An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3028 feet and Plane B is at an altitude of 4000 feet. Plane A is gaining altitude at 55.75 feet per second and Plane B is gaining altitude at 35.5 feet per second. How many seconds will pass before the planes are at the same altitude? seconds What will their altitude be when they're at the same altitude? feet
Answers
Consider plane A with respect to B,
initial relative Altitude [tex] h_{a, b}=h_a-h_b=-972 [/tex]
relative rate of altitude(speed) $r_{a,b}= 55.75-35.5=20.25$
To get at same altitude, they'll take same time, and their relative height will be $0$ So,
$H_{a,b}=h_{a,b}+r_{a,b}t$
$0=-972+20.25t$
$t=48$
and altitude will be, $3028+55.75\cdot 48=5704$
Answer:
48 seconds5704 feetStep-by-step explanation:
We can write equations for the altitude of each plane:
A(t) = 3028 +55.75t . . . . . initially at 3028 ft; gaining at 55.75 ft/s
B(t) = 4000 +35.5t . . . . . initially at 4000 ft; gaining at 35.5 ft/s
The two altitudes will be equal when ...
A(t) = B(t)
3028 +55.75t = 4000 +35.5t . . . . substitute the expressions for A and B
20.25t = 972 . . . . . . subtract 3028+35.5t
t = 48 . . . . . . . . . . . . divide by 20.25
The common altitude will be ...
B(48) = 4000 +35.5(48) = 5704 . . . . feet
The planes will both be at an altitude of 5704 feet after 48 seconds.
Related Questions
cual es el area de un rectangulo
Answers
Answer:
Use this formula:
a = b * h
Where: "a", the area of the rectangle is equal to its "b" (base), multiplied by "h" (height)
Step-by-step explanation:
Usa esta formula:
a = b * h
Donde: "a", el área del rectángulo es igual a su "b" (base), multiplicado por "h" (su altura).
When a boy pulls his sled with a rope, the rope makes an angle of 70° with the horizontal. If a pull of 20 pounds on the rope is needed to move the sled, what is the horizontal component force?
7 lb
19 lb
20 lb
24 lb
Answers
Answer:
The answer to your question is 7 lbs.
Step-by-step explanation:
Data
angle = 70°
force = 20 lb
horizontal component
Process
To solve this problem just imagine a right triangle, where the force is the hypotenuse and the horizontal component is the adjacent side.
1.- Look for a trigonometric function that relates the adjacent side and the hypotenuse.
cos Ф = adjacent side / hypotenuse
- Solve for the adjacent side
adjacent side = hypotenuse x cosФ
- Substitution
adjacent side = 20 x cos 70
- Simplification
adjacent side = 20 x 0.342
- Result
adjacent side = 6.84 ≈ 7 lb
(3-1) (4+2) + 9 - 3 I need help
Answers
Answer:
18
Step-by-step explanation:
(3-1) (4+2) + 9-3 =
2 • 6 + 6 = 12 + 6
= 18
Answer:
[tex]\displaystyle 18[/tex]
Step-by-step explanation:
[tex]\displaystyle (3 - 1)(4 + 2) + 9 - 3 = [(2)(6)] + 9 - 3 = 12 + 9 - 3 = 12 + 6 = 18\:[OR\:21 - 3 = 18][/tex]
G - Grouping Symbols
E - Exponents
M\D - Division & Multiplication [left to right]
A - Subtraction & Addition [right to left OR vice versa]
I am joyous to assist you at any time.
How many real solutions does this system of equations have?
y=x^2+1
y=x
Answers
Answer:
none
Step-by-step explanation:
y=x²+1
y=x
x²+1=x
x²-x+1=0
Disc.=b²-4ac=(-1)²-4×1×1=1-4=-3<0
so roots are imaginary.
Verify the identity. cos quanity x plus pi divided by two = -sin x
Answers
Answer:
see below
Step-by-step explanation:
cos ( x+pi/2) = -sinx
We know that
cos(A + B) = cos A cos B - sin A sin B
Let x = A and pi/2 = B
cos x cos pi/2 - sin x sin pi/2 = -sin x
We know cos pi/2 = 0 and sin pi/2 = 1
cos x * 0 - sin x *1 = -sin x
- sin x = - sin x
Xian and his cousin Kai both collected stamps. Xian has 56 stamps, and Kai has 80 stamps. They boys recently joined different stamp-collecting clubs. Xian’s club will send him 12 new stamps per month. Kai’s club will send him 8 new stamps per month. after how many months will Xian and Kai have the same number of stamps? How many stamps will each have?
Answers
Answer:
After 4 months Xian will have 104 stamps,
But after three months Kai will also have 104 stamps
Step-by-step explanation:
There are (43)2⋅ 40 strawberries on a farm. What is the total number of strawberries on the farm?
Answers
Answer:
3,440 strawberries
Step-by-step explanation:
Because of PEMDAS you want to start with the parentheses, and want to treat them like the distributive property.
So,
43 x 2 = 86
Then,
86 x 40 = 3440.
I hope that helps!!
Answer: 3440 strawberries on the farm.
Step-by-step explanation: (43)(2)⋅40 (86)(40) 3440
A card is chosen at random from a standard deck of 52 cards. What is the probability that the card is a Queen or a $\diamondsuit$ (or both)?
Answers
Answer:
probability that the card is a Queen or a diamond= 0.3269
Step-by-step explanation:
There are 4 queen in a deck of cards and 13 diamond in a deck of cards.
And a deck of cards contains 52 cards total.
Probability of the card selected to be a queen = number of queen/total number of cards
Probability of the card selected to be a queen =4/52
Probability of the card selected to be a queen= 1/13
Probability of the card selected to be a diamond= number of diamond/ total number of cards
Probability of the card selected to be a diamond=13/52
Probability of the card selected to be a diamond=1/4
probability that the card is a Queen or a diamond= Probability of the card selected to be a queen + Probability of the card selected to be a diamond
probability that the card is a Queen or a diamond= 1/13+1/4
probability that the card is a Queen or a diamond= 0.3269
If Jim Roller can paint a room in 3 hours while John Brush would take 5 hours, how long will they take if they work together?
Answers
Answer:
4 hrs
Step-by-step explanation:
half of Jim Rollers time is 1.5 hrs, and half of John Brushs time is 2.5 hrs. The two combined is 4 hrs. Therefore, the answer is four hours.
This is basically finding the average of two numbers, and you can use multiple different equations to find the same answer.
3/2 + 5/2 =4
(3+5)/2 =4
5-3=2, then 2/2=1, 5-1=4
Answer:
1 7/8 hours
Step-by-step explanation:
Use the Law of Sines to find the missing angle of the triangle.
Find m < C to the nearest tenth if the c= 102, a = 71 and m < A=40
Answers
Answer:
66.9 degrees
Step-by-step explanation:
The Law of Sines states that a/sinA = c/sinC. Plugging in the values for c, a, and M < A, we get:
71/sin40 = 102/sinC
Cross multiplying, we get:
102(sin40deg) = 71(sinC)
Now, we simplify the left side and get:
65.56 = 71(sinC)
Next, we divide 65.56 by 71 to get:
0.92 = sinC
Taking the inverse sign we get:
C = 66.9 degrees
An online company wants to establish ratings for the products they provide. To do so, they ask visitors to their website to evaluate the products and leave a "thumbs up" or a "thumbs down." What type of sample is this? Explain why.
Answers
Answer:
This is a group specific influence sample, it only shows a demographic sample of those that are influenced by the reviews in the first place.
Step-by-step explanation:
find the positive square root of 26.77
Answers
Answer:5.173973328
Step-by-step explanation:
Thus: 5.1739733 x 5.1739733 = 26.77
Help pleasee!!! Tyyyyy
Answers
Answer:
G. 7
Explanation:
The longest side must be less than the sum of the two shorter sides.
The difference between the longest and shortest sides must be less than the middle side.
l+a = 11
l < (a + 4) ... l < (11 - l + 4)
... 2 l < 15 ... l < 7.5
--Variables
l = 7 (Longest Side/Answer)
a = 4 (Other Missing Length)
m = 4 (Side Given)
After taking off from the landing pad, a helicopter flies 3 miles west, then 2 miles southeast. How far is the helicopter from the landing pad? If someone could explain to that would be very helpful
Answers
Answer:
When the plane makes its turn to fly southeast, it makes a 45º angle at point a, making angle abc also equal to 45º.
Line ab is the 2 miles southeast the plane flies.
Line ac = line cb
sine (45º) = opposite / hypotenuse = cb / 2
.70711 = cb / 2
cb = 1.41422 miles = line ac
Line cs = 3 - 1.41422 = 1.58578
Line x^2 = cs^2 + cb^2
Line x^2 = 2.5146982084 + 2.0000182084
Line x^2 = 4.5147
Line x = 2.1248
Step-by-step explanation:
Describe the transformation. A. (x,y)→(x+5,y−3) B. (x,y)→(x−3,y+5) C. (x,y)→(x+3,y−5) D. (x,y)→(x−5,y+3)
Answers
Answer:
Option(A)
Step-by-step explanation:
From the graph attached,
Quadrilateral USTR has been transformed to get the image quadrilateral U'S'T'R'.
Coordinates of point U → (-2, 6)
Coordinates of point U' → (3, 3)
Coordinates of U and U' show that quadrilateral USTR has been shifted by 5 units to the right and 3 units down.
Rule to be followed for the translation,
U(-2, 6) → U'[(-2 + 5), (6 - 3)]
U(x, y) → U'[(x + 5), (y - 3)]
Therefore, Option (A) describes the correct rule of transformation.
multiplying polinomiyal(5x+2)(3x+4)
Answers
Answer:
(5x+2) (3x+4)
= 15x²+20x+6x+8
= 15 x²+ 26x+8
Hope this helps ^_^
Answer:
Step-by-step explanation:
Use FOIL method
(5x + 2)(3x + 4) = 5x * 3x + 5x *4 + 2*3x +2*4
= 15x² + 20x + 6x + 8 { now add like terms}
= 15x² + 26x + 8
How many equations are thereof: 70 divided by h equals 10?
What are those equations?
Answers
Answer:
We have:
"70 divided by h equals 10"
We can write it in only one equation:
70/h = 10.
This is a rational equation because our variable is in the denominator of a quotient.
To solve it we can multiply by h on both sides of the equation and get:
(70/h)*h = 10*h
70 = 10*h
now we divide both sides by 10.
70/10 = (10*h)/10
7 = h.
1/4x + 2/3 =19/12 I don’t understand how to do this equation
Answers
Answer:
X=11/13
Step-by-step explanation:
First, convert the non-variable fractions to a common denominator.
1/4x+8/12=19/12
1/4x=19/12-8/12
1/4x=11/12
x=11/12*4/1
x=44/12
x=11/3
Determine the measure of the interior angle at vertex D. A. 27 B. 162 C. 20 D. 36
Answers
Answer:
162°
Step-by-step explanation:
The shape is a hexagon, so the interior angles equal 720. (N-2)*180=720
9x+9x+9x+2x+9x+2x=720
40x=720
x=720/40
x=18
D=9x=9(18)=162°
The sum of interior angles of a polygon with n sides is [tex](n-2)\cdot180[/tex]
In this case [tex]n=6[/tex]
Therefore
[tex]4\cdot9x+2\cdot2x=(6-2)\cdot180\\36x+4x=4\cdot180\\40x=720\\x=18[/tex]
[tex]9x=9\cdot18=162[/tex]
So B
hi! i need to know the cube root of minus one!! just let me know down there!
Answers
Answer:
[tex]\large \boxed{\mathrm{-1}}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{-1}[/tex]
Apply radical rule:
[tex]\sqrt[n]{-1}=-1[/tex]
If [tex]n[/tex] is odd.
[tex]\sqrt[3]{-1}=-1[/tex]
To celebrate the first day of a leap year, I taught my dog to jump through a hoop. It was a Sunday. When he taught me the same trick the first day of the next year, it was a ?
Answers
Answer:
Tuesday
Step-by-step explanation:
364/7 = 52, meaning that 364 days later will also be a Sunday. 2 days after that (366 as it is a leap year) would be a Tuesday.
There will be Tuesday when the dog jumps the next year.
What is the reasoning?the process of applying logical reasoning to examine a situation in order to identify the optimal strategy for solving a specific problem, then using this approach to develop and justify a solution.
Reasoning is a tricky but interesting problem in mathematics that required relations of variables to solve.
Since when the dog jumped it was Sunday
Next Sunday will be at
364/7 = 52
So, after 52 weeks or 364 days, there will be next Sunday.
Since leap year is 366 days years
366 - 364 = 2
So, two days after Sunday is Tuesday.
Hence the day after next year when the dog jump will be Tuesday.
For more about reasoning,
https://brainly.com/question/2923977
#SPJ2
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 4 centimeters long, and the height of the equilateral triangle is 3.5 centimeters. The pyramid's slant height is 8 centimeters. What is its surface area?
Answers
Answer:
The surface area is 55 cm².
Step-by-step explanation:
The formula to compute the surface area of the triangular pyramid is:
[tex]SA=(0.50\times \text{Base Perimeter}\times h)+\text{Base Area}[/tex]
Here h is the slant height.
Compute the Base perimeter as follows:
Perimeter of the equilateral triangle = 3 × side
= 3 × 4
= 12 cm
Compute the Base area as follows:
Area of the equilateral triangle = 0.50 × side × height
= 0.50 × 4 × 3.50
= 7 cm²
Compute the surface area as follows:
[tex]SA=(0.50\times \text{Base Perimeter}\times h)+\text{Base Area}[/tex]
[tex]=(0.50\times 12\times 8)+7\\=48+7\\=55\ \text{cm}^{2}[/tex]
Thus, the surface area is 55 cm².
5 of 17Questions Question 5 Safiya needs to find a number that can be multiplied by 18−−√3 to result in a rational product. Which values could she use? Select all that apply.
Answers
Answer:
18 + √3
Step-by-step explanation:
The product of a surd and its conjugate gives a rational number. Hence;
(18 - √3) (18 + √3)
=324 + 18√3 - 18√3 - 3
=321
A rational number does not contain any surd, hence the answer.
Answer: cube root 1/18 & cube root 12
Alexander bought a box of crackers at the store. He ate half of the crackers in the box on Monday, and he ate 1/2 of what was left on Tuesday. On Wednesday, he ate 1/3 of what was left after he was finished eating the crackers on Tuesday.
1) What fractional part of the total crackers originally in the box did Alexander
eat on Wednesday?
2) what fractional part of the total crackers originally in the box are left. 3) if there are 4 crackers left in the box after Alexander finished eating crackers on wensday, how many crackers were in the box before it was opened. (Please help!)
Answers
Answer:
1. 1/12x
2.1/6x
3. 18
Step-by-step explanation:
Let
x=number of crackers in the box
On Monday, Alexander are 1/2 of the crackers
1/2 of x
=1/2x
Remaining
x-1/2x=2x-1/2
=1/2x
Tuesday=1/2 of what was left
=1/2 of 1/2x
=1/2×1/2x
=1/4x
Remaining
1/2x-1/4x
=2x-x/4
=1/4x
Wednesday=1/3 of what was left
=1/3 of 1/4x
=1/12x
Remaining
1/4x-1/12x
=3x-x/12
=2/12x
=1/6x
1. What fractional part of the total crackers originally in the box did Alexander eat on Wednesday?
1/12x
2. what fractional part of the total crackers originally in the box are left.
1/6x
3. if there are 4 crackers left in the box after Alexander finished eating crackers on wensday, how many crackers were in the box before it was opened.
1/6x=3
Divide both sides by 1/6
1/6x ÷ 1/6 = 3 ÷ 1/6
x=3÷1/6
=3 × 6/1
=18
x=18
Answer:
1) 1/12
2) 1/6
3) 18
Step-by-step explanation:
8 times the sum of a and b
Answers
Answer:
c
Step-by-step explanation:
i did the quiz
Answer:
8(a + b)
Step-by-step explanation:
Sun of a and b = a + b
8 times of (a + b) = 8(a + b)
1,400 is 10 times as much as 140- true or false
Answers
Answer:
True
Step-by-step explanation:
140 * 10 = 1400
True
what is the common number to be subtracted from each term of the ratio 11:8 to get the new ratio 2:1.?
Answers
Answer:
5 should be subtracted from each term
Step-by-step explanation:
[tex]\frac{11-x}{8-x}=\frac{2}{1}[/tex]
Cross multiply,
1 * (11 - x) = 2*(8-x)
11 -x = 2*8 - 2*x
11 - x = 16 - 2x
Subtract 11 from both sides,
-x = 16 - 2x - 11
-x = 5 - 2x
Add 2x to both sides
-x +2x = 5 - 2 + 2x
x = 5
a pizza shop offers 30% of the price of a large pizza every tuesday night. if the regular price is 25, what is the discount price?
Answers
Answer:
17.50
Step-by-step explanation:
First find the discount
25 * .3
7.5
Subtract this from the original price
25-7.5
17.50
Area of a trapeziod with a top base length of 6 cm a bottom base length of 12 cm and a height of 5 cm
Answers
Answer:
A=45cm^2
Step-by-step explanation:
A= h/2(b1 + b2) for trapezoid
A=(5/2(6+12))cm^2
A=(2.5(18))cm^2
A=45cm^2
which phrase matches the algebraic expression bellow? 2(x+7)+10
Answers
Answer:
i think your answer is two times the sum of x and seven plus ten
if i am wrong than tell me
Step-by-step explanation:
hope this will help :)
