Two people start from the same point. One walks east at 4 mi/h and the other walks northeast at 8 mi/h. How fast is the distance between the people changing after 15 minutes?

Answers

Answer 1

Answer:

5.89 mi/h

Step-by-step explanation:

This problem can be solved by using different methods. I will use vectors since it's the simplest way in which we can solve it. This can be solved by using related rates of change though.

First, we start by drawing a diagram with the velocity vectors.

A= velocity of the first person

B= velocity of the second person

C= velocity in which they are moving away from each other.

Since there is no acceleration in the problem, we can suppose we are talking about constant speeds, so the velocity at which they are moving away from each other will always remain constant. (It doesn't matter what time it is, the velocity will always be the same)

Having said this we can solve this problem by using the components, by using law of cosines or graphically. I will use law of cosines. The idea is to find the length of side c.

Law of cosines:

[tex]C^{2}=A^{2}+B^{2}-2ABcos \gamma[/tex]

so we can solve the formula for C so we get:

[tex]C=\sqrt{A^{2}+B^{2}-2ABcos \gamma}[/tex]

and now we can substitute the values we know:

[tex]C=\sqrt{(4)^{2}+(8)^{2}-2(4)(8)cos 45^{o}}[/tex]

[tex]C=\sqrt{16+64-32\sqrt{2}}[/tex]

[tex]C=\sqrt{80-32\sqrt{2}} mph[/tex]

if we want an exact answer, then that will be the exact answer, which approximates to:

C=5.89 mph

Two People Start From The Same Point. One Walks East At 4 Mi/h And The Other Walks Northeast At 8 Mi/h.

Related Questions

Given f (x) = 4x-3, g(x) = x^3 +2x
Find (f-g) (4)

Answers

Answer:

[tex](f-g)(4) = -59[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]f(x)=4x-3\text{ and } g(x) = x^3 +2x[/tex]

And we want to find the value of:

[tex](f-g)(4)[/tex]

Recall that this is equivalent to:

[tex](f-g)(4) = f(4) - g(4)[/tex]

Find f(4):

[tex]f(4) = 4(4)-3 = 13[/tex]

And find g(4):

[tex]g(4) = (4)^3 + 2(4) =72[/tex]

Substitute:

[tex](f-g)(4) = (13)-(72)[/tex]

And subtract. Hence:

[tex](f-g)(4) = -59[/tex]

Step-by-step explanation:

I love this question!

So there are a couple different ways of solving this. You feel free to ignore whichever one makes less sense.

Subtracting First

The first option is taking f(x) and g(x) and subtracting them, then introducing the number.

The calculation:

f(x) - g(x)

Substitute.

4x - 3 - (x^3 + 2x)

Multiply out the negative.

4x - 3 - x^3 - 2x

Rewrite.

-x^3 + 4x - 2x - 3

Simplify.

-x^3 + 2x - 3

Then, replace x with 4.

-(4)^3 + 2(4) - 3

Simplify.

-64 + 8 - 3

Add.

-59

Making x = 4 first

Here, we'll do what's on the tin. Find f(4) and g(4), then subtract them.

f(x) = 4x - 3

f(4) = 4(4) - 3

f(4) = 16 - 3

f(4) = 13

Then find g(4):

g(x) = x^3 + 2x

g(4) = (4)^3 + 2(4)

g(4) = 64 + 8

g(4) = 72

Then, subtract these two:

f(4) - g(4) = 13 - 72

f(4) - g(4) = -59

Answer:

Either way, the answer is -59

What is the length of the line?
WILL GIVE BRAINLIEST!!

Answers

Answer:

18

Step-by-step explanation:

6^2 plus 3^2 = 324, square root 324 =18

Answer:

[tex]\sqrt{45}[/tex]

Step-by-step explanation:

The line represents the hypotenuse of a right triangle with legs 6 and 3. For any right triangle, the Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle and [tex]c[/tex] is the hypotenuse.

Therefore, we have:

[tex]6^2+3^2=c^2,\\c^2=36+9,\\c=\boxed{\sqrt{45}}[/tex]

Find the second partial derivatives of the following functions
a) z = 3x^2 − 4xy + 15y^2
b) z = 4xe^y
c) z = 6xln(y)

Answers

(a) z = 3x ² - 4xy + 15y ²

has first-order partial derivatives

z/∂x = 6x - 4y

z/∂y = -4x + 30y

and thus second-order partial derivatives

∂²z/∂x ² = 6

∂²z/∂xy = -4

∂²z/∂yx = -4

∂²z/∂y ² = 30

where ∂²z/∂xy = ∂/∂x [∂z/∂y] and ∂²z/∂yx = ∂/∂y [∂z/∂x].

(b) z = 4x

z/∂x = 4

z/∂y = 4x

∂²z/∂x ² = 0

∂²z/∂xy = 4

∂²z/∂yx = 4

∂²z/∂y ² = 4x

(c) z = 6x ln(y)

z/∂x = 6 ln(y)

z/∂y = 6x/y

∂²z/∂x ² = 0

∂²z/∂xy = 6/y

∂²z/∂yx = 6/y

∂²z/∂y ² = -6x/y ²

Find two numbers nearest to 8888888 which are exactly divisible by 2915 explain step by step​

Answers

Answer: 88,87,835 and 88,90,750.
Step-by-step explanation: 88,87,835 =2915*3049 , 8890750 = 2915*3050.

Two sides of a triangle are 24 inches in length, what is the length of the third side

Answers

The answer should be 24 inches

How far apart are the 2 cities? See picture.
Show steps

Answers

9514 1404 393

Answer:

  373 miles

Step-by-step explanation:

The difference in latitude is ...

  39.1° -33.7° = 5.4° = 0.54°(π/180°) radians = 0.03π radians

The arc length is given by ...

  s = rθ, where θ is the angle in radians

The length of the arc along the longitude line is ...

  s = (3960 mi)(0.03π) ≈ 373 mi

The distance from Atlanta to Cincinnati is about 373 miles.

Can somebody help me find the answer to this problem please ?

Answers

Answer:

Step-by-step explanation:

Answer:

D. x = -2y + 4

Step-by-step explanation:

4x + 8y = 16

Solve for x

Our objective here is to isolate x ( in other words we want to get x by itself ) using inverse operations.

So let's begin

4x + 8y = 16

First we want to get rid of 8y

Notice how 8y is being added to 4x

Well we can get rid of it by applying it's inverse operation. The opposite of addition is subtraction. So to get rid of 8y we would simply subtract 8y.

Important note! Whatever we do to one side we must do to the other

So we would subtract 8y from both sides

4x + 8y - 8y = 16 - 8y

The 8y on the left hand side cancels out and the 8y on the right side stays as it is as you can't subtract 8y from 16

We then have 4x = 16 - 8y

Next we want to get rid of 4 from 4x.

4x is the same as 4*x which is multiplication

The inverse of multiplication is division so to get rid of the 4 we divide both sides by 4

4x/4 = (16-8y)/4

4x/4 = x

16-8y/4 ( simply divide 16 by 4 and -8y by 4 )

16-8y/4 = 4 - 2y

We're left with x = 4 - 2y which can also be written as x = -2y + 4

A normal distribution has a mean of 15 and a standard deviation of 2. Find the value that corresponds to the 75th
percentile. Round your answer to two decimal places.
N
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.5
0.6915
0.6950
0.6985
0.7019
0.7054
0.7088
0.7123
0.7157
0.7190
0.7224
0.6 0.7257
0.7291
0.7324
0.7357
0.7389 0.7422
0.7454
0.7486
0.7517
0.7549
0.7 0.7580
0.7611
0.76420.7673
0.7704
0.7734
0.7764
0.7794
0.7823
0.7852
0.8
0.7881
0.7910
0.7939
0.7967
0.7995
0.8023
0.8051
0.8078
0.8106
0.8133

Answers

I am sorry, I am so confused
I wish I could help

List the sides of the triangle in order from largest to smallest.

Answers

translate it to english

A police officer investigating a car accident finds a skid mark of 115 ft in length.

How fast was the car going when the driver hit the brakes?
Round your answer to the nearest mile per hour.

mph

Answers

Answer:

Speed of car = 49 mph (Approx.)

Step-by-step explanation:

Given:

Length of skid marked = 115 ft

Formula for skid mark = S = √21d

Where d = Length of skid marked

Find:

Speed of car

Computation:

Speed of car = √21d

Speed of car = √21(115)

Speed of car = √2,415

Speed of car = 49.1426

Speed of car = 49 mph (Approx.)

One angle of a triangle measures 108°. The other two angles are congruent.
Enter and solve an equation to find the measure x of the congruent angles.

Answers

Congruent means the same. So (180-108)/2 equals to 36.

Find the value of x.
A. 86
B. 172
C. 94
D. 188

Answers

Answer:

188

Step-by-step explanation:

Tangent Chord Angle = 1/2Intercepted Arc

94 = 1/2 x

Multiply by 2

2*94 =x

188 =x

If f:X is 3x + b and ff(2) = 12, find the value of b​

Answers

Answer:

[tex]b =6[/tex]

Step-by-step explanation:

Given

[tex]f(x) =3x + b[/tex]

[tex]f(2) = 12[/tex]

Required

Find b

[tex]f(2) = 12[/tex] implies that:

[tex]12 = 3 * 2 + b[/tex]

[tex]12 = 6 + b[/tex]

Collect like terms

[tex]b = 12 - 6[/tex]

[tex]b =6[/tex]

6 + 7* log base 2 of x = 21

Answers

6 + 7* log base 2 of x = 21

Answer:

Step-by-step explanation:

A+ Series - Core Mathematics THEORY QUESTIONS Question 1 (SSSCE 2000 Ou 12a) Four angles of a hexagon are 130°, 160°, 112° and 80°. If the remaining angles are equal, find the size of each of them ​

Answers

To solve this question, we have to understand the sum of all angles of a polygon, identify the polygon and doing this, we get that the size of each of the angles are: 119º.

Sum of angles:

The sum of angles of a polygon of n sides is given by:

[tex]S_n = 180(n-2)[/tex]

Hexagon:

6 sides, thus [tex]n = 6[/tex], and:

[tex]S_n = 180(6-2) = 180*4 = 720[/tex]

Angles:

Four are 130°, 160°, 112° and 80°, the other two are equal, so both are x. Then:

[tex]130 + 160 + 112 + 80 + x + x = 720[/tex]

[tex]482 + 2x = 720[/tex]

[tex]2x = 238[/tex]

[tex]x = \frac{238}{2}[/tex]

[tex]x = 119[/tex]

Thus, the size of each of them is of 119º.

For more of the angles of a polygon, you can check https://brainly.com/question/19023938

If the price of a stapler increase from Rs 50 to Rs 54, find the percentage increase?

Answers

Hope this helps have a nice day
We can use proportions to solve this. We need to subtract 54 from 50. This gives us 4. Therefore, our fraction can be 4/50. Then, our next fraction is x/100. We can cross multiply 4*100 is 400. 400/50 is 8. The percentage increase is 8.

a bus carry 53 passengar on a trif. how many passenger can 9 such carry if each dose 2 trif

Answers

Answer:

954 passengers

Step-by-step explanation:

(Assuming I read the question correctly)

1 bus can carry in 1 trip = 53 passengers

1 bus can carry in 2 trips : 106 passsengers

9 busses can carry in 2 trips = 106 x 9 = 954

Answred by Gauthmath

Rules for multiplying exponents

Answers

Answer and Step-by-step explanation:

When multiplying exponents:

- Product of Powers: When the base of the exponents are the same, and the bases are being multiplied to each other, the exponents are added together.

Example: [tex]a^x + a^y = a^{x+y}[/tex]

- Different bases Same Exponents: When the bases of the exponents are different, but the exponents are the same, the bases multiply together (within a parenthesis) with the exponent on the parenthesis.

Example: [tex]a^x*b^x = (a*b)^x[/tex]

- Quotient of Powers: When the base of the exponents are the same, and they are being divided by each other, the exponents will subtract from each other.

Example: [tex]\frac{a^x}{a^y}= a^{x-y}[/tex]

- Power of a Power: When a base has an exponent, and that entire term has and exponent, the exponents multiply together.

Example: [tex](a^x)^y = a^{x*y}[/tex]

- Power of a Product: The opposite of Different bases Same Exponents. Distribute the exponent onto the different bases.

Example: [tex](ab)^x = a^x*b^x[/tex]

- Power of a Quotient: The opposite of Quotient of Powers. Distribute the exponent to the dividing bases.

Example: [tex](\frac{a}{b} )^x = \frac{a^x}{b^x}[/tex]

- Zero Power: Any number raised to the 0 power equals 1.

Example: [tex]a^0 = 1\\999999^0=1[/tex]

- Negative Exponent: Any number raised by a negative number goes to the denominator of a fraction (if not already in the denominator), and vise versa (goes to the numerator if not already in the numerator).

Example: [tex]a^-2 = \frac{1}{a^2} \\\\\frac{1}{b^-3} = b^3[/tex]

- Power of One: Any number raised to the power of 1 is the same number.

Example: [tex]a^1 = a\\\\999^1 = 999[/tex]

I hope this helps!

#teamtrees #PAW (Plant And Water)

Please help 20 points. I will give Brainly to who ever get it right.

Answers

Answer:

Step-by-step explanation:

(-∞,2)

Here are some photos of my math home work please show some work.

Answers

Answer:

I can answer 2-19.

Step-by-step explanation:

The first equation is x=0.

the second equation has no solution.

A large cable company reports that 42% of its customers subscribe to its Internet service, 32% subscribe to its phone service and 23% subscribe to both its Internet service and phone service.
a) What is the probability that a randomly selected customer subscribes to the Internet service or the phone service?
b) What percent of customers subscribe to neither the Internet service nor the phone service?

Answers

9514 1404 393

Answer:

  a) 51%

  b) 49%

Step-by-step explanation:

a) P(A∪B) = P(A) +P(B) - P(A∩B)

  P(A∪B) = 42% +32% -23% = 74% -23% = 51%

51% subscribe to one or the other.

__

b) P(¬A∩¬B) = P(¬(A∪B)) = 1 -P(A∪B) = 1 -51% = 49%

49% of customers subscribe to neither service.

For this problem I thought the answer would be 1.3 for part C since it said to find the mean. However, I am wrong. Can someone help me with the problem please? Thank you for your help!

Answers

Answer:

Step-by-step explanation:

the mean is

{(12x1)+(13x1)+(14x2)+(15x2)+(17)+(18)+(19x2)+(20)+(21x2)+(22)+(24)}/11

mean=264/11

mean=24

Solve for x.
Sqrt8 (Sqrt2 - x) = 11

Answers

Answer:[tex]\frac{-7\sqrt{2} }{4}[/tex]

Step-by-step explanation:

So first, let's get rid of the parentheses. We can multiply it out to get [tex]\sqrt{16}-x\sqrt{8} =11[/tex]. We know that the square root of 16 is ±4, so now our equation is ±4 - [tex]x\sqrt{8}[/tex]=11. I'm guessing since the problem only has one solution it's most likely only positive 4, so let's revise our equation to 4 - [tex]x\sqrt{8}[/tex]=11. We can use inverse operations to make the a little easier to solve: -7= [tex]x\sqrt{8}[/tex]. We divide both sides by [tex]\sqrt{8}[/tex] to get [tex]\frac{-7}{\sqrt{8} } =x[/tex], which we can rationalize (remove the square root from the denominator so that it's a proper answer) by multiplying by [tex]\frac{\sqrt{8} }{\sqrt{8} }[/tex] (which is equal to one so we can use it) which is equal to [tex]\frac{-7\sqrt{8} }{8}[/tex]. Let's finish this by simplifying it. [tex]\sqrt{8} =2\sqrt{2}[/tex] (2x[tex]2^{2}[/tex]). We can simplify it further by simplifying the 2, making it [tex]\frac{-7\sqrt{2} }{4}[/tex].

Hope this wasn't too confusing! I'll answer any questions.

Answer:

x = -7 sqrt(2)/4

Step-by-step explanation:

Sqrt8 (Sqrt2 - x) = 11

Simplify sqrt(8) = sqrt(4*2) = 2 sqrt(2)

2 sqrt(2) (Sqrt2 - x) = 11

Distribute

2 *2 - 2 sqrt(2) x = 11

4 - 2 sqrt(2)x = 11

Subtract 4 from each side

4-2sqrt(2)x -4 = 11-4

-2 sqrt(2)x = 7

Divide each side by -2 sqrt(2)

-2 sqrt(2)x /-2 sqrt(2) = 7/ -2 sqrt(2)

x = - 7/ 2 sqrt(2)

Multiply top and bottom by sqrt(2)

x = - 7/ 2 sqrt(2)  * sqrt(2)/ sqrt(2)

x = -7 sqrt(2)/4

What is the shape of a sorbital

Answers

Answer:

Spherical-Like Shape

Step-by-step explanation:

An s-orbital is spherical with the nucleus at its center.

Please help me to find this answer

Answers

Answer:

Look in Step by Step Explanation

Step-by-step explanation:

3)SOHCAHTOA

tan=opposite/adjacent

tan(20)=x/83

83tan(20)=x

x=30.209

2) SOHCAHTOA

Tangent=opposite/adjacent

Tan(62)=x/8

8tan(62)=x

x=15.04

3)SOHCAHTOA

Sin=opposite/hypotonouse

sin(25)=30/x

x=30/sin(25)

x=70.986

PLEASE HELP!! URGENT

Answers

Answer:

y=105

Step-by-step explanation:

82+75+x=180

157+x=180

x=23

82+23=y

105=y

ILL GIVE BRAINLIEST

Combine like terms.
4x – 7y + 2x – 4 = [ ? ]x + [ ]y + [ ]

Answers

Answer:

[6x] + [-7y] + [-4]

Step-by-step explanation:

There are only two like terms in this expression "4x" and "2x." Since they are like terms we can combine them by adding the coefficients and keeping the variable attached. Therefore we can combine 4x and 2x into 6x. Since there are no more like terms, this expression can be simplified to 6x - 7y - 4.

Answer:

6x - 7y - 4

Step-by-step explanation:

4x - 7y + 2x - 4

Combine like terms (by either subtracting or adding a number with the same variable)

4x + 2x = 6x

Thus, only one like term so the final answer is

6x - 7y - 4

A noted psychic was tested for extrasensory perception. The psychic was presented with 200 cards face down and asked to determine if each card were one of five symbols: a star, a cross, a circle, a square, or three wavy lines. The psychic was correct in 50 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 200 trials can be treated as a simple random sample from the population of all guesses the psychic would make in his lifetime. How large a sample n would you need to estimate p with a margin of error of 0.01 with 95% confidence? Use the hypothesized value p = 0.20 as the value for p*.

Answers

Answer:

r3jehejn wbbwbwbbwmwkwkwjwjwhhejehehehhe

i need help on this pls

Answers

Answer:

Shawn earns $11 per hour.

Step-by-step explanation:

When looking at the x axis (hours), and find where 1 hour intersects with the y axis It intersects with the point labeled at $11. This means after working for 1 hour, Shawn earned $11.

The average fish at a fishing tournament was 12.4 pounds. Some of the weight last of the fish are shown on the table:


What was the weight of the heaviest fish?

Answers

Answer:

15.5kg

Step-by-step explanation:

12.4kg × 5 = 62kg,

= 62kg - (14.6kg + 11.4kg + 10.3kg + 10.2kg)

= 62kg - 46.5kg

= 15.5kg

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