Santos is a lifeguard and spots a drowning child 50 meters along the shore and 60 meters from the shore to the child. Santos runs along the shore for a while and then jumps into the water and swims from there directly to the child. Santos can run at a rate of 4 meters per second and swim at a rate of 0.9 meters per second. How far along the shore should Santos run before jumping into the water in order to save the child
Answers
Answer:
Santos should run approximately 36.145 meters along the shore
Step-by-step explanation:
The given parameters are;
The distance along the shore of the child = 50 meters
The distance from the shore of the child = 60 meters
The rate at which Santos can run = 4 m/s
The rate he can swim = 0.9 m/s
Let 'x' represent the distance he runs along the shore
We have;
The time he spends running on the shore, t₁ = x/4
The time he spends swimming, t₂ = (√(60² + (50 - x)²)/0.9
The total time, T = t₁ + t₂ = x/4 + (√(60² + (50 - x)²)/0.9
To find the maximum, we have;
dT/dx = 0 = d(x/4 + (√(60² + (50 - x)²)/0.9)/dx = 1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0
1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0
Simplifying using a graphing calculator gives;
[tex]\dfrac{x - 2000}{9} = \sqrt{x^2-100\cdot x+6,100}[/tex]
1519·x² - 151900·x + 3505900 = 0
x = (151900 ± √((-151900)² - 4×1519×3505900))/(2 × 1519)
x ≈ 63.86 m or x ≈ 36.145 m
We note that the distance from a point x = 63.83 meters and 36.145 meters from where Santos spots the girl to the location of the girl are the same
Therefore, Santos should run approximately 36.145 meters along the shore before jumping into to the water in order to save the child
Related Questions
Peter wallpapered a wall that was 9 feet wide and 8 feet high. He had 27 square feet of wallpaper left over. How many square feet of wallpaper did he start with?
Answers
Answer:
99 square feet
Step-by-step explanation:
Because 8 times 9=72+27=99
Explanation:
1.) Find the area of the wall:
8 feet x 9 feet = 72 square feet
2.) To find out how many square feet of wallpaper he had at first, add the area of the wall to the wallpaper he has left:
72 square feet + 27 square feet = 99 ft2
SOMEBODY CORRECT ME IF IM WRONG
And if I am right (pls say if my answer was right after this) Mark me brainliest tysm!
Another Easy One, 50 points and a brainliest to anyone who gives the best answer.
Answers
[tex]5^{-2}=\frac{1}{5²}[/tex]
Answer:
Solutions given:
[tex]5^{-2}=\frac{1}{5²}[/tex]
since
we have rule of indices
[tex]x^{-a}=\frac{1}{x^{a}}[/tex]
Answer: It's 1/25 or 0.04 That's what I got
Step-by-step explanation:
Since 1/5^-2 = 0.04 I think its the first one
Math Problem Solving
statistics and probability
Answers
Answer:
Standard Deviation = 3.22
Variance = 10.36
Step-by-step explanation:
x P(x) x × P(x) x² x² × P(x)
19 0.20 3.8 361 72.2
10 0.20 2 100 20
11 0.30 3.3 121 36.3
12 0.20 2.4 144 28.8
13 0.10 1.3 169 16.9
____________________________________________
12.8 174.2 => Total
Mean Formula
[tex]\mu_x = \sum(x \times P(x))[/tex] [tex]= 12.8[/tex]
[tex]\mu_x^2 = 163.84[/tex]
Variance Formula
[tex]\sigma _x^2 = \sum[x^2 \times P(x)] - \mu_x^2[/tex]
[tex]= 174.2- 163.84\\\\=10.36[/tex]
Standard Deviation Formula
[tex]Standard\ deviation, \ \sigma_x = \sqrt{Variance}[/tex]
[tex]=\sqrt{10.36}\\\\=3.218[/tex]
The value of a piece of property is growing at a rate of 3.5% annually if the property was worth $77,000 when it was purchased, which equation could be used to determine the value of the property, y, x years after it was purchased?
A. y=77,000+3.5x
B. y=77,000(3.5)x
C. y=77,000(1.035)x
D. y=77,000(0.035)x
Answers
What is the area of the sail?
Answers
Area of a triangle is found by multiplying both sides and then dividing that answer by 2.
So 6 times 10 is 60, and 60 divided by 2 is 30.
Answer:
I agree other students
Step-by-step explanation:
congrats
what is the value of x to the nearest tenth
Answers
Answer:
x ≈ 24.7
Step-by-step explanation:
Using the Sine rule in the triangle , that is
[tex]\frac{x}{sin71}[/tex] = [tex]\frac{15}{sin35}[/tex] ( cross- multiply )
x × sin35° = 15 × sin71° ( divide both sides by sin35° )
x = [tex]\frac{15sin71}{sin35}[/tex] ≈ 24.7 ( to the nearest tenth )
Find the volume of the shape with the given dimensions 8 in by 5 in by 3 in
Answers
Answer:
V = (8 in)(5 in)(3 in) = 120 in^3
Step-by-step explanation:
The likeliest name for this shape is "rectangular prism." Let's assume that the length, L, is 8 in; the width, W, is 5 in; and the height, H, is 3 in.
Then the volume of this rectangular prism is V = L * W * H, or
V = (8 in)(5 in)(3 in) = 120 in^3
The Thomson family spends money each month on the expenses shown.
Drag each expense to show whether it is a fixed expense, a variable expense, or if it is neither of these from month to month.
Answers
6.2x6.2x6.2x6.2=1,477.6336 HOW DOES IT BECOME THAT
Answers
Answer:
So, you multiply them.
Step-by-step explanation:
Try it yourself….. Use table multiplication or somthin
Answer:
Well 6.2 x 6.2 is 38.44 and if you do 38.44 x 38.44 it is 1,477.6336
how do you do this?
Answers
Answer:
by increasing the size ez
Find three consecutive odd integers where the sum of the first two numbers multiplied by the last number is 3116.
a. -42, -44, - 46
b. None of these.
c. 37, 39, 41
d. 42, 44, 46
e. 33, 35, 37
Answers
What is the volume of this triangular prism? A triangular prism. The triangular base has a base of 28 centimeters and height of 22.4 centimeters. The height of the prism is 18.1 centimeters. 313.6 506.8 5,676.16 11,352.32
Answers
Answer:
The volume of the triangular prism is 5676.16 cm³
Step-by-step explanation:
The area of the triangular base A = bh/2 where b = base = 28 cm and h = height = 22.4 cm.
Now, the volume of the triangular prism, V = area of triangular base, A × height of prism, h'
V = Ah' where h = height of prism = 18.1 cm
So, V = bhh'/2
Substituting the values of the variables into the equation for V, we have
V = bhh'/2
V = 28 cm × 22.4 cm × 18.1 cm/2
V = 14 cm × 22.4 cm × 18.1 cm
V = 5676.16 cm³
So, the volume of the triangular prism is 5676.16 cm³
Answer:
5676.16 cm³
Step-by-step explanation:
CE and FI are parallel. Giving reasons prove that DGH is isosceles
Answers
9514 1404 393
Answer:
∠GDH = ∠GHD = 50°
Step-by-step explanation:
Angles FGD and EDG are alternate interior angles, so are congruent. That means angle EDG is 100°. The angle sum theorem tells us ...
∠EDG = ∠EDH +∠HDG
100° = 50° +∠HDG
50° = ∠HDG
You can find the measure of ∠DHG a couple of different ways. It is an alternate interior angle congruent to ∠EDH, so is 50°. It is one of two remote interior angles that have a sum equal to the exterior angle FGD, so is ...
∠DHG = ∠FGD -∠HDG = 100° -50° = 50°
So, angles DHG and HGD both have measures of 50°. When a triangle has two angles with the same measure, it is an isosceles triangle.
What is the sum of 3/10 and 1/3
Answers
Answer:
19/30
Step-by-step explanation:
3/10 + 1/3
Get a common denominator of 30
3/10 * 3/3 + 1/3 * 10/10
9/30 + 10/30
19/30
Answer:
19 / 13
Step-by-step explanation:
➟ 3 / 10 + 1 / 3
➟ 3 / 10 × 3/3 + 1 /3 × 10 /10
➟ 3 × 3 / 10 × 3 + 1 × 10 / 3 × 10
➟ 9 / 30 + 10 / 30
➟ 9 + 10 / 30
➟ 19 / 30
Analyze the diagram below and complete the instructions that follow.
3
3
4
45°
h
x
Find the value of x and the value of y.
A X= 4, y = 8
B. x = 7, y = 42
C. x = 413, y = 7/2
D. -73.7=42
Answers
Answer:
B) x = 7, y = 4√2
Step-by-step explanation:
Drop a line from the upper left vertex
This creates a rectangle with a bottom side of 3
and an isosceles right triangle with legs of 4
Therefor
x = 4 + 3
x = 7
y = √(4² + 4²)
y = 4√2
The values of x and y from figure are 7 and 4√2 respectively, option B is correct.
When we analyze the diagram, there is a right angle triangle with opposite side of 4 units.
We have to find the values of x and y.
Sine function is a ratio of opposite side and hypotenuse.
sin45=4/y
1/√2 = 4/y
Apply cross multiplication:
y=4√2.
Now let us find the value of x by cosine function.
Cosine is a ratio of adjacent side and hypotenuse.
cos 45 =x/y
1/√2 = x/4√2
Apply cross multiplication:
x=4
Now from diagram x=4+3 =7
Hence, the values of x and y from figure are 7 and 4√2 respectively.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ7
What are the coordinates?
Answers
Answer:
J - (0, 4) K - (2, 3) L - (3, 4) M - (4, 1) N - (1, 2)
Step-by-step explanation:
So, the first number, is the value on the x axis, The second number, is the value on the y axis.
So lets look at each point. J is at 0 on the x axis, and 4 on the y axis.
K is at 2 on the x axis, and 3 on the y axis.
L is at 3 on the x axis, and 4 on the y axis.
M is at 4 on the x axis, and 1 on the y axis.
Finally, n is at 1 on the x axis, and 2 on the y axis.
Since we write coordinates as (x, y):
K is (2, 3)
L is (3, 4)
M is (4, 1)
N is (1, 2)
Hope this helps!
I need help with this math question: 15x+ 60 < 240
Answers
12
15x + 60 <240
-60
15 veces <180/15
x <12
Step-by-step explanation:
A recipe for a smoothie for 0.75 pound of strawberries. If Kerry has 3.15 pounds of strawberries, how many batches of the recipe can She make
Answers
Answer:
4 batches
Step-by-step explanation:
To obtain the number of batches of the recipe that can be made ;
We take the divison of the total amount of strawberry by the amount of strawberry required per batch :
Pounds of strawberry per recipe = 0.75 pound
Total pounds of strawberry = 3.15 pound
= 3.15 / 0.75
= 4.2
We round down :
4.2 batches = 4 batches of the recipe can be made
Hi could someone tell me how to solve this, you don’t even have to tell me the answer I’m just confused on this math and need help with how to do it! (Will give 33 points (and POSSIBLY Brainliest if I’m able to)!
Answers
Answer:
132 ft
Step-by-step explanation:
The radius is 21 ft
We want to find the circumference
C = 2 * pi *r
Letting pi = 22/7
C = 2 * 22/7 * 21
C = 132 ft
Answer:
[tex]{\Huge{\underline{\underline{\textbf{\textsf{Answer}}}}}}[/tex]The radius is 21 ftWe want to find the circumference
C = 2 * pi *rLetting pi = 22/7C = 2 * 22/7 * 21C = 132 ftFrank is making chocolate chip pancakes for his whole family. He wants to make 20 pancakes using a 3-cup bag of chocolate chips. How many cups of chocolate chips will be in each pancake? Write your answer as a proper fraction or mixed number.
Answers
im pretty sure that the answer is 6 2/3
9. Rachel wants to draw a triangle with
sides of length 4 cm and 5 cm. What is
a possible length of the third side?
Answers
I think its 6 cm for the 3rd side
more help srry if its annoying
Answers
Answer:
4^5
4 by the power of 5
Step-by-step explanation:
4 times the amount of 4's
4 times 5 does not equal 4^5 and is not the answer
it is 4 by the power of 5
A right-angled triangle D E F, angle E marked right angle, side E F labeled 7, side D E labeled 24 and hypotenuse D F labeled 25.
Answers
Answer:
Ya está resuelto ya
Step-by-step explanation:
Please answer the question below
Answers
Answer:
320
Step-by-step explanation:
(2 / 50) * 8000 = 320
Answer:
320
Step-by-step explanation:
please help me u guys!!
Answers
pls help (ty and I just clicked sas cause I don’t know sorry)
Answers
Explanation: the 2 congruent sides are next to one another and SAA ≈ SAA is never right
That was kind of bad but I’m not really sure how else to explain it
You are given a bag with 3 cubes (1 green and 2 white). You put all 3 cubes in a bag and shake the
bag and pick a cube. If you pick a green cube, you get 2 points. If you pick a white cube, you lose 1
point. What is the expected value for the game?
Answers
Answer:
-1 (losing a point)
Step-by-step explanation:
it is a probability question
total possible outcomes= 3
favourable outcome(white) = 2
probability of getting a white is 2/3
probability of getting a green is 1/3
so the expected value of the game will be -1
ZA — 5х – 12°
ZB = 2х + 24°
B
4
Answers
Answer:
Step-by-step explanation:
angle A =angle B (because they are alternate interior angles)
5x-12=2x+24
5x-2x=24+12
3x=36
x=36/3
x=12
angle A=5x-12
5*12-12
60-12
48
angle B=2x+24
2*12+24
24+24
48
Write as an equation in two variables: k(x) = -4x-1
Answers
Answer:
y = -4x - 1
Step-by-step explanation:
k(x) = -4x - 1
replace k(x) with y
y = -4x - 1
Answer:
y = -4x - 1
Step-by-step explanation:
identify one solution for this graph
Answers
Basically, any point that is shaded.
