividend to the nearest whole numbers.
ANSWER:
try 2.721....................
What is the slope of this line?
5
1/5
-1/5
-5
Answer:
1/5
Step-by-step explanation:
You do rise over run so your rise is 1 and your run is 5 so the answer is 1/5.
And it is positive because it is pointed to the right side.
Hope this helps
can someone help me !?
Talya wanted to hit 20 homeruns this season. She ended up hitting 150% of her goal. How many homeruns did Talya hit this season?
Answer:
30
Step-by-step explanation:
tell me if im wrong
sorry if i am TmT
Help I Dont Understand?
GIVING BRAINLIEST IF CORRECT PLEASE HELP ASA[P
Answer:
A) b= 8 students
B) 1) 19/55 2) 28/55
Step-by-step explanation:
I'm sorry if I'm getting this whole concept wrong cause it felt way too easy to be right so I'm sorry if you get it wrong.
The reason the first question is 8 is because of the fact that you first have to add the students charted on the Venn-diagram and subtract that from 55, getting you to 8 students.
For the second one, the first part would be 19/55 becuase in the Venn-diagram it is shown that only 19 people passed both and so that be the numerator and the denominator would be the total of students, so it would be 55.
Same thing for part two except the fact that you have to add the students who only passed one subject, so combine 17 and 11, getting you to 28, thus getting the answer 28/55.
Identify the constant in the expression.
4w – 3r + 6
6
because it is the only number that isn't being multiplied by a letter
which number are composite numbers-49,35,32,41,47
Answer:
49, 35, 32
Step-by-step explanation:
A prime number is a number whose factors are 1 and itself
Eg 7
7 is a prime number because it only comes in table one and 7
Or it’s only factors are 1 and itself
A composite number comes in 1, itself and other tables
Eg. 16
It comes in table 1, 2, 4 and 16
Answer: 49,32,35.
Hope this helps!
If there are 12 inches in a foot, how many inches are in 64 feet?
Answer:
768
Step-by-step explanation:
64*12
Answer:
768
Step-by-step explanation:
12x64=768
What are the solutions to the quadratic equation 4(x + 2)2 = 36 x = −11 and x = 7 x = −7 and x = 11 x = −5 and x = 1 x = −1 and x = 5
Answer:
c
Step-by-step explanation:
edge2020
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
What is a Quadratic Equation?
Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given that;
4(x + 2)² = 36
4( x(x + 2) + 2(x+2) ) = 36
4( x² + 2x + 2x + 4 ) = 36
4( x² + 4x + 4 ) = 36
4x² + 16x + 16 = 36
4x² + 16x + 16 - 36 = 0
4x² + 16x - 20 = 0
We can further simply ( divide through by 4 )
x² + 4x - 5 = 0
Hence,
a = 1b = 4c = -5x = (-b±√(b² - 4ac)) / (2a)
x = (-4±√(4² - (4 × 1 × -5)) / (2×1)
x = (-4±√(16 - (-20)) / (2)
x = (-4±√(16 + 20)) / (2)
x = (-4±√(36)) / 2
x = (-4±6)) / 2
Hence
x = (-4-6)) / 2 and x = (-4+6)) / 2
x = -10/2 and x = 2/2
x = -5 and x = 1
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
Learn more about quadratic equations here: brainly.com/question/1863222
#SPJ2
Convert 12 ounces to pounds use the conversion rate 16 ounces = 1 pound
Answer:
3/4 pound
Step-by-step explanation:
12/ 16
÷4 on top and bottom
Answer:
0.75lbs
Step-by-step explanation:
HELP!!!!i will give BRAINLIEST
Answer:
2.9
Step-by-step explanation:
2 9/10 as an improper fraction is 29/10
29/10 as a decimal is 2.9
Answer:
2.9
Step-by-step explanation:
Math. Pls give brainliest:)!
Three cards—one red, one green, and one blue—are to be arranged in a stack. Using R for red, G for green, and B for blue, make a list of all the different stacks that can be formed. (Some computer monitors are called RGB monitors for the colors red, green, and blue. Enter your answers as a comma-separated list.)
Answer:
RGB. RBG, BRG, BGR, GBR, GRB
Step-by-step explanation:
Given
R, G and B
Required
List all possible arrangement
First, we need to calculate the number of arrangement
There are 3 letters and they are to be arranged in order of 3.
So, we have:
[tex]n = 3[/tex] and [tex]r =3[/tex]
Number of arrangement is:
[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]
[tex]^3P_3 = \frac{3!}{(3 - 3)!}[/tex]
[tex]^3P_3 = \frac{3!}{0!}[/tex]
[tex]^3P_3 = \frac{3*2*1}{1}[/tex]
[tex]^3P_3 = \frac{6}{1}[/tex]
[tex]^3P_3 = 6[/tex]
Hence, number of arrangements is 6 and the arrangements are:
RGB. RBG, BRG, BGR, GBR, GRB
