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pav-90 [236]
3 years ago
12

A log is 20 m long, correct to the nearest metre.

Mathematics
1 answer:
Marat540 [252]3 years ago
4 0

Answer:

222 fence posts

Step-by-step explanation:

Since the log is 20 m long, correct to the nearest metre and has to be cut into fence posts which must be 90 cm long, correct  to the nearest 10 centimetres, there can be x fence posts 90 cm long.

So, we have x × 90 cm = 20 m

x × 0.9 m = 20 m

x = 20 m/0.9 m

x = 222.22

x ≅ 222 fence posts

So, the largest number of fence posts that can possibly be cut from the log is 222 fence posts.

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The angle of elevation of a cliff top from a small boat on the sea is 36º. The boat is 100m from the foot of the vertical cliff.
storchak [24]

Answer:

72.65m (2dp) is the height of the cliff

Step-by-step explanation:

The height of the cliff can be calculated using trigonometry

Since we know the angle of elevation and the adjacent = side of the angle, and we are looking for the opposite side of the angle, which say is h, we will use tan since we are not dealing with the hypotenuse

tan(36) = h/100

100tan(36) = h

h = 72.65m (2dp)

I have attached a diagram as reference

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3 years ago
What is the pythagoras theorem?
statuscvo [17]
Pythagoras theorem is used in scalene triangles to work out the other side length to do this you would need to follow the rule a2+b2=c2 in order to calculate the hypotenuse
3 0
3 years ago
Can someone help me?! ​
Sever21 [200]

Answer:

10 km

Step-by-step explanation:

5 0
2 years ago
(Please Answer Quickly)
iren2701 [21]
For an airplane we need to create a function. The airplane flies in straight line so this means that we will have linear function. The airplane starts left of the rainbow. So let's take the following function:
y=x+8

"<span>Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow."
To find the intersection points we need to solve system of two equations:
</span>y=- x^{2} +36 \\ y=x+36
Solution are two points:
(-1,35) and (0,36)
Now we can create a table
x        -1    0     1    2
f(x)    35    36   37  38    
<span>

"</span><span>What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not?"

The domain represents all possible values that x can have. The range represents all possible values that y can have.
In this example not all values make sense. Rainbow goes above ground and touches it.
Limitations exist if we have fraction, root, logarithm, trigonometric function... We do not have any of these so there are no limitations, so x can have any value.
Domain:  -6</span>≤x≤6   because x can not have smaller values than those at ground touch.
The formula for parabola is:
y=a x^{2} +b
Depending on sign of x^{2} the maximum or minimum value of y is equal to b. All other smaller or greater values are possible.
Range: 0≤y≤36     because y can not have smaller values than those at ground touch.

"<span>What are the x- and y-intercepts of the rainbow? Explain what each intercept represents."
x- and y- intercepts represent points at which function touches x- and y- axis.
To find y- intercept we insert x=0 into equation:
y=0+36
y=36
To find x- intercept we insert y=0
0=-</span>x^{2}+36
x^{2} =36 \\  x_{1} =-6 \\  x_{2} =6

"<span>Is the linear function you created with your table positive or negative? Explain."

Function is positive if it lies above x-axis. Function is negative if it lies below x-axis.
Positive on interval:  x </span>∈ <-6,∞>
Negative on interval: x ∈ <-∞,-6>
Not defined: x= -6


"What are the solutions or solution to the system of equations created?Explain what it or they represent."

We already found these solutions:
y=- x^{2} +36 \\ y=x+36
Solution are two points:
(-1,35) and (0,36)
These solutions represent points of intersection of linear function and parabola.

"Explain, using complete sentences, the steps for graphing the function."

Step 1) we need to find domain and range
Step 2) we need to find x- and y- intercepts
Step 3) if the function is exponential we find minima and maxima
Step 4) we find at least three values for the function

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3 years ago
Use the Product Property for Exponents to explain why x · x = x2.
Lubov Fominskaja [6]

Whenever there is no exponent on a variable,

you can give it an exponent of 1.

So we can rewrite the x's in this problem as x¹.

When we multiply two terms together

with like bases, we add their exponents.

So now just add their exponents to get x².

3 0
2 years ago
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