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2 years ago

Determine when both options will cost you the same amount and how much is that?

Mathematics

1 answer:

Mrac [35]2 years ago

8 0

Answer:

after 25 months both options cost $2000

Step-by-step explanation:

the options are the same at the point of intersection of the 2 lines

the lines intersect at (25, 2000)

That is after 25 months both options will cost $2000

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If h(x)=(fog)(x) and h(x)=³√x+3, find g(x) if f(x) =³√x+2

ipn [44]

Answer:

$g(x)=x+1$

The problem:

Find $g(x)$ if $h(x)=(f \circ g)(x)$ ,

$h(x)=\sqrt[3]{x+3}$ , and

$f(x)=\sqrt[3]{x+2}$ .

Step-by-step explanation:

$h(x)=(f \circ g)(x)$

$h(x)=f(g(x))$

Replace $x$ in $f(x)=\sqrt[3]{x+2}$ with $g(x)$ since we are asked to find $f(g(x))$ :

$\sqrt[3]{x+3}=\sqrt[3]{g(x)+2}$

$\sqrt[3]{x+1+2}=\sqrt[3]{g(x)+2}$

This implies that $x+1=g(x)$

Let's check:

$(f \circ g)(x)$

$f(g(x))$

$f(x+1)$

$\sqrt[3]{(x+1)+2}$

$\sqrt[3]{x+1+2}$

$\sqrt[3]{x+3}$ which is the required result for $h(x)$ .

6 0

3 years ago

The base of a solid is bounded by the curve y = sqrt (x+1) the x-axis and the line x = 1. the cross sections, taken perpendicula

Andrei [34K]

See attached for a sketch of some of the cross sections.

Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).

If the thickness of each cross section is ∆x, then the volume of each cross section is

∆V = (√(x + 1))² ∆x = (x + 1) ∆x

As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,

$\displaystyle \int_{-1}^1 (x+1) \, dx = \left(\frac{x^2}2 + x\right) \bigg|_{-1}^1 = \boxed{2} ~~~~ (B)$

3 0

3 years ago

A 8-foot tall man is standing beside a 32-foot flagpole. The flagpole is

kipiarov [429]

Answer:

The flagpole's shadow is 16.875 feet longer than the man's shadow

Step-by-step explanation:

The total length of the shadow is expressed by taking its actual length by a factor that depends on the position of the sun which is constant for the man too. The expression is as follows;

Height of the shadow=actual height of the flagpole×factor

where;

length of the flagpole's shadow=22.5 feet

actual height of the flagpole=32 feet

factor=f

replacing;

22.5=32×f

32 f=22.5

f=22.5/32

f=0.703125

Using this factor in the expression below;

Length of man's shadow=actual height of man×factor