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2 years ago

What is the value of x? Enter your answer in the box. x =

Mathematics

1 answer:

Bezzdna [24]2 years ago

3 0

Answer:

Step-by-step explanation:

The shape in image is an equilateral triangle which means all of it's angles has equal measurements:

2x - 4 = 5y and that is equal to 60 degrees

2x - 4 = 60 add 4 to both sides

2x = 64 divide both sides by 2

x = 32

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James drove 986 miles from Philadelphia to Orlando in 14.5 hours. He continued to drive at the same average speed and drove anot

VMariaS [17]

Answer:

James Spent 25 hours driving from Philadelphia to New Orleans.

Step-by-step explanation:

Given:

Distance from Philadelphia to Orlando = 986 miles

Time required to travel Philadelphia to Orlando = 14.5 hrs

Distance from Orlando to New Orleans = 714 mile.

We need to find the total amount of time James spent driving from Philadelphia to New Orleans.

Solution:

First we will find the average speed from Philadelphia to Orlando.

We know that;

Speed is equal to distance divided by time.

framing in equation form we get;

average speed from Philadelphia to Orlando = $\frac{986}{14.5}=68\ mi/hrs$

Now given that he traveled with same speed from Orlando to New Orleans.

So we will find the time required from Orlando to New Orleans.

We know that;

Time is equal to Distance divided by speed.

framing in equation form we get;

time required from Orlando to New Orleans = $\frac{714}{68}= 10.5 \ hrs$

Now we will find the total time James spent on driving from Philadelphia to New Orleans.

the total time James spent on driving from Philadelphia to New Orleans is equal to sum of Time required to travel Philadelphia to Orlando and time required from Orlando to New Orleans.

framing in equation form we get;

the total time James spent on driving from Philadelphia to New Orleans = 14.5 + 10.5 = 25 hours.

Hence James Spent 25 hours driving from Philadelphia to New Orleans.

6 0

3 years ago

Robin earned $4,320 in 9 weeks and worked 40 hours in each week. How much did he earn per hour? $ per hour

lys-0071 [83]

Hi.............

Good luck :) ........

8 0

3 years ago

Read 2 more answers

Jamie is riding a Ferris wheel that takes fifteen seconds for each complete revolution. The diameter of the wheel is 10 meters a

Agata [3.3K]

Answer:

The answers to the question is

(a) Jamie is gaining altitude at 1.676 m/s

(b) Jamie rising most rapidly at t = 15 s

At a rate of 2.094 m/s.

Step-by-step explanation:

(a) The time to make one complete revolution = period T = 15 seconds

Here will be required to develop the periodic motion equation thus

One complete revolution = 2π,

therefore the we have T = 2π/k = 15

Therefore k = 2π/15

The diameter = radius of the wheel = (diameter of wheel)/2 = 5

also we note that the center of the wheel is 6 m above ground

We write our equation in the form

y = $5*sin(\frac{2*\pi*t}{15} )+6$

When Jamie is 9 meters above the ground and rising we have

9 = $5*sin(\frac{2*\pi*t}{15} )+6$ or 3/5 = $sin(\frac{2*\pi*t}{15} )$ = 0.6

which gives sin⁻¹(0.6) = 0.643 = $\frac{2*\pi*t}{15}$

from where t = 1.536 s

Therefore Jamie is gaining altitude at

$\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) =$ 1.676 m/s.

(b) Jamie is rising most rapidly when the velocity curve is at the highest point, that is where the slope is zero

Therefore we differentiate the equation for the velocity again to get

$\frac{d^2y}{dx^2} = -5*(\frac{\pi *2}{15} )^2*sin(\frac{2\pi t}{15})$ =0, π, 2π

Therefore $-sin(\frac{2\pi t}{15} )$ = 0 whereby t = 0 or

$\frac{2\pi t}{15}$ = π and t = 7.5 s, at 2·π t = 15 s

Plugging the value of t into the velocity equation we have

$\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) =$ - 2/3π m/s which is decreasing

so we try at t = 15 s and we have $\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi *15}{15}) = \frac{2}{3} \pi$ m/s

Hence Jamie is rising most rapidly at t = 15 s

The maximum rate of Jamie's rise is 2/3π m/s or 2.094 m/s.

7 0

3 years ago

For which acute angle are the sine of the angle and cosine of the angle equal? 30º 45º 60º 75º

Damm [24]

Hello

sin ..... | 0° |30°|45°|60°|90°|
...........| 0...| 1..| 2..| 3..| 4..| write numbers
...........| 0...| 1..|√2.| √3 | 2..| take root square
...........| 0...|1/2|√2/2|√3/2|1| divide by 2
...........| 0...|1/2|√2/2|√3/2|1| .....
cos.....| 90°|60°|45°|30°| 0°|

sin (75°)
=sin(30°+45°)=sin 30°*cos 45° +cos 30°*sin 45°
.................... =1/2*√2/2 + √3/2*√2/2
.................... = √2(1+√3)/4

cos 75°
=cos(30°+45°)=cos 30°*cos 45°-sin 30°*cos 45°
=√3/2*√2/2-1/2*√2/2
=√6/4-√2/4=√2/4*(√3 -1 )

5 0

2 years ago

What do you call it when 50 people stand on a wooden dock

Helen [10]

Pier pressure lolllllllllllllllllllllllll

3 0

3 years ago

Read 2 more answers