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2 years ago

Given f(x)=x-7 and g(x)=x^2 Find g(f(-1)) Find f(g(-1)) With explanation

Mathematics

1 answer:

Arlecino [84]2 years ago

4 0

Step-by-step explanation:

f (x)= x-7

= -1-7

= -6

g (x)= x^2

= (-1)^2

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How would you use the Fundamental Theorem of Calculus to determine the value(s) of b if the area under the graph g(x)=4x between

-BARSIC- [3]

The Fundamental Theorem of Calculus regarding geometry states that
$\int\limits^b_a g{(x)} \, dx = F(b)-F(a)$

Where F is the indefinite integral of $g(x)$

The first step is to integrate $g(x)$
$\int\ {4x} \, dx = \frac{4x^{1+1} }{1+1} = \frac{4x^{2} }{2} =2 x^{2}$

Then substitute the value of $b$ and $a=1$ into $2x^{2}$

$[2 (b)^{2}]-[2 (1)^{2}] = 240$
$2b^{2} -2=240$
$2b^{2}=240+2$
$2b^{2}=242$
$b^{2}= \frac{242}{2}$
$b^{2}=121$
$b=11$

Hence the limit of the area under $g(x)$ is between $a=1$ and $b=11$

6 0

3 years ago

A sample of 1800 computer chips revealed that 53% of the chips do not fail in the first 1000 hours of their use. The company's p

charle [14.2K]

Answer:

So the value of the test statistic is -0.85.

Step-by-step explanation:

We know that a sample of 1800 computer chips revealed that 53% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 54% of the chips do not fail in the first 1000 hours of their use.

We get that:

$n=1800\\\\p_1=53\%=0.53\\\\p_2=54\%=0.54\\$

We calculate the standar deviation:

$\sigma=\sqrt{\frac{0.53 \cdot (1-0.53)}{n}}=\sqrt{\frac{0.53 \cdot 0.47}{1800}}=0.01176$

We calculate the value of the test statistic:

$z=\frac{p_1-p_2}{\sigma}=\frac{0.53-0.54}{0.01176}=-0.85$

So the value of the test statistic is -0.85.

5 0

4 years ago

A golfer exerts a force of 15.0 N on a golf ball that has a mass of 0.42 kg. What is the golf

Gala2k [10]

Answer:

35.71m/s²

Step-by-step explanation:

using the formula force(F)=mass(m)×acceleration(a)

a =

$\frac{f}{m}$

F=15.0N

m=0.42kg

a=?

a=15÷0.42

a=35.71m/s²

5 0

4 years ago

Read 2 more answers

Here's the result of this question

Dafna11 [192]

We have been given that Anil borrows $80 000 to buy a business. The bank gives him a loan, with an interest rate of 2% each year. We are asked to find the total amount paid back by Anil to bank after 10 years.

We will use simple interest formula to solve our given problem.

$A=P(1+rt)$ , where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

Let us convert 2% into decimal.

$2\%=\frac{2}{100}=0.02$

We have $P=\$80,000$ and $t=10$ , so we will get:

$A=\$80000\left(1+0.02\cdot 10\right)$

$A=\$80000(1+0.2)$

$A=\$80000(1.2)$

$A=\$96,000$

Therefore, Anil will pay $\$96,000$ to the bank after 10 years.

8 0

3 years ago

What are the coordinates of the vertex of the parabola described by the equation below? y = -7(x - 4)2 - 5

pochemuha

To get the vertex of the parabola we proceed as follows;
y=-7(x-4)^2-5
The above can be written as:
y=-7x^2+56x-117
The values of a,b and c are:
a=-7, b=56 and c=-117
x=-b/(2a)
x=-56/(-7*2)=4
but;
y=-7x^2+56x-117
y=-7(4)^2+56(4)-117
y=-5
Thus;
x=4 and y=-5
The vertex will be at point (4,-5)

7 0

4 years ago

Read 2 more answers