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2 years ago

Austin takes 1 minute and 45 seconds to run three-quarters of a circular track. His rate of motion is π/ radians per second.

1 answer:

6 0

Length of circular track is:

L = 2*r*pi

He run 3/4 of it so length is:
L' = 3*2/4*r*pi = 3/2*r*pi

To calculate speed of his movement we use formula:
v = s/t where s = L' and t = 1 minute 45 seconds = 105 seconds

v = L'/t = $\frac{3*r*pi}{2*105}$

v = r* pi/70

If we take that r = 1 answer is $\pi /70$

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-3^(-x)-6=-3^x+10<br><br>Solve the equation below for x by graphing plz

vitfil [10]

To graph it, just graph $y=-3^{-x}-6$ and $y=-3^x+10$ and see where they intersect

I would like to solve it by using math and not graphing
if you don't want to see the math, just don't scroll down
the graphical meathod is above, first line, just read it

hmm
multiply both sides by -1
$3^{-x}+6=3^x-10$
multiply both sides by $3^x$
$3^0+6(3^x)=3^{2x}-10(3^x)$
$1+6(3^x)=3^{2x}-10(3^x)$
minus 1 from both sides and minus 6(3^x) from both sides
$0=3^{2x}-16(3^x)-1$
use u subsitution
$u=3^x$
we can rewrite it as
$0=u^2-16u-1$
now factor
I mean use quadratic formula
for $ax^2+bx+c=0$ $x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}$
so for 0=u^2-16u-1, a=1, b=-16, c=-1
$u=\frac{-(-16)+/-\sqrt{(-16)^2-4(1)(-1)}{2(1)}$
$u=8+/-\sqrt{65}$
remember that u=3^x so u>0
if we have u=8+√65, it's fine, but u=8-√65 is negative and not allowed
so therfor
$u=8+\sqrt{65}=3^x$
$8+\sqrt{65}=3^x$
if you take the log base 3 of both sides you get
$log_3(8+\sqrt{65})=x$
if you use ln then
$ln(8+\sqrt{65})=xln(3)$
then
$\frac{ln(8+\sqrt{65})}{ln(3)}=x$

8 0

2 years ago

Read 2 more answers

An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall, and the initial velocity of the ball is 40

satela [25.4K]

Answer:

0.14 s

Step-by-step explanation:

s = -2.7 t² + 40t + 6.5

Let s = 12

12 = -2.7t² + 40t + 6.5 Subtract 12 from each side

-2.7t² + 40t + 6.5 - 12 = 0

-2.7t² + 40t - 5.5 = 0

Apply the <em>quadratic formula </em>

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a = -2.7; b = 40; c = -5.5

$x = \frac{-40\pm\sqrt{40^2 - 4\times (-2.7) \times (-5.5)}} {2(-2.7)}$

$x = \frac{-40\pm\sqrt{1600-59.4}}{-5.4}$

$x = \frac{-40\pm\sqrt{1540.6}}{-5.4}$

$x = \frac{-40\pm 39.25}{-5.4}$

x = 7.41 ± 7.27

x₁ = 0.14; x₂ = 14.68

The graph below shows the roots at x₁ = 0.134 and x₂ = 14.68.

The Moon’s surface is at -12 ft. The ball will be 12 ft above the Moon’s surface (crossing the x-axis) in 0.14 s.

The second root gives the time the ball will be 12 ft above the Moon’s surface on its way back down.

6 0

2 years ago

A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over

marishachu [46]

Answer:

employment plan for the next 12 months is not independent of the type of company

Step-by-step explanation:

H0 : employment plan for the next 12 months is independent of the type of company

H1 : employment plan for the next 12 months is not independent of the type of company

The Chisquare statistic, χ² :

χ² = (observed - Expected)²/ Expected

Given the data:

Observed values :

_________________ Company

Emp plan ________ private _____ public _total

Add employees _____ 37 ________ 32 __ 69

No change__________19 ________ 34 __53

Layoff employees ____ 16 ________ 42__58

Total ______________72 ________108 _ 180

The expected value counts :

(Row total * column total) / grand total

Expected Values:

27.6 ___41.4

21.2 ___ 31.8

23.2 ___34.8

Chi-Squared Values:

3.20145 ___2.1343

0.228302__ 0.152201

2.23448 ____1.48965

χ² = (3.20145 + 2.1343 + 0.228302 + 0.152201 + 2.23448 + 1.48965)

χ² = 9.440383

Degree of freedom, df (row - 1) * (column - 1) = (3-1) * (2 - 1) = 2 * 1 = 2

Pvalue from Chisquare statistic, df = 2

Pvalue = 0.008913

Since ;

Pvalue < α ; We reject the null and conclude that employment plan for the next 12 months is not independent of the type of company.

4 0

2 years ago

If the test scores of a class of 35 students have a mean of 74.3 and the test scores of another class of 28 students have a mean

STALIN [3.7K]

Let the total sum of the scores of the first class of 35 students be a. The mean is 74.3 .

So
$\frac{a}{35}=74.3\\\\a=35\cdot74.3= 2600.5$

Also, let the total sum of the scores of the second class of 28 students be b. The mean is 67.6 .

so
$\frac{b}{28}=67.6\\\\ b=28\cdot67.6= 1892.8$

The combined group has 35+28=63 students. The sum of their scores is

a+b=2600.5+1892.8=4493.3

Thus, the mean of the combined group is $\frac{4493.3}{63}= 71.32$

6 0

2 years ago

Alejandro would like to start a new business. His friends have suggested he go into merchandising. But he's confused about what

Andreyy89

Answer:

Step-by-step explanation:

This is the complete question

(Alejandro would like to start a new business. his friends have suggested he go into merchandising. but he's confused about what exactly

merchandising is. which sentence provides alejandro with the most accurate description of merchandising?

merchandising is selling your skills, expertise, knowledge, and experience for money

merchandising is selling a product bought at a wholesale price at a higher retail price

merchandising is selling a product that you have created directly to your target customer.

d. merchandising is selling marketing ideas and advertising campaigns to other companies.

e. merchandising is selling a customized service to cater to a customer's needs and wants).

The most accurate description of what merchandising is option B, because it entails the selling of a product, bought at a whole sale price at a higher retail price through different approach such as offering promos or discounts, bargaining and even giving the customer first hand information about the product they are about to buy. Merchandising involves convincing the customer to buy a product in your shop while making profit from it.

7 0

2 years ago

Read 2 more answers