Running at an average rate of 10 m/s, a sprinter ran to the end of a track and then jogged back to the starting point at an average of 5 m/s. The sprinter took 60 s to run to the end of the track and jog back. Find the length of the track.

d=300md is equal to 300 m

d=200md is equal to 200 m

d=600md is equal to 600 m

d=150md is equal to 150 m

Answer:

(1) 13.0 years

(2) [tex]y^{3} =[/tex] {-1728, 1728}

Step-by-step explanation:

(1)

Compound annually:

[tex]Pe^{rt}[/tex] = A

(47000)[tex]e^{(0.04)(t)}[/tex] = 79200

[tex]e^{(0.04)(t)}[/tex] = [tex]\frac{79200}{47000}[/tex]

ln([tex]e^{(0.04)(t)}[/tex]) = ln([tex]\frac{79200}{47000}[/tex])

ln and e cancel out.

(0.04)(t) = ln([tex]\frac{79200}{47000}[/tex])

t = [tex]\frac{ln(\frac{79200}{47000})}{0.04}[/tex]

t = 13.0 years

(2)

[tex]x^{2} +y^{2} = 153\\y = -4x[/tex]

Substitute y with -4x.

[tex]x^{2} + (-4x)^{2} = 153[/tex]

Solve for x.

x = {-3, 3}

Plug in x values into any equation to find y.

y = -4(-3) and y = -4(3)

y = {-12, 12}

[tex]y^{3}[/tex] = [tex]-12^{3}[/tex] = -1728

[tex]y^{3}[/tex] = [tex]12^{3}[/tex] = 1728

Answer:

13.3    

Step-by-step explanation:

I got it right  

Answer:

A≈1130.97

------------------------------------------------------

Step-by-step explanation:

A=2πrh+2πr2=2·π·12·3+2·π·122≈1130.97336

Answer:

16.66 %

Step-by-step explanation:

1 / 6 as a percent

= ( 1 / 6 ) x 100

= 100 / 6

= 16.66 %

9514 1404 393

Answer:

Step-by-step explanation:

When calculations are repetitive, I like to let a calculator or spreadsheet do them. Here we have used the formula for the base area:

  B = πr² = 3.14×r²

In the second figure, the radius is half the diameter, so is 5 units.

The table in the attachment lists the base area B, the height h (from the figures), and the volume V. These are the values that you need to drag and drop to the boxes in your problem.

  V = 113.04 · 4

  V = 452.16 units³ . . . showing how the numbers are used in the first figure

Answer:

2.75 miles in 1 hour

Step-by-step explanation:

Answer:

C) 972π

Step-by-step explanation:

Volume of a sphere formula:

V = 4/3πr³

Given:

r = 9

Work:

V = 4/3πr³

V = 4/3π9³

V = 4/3(729)π

V = 972π

E⁣⁣⁣xplanation i⁣⁣⁣s i⁣⁣⁣n a f⁣⁣⁣ile

bit.[tex]^{}[/tex]ly/3a8Nt8n

Answer: 30+4x

Step-by-step explanation: Expanding the expression you would get 30+6x-2x and then you subtract the 6x and 2x to get 4x

Answer:

30+4x.

Step-by-step explanation:

yehdbebdbejeiiwiwuebdbsjjjwiwjeurnfnd

Answer:

1, 1, 3, 3

Step-by-step explanation:

For an even function, f(-x) = f(x).

So, f(-1) = f(1) = 1.

Similarly, the other three blanks are 1, 3, and 3, respectively.

Answer:

The flow rate will be say around 10000 liters per hour. Or 180 liters per minute.

Step-by-step explanation:

Answer:

583

Step-by-step explanation:

The mean of a data set is the average of the data set. It can be found by adding up all of the values and then dividing by the total number of values added. In this case, one is given the mean, and one needs to find a missing value. Since there is a missing element, add one to the total number of values in the data set. The missing element is represented by the parameter (x). Set up an equation and solve:

[tex]\frac{(236)+(342)+(328)+(352)+(352)+(306)+(317)+(x)}{8}=325\\[/tex]

Simplify,

[tex]\frac{2233+x}{8}=352[/tex]

Inverse operations,

[tex]2233+x=2816\\\\x = 583[/tex]

Answer:

It’s 367

Step-by-step explanation:

A basis of the subspace that consists of all vectors perpendicular to both [1,0,5,-9] and [0,1,9,-7] is [-5, -9, 5].

To find a basis of the subspace that consists of all vectors perpendicular to both [1,0,5,-9] and [0,1,9,-7], we can use the concept of the cross product.

Let's consider the vectors [1,0,5,-9] and [0,1,9,-7] as vectors A and B, respectively.

We can find a vector C that is perpendicular to both A and B by taking the cross product of A and B.

C = A × B

To compute the cross product, we can use the following determinant formula:

C = [i, j, k]

[1, 0, 5]

[0, 1, 9]

Expanding the determinant, we have:

C = (0 × 9 - 1 × 5)i - (1 × 9 - 0 × 5)j + (1 × 5 - 0 × 1)k

= -5i - 9j + 5k

Therefore, we have found a vector C that is perpendicular to both [1,0,5,-9] and [0,1,9,-7], which is C = [-5, -9, 5].

To find a basis of the subspace, we can use this vector C as the basis vector. Since it is the only vector in the subspace, it forms a basis.

So, a basis of the subspace that consists of all vectors perpendicular to both [1,0,5,-9] and [0,1,9,-7] is [-5, -9, 5].

for such more question on vectors perpendicular

https://brainly.com/question/11353587

#SPJ8

Answer:

Jesse eats lunch at 11:45 a.m.

Answer:

1.) M=9,-9  2.) x=10,-10  3.) n=3,-3  4.) x=2,-2

Step-by-step explanation:

Answer:

pirwvjihpwrugh

Step-by-step explanation:

wrhfuwhfuhugfrifhi

Answer:

not possible

Step-by-step explanation:

It can't be possible because the ratio would be 50:1 is possible

Answer:

Normal/standard

Step-by-step explanation:

Answer:

Ordinary

Step-by-step explanation:

The area of triangle ABC is 23.5 square units and the perimeter is 20.4174 units.

To find the area and perimeter of the given triangle ABC, we need to apply the following formulas:Formula for Distance between two points:

The distance between two points (x1, y1) and (x2, y2) is given by:

AB = √(x2-x1)²+(y2-y1)²BC = √(x3-x2)²+(y3-y2)²AC = √(x3-x1)²+(y3-y1)²

Formula for Area of Triangle: If we know the length of the three sides of a triangle then,

using Heron's formula, we can calculate the area of the triangle as:

area = √s(s-a)(s-b)(s-c)where a, b, and c are the lengths of the sides of the triangle and s is the semi-perimeter of the triangle, which is given as s = (a+b+c)/2

Formula for Perimeter of Triangle: The perimeter of the triangle is the sum of the lengths of its sides.

That is: perimeter = AB + BC + ACArea of ΔABCAB

= √(1 - (-2))² + (5 - (-4))²AB

= √3²+9² = √90BC

= √(2 - 1)² + (2 - 5)²BC

= √1²+3² = √10AC

= √(2 - (-2))² + (2 - (-4))²AC

= √4²+6²

= √52Semi-Perimeter (s)

= (AB + BC + AC)/2

= (√90 + √10 + √52)/2

= 12.8572Area of ΔABC

= √s(s-a)(s-b)(s-c)

= √12.8572(12.8572-√90)(12.8572-√10)(12.8572-√52)

= 23.5

Perimeter of ΔABC = AB + BC + AC = √90 + √10 + √52 = 20.4174

To learn more about : area

https://brainly.com/question/25292087

#SPJ8

Step-by-step explanation:

area of a parallelogram is bh

so if a parallelogram has a base of b and a height of 10 and an area of 140

b(10)=140

b=14

Hope that helps :)

Complete question is;

The polynomial -16t² + v_o(t) + s_o represents the height (in feet) of an object, where v_o is the initial vertical

velocity (in feet per second), s_o is the initial height of the object (in feet), and t is the time in seconds. Write a polynomial that represents the height of the object that has an initial velocity of 25 ft/s and initial height of 4ft. Then find the height of the object after 1 second.

Answer:

A) Polynomial is h(t) = -16t² + 25t+ 4

B) h(1) = 13 ft

Step-by-step explanation:

A) We are given;

h = -16t² + v_o(t) + s_o

Where;

v_o = the initial vertical velocity

s_o = the initial height of the object

t = the time

We are given;

v_o = 25 ft/s

s_o = 4 ft

Thus, polynomial that represents the height is;

h(t) = -16t² + 25t+ 4

B) after a time of 1 second, height is;

h(1) = -16(1²) + 25(1) + 4

h(1) = -16 + 25 + 4

h(1) = 13 ft

Answer:

the area of the large rectangle is 120m squared in the area of the smaller triangle is 14m squared

Answer:

Area of large rectangle = 120m²

Area of small rectangle = 14m²

Step-by-step explanation:

Large rectangle:

Length = 12m

Breadth = 10m

Area of rectangle = l × b

Area = 12 × 10

Area = 120m²

Small rectangle:

Length = 7m

Breadth = 2m

Area of rectangle = l × b

Area = 7 × 2

Area = 14m²

Answer:

6

Step-by-step explanation:

Answer:

first day. yehahhhhhhhh

Answer:

School isn't exciting for me, lol.

Step-by-step explanation:

Answer:

7.20

Step-by-step explanation:

Answer:

7.20 or 6.90

Step-by-step explanation: most likely 7.20 because 3 pounds of apples is 6.90 so adding a half to that would be 7.20

Answer:

y = 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Mean,median, mode, rule, par, normal etc.

Step-by-step explanation:

PQ are the first two letters and AB are the first two letters.

Since the windows are similar the letters in one are in the same orientation as the other ones.

This means PQ would be the same as AB

PQ = 60

The answer is A. 60 in.

Answer:

a

Step-by-step explanation:

Step-by-step explanation:

s =   a+b+c  / 2

=   14+6+9  / 2

=  14.5 feet

Area =  √s(s-a)(s-b)(s-c)

=  √14.5×(14.5 - 14)×(14.5 - 6)×(14.5 - 9)

ANSWER: 18.410255294265 feet^2

Answer:b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

because it has two parallel side and and other are just lines but being quadrilateral its sum is 360

Answer:

c

Step-by-step explanation:

supplementary means together that equal 180°, implying that 4 and 1 are equal, five and three are equal, which makes line k in line j parallel to each other.