Answer:
The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient of consecutive terms is the same. The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term and [tex]q[/tex] is the common ratio.
A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again.
This means that:
[tex]q = 0.7, a_1 = 25*0.7 = 17.5[/tex]
Then
[tex]a_n = a_1q^{n-1}[/tex]
[tex]a_n = 17.5(0.7)^{n-1}[/tex]
First 5 terms:
[tex]a_1 = 17.5[/tex]
[tex]a_2 = 17.5(0.7)^{2-1} = 12.25[/tex]
[tex]a_3 = 17.5(0.7)^{3-1} = 8.58[/tex]
[tex]a_4 = 17.5(0.7)^{4-1} = 6[/tex]
[tex]a_5 = 17.5(0.7)^{5-1} = 4.2[/tex]
Find the total distance the ball has travelled after it hits the ground the 5th time.
[tex]T = 17.5 + 12.25 + 8.58 + 6 + 4.2 = 48.53[/tex]
The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.
PLEASE HELP WILL MARK BRAINLIEST - An airplane travels 150 miles horizontally during a decrease of 35,000 feet vertically.
1. What is the angle of descent?
2. How long is the plane's path?
Answer:
[tex]\text{1. }2.53^{\circ},\\\text{2. }792,772.98\:\mathrm{ft}[/tex]
Step-by-step explanation:
Start by converting miles to feet:
[tex]150\text{ miles}=150\cdot 5280\text{ feet}=792000\text{ feet}[/tex]
Form a right triangle with the plane's displacement marking the hypotenuse of this triangle. We can now use basic trig for a right triangle to solve for the angle of descent.
Let the angle of descent be [tex]\theta[/tex]. In a right triangle, the tangent of an angle is equal to its opposite side divide by its adjacent side.
Therefore, we have:
[tex]\tan \theta=\frac{35000}{792000},\\\\\theta =\arctan(\frac{35000}{792000})=2.53036411\approx \boxed{2.53^{\circ}}[/tex]
In all right triangles, [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle (Pythagorean Theorem).
Therefore, the length of the plane's path is:
[tex]35,000^2+792,000^2=c^2,\\c^2=628489000000,\\c=\sqrt{628489000000}=792772.981376\approx \boxed{792,772.98\:\mathrm{ft}}[/tex]
I have a bag of coins.In it, one third is gold, one fifth of them are silver, two seventh are bronze the rest are copper. My bag can only fit 200 coins how many coins do i have in my bag?
Answer:
Copper = x= 36.19
Step-by-step explanation:
The number of copper is unknown
Gold = 1/3
Silver = 1/5
Bronze =2/7
Copper = x
Total coins = 200
Gold = 1/3 of 200
= 1/3 × 200
= 200/3
= 66.67
Silver = 1/5 × 200
= 200/5
= 40
Bronze = 2/7 × 200
= 400/7
= 57.14
Total = gold + silver + bronze + copper
200 = 66.67 + 40 + 57.14 + x
200 = 163.81 + x
200 - 163.81 = x
x = 36.19
Copper = x= 36.19
WILL GIVE BRAINLIEST IF CORRECT!!!
Write an equation that represents the line.
Use exact numbers.
Answer:
y = 3/4 x - 9/2
Step-by-step explanation:
Slope = 3/4
y = mx + b
y = 3/4x + b
0 = 3/4 (6) + b
0 = 18/4 + b
-9/2 = b
y = 3/4 x - 9/2
Simplify the expressions. 3p+-q-7r--8p-q+2r
Answer:
=11p-5r
Step-by-step explanation:
3p+(-q)-7r-(-8p)-q+2r=
3p-q-7r+8p-q+2r=
3p+8p-q-q-7r+2r=
11p-5r=
Find the length of "b" to the nearest tenth.
Answer:
11.2
Step-by-step explanation:
(AB) ^2 - (BC) ^2 = b^2 (Pythogoras Theorem)
(15)^2 - (10)^2 = (b) ^2
b^2=225-100
b^2=125
b=root (125)
b=11.18
b=11.2
14: A popular retailer offered 20% off their store for the entire weekend. Which of the following is the fraction equivalent of 20%?
Answer:
1/5
Step-by-step explanation:
20/100 or 1/5
what is the value of x in a circle
Answer:
30°
Step-by-step explanation:
x = 180° -60°-90° = 30°
in circle p, which arc is a major arc?
If your asking to select all that apply, The formula is arc length = θ ( r ) {\displaystyle {\text{arc length}}=\theta (r)} , where equals the measurement of the arc's central angle in radians, and r {\displaystyle r} equals the length of the circle's radius. Plug the length of the circle's radius into the formula.ABC,BAD,DCB
More
For the points A and B, the major arc is the part of the circumference from A to B which contains the points E, D and C
What is arc in a circle and what are its classifications?For a circle, take two points on its circumference. That divides the circumference of the considered circle in two parts. Those both parts are called arcs of the circle. The bigger part will be called the major arc, and the smaller one will be called the minor arc.
When the two points are chosen such that they're the endpoints of one of the diameters of the considered circle, then both the arcs are of same length due to symmetry, so there is no concept of major or minor between them.
For this case, there are 5 points, as A, B, C, D, and E.
Since no option is given, so let we take two points which are not on the ends of any diameter.
The points A and B are good enough.
So, the smaller part of the circumference between A and B is the minor arc and the bigger part which contains points like E, D and C is the major arc.
A demonstration is given in the image attached below.
Thus, for the points A and B, the major arc is the part of the circumference from A to B which contains the points E, D and C (the bigger part).
Learn more about major and minor arcs here:
https://brainly.com/question/9288523
3/4 part of a rope is 150m. find the length of 7/10 part of the rope
Please help ASAP with step by step explanation.
Answer:
140m
Step-by-step explanation:
3/4 = .75
x/.7 = 150/.75
multiply both sides by .7
x = 150/.75 * .7
x = 140m
Sal knows the volume of a cylinder is 500 cubic units. He wants to create a cylinder with twice the volume. Which variation of the original cylinder will have a volume of exactly 1,000 cubic units?
Evaluate e^4 to one decimal place
Answer:
The answer is going to be the general form for e^x = 1 + x/(1!) + + x^2/(2!) + x^3/(3!) +.....,. till infinity so : e^4 = 1 + 4/1 + 16/ 2 + 64/6 + 256/24 + 1024/ 120 + 4096/720 + 16384/5040 +...till the fraction is<0.1 = 54.6
10. What are the coordinates of point on the directed segment from A(2,-3) to B(8,-6) that
partitions the segment such that AC:CB is 4:2?
(1) (6,-5)
(3) (2,0)
(2) (-2, 2)
(4) (1, 1)
Answer:
(4, -4)
Step-by-step explanation:
Using the midpoint formula;
M(X,Y) = {(ax1+bx2)/a+b, (ay1+by2)/a+b}
X = (ax1+bx2)/a+b
Y = (ay1+by2)/a+b
Substitute
X = 4(2)+2(8)/4+2
X = 8+16/6
X = 24/6
X = 4
Also
Y = 4(-3)+2(-6)/6
Y = -12-12/6
Y = -24/6
Y = -4
Hence the required partition is (4, -4)
a man spends ⅕ of his salary on shoes and ⅔ on school fees. what is the fraction of his salary left. pls help asap
Answer:
2/15
Step-by-step explanation:
1/5 + 2/3
= 3/15 + 10/15
= 13/15
15/15 - 13/15
= 2/15
what is the 1QR 14,11,8,1,23,20,17,5,19,10,12,22
Answer:
Step 1: Put the numbers in order.
1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.
Step 2: Find the median.
1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.
Step 3: Place parentheses around the numbers above and below the median.
Not necessary statistically, but it makes Q1 and Q3 easier to spot.
(1, 2, 5, 6, 7), 9, (12, 15, 18, 19, 27).
Step 4: Find Q1 and Q3
Think of Q1 as a median in the lower half of the data and think of Q3 as a median for the upper half of data.
(1, 2, 5, 6, 7), 9, ( 12, 15, 18, 19, 27). Q1 = 5 and Q3 = 18.
Step 5: Subtract Q1 from Q3 to find the interquartile range.
18 – 5 = 13.
Step-by-step explanation:
What is the maximum value of the objective function, P, with the given constraints? P=25x+45y 4x+y≤16 x+y≤10 x≥0 y≥0
Answer:
the maximum is 450 and the minimum is 0.
Step-by-step explanation:
We know that:
P(x, y) = 25*x + 45*y
First, is easy to see that as x and y increase, also does the value of P(x, y)
So we just need to find the largest and smallest possible values of these variables. We also can notice that the variable y is being multiplicated by a larger coefficient than x, so we prioritize larger values of y when we can.
We know that:
4x+y ≤ 16
x + y ≤10
x≥0
y≥0
Let's start with the second inequality, let's solve this for y:
y ≤ 10 - x
and from the first one we get:
y ≤ 16 - 4*x
Just to show that maximizing x does not work, let's do it:
from the second one, knowing that the minimum value of y is y = 0
we have that:
0 ≤ 16 - 4*x
Here the maximum value that y can take is x = 1
0 ≤ 16 - 4*1 = 0
So we can have the combination y = 0 and x = 1, when we maximize x (here we can see that we should not maximize x)
in this case we get:
P(1, 0) = 25*1 + 47*0 = 25
let's write again our inequalities:
y ≤ 10 - x
y ≤ 16 - 4*x
If now we take the minimum value of x, x = 0, we get:
y ≤ 10
y ≤ 16
Because the first one is more restrictive, we know that the maximum value that y can take (when x = 0) is y = 10
in this case we get:
P(0, 10) = 25*0 + 45*10 = 450
As expected, here is the actual maximum for the given restrictions.
For the minimum, we just need to take the two lowest possible values of x and y, which are the two given by the equalities on:
x≥0
y≥0
The smallest values are:
x = 0
y = 0
Replacing that in the equation we get:
P(0, 0) = 25*0 + 47*0 = 0
So the maximum is 450 and the minimum is 0. (with the given restrictions)
What is m angle A? Enter your answer in the box.
Answer:
ANSWER: 22
Step-by-step explanation:
hope it helps thankks
Answer:
I agree with the person above
What is the circumference of a circle with a diameter of 12 feet? (use 3.14 for pi)
36 ft.
37.68 ft.
36.26 ft.
38 ft.
Answer:
37.68ft
Step-by-step explanation:
Answer:
37.68 ft
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d where d is the diameter
C = 3.14 * 12
C =37.68 ft
If m(y) = 12 + 3 and nl) = 5% +9, which expression is equivalent to (n))?
5x + y2 + 15% - 27
2542 - 90% - 84
745x + 12
587 +24
Answer:
Option (2)
Step-by-step explanation:
Two functions have been given as,
m(x) = x² + 3
n(x) = 5x + 9
And we have to find the value of (mn)(x).
Since, (mn)(x) = m[n(x)]
Therefore, m[n(x)] = (5x + 9)² + 3
= 25x² + 90x + 81 + 3
= 25x² + 90x + 84
This expression matches with the expression given in option (2).
Therefore, Option (2) will be the answer.
Eliza says, “Every member of the population is equally likely to be selected for the sample”. Which type of sample is Eliza describing?
a
a random sample
b
a biased sample
c
a stratified sample
d
a quota sample
Answer: A. A random sample
Step-by-step explanation:
Since everyone is equally as likely yo be selected for this sample, is has to be random because there won't be any interference to the probability of your chances of being selected in the population
I hope this helps!
Evaluate angles s and r, giving reason for your answer
Answer:
r=42 degrees
This is because of vertically opposite angles
s=68
This is because 180( angles in a triangle) minus ( 70 + 42) is equal to 68 degrees
Answer:
r = 42° , s = 68°
Step-by-step explanation:
r and 42° are vertical angles and are congruent , then
r = 42°
The sum of the 3 angles in a triangle = 180° , then
s = 180° - (70 + 42)° = 180° - 112° = 68°
The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm
The height of the open box is (x - 2) cm.
a) Show that 2x + 5x -58 = 0
) Solve the equation 2x + 5x -58 = 0, giving your answers correct
to 2 decimal places
D) Hence calculate the volume of the box, stating the units of your answer.
Answer:
a) x = 8.29 cm
D) V = 1125.27 cm³
Step-by-step explanation:
a) We can solve the equation as follows:
[tex] 2x + 5x - 58 = 0 [/tex]
[tex] 2x + 5x = 58 [/tex]
[tex] x = \frac{58}{7} = 8.29 [/tex]
D) The volume of the box is given by:
[tex] V = l*w*h [/tex]
Where:
l: is the length
w: is the width
h: is the height
The length of the rectangular box is:
[tex] l = (2x + 5) cm = (2*8.29 + 5) cm = 21.58 cm [/tex]
The width is x = 8.29 cm.
And the height is:
[tex] h = (x - 2) cm = (8.29 - 2) cm = 6.29 cm [/tex]
Hence, the volume is:
[tex] V = l*w*h = (21.58*8.29*6.29) cm^{3} = 1125.27 cm^{3} [/tex]
I hope it helps you!
What expression is equivalent to (5z^2+3z+2)^2
?
Answer:
[tex]{ \tt{ {(5 {z}^{2} + 3z + 2)}^{2} }} \\ = (5 {z}^{2} + 3z + 2)(5 {z}^{2} + 3z + 2) \\ = (25 {z}^{4} + 30 {z}^{3} + 29 {z}^{2} + 12z + 4)[/tex]
By writing each number correct to 1 significant figure, estimate the value of
37.8 x 13.2
28,5 + 22.1
You must show all your working.
Answer:
37.8 x 13.2 =4988.6
28,5 + 22.1 = 50.6
A+b=25
What is the value of 2a + 2b + 4
Answer:
THE ANSWER IS 54
Step-by-step explanation:
8p²-18p² need help from brainliest
Answer:
- 10p2
Step-by-step explanation:
p(8p - 18 p)
p x -10p
ans = -10p2
Answer: -10p²
This is the same as saying -10p^2
============================================
Explanation:
Both terms 8p² and -18p² are like terms.
We combine them in much the same way as 8-18 = -10, just with a p² attached to everything.
So 8p² - 18p² = (8-18)p² = -10p²
The coefficient -10 is negative because we're subtracting small minus big. If it was the other way around, then we'd get a positive value.
( Answer Honestly Please )
B. Translate the following English phrases to mathematical statements:
6. 3 times a number (x) is greater than 10
7. A number (x) added by 4 is less than or equal to 7
8. 6 is less than a number (x) divided by 6
9. The ratio of 10 and a number (x) is greater than or equal to 5
10.The sum of x and 7 is less than 4
Answer:
See below.
Step-by-step explanation:
6. 3 times a number (x) is greater than 10
3x > 10
7. A number (x) added by 4 is less than or equal to 7
x+4[tex]\leq[/tex]7
8. 6 is less than a number (x) divided by 6
6 < x/6
9. The ratio of 10 and a number (x) is greater than or equal to 5
(10/x) [tex]\geq[/tex] 5
10.The sum of x and 7 is less than 4
x + 7 < 4
PLSSS, NEED ANSWER. Find the midpoint of the line segment with end coordinates of (-2,-5 and 3,-2
). Give coordinates as decimals where apropriate
Answer:
(0.5, -3.5)
Step-by-step explanation:
(x1 + x2/2, y1 + y2/2)
(-2 + 3 / 2, -5 - 2 / 2)
(1/2, -7/2)
how do I solve this?
Answer: I cant see the problem
Step-by-step explanation:
Answer:
Where is the question?
Step-by-step explanation:
The plastic straws were placed under the wooden block to
Answer:
What? Your not even done.
Step-by-step explanation:
(x+4)+(x-3)+(2x+2)+(x^2+3x+1)
Answer:
X^2+7x+4
Step-by-step explanation:
