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3 years ago

Let f(x) = 4 – x^2, g(x) = 2 – x. Find (f + g)(x) and its domain.

Mathematics

1 answer:

PtichkaEL [24]3 years ago

8 0

Step-by-step explanation:

$f(x)=4-x^2,\ g(x)=2-x\\\\(f+g)(x)=f(x)+g(x)\\\\\text{therefore}\\\\(f+g)(x)=(4-x^2)+(2-x)=-x^2-x+(4+2)=-x^2-x+6\\\\\text{It's the quadratic function. The domain is the set of all real numbers}\ x\in\mathbb{R}$

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Pls help

KATRIN_1 [288]

Answer:

169.04 in² (nearest hundredth)

Step-by-step explanation:

Surface area of a cone = $\pi$ r² + $\pi$ r $l$

(where r = radius of the base and $l$ = slant height)

Given slant height $l$ = 10 and surface area = 188.5

Surface area = $\pi$ r² + $\pi$ r $l$

188.5 = $\pi$ r² + 10 $\pi$ r

$\pi$ r² + 10 $\pi$ r - 188.5 = 0

r = $\frac{-10\pi +\sqrt{(10\pi )^2-(4\times\pi \times-188.5)} }{2\pi }$ = 4.219621117...

Volume of a cone = (1/3) $\pi$ r²h

(where r = radius of the base and h = height)

We need to find an expression for h in terms of $l$ using Pythagoras' Theorem a² + b² = c², where a = radius, b = height and c = slant height

r² + h² = $l$ ²

h² = $l$ ² - r²

h = √( $l$ ² - r²)

Therefore, substituting found expression for h:

volume of a cone = (1/3) $\pi$ r²√( $l$ ² - r²)

Given slant height $l$ = 10 and r = 4.219621117...

volume = 169.0431969... = 169.04 in² (nearest hundredth)

5 0

2 years ago

Read 2 more answers

What is the perimeter of triangle ABC? 20 units 22 units 24 units 26 units

Alex777 [14]

8[2] + 6[2] = c[2]
64 + 36 = c[2]
100 = c[2]
c = 10

8 + 6 + 10 = 24 units

8 0

3 years ago

Read 2 more answers

Nine times a number decreased by four is at least twenty three

Andru [333]

The answer is any whole number larger than 3

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3 years ago

A large spherical balloon is being deflated

artcher [175]

The formula for volume of a sphere is V = 4 /3 x π x r3 (cubed).

The original radius of the balloon is 10 ft, so when we plug that value into the equation we get 4188.79. When the balloon deflated, the new radius was 5 ft, so the new volume is 523.6. The question asks how much volume was lost, so we need to subtract 4188.79 - 523.6 and get approximately 3665.

Hope this helps! I hate taking usa test prep quizzes too haha.

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3 years ago

Six Republicans and four Democrats have applied for two open positions on a planning committee. Since all the applicants are qua

Dafna11 [192]

Answer:

$\displaystyle P=\frac{7}{15}=0.467$

Step-by-step explanation:

<u>Probabilities</u>

When we choose from two different sets to form a new set of n elements, we use the so-called hypergeometric distribution. We'll use an easier and more simple approach by the use of logic.

We have 6 republicans and 4 democrats applying for two positions. Let's call R to a republican member and D to a democrat member. There are three possibilities to choose two people from the two sets: DD, DR, RR. Both republicans, both democrats and one of each. We are asked to compute the probability of both being from the same party, i.e. the probability is

$P=P(DD)+P(RR)$