A circular garden has a radius of 4 meters. What is the area of the garden? Use 3.14 as an approximation for .a. 38.74 m2
b. 45.81 m2
c. 50.24 m2
d. 62.58 m2

Answers

Answer 1

Answer: A=pir^2
r=4
pi=3.14 for this problem
A=3.14(4^2)
A=3.14(16)
A=50.24 m^2

C

Answer 2

Answer: Area of a circle = pi (radius^2)

A = 3.14(4^2)
A = 3.14(16)
A = 50.24 m^2

Answer C

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Bret threw a baseball up in the air. The following table represents the height f(t), in meters, of the ball above the ground at time t seconds: Time (t)
(in seconds) Height f(t)
(in meters)
0 3
2 4
4 3
6 0

Which of the following is represented by the y-intercept of f(t)?
(A)The ball touches the ground after 6 seconds.
(B)The ball was thrown from a height of 3 meters.
(C)The ball reaches a maximum height of 4 meters.
(D)The ball reaches the maximum height in 2 seconds.

Answers

The answer is B. The y-intercept is the number on the y axis when x=0. you can see that when x=0, y=3, therefore B is the answer

The statement that represents the y-intercept of f(t) is (B)The ball was thrown from a height of 3 meters.

How to determine the y-intercept?

The table of values is given as:

t f(t)

0 3

2 4

4 3

6 0

The y-intercept is when x = 0.

From the table, we have:

f(0) = 3

This means that: The ball was thrown from a height of 3 meters.

Answers

Answer:

look at the pivots (the leading 1's of the rows)

Step-by-step explanation:

Then, look at the pivots (the leading 1's of the rows). If we have a pivot in every column, then the nullspace of the matrix (and hence the kernel of T) is zero-dimensional. So, T is one-to-one if and only if the REF has pivot in every column.

Final answer:

To check if a matrix is one-to-one using a calculator, you need to enter the matrix values into the calculator, find the reduced row echelon form (RREF) of the matrix, and if the RREF is the identity matrix, the matrix is one-to-one.

Explanation:

In Linear Algebra, a matrix is considered one-to-one if each input vector from a given set of vectors gives a unique output vector. In other words, no two different input vectors can yield the same output vector. To check whether a matrix is one-to-one using a calculator, you’re essentially checking if the transformation represented by the matrix is injective. Here are the steps:

Enter the values of your matrix into the calculator.
Find the reduced row echelon form (RREF) of the matrix. You can do this by row reducing the matrix.
If the RREF of the matrix is the identity matrix, then the matrix is one-to-one. This means that every column of the matrix will have a leading 1, with zeros everywhere else in that column and row.

Note: These steps can often be performed on a calculator that has capabilities for matrix operations, like a TI-83 or TI-84.

Learn more about Matrix here:

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A complex number, (a + bi), multiplied by (2 + 3i) and added to -i gives the product of (-11 + 5i) and (1 – i).a = and b =

Answers

Answer:

Hence, we have:

a= 3 and b= 4

Step-by-step explanation:

It is given that:

A complex number, (a + bi), multiplied by (2 + 3i) and added to -i gives the product of (-11 + 5i) and (1 – i).

i.e.

$(a+ib)(2+3i)-i=(-11+5i)(1-i)\n\ni.e.\n\na(2+3i)+ib(2+3i)-i=-11(1-i)+5i(1-i)\n\ni.e.\n\n2a+3ai+2bi+3bi^2-i=-11+11i+5i-5i^2$

Since, we know that :

$i^2=-1$

Hence, we have:

$2a+3ai+2bi-3b-i=-11+11i+5i+5\n\ni.e.\n\n(2a-3b)+i(3a+2b-1)=-11+5+11i+5i\n\ni.e.\n\n(2a-3b)+i(3a+2b-1)=-6+16i$

i.e. we have:

$2a-3b=-6---------(1)$

and

$3a+2b-1=16\n\ni.e.\n\n3a+2b=16+1\n\ni.e.\n\n3a+2b=17------------(2)$

On multiplying equation (1) by 2 and equation (2) by 3 we get:

$13a=39\n\ni.e.\n\na=3$

on putting the value of a into equation (1) we get:

$2* 3-3b=-6\n\ni.e.\n\n6-3b=-6\n\ni.e.\n\n-3b=-6-6\n\ni.e.\n\n-3b=-12\n\ni.e.\n\nb=4$

(a+bi)(2+3i)-i=(-11+5i)(1-i)
2a+3ai+2bi+3bi²-i=-11+11i+5i-5i²
2a+(3a+2b-1)i-3b=-11+16i+5
(2a-3b)+(3a+2b-1)i=-6+16i
Therefore; we have the next system of equations:
2a-3b=-6
3a+2b-1=16

Finally, the system of equations is:
2a-3b=-6
3a+2b=17
We can solve this system of equations by reduction method
2(2a-3b=-6)
3(3a+2b=17)
----------------------
   13a=39 ⇒a=39/13=3

3(2a-3b=-6)
-2(3a+2b=17)
----------------------
   -13b=-52 ⇒ b=52/13=4

Answer: a=3;    b=4

If Jimmy has 530 pieces of paper and Kit comes along and gives him 18 times as much, how many pieces of paper Jimmy have? And if Kit takes 23 pieces away how much does Jimmy have now?

Answers

Answer:

10,070 and 10,047 pieces respectively

Step-by-step explanation:

In this question, we have 2 questions to answer.

Firstly, we are told that Jimmy has 530 pieces of paper and kit comes along to give him 18 times as much, we need to know how much he has now.

Since he was given 18 times as much, the amount given would be 18 * 530 = 9,540

The amount he has now would be 9,540 + 530 = 10,070 paper pieces

Secondly, Kim comes along to take 23 pieces away, we need to know how much pieces he has now. What to do is simply to

Subtract 23 from the previous pieces = 10,070 - 23 = 10,047 pieces of paper

The radius of the Earth is approximately 3,960 miles. Find the approximate surface-area-to-volume ratio of the Earth.

Answers

The surface area of a sphere is A = 4π R²

The volume of a sphere is V = (4/3) ( π) (R³)

The ratio of (surface area) to (volume) is

      4 π R² / (4/3) (π) (R³)

Divide top and bottom by 4π :    R² / (1/3) (R³)

Multiply top and bottom by 3: 3 R² / R³

Divide top and bottom by R² :    3 / R .

For the Earth,

   A / V = (3) / (3,960 miles) = 0.00076 per mile (rounded)

Answer:

B. 0.00076

Step-by-step explanation:

Unit test on e2020

Write the phrase as an expression. The difference of a number x and 6.4