Answer:
<em> The distance from your eyes to the stage is 8.85 ft</em>
Step-by-step explanation:
Your distance to the stage is 6 feet
Your eyes are 6.5 feet tall
You need to find the distance of your eyes towards the stage.
This situation can be modeled using a rectangle triangle, where the adjacent side x is the horizontal distance to the stage and the opposite side h is the vertical distance of your eyes to the stage.
<u>Observe the attached image.</u>
Then, we look for the distance z from your eyes to the stage. This distance is the hypotenuse of the right triangle.
So, using the Pythagorean theorem we have:
Where
therefore:
Answer:
y = 4x + 32
Step-by-step explanation:
Given: Temperature at sunrise = 32°F
y is the temperature after x hours of sunrise
Temperature change is 4°F/hour.
The equation of a line in slope intercept form is given by
y = mx +c
where m is the slope, which is the change in value of y to the value of x
and c is the value of y at x = 0
At sunrise, x =0 and y =32
∴ c = 32
Also we see that the change in temperature to that of time is 4/1 = 4
∴ m = 4
Substituting the values of m and c in the equation of line, we have
y = 4x +32
Answer:
Use the Pythagorean theorem
Step-by-step explanation:
The pythagorean theorem is 
where a is a height, b is a height, and c is the hypotenuse, which is the longest side of a triangle. For example, if the triangle has two side with lengths of three and four we would put them into the equation to get:
Simplify the equation to get:
Add 16 and 9 to get 25 and take the square root of both sides:
The sqrt of 25 is 5. Therefore, the length of the hypotenuse, or c, is 5.
Answer:
Step-by-step explanation:
a. Since the parabola is compressed by a factor of 1/3 we can state:
- a parabola is written this way : y=(x-h)²+k
- h stands for the translation to the left ⇒ 2*3=6
- k for the units down ⇒4*3=12
So the equation is : y=(x-6)²+12
b.Here the parabola is stretched by a factor of 2 so we must multiply by 1/2
- We khow that a parabola is written this way : y=(x-h)²+k
- (h,k) are the coordinates of the vertex
- the maximum value is 7*0.5=3.5
- we khow tha the derivative of a quadratic function is null in the maximum value
- so let's derivate (x-h)²+k= x²+h²-2xh+k
- f'(x)= 2x-2h h is 1 since the axe of simmetry is x=1
- f'(x)=2x-2 ⇒2x-2=0⇒ x= 1
- Now we khow that 1 is the point where the derivative is null
- f(1)=3.5
- 3.5=(x-1)²+k
- 3.5= (1-1)²+k⇒ k=3.5
So the equation is : y=(x-1)²+3.5
7.
the maximum height is where the derivative equals 0
- h= -5.25(t-4)²+86
- h= -5.25(t²-8t+16)+86
- h=-5.25t²+42t-84+86
- h=-5.25t²+42t+2
Let's derivate it :
- f(x)= -10.5t+42
- -10.5t+42=0
- 42=10.5t
- t= 42/10.5=4
When the height was at max t=4s
- h(max)= -5.25(4-4)²+86 = 86 m
h was 86m
Answer:
2x + y = 3.75
3x + 2y = 6
Step-by-step explanation:
x = cost of 1 hot dog
y = cost of 1 drink
Neveah: 2x + y = 3.75
Jason: 3x + 2y = 6
