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4 years ago

Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(1).

Mathematics

1 answer:

anastassius [24]4 years ago

5 0

Answer:

$\large\boxed{(h\circ g)(1)=8}$

Step-by-step explanation:

$(f\circ g)(x)=f\bigg(g(x)\bigg)\\===================\\\\(h\circ g)(1)=h\bigg(g(1)\bigg)\\\\g(1)-\text{put}\ x=1\ \text{to the equation of the function}\ g(x)=2x:\\\\g(1)=2(1)=2\\\\h\bigg(g(1)\bigg)=h(2)-\text{put}\ x=2\ \text{to the equation of the function}\ h(x)=x^2+4:\\\\h(2)=2^2+4=4+4=8$

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A solid right circular cone of diameter 14cm and height 8cm is melted to form a hollow sphere. If the external diameter of the s

Pani-rosa [81]

Answer:

The internal diameter of the sphere is 6 cm.

Step-by-step explanation:

Given that, a solid right circular cone of diameter 14 cm and height 8 cm.

The radius of the cone is $=\frac{diameter}{2}$

$=\frac{14}{2} \ cm$

= 7 cm.

The volume of the cone is $= \frac13 \pi r^2 h$

$=(\frac1 3\times \pi \times 7^2\times 8) \ cm^3$

$=\frac{392}{3}\pi \ cm^3$

Let the internal radius of the sphere be r.

The external diameter of the sphere is = 10 cm

The external radius of the sphere is(R) = 5 cm

The volume of the sphere is $= \frac43 \pi(R^3-r^3)$

$=\frac43 \pi (5^3-r^3) \ cm^3$

The sphere is formed by the solid right circular cone.

∴The volume of the sphere = The volume of the cone

According to the problem,

$\frac43 \pi (5^3-r^3) =\frac{392}{3}\pi$

$\Rightarrow 4(5^3-r^3)= 392$

$\Rightarrow 5^3-r^3=\frac{392}{4}$

$\Rightarrow 5^3-r^3=98$

$\Rightarrow -r^3=98-125$

$\Rightarrow-r^3= -27$

⇒r= 3

The internal radius of the sphere is = 3 cm.

The internal diameter of the given sphere is = (2×3) cm =6 cm.

7 0

4 years ago

How many seconds will it take an echo to reach your ears if you yell toward a mountain

DiKsa [7]

It will take 0.556 seconds for an echo to reach one's ears

<h3>Calculating the time to hear an echo</h3>

From the question, we are to determine how long it would take an echo to reach one's ears

From the formula,

$Speed = \frac{2 \times distance \ travelled\ by \ sound}{Time}$

NOTE: To hear an echo, the sound will travel to and fro, hence, it will cover twice the distance

From the given information,

Distance = 92.0 m

NOTE: Speed of sound in air at 0 °C ≅ 331 m/s

Putting the parameters into the formula, we get

$331 = \frac{2 \times 92.0}{Time}$

$Time = \frac{2 \times 92.0}{331}$

Time = 0.556 secs

Hence, it will take 0.556 seconds for an echo to reach one's ears.

Learn more on Calculating the time to hear an echo here: brainly.com/question/16676723

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6 0

2 years ago

RATING BRAINLIEST Which of the following demonstrates the Distributive Property?

ra1l [238]

Answer:

D: 4(2a+3)=8a+3

Step-by-step explanation:

4x2a = 8a and 4x3 = 12

4 0

2 years ago

Read 2 more answers

The length,l of a rectangle is 5/2 its width, w. The length, l, of the rectangle is 10 inches. what is the perimeter and the are

guapka [62]

P=2(L+W)
=2(2.05+10)
=2(12.05)
=24.1
A=LW
=2.05 x 10
=20.5

4 0

3 years ago

In her freshman year, Wilhelmina earned a B+ in algebra, a B+ in English, an A- in science, and a B- in geography. As a sophomor

Lana71 [14]

Answer:

Freshman: 3.245

Sophomore: 3.0775

All: 3.16125

Step-by-step explanation:

Freshman: (B+) + (B+) + (A-) + (B-) /(4lessons)

(3.33 + 3.33 + 3.66 + 2.66)/4=12.98/4=3.245

Sophomore: (B-) + (C+) + (A-) +(A-) /4

(2.66 + 2.33 + 3.66 + 3.66)/4 = 12.31/4= 3.0775

All: (3.245 + 3.0775)/2=6.3225/2=3.16125

8 0

3 years ago