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2 years ago

Lesson 4: Practice Problems

Mathematics

1 answer:

gtnhenbr [62]2 years ago

3 0

Answer:

a).1

b).1

c).111

Step-by-step explanation:

a) anything to the zero power is 1

b) any number divided by itself is one

c) 100+10+1=111

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Mary is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect? Which coordinates if they do? Negat

Umnica [9.8K]

Answer:

The graphs of the two function will not intersect.

Step-by-step explanation:

We are given a quadratic function f(x).

Also g(x) is given by a set of values as:

x g(x)

1 -1

2 0

3 1

As g(x) is a linear function hence we find out the equation of g(x) by the slope intercept form of a line: y=mx+c

let g(x)=y

when x=1 , g(x)=-1

-1=m+c----(1)

when x=2 , g(x)=0

0=2m+c------(2)

Hence, on solving (1) and (2) by method of elimination we get:

m=1 and c=-2

Hence, the equation of g(x) is:

g(x)=x-2

So clearly from the graph we could see that the graph of the two functions will never intersect.

3 0

3 years ago

Read 2 more answers

At the sewing store ashly bought a bag of mixed buttons she got 25 buttons in all 5 of the buttons were large what percentage of

iren [92.7K]

Answer:

20%

Step-by-step explanation:

You have to do 5/25, giving you 20%.

8 0

3 years ago

Read 2 more answers

Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your

Veronika [31]

The expression of integral as a limit of Riemann sums of given integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ is 4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$ from i=1 to i=n.

Given an integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ .

We are required to express the integral as a limit of Riemann sums.

An integral basically assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinite data.

A Riemann sum is basically a certain kind of approximation of an integral by a finite sum.

Using Riemann sums, we have :

$\int\limits^b_a {f(x)} \, dx$ = $\lim_{n \to \infty}$ ∑f(a+iΔx)Δx ,here Δx=(b-a)/n

$\int\limits^5_1 {x/(2+x^{3}) } \, dx$ =f(x)= $x/2+x^{3}$

⇒Δx=(5-1)/n=4/n

f(a+iΔx)=f(1+4i/n)

f(1+4i/n)= $[n^{2}(n+4i)]/2n^{3}+(n+4i)^{3}$

$\lim_{n \to \infty}$ ∑f(a+iΔx)Δx=

$\lim_{n \to \infty}$ ∑ $n^{2}(n+4i)/2n^{3}+(n+4i)^{3}4/n$

=4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$

Hence the expression of integral as a limit of Riemann sums of given integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ is 4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$ from i=1 to i=n.

Learn more about integral at brainly.com/question/27419605

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5 0

1 year ago

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 4 inches, and the larger gear has a ra

pychu [463]

Draw a diagram to illustrate the problem as shown below.

When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.

Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°

Answer: 205.7° (nearest tenth)

Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions

Answer:
The smaller gear makes 1.75 rotations

7 0

3 years ago

240 fluid ounces = ____ cups

katen-ka-za [31]

Answer:

Step-by-step explanation:

for every 1 fluid once it is 0.125 cup. So keep adding up and you will get to 240 and the amount will be 30.

8 0

2 years ago