5) Obtuse triangle because the top angle is more than 90 degrees
Answer:
f(x)=(1.023) ⋅ 3^x Growth
f(x)=3 ⋅ (0.072)^x Decay
f(x)=4 ⋅ (0.035)^x Decay
f(x)=2 ⋅ (1.34)^x Growth
Step-by-step explanation:
An exponential function at its heart has a base number of rate. If the rate is less than 1, then the function decays. If the base number or rate is greater than 1, then the function grows and increase.
f(x)=(1.023) ⋅ 3^x Rate 3 - Growth
f(x)=3 ⋅ (0.072)^x Rate 0.072 - Decay
f(x)=4 ⋅ (0.035)^x Rate 0.035 - Decay
f(x)=2 ⋅ (1.34)^x Rate 1.34 - Growth
This is a problem of maxima and minima using derivative.
In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:
V = length x width x height
That is:

We also know that the <span>bin is constructed from 48 square feet of sheet metal, s</span>o:
Surface area of the square base =

Surface area of the rectangular sides =

Therefore, the total area of the cube is:

Isolating the variable y in terms of x:

Substituting this value in V:

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

Solving for x:

Solving for y:

Then, <span>the dimensions of the largest volume of such a bin is:
</span>
Length = 4 ftWidth = 4 ftHeight = 2 ftAnd its volume is:
Answer:
the hypotenuse of the given triangle is 48.5 ft
Step-by-step explanation:
the ways to detect the hypotenuse of a triangle are :
- longest side of a right angled triangle is the hypotenuse of the triangle .
- side opposite to the right angle ( 90° ) is the hypotenuse of the right angled triangle .
<em> </em><em>in</em><em> </em><em>the</em><em> </em><em>given</em><em> </em><em>figure</em><em> </em><em>the</em><em> </em><em>longest</em><em> </em><em>side</em><em> </em><em>is</em><em> </em><em>48</em><em>.</em><em>5</em><em>,</em><em> </em><em>hence</em><em> </em><em>it's</em><em> </em><em>the</em><em> </em><em>hypotenuse</em><em>.</em><em>.</em><em>.</em><em>.</em>
Answer:
y-4=-5/4(x-(-4))
Step-by-step explanation:
Slope form is y-y1=m(x-x1)
X1and Y1 are a point on the line and M is the slope