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3 years ago

Which of the following will form the composite function?

Mathematics

1 answer:

zhuklara [117]3 years ago

5 0

Answer:

Step-by-step explanation:

In the composition of <em>f</em><em> </em>and <em>g</em>, the equation is telling us to place the function <em>f</em> inside <em>g</em>. Observing in B that <em>f</em> is (x + 4), then this can be put in place of the x in 3x^2, making it 3(x + 4)^2 and finally the minus 5.

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The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volum

Mariana [72]

The volume of any "pointy" solid will be 1/3 that of the corresponding prism or cylinder (with same height and base area). The only caveat is that the slope of the sides of the pointy solid is constant.

For your figures: 1/3.

8 0

3 years ago

Read 2 more answers

Two bottles are selected at random, without replacement from a drawer containing 2 bottles of coke, 3 bottles of fanta and 4 bot

AVprozaik [17]

To find : outcomes for choosing 2 bottles (without replacement) from 3 various soft drink bottles in different numbers - coke , fanta , sprite

There can be total 2 x 3 , ie = 6 outcomes in this case.

Like two alphabets from A,B,C can be chosen without replacement in following 6 cases - A B & B A , A C & C A , B C & C B

Similarly for Coke , Fanta , Sprite case ; total <u>outcomes</u><u> </u>are :-

Coke, Fanta
Fanta, Coke
Coke, Sprite
Sprite , Coke
Fanta , Sprite
Sprite , Fanta

For more information, refer brainly.com/question/23489473?referrer=searchResults

5 0

2 years ago

Use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 + y2 and the sphere x2 + y2 + z2 =

sashaice [31]

Let $R$ be the solid. Then the volume is

$\displaystyle\iiint_R\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$

which follows from the facts that

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=\zeta\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta$
(by computing the Jacobian)

and

$z=x^2+y^2=r^2\implies z+z^2=72\implies z=-9\text{ or }z=8$
(we take the positive solution, since it's clear that $R$ lies above the $x$ - $y$ plane)
$r^2+z^2=72\implies z=\pm\sqrt{72-r^2}$
(again, taking the positive root for the same reason)
$z=r^2\implies 8=r^2\implies r=\sqrt8$

$\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}r(\sqrt{72-r^2}-r^2)\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}(r\sqrt{72-r^2}-r^3)\,\mathrm dr$
$=\dfrac{32(27\sqrt2-35)\pi}3$

7 0

3 years ago

The area of a storage shed floor is 20 ft2. The length is 3 more than twice the width. Find the dimensions of the storage shed f

vladimir1956 [14]

Answer:

2.5 ft wide
8 ft long

Step-by-step explanation:

The given relation between length and width can be used to write an expression for area. The equation setting that equal to the given area can be solved to find the shed dimensions.

<h3>Given relation</h3>

Let x represent the width of the shed. Then the length is (2x+3), and the area is ...

A = LW

20 = (2x+3)(x) . . . . . area of the shed

<h3>Solution</h3>

Completing the square gives ...

2x² +3x +1.125 = 21.125 . . . . . . add 2(9/16) to both sides

2(x +0.75)² = 21.125 . . . . . . . write as a square

x +0.75 = √10.5625 . . . . . divide by 2, take the square root

x = -0.75 +3.25 = 2.50 . . . . . subtract 0.75, keep the positive solution

The width of the shed is 2.5 feet; the length is 2(2.5)+3 = 8 feet.

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2 years ago

The diagram shows the length and width of a laptop, and the length of a larger version of the same brand of a smaller laptop.

Snowcat [4.5K]

Answer:

11.04 in taylor brown

Step-by-step explanation:

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2 years ago