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3 years ago

Given the function f(x) = 4" + 3, what is the value of f(3)?

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

8 0

Note:

Your function is a little ambiguous. I think you may have tried to write your function such as:

I am assuming your function as:

f(x) = 4x + 3

Answer:

The value of f(3) = 15

Step-by-step explanation:

Given

Assuming the function is

f(x) = 4x + 3

To determine

The value of f(3)

The value of f(3) can be determined by substituting x = 3 in the function

f(x) = 4x + 3

substitue x = 3 in the function

f(3) = 4(3) + 3

f(3) = 12 + 3

f(3) = 15

Therefore, the value of f(3) = 15

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An athlete has run 200m in a 1.5km race. What fraction is she through the race

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Answer:

2/15

Step-by-step explanation:

So 1 km is 1000m

Meaning the race is 1500m

200m out of 1500m = $\frac{200}{1500}$

Simplified down to 2/15

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3 years ago

You must design a closed rectangular box of width w, length l and height h, whose volume is 504 cm3. The sides of the box cost 3

Charra [1.4K]

Answer:

Dimensions will be

Length = 7.23 cm

Width = 7.23 cm

Height = 9.64 cm

Step-by-step explanation:

A closed box has length = l cm

width of the box = w cm

height of the box = h cm

Volume of the rectangular box = lwh

504 = lwh

$h=\frac{504}{lw}$

Sides which involve length and width and height, cost = 3 cents per cm²

Top and bottom of the box costs = 4 cents per cm²

Cost of the sides $C_{s}$ = 3[2(l + w)h] = 6(l + w)h

$C_{s}$ = 3[2(l + w)h]

$C_{s}=6(l+w)(\frac{504}{lw} )$

Cost of the top and the bottom $C_{(t,p)}$ = 4(2lw) = 8lw

Total cost of the box C = $3024\frac{(l+w)}{lw}$ + 8lw

= $3024[\frac{1}{l}+\frac{1}{w}]$ + 8lw

To minimize the cost of the sides

$\frac{dC}{dl}=3024(-l^{-2}+0)+8w=0$

$\frac{3024}{l^{2}}=8w$

$\frac{378}{l^{2}}=w$ ---------(1)

$\frac{dC}{dw}=3024(-w^{-2})+8l=0$

$\frac{3024}{w^{2}}=8l$

$\frac{378}{w^{2}}=l$

$w^{2}=\frac{378}{l}$ -------(2)

Now place the value of w from equation (1) to equation (2)

$(\frac{378}{l^{2}})^{2}=\frac{378}{l}$

$\frac{(378)^{2} }{l^{4}}=\frac{378}{l}$

l³ = 378

l = ∛378 = 7.23 cm

From equation (2)

$w^{2}=\frac{378}{7.23}$

$w^{2}=52.28$

w = 7.23 cm

As lwh = 504 cm³

(7.23)²h = 504

$h=\frac{504}{(7.23)^{2}}$

h = 9.64 cm

6 0

4 years ago

a country's population in 1990 was 134 million. in 2000 it was a 139 million. estimate the population in 2014 using the exponent

yuradex [85]

F=ir^t

139=134r^10

139/134=r^10

r=(139/134)^(1/10) then:

f=134(139/134)^(t/10) so in 2014, t=24 so

f=134(139/134)^(2.4)

f≈146 million (to nearest million)

Some will say that you have to use the exponential function, but it really gives you the same answer...even for continuous compounding :)...

A=Pe^(kt)

139=134e^(10k)

139/134=e^(10k)

ln(139/134)=10k

k=ln(139/134)/10 so

A=134e^(t*ln(139/134)/10) when t=24

A=134e^(2.4*ln(139/134))

A≈146 million (to nearest million)

The only real reason or advantage to using A=Pe^(kt) is when you start getting into differential equations...

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3 years ago