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2 years ago

Which circle has a radius that measures 10 units?

Mathematics

2 answers:

ZanzabumX [31]2 years ago

5 0

Answer:

dav d

Step-by-step explanation:

podryga [215]2 years ago

5 0

Answer:

Step-by-step explanation:

Diameter of 20

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What dividend is represented by the synthetic division below?

Mashcka [7]

Answer:

2x³ + 10x² + x + 5

Step-by-step explanation:

The coefficients of the dividend are represented by the top row, that is

2 10 1 5 → 2x³ + 10x² + x + 5

The divisor is ( x + 5) and

the quotient is represented by the first 3 numbers on the bottom row

2 0 1 → 2x² + 1

The last zero on the same row is the remainder

Since zero this indicates that (x + 5) is a factor of 2x³ + 10x² + x + 5

6 0

2 years ago

Read 2 more answers

Suppose that 5 out of 13 people are to be chosen to go on a mission trip. In how many ways can these 5 be chosen if the order in

algol [13]

5 People can be chosen in 1287 ways if the order in which they are chosen is not important.

Step-by-step explanation:

Given:

Total number of students= 13

Number of Students to be selected= 5

To Find :

The number of ways in which the 5 people can be selected=?

Solution:

Let us use the permutation and combination to solve this problem

$nCr=\frac{(n)!}{(n-r)!(r)!}$

So here , n =13 and r=5 ,

So after putting the value of n and r , the equation will be

$13C_5=\frac{(13)!}{(13-5)!(5)!}$

$13C_5=\frac{(13 \times12 \times11 \times10 \times9 \times8\times7 \times6 \times5 \times4 \times3 \times2 \times1)}{(8 \times7 \times6 \times5 \times4 \times3 \times2 \times1)(5 \times4 \times3 \times2 \times1)}$

$13C_5=\frac{(13 \times12 \times11 \times10 \times9 )}{((5 \times4 \times3 \times2 \times1)}$

$13C_5=\frac{154440}{120}$

$13C_5= 1287$

8 0

2 years ago

QUICK! 75 POINTS !!Select all that are part of the solution set of csc(x) > 1 and over 0 ≤ x ≤ 2π.

Vladimir79 [104]

Answer:

$\frac{\pi}{4}$

$\frac{5\pi}{6}$

Step-by-step explanation:

The answer uses the unit circle and that sine and cosecant are reciprocals.

The first choice doesn't even fit the criteria that $x$ is between $0$ and $2\pi$ (inclusive of both endpoints) because of the $x=\frac{-7\pi}{6}$ .

Let's check the second choice.

$\csc(\frac{\pi}{4})=\frac{2}{\sqrt{2}} \text{ since } \sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$ .

$\csc(\frac{\pi}{4})>1 \text{ since } \frac{2}{\sqrt{2}}>1$

$\csc(\frac{\pi}{2})=1 \text{ since } \sin(\frac{\pi}{2})=1$ which means $\csc(\frac{\pi}{2})=1$ which is not greater than 1.

So we can eliminate second choice.

Let's look at the third.

$\csc(\frac{5\pi}{6})=2 \text{ since } \sin(\frac{5\pi}{6})=\frac{1}{2}$ which means $\csc(\frac{5\pi}{6})>1$ .

$\csc(\pi)$ isn't defined because $\sin(\pi)=0$ .

So we are eliminating 3rd choice now.

Let's look at the fourth choice.

$\csc(\frac{7\pi}{6})=-2 \text{ since } \sin(\frac{7\pi}{6})=\frac{-1}{2}$ which means $\csc(\frac{7\pi}{6})$ and not greater than 1.

I was looking at the rows as if they were choices.

Let me break up my choices.

So we said $x=-\frac{7\pi}{6}$ doesn't work because it is not included in the inequality $0\le x \le 2\pi$ .

How about $x=0$ ? This leads to $\csc(0)$ which doesn't exist because $\sin(0)=0$ .

So neither of the first two choices on the first row.

Let's look at the second row again.

We said $\frac{\pi}{4}$ worked but not $\frac{\pi}{2}$

Let's look at the choices on the third row.

We said $\frac{5\pi}{6}$ worked but not $x=\pi$

Let's look at at the last choice.

We said it gave something less than 1 so this choice doesn't work.

6 0

2 years ago

Read 2 more answers

Paula invited some friends to dinner and she plans to make fajitas at the grocery store she spent $2.56 on red bell peppers and

densk [106]

Answer: 2.8

Step-by-step explanation:

Given Data:

Money spent by Paula for red bell peppers = $2.56

Money spent by Paula on green bell peppers = $1.92

Both pepper cost = $1.60/ pound

Therefore:

Total pounds of bell peppers bought by Paula

= cost of green bell pepper + red red bell pepper / price/pound

= $2.56 + $1.92 / $1.60

= $4.48 / $1.60

= 2.8 pounds

Paula bought 2.8pounds of pepper

6 0

2 years ago

Read 2 more answers

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

2 years ago