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3 years ago

Identify the vertex of g(x) = (x+10)^2+2

Mathematics

1 answer:

RoseWind [281]3 years ago

7 0

Answer:

(-10, 2)

Step-by-step explanation:

Compare:

g(x) = (x+10)^2+2

f(x) = (x - h)^2 + k

Matching these up, term by term, we see that h = -10 and k = 2. (h, k) represents the vertex of the parabola f(x) = (x - h)^2 + k.

We conclude that the vertex of this parabola is (-10, 2).

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A toy train has 8 compartments and an engine that is 8 inches long. Each compartment is 4 inches long. Each compartment is joine

luda_lava [24]

Answer:

64in

Step-by-step explanation:

links=8*3=24

compartments + engine=4*8+8=40

40+24=64

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3 years ago

A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h a

kkurt [141]

Answer:

$b=h=\sqrt{6}$ m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box= $2b^2+4bh$

$2b^2+4bh=36$

$b^2+2bh=18$

$2bh=18-b^2$

$h=\frac{18-b^2}{2b}$

Volume of box, V= $b^2h$

Substitute the values

$V=b^2\times \frac{18-b^2}{2b}$

$V=\frac{1}{2}(18b-b^3)$

Differentiate w. r.t b

$\frac{dV}{db}=\frac{1}{2}(18-3b^2)$

$\frac{dV}{db}=0$

$\frac{1}{2}(18-3b^2)=0$

$\implies 18-3b^2=0$

$\implies 3b^2=18$

$b^2=6$

$b=\pm \sqrt{6}$

$b=\sqrt{6}$

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

$\frac{d^2V}{db^2}=-3b$

At $b=\sqrt{6}$

$\frac{d^2V}{db^2}=-3\sqrt{6}$

Hence, the volume of box is maximum at $b=\sqrt{6}$ .

$h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}$

$h=\frac{18-6}{2\sqrt{6}}$

$h=\frac{12}{2\sqrt{6}}$

$h=\sqrt{6}$

$b=h=\sqrt{6}$ m

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3 years ago

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Answer:

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Step-by-step explanation:

4:20+67 minutes= 5:27

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