Answer: 49.25
Step-by-step explanation:
One airplane is approaching an airport from the north at 164 km/hr. A second airplane approaches from the east at 271 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 28 km away from the airport and the westbound plane is 17 km from the airport.
Answer:
The rate of change of the distance between the airplanes is approximately 316.760 kilometers.
Step-by-step explanation:
The distance between both airplanes (r), in kilometers, can be determined by the Pythagorean Theorem, that is:
[tex]r^{2} = x^{2}+y^{2}[/tex] (1)
Where:
[tex]x[/tex] - Distance of the westbound airplane from airport, in kilometers.
[tex]y[/tex] - Distance of the southbound airplane from airport, in kilometers.
By Differential Calculus, we derive an expression for the rate of change of the distance between the airplanes ([tex]\dot r[/tex]), in kilometers per hour:
[tex]2\cdot r\cdot \dot r = 2\cdot x \cdot \dot x + 2\cdot y \cdot \dot y[/tex]
[tex]\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
Where:
[tex]\dot x[/tex] - Rate of change of the distance of the westbound airplane, in kilometers per hour.
[tex]\dot y[/tex] - Rate of change of the distance of the southbound airplane, in kilometers per hour.
If we know that [tex]x = 17\,km[/tex], [tex]y = 28\,km[/tex], [tex]\dot x = -164\,\frac{km}{h}[/tex] and [tex]\dot y = -271\,\frac{km}{h}[/tex], then the rate of change of the distance between the airplanes is:
[tex]\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}[/tex]
[tex]\dot r \approx -316.760\,km[/tex]
The rate of change of the distance between the airplanes is approximately 316.760 kilometers.
If a 50 kg car accelerates at a speed of 10 miles per second squared, what will the force of the car be? (Remember: Force = mass x acceleration) *
Answer:
500N
Step-by-step explanation:
Given data
Mass m= 50kg
Acceleration a= 10m/s^2
We know that the expression for the force is
F=ma
Substitute
F= 50*10
F= 500N
Hence the applied force is 500N
HELP ME giving brainlest
Answer:
The answer is false.
Step-by-step explanation:
THE reason why it is false is because if so that wouldnt make any sense.
need help thank u
:)
The area of the base is 1/2 x s x s = 1/2 x 12 x 12 = 72 square cm
Volume = area of base x height/3
Volume = 72 x 14/3 = 336 cm^3
find the total surface area of the shape
Answer:
510 ft²
Step-by-step explanation:
in the triangle
base (b) = 5 ft
height of the triangle (h1) = 12 ft
height of the prism = 15 ft
Now
Lateral surface area (LSA)
= perimeter of triangular base * height
= ( 13 + 5 + 12) * 15
= 450 ft²
Total surface area
= LSA + 2 * area of triangular base
= 450 + 2 * 1 / 2 * b * h1
= 450 + 5 * 12
= 450 + 60
= 510 ft²
Hope it will help :)❤
HELP CAN SOMEONE HELP ME MATH I'LL GIVE BRAINLIEST
Answer:
Student C wrote the correct inequality
the inequality will be less than or equal to since we want to spend (exactly) 300 or less. We only buy one jacket for 60 dollars so it will be added seperately to the total number of jackets. We are buying multiple jackets and each jacket costs $40. P = # of pants. So the inequality will look like
60 + 40P (less than or equal to symbol) 300
Hope I'm not too late :)
Nancy watches her dad fix a broken chair with a nail and a hammer, but she finds the hammering sound too loud. So, she decides to go back to her room, which is next door. On entering her room, she finds the hammering does not sound as loud. Why does the sound become faint?
Answer:
The sound of hammering becomes fainter as Nancy goes into her room because some of the sound waves are absorbed by the walls. Only part of the sound waves coming from the other room comes into her room, so the hammering sounds quieter.
I hope this helps. Good luck ^^
Belinda has 7 pieces of wood. Each piece of wood measures 3/4 yards. How many yards of wood does she have all together?
Answer:
each wood is 3/4 and there is 7wood so it's 7*3/4
Step-by-step explanation:
7×3/4
=21/4
PLEEEASE HELP! TEST TMRW AND I MIGHT FAIL.
HELP ASAP!!!!!! AND NO LINKS!!! The Utah Bees discounts tickets 30% for students 14 or younger. If adult tickets cost $23, how much will a student ticket cost after being discounted? Round to the nearest cent if necessary.
Answer:
$6.90
Step-by-step explanation:
30/100 = x/23
100x = 690
x= $6.90
PLEASE HELP I WILL MARK BRANLIEST FOR FIRST AND CORRECT ANSWER AND NO LINKS
Answer:
I think the Las t answer
Step-by-step explanation:
prime minister and members of the legislature
Answer:
Prime ministierer only :P
Patricia tiene $80.000 sólo en billetes de $5.000, Camila tiene $60.000 sólo en billetes de $2.000 y Andrea tiene $120.000 sólo en billetes de $10.000. Cada una aportará la misma cantidad de dinero a un fondo para comprar un regalo a su madre, que tiene un valor de $90.000. ¿Con cuántos billetes se quedará Camila después de pagar su parte de la cuota?
Answer:
mmmm
Step-by-step explanation:
7-4 pls help pleasssssssssssssssse
Answer:
for what subject?
geometry
trig
algebra
Answer:
I think it's 3 but maybe ask your teacher to check :o
Step-by-step explanation:
does anyone know the answer?
Answer:
E
Step-by-step explanation:
Answer:
It's E l did that before
Multiply polynomials
Step-by-step explanation:
[tex] {x}^{2} \times (3 {x}^{3} + 15) \\3 {x}^{2} + 15 {x}^{2} [/tex]
hope it helps
[tex] \huge \frak \green{question}[/tex]
Multiply the polynomials :-
x² ( 5x³ - 2x³ + 15)
[tex] \huge \frak \green{solution}[/tex]
→ x² ( 5x³ - 2x³ + 15)
→ x² × (3x³ + 15)
→ 3x² + 15x²
This can be further solved as :-
→ 3x² + 15x²
→ 18x²
[tex] \huge \frak \red{answer}[/tex]
18x²
The scatter plot shows how much puppy weighs within a certain time period. about how much did the puppy gain during this time period?
PLEADE HELP I WILL MARK YOU AS BRAINEIST
Answer:
83
Step-by-step explanation:
a = 25
The biggest angle is (3a+8) = 83
Answer:
83
Step-by-step explanation:
(3a+8)+(60-a)+(4a-38)=180
combine like terms, 6a+30=180
inverse operation to isolate the variable, 6a=150
divide six on both sides, a=25
replace a in every expression, 3(25)+8=83
60-25=35
4(25)-38=62
83 is biggest out of the three, therefore 83 is the answer.
pLEASE HELP I'LL GIVE BRAINLIEST
Hope it helps you......
Winston earns $140.00 by selling 56 hot dogs at a concession stand at school. Using the same rate for the cost of one hot dog, How many more hot dogs would Winston needto sell to earn a total of $175.00 ?
Answer:
Winston would need to sell 14 more hot dogs to earn a total $175
Step-by-step explanation:
If Sally purchases a car for $22,000 with a 5 year loan having a 2.5% interest rate, how much simple
interest will she have to pay on the loan?
A.$2,750.00
B.$19,250.00
C.$24,750.00
D.$275,000.00
solve for k. -5/6k = -10
Answer:
k = 12
Step-by-step explanation:
-5/6k = -10
Multiply both sides by 6k
-5/6k x 6k= -10 x6k
simplify
-5 = -60k
Switch sides
-60k = -5
Divide both sides by -60
-60k/-60 = -5/-60
Simplify to get your answer of
1/12 or 12
If you have any questions revolving around this topic,feel free to ask me :)
2x - 42 = 94
Solve for x
Answer:
x = 68
Step-by-step explanation:
2x - 42 = 94
Use inverse operations to add 42 to both sides of the equation.
2x - 42 + 42 = 94 + 42
Simplify this to-
2x = 136
Now divide 2x and 136 by two for-
2x/2 = 136/2
Simplify.
x = 68
The answer, then, is x = 68.
I hope this helps ^^
Good luck :]
A farmer plants the same amount every day, adding up to 134 acres at the end of the year. If the year is 12 over, how many acres has the farmer planted?
fAnswer:
1608 acres
Step-by-step explanation:
total acres planted in 12 years = acres planted per year x number of years
134 x 12 = 1608
Answer:
5/6
Step-by-step explanation:
1 2/3 x 1/2 = 5/6
El largo de una casa es el triple de su ancho. Si a la longitud se suma 40 metros y al ancho 1 metro, el área se triplica
Answer:
el ancho es de 8 metros y el largo es 3 * 8 = 24 metros
width is 8 meters and length is 3*8= 24 meters
Step-by-step explanation:
Spanish
Si el ancho de la casa de la casa es x, entonces el largo de la casa es 3x.
Entonces el área = largo * ancho
área = 3x * x = 3x²
3 multiplicado por área = 9x²
9x² = (3x + 40) (x + 1)
9x² = 3x² + 3x + 40x +40
9x² = 3x² + 43x +40
0 = -6x² + 43x +40
0 = 6x²- 43x - 40
6x²- 43x - 40 = 0
Usando ecuación cuadrática
a = 6, b = -43, c- = -40
x = - b ± √b²- 4ac / 2a
x = 43 ± √1849- 4 (6) (- 40) / 12
x = 43 ± √1849 + 960/12
x = 43 ± 53/12
x = 43+ 53/12 y x = 43-53 / 12
x = 96/12 y x = -10/12
x = 8 y x = - 5/6
Ignorando el valor negativo x = 8 el ancho es de 8 metros y el largo es 3 * 8 = 24 metros
English
The length of a house is three times its width. If 40 meters are added to the length and 1 meter to the width, the area is tripled
If the width of the house of the house is x then the length of the house is 3x.
Then the area = length * breadth
area= 3x*x= 3x²
3 times area= 9x²
9x²= (3x+40 )(x+1)
9x²= 3x²+ 3x +40x +40
9x²= 3x²+ 43x +40
0 = -6x²+ 43x +40
0 = 6x²- 43x - 40
6x²- 43x - 40= 0
Using quadratic equation
a= 6 , b= -43 , c-= -40
x= - b±√b²- 4ac/ 2a
x= 43±√1849- 4(6)(-40)/ 12
x= 43±√1849+960/ 12
x= 43± 53/ 12
x= 43+ 53/ 12 and x= 43- 53/ 12
x= 96/ 12 and x= -10/ 12
x= 8 and x= - 5/6
Ignoring the negative value x= 8 width is 8 meters and length is 3*8= 24 meters
???Anyone knows answer??
Answer:
30feet
Step-by-step explanation:
I don't know the requirement to get full mark but can work through the equation but:
The man is creating a small triangle as information about the small triangle is given. The small triangle is a miniature size of the bigger triangle. So,
let x be the height of the tree
6/4=x/20
6/4*20=x
x=30 feet
A student number system for a county requires that the student number be 5
characters. The first character is a consonant, the second through the fourth characters can be any digit but no digit can repeat and the last character must be a
letter. How many unique student numbers are possible?
546,000 student numbers
393,120 student numbers
302,400 student numbers
468,000 student numbers
Answer:
B
Step-by-step explanation:
First Character: 21 consonant
2nd 3rd and 4th: 10* 9* 8 = 720
Last Character: 26
Total Ways 21 * 720 * 26 = 393120
Find the value of X?
Answer:
Using this to get my answer done ;)
Step-by-step explanation:
hehe
What is the equation of the line that passes through the point (6,6) and has a slope of 5/3??
Answer:
y = 5/3x - 4
Step-by-step explanation:
(6, 6)
m = 5/3
Slope-intercept:
y - y1 = m(x - x1)
y - 6 = 5/3(x - 6)
y - 6 = 5/3x - 10
y = 5/3x - 10 + 6
y = 5/3x - 4
Find x. Round to the nearest tenth and only type the number for your
answer.
25
X
16
22
Answer:
10.7
Step-by-step explanation:
To find x we have to basically do pythagoream theorem twice. Both the traingles share the same long side. The find the long side of the top traingle do, [tex]a^{2} +16^{2} =25^{2}[/tex], and we find the long side to be [tex]\sqrt{369}[/tex]. Using this we now plug it into the pythagoream theorem for the bottom triangle. [tex]\sqrt{369} ^{2} +x^{2} =22^{2}[/tex], and doing this out we find that x=[tex]\sqrt{115}[/tex] or about 10.7.
2x+1=5x-8 Solving Equations with Many or No Solutions
Hello!
[tex]\large\boxed{x = 3}[/tex]
2x + 1 = 5x - 8
Solve by subtracting both sides by 2x:
2x - 2x + 1 = 5x - 2x - 8
1 = 3x - 8
Add 8 to both sides:
1 + 8 = 3x - 8 + 8
9 = 3x
Divide both sides by 3:
9/3 = 3x/3
x = 3
Answer:
x = 3
Step-by-step explanation:
1. Write the equation
2x + 1 + 5x - 8
2. Add 8 on both sides
2x + 9 = 5x
3. Get the variables together
9 = 3x
4. Solve for x and divide both sides by 3
x = 3