Answer:
17π
Step-by-step explanation:
Equation of a circle is:
(x − h)² + (y − k)² = r²
Area of a circle is:
A = πr²
r² = 17, so A = 17π.
A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the third square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares.
Once George has put rice on the 10th square, he has placed a total of _____ grains of rice on the chess board.
Hey there! I'm happy to help out!
As you can see, our number keeps on doubling. It's like 2×2×2×2.... so on and so forth. Whenever we multiply a number by itself, we can model it as an exponent, so if we had 2², it is two twos being multiplied, and 2×2=4. If it was 2³, it would be 2×2×2=8.
However, we have a one. This signifies a starting point and exponents have our back. Anything to the 0th power is always equal to one! So, this situation would look something like this:
[tex]2^0, 2^1, 2^2, 2^3,2^4,... etc.[/tex]
So, for the second square, we are going to the first power. For the fourth square it's going to the third power. Therefore, the 10th square will be the 9th power!
[tex]2^9=[/tex] 2×2×2×2×2×2×2×2×2= 512
However, we want to find how much he has done in total! So, let's find how much he did on the other squares!
[tex]2^8[/tex]= 256
[tex]2^7[/tex]=128
[tex]2^6[/tex]=64
[tex]2^5[/tex]=32
[tex]2^4[/tex]=16
2³=8
2²=4
[tex]2^1[/tex]=2
[tex]2^0[/tex]=1
Now, we add these all up to find the total grains of rice!
512+256+64+32+16+8+4+2+1=895
Therefore, George has placed a total of 895 grains of rice on the chess board.
I hope that this helps! Have a wonderful day!
Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
We have,
On the first square, George placed 1 grain of rice.
On the second square, he placed 2 grains.
On the third square, he placed 4 grains.
On the fourth square, he placed 8 grains.
In general, on the nth square, he places [tex]2^{n-1}[/tex] grains.
So,
On the first 10 squares,
1 + 2 + 4 + 8 + ... + [tex]2^9[/tex]
This is a geometric series with a first term of 1 and a common ratio of 2.
The sum of the first n terms of a geometric series.
[tex]S_n[/tex] =[tex]a(1 - r^n) / (1 - r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
Substituting the values,
[tex]S_{10}[/tex] = 1(1 - 2^10) / (1 - 2)
= 1(1 - 1024) / (-1)
= 1023
Therefore,
Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.
Learn more about geometric sequence here:
https://brainly.com/question/2321576
#SPJ7
Write the following trigonometric ratio using an acute angle: tan 162 degrees
Answer:
-tan(18°) or tan(-18°)
Step-by-step explanation:
The angle given is in the 3rd quadrant, so the tangent is negative. The reference angle is ...
180° -162° = 18°
Tangent is an odd function, so ...
tan(-x) = -tan(x)
This means we can write the required ratio two ways:
tan(-18°)-tan(18°)Factorise 2y^2 + y + 6xy + 9x - 3
Answer: (2y+3)(3x+y-1)
Step-by-step explanation:
First regroup the terms.
6xy+9x+2y^2+y-3
Second factor 3x out of 6xy+9x
3x(2y)+9x+2y^2+y-3
3x(2y)+3x(3)+2y^2+y-3
And you get
3x(2y+3)+2y^2+y-3
Third factor by grouping
Distance between (-1,0) and (8,6)
Answer:
3 √ 13
Step-by-step explanation:
Answer:
3√13
Step-by-step explanation:
We want to find the distance between these two points. To do so, we need to use the distance formula which states that the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is:
d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
Here, [tex]x_1=-1,x_2=8,y_1=0[/tex], and [tex]y_2=6[/tex]. So:
d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
d = [tex]\sqrt{(-1-8)^2+(0-6)^2}=\sqrt{(-9)^2+(-6)^2} =\sqrt{81+36} =\sqrt{117} =3\sqrt{13}[/tex]
Thus, the answer is 3√13.
~ an aesthetics lover
Classify each representation shown below as either linear or exponential.
x y
0 5
1 7.5
2 11.25
y = 2x + 4
One person sends an email to 2 people. Those 2 people send it to 4 people, and those 4 send it to 8 people.
1. Exponential
2. Linear
3. Exponential
The sum of five consecutive integers is 70. What are the numbers?
Answer: The numbers are 12, 13, 14, 15, and 16.
Step-by-step explanation:
Write an algebraic equation.
x + (x+1) + (x+2) + (x+3) + (x+4) = 70
5x + 10 = 70
subtract 10 from both sides
5x = 60
divide each side by 5
x = 12
The numbers are 12, 13, 14, 15, and 16.
Answer:
12 to 16 :) hope it helped
solve for the coefficient -5=a(0-2)(0-3)(0-5)
Answer:
a = 1/6
Step-by-step explanation:
-5=a(0-2)(0-3)(0-5)
Simplify
-5=a(-2)(-3)(-5)
-5 = a(-30)
Divide each side by -30
-5/-30 = -30a/-30
1/6 =a
Answer:
1/6
Step-by-step explanation:
1. Terry made $53
washing cars. She made
some money selling
cookies. In total she has
$67. How much money
did she make selling
cookies?
Answer:
Terry made $14 selling cookies.
Step-by-step explanation:
[tex]67-53=14[/tex]
Answer:
$14
Step-by-step explanation:
She made $14 selling cookies.
$67-$53=$14
1. Si pide prestado $ 600 por siete años a una tasa de interés del 7%, ¿cuánto interés pagará?
Answer:
Su pago mensual sería de $9.06 (Espero que esto ayude)
Step-by-step explanation:
The formula A=12(b+c)h. Write the equation in term of c?
Answer:
[tex]c = \frac{A}{12h} - b[/tex]
Step-by-step explanation:
Okay, so the goal is to isolate c on one side with all the other terms on the other side. So, let's start by dividing both sides with 12h. After we do that, we will be left with [tex]\frac{A}{12h} = b+c[/tex]. Now, we can subtract both sides by b, and we will be left with [tex]\frac{A}{12h} - b = c[/tex]. Yay! We've now isolated c and that is our final answer!
Hope this helped! :)
Look at recent question
Answer:
ok was it college math if so the I don't know
One brand of coffee is packaged in cylinders where the height is equal to the radius, r. The volume of the package, in cubic centimeters, can be found using the function V(r) = πr3. The number of ounces of coffee in the cylinder depends on the volume of the cylinder, V, in cubic centimeters. This can be modeled by the function C(V) = 3.2V. Which function can be used to find the number of ounces of coffee in the can based on its radius? C(V(r)) = 32.768πr3 C(V(r)) = 3.2πr3
Answer:
C(V(r)) = 3.2πr3Step-by-step explanation:
This problem is a composition of function defined by C(V(r)), now we have the functions [tex]V(r)= \pi r^{3}[/tex] and [tex]C(V)=3.2V[/tex], where the first depends on the radius, and the second dependes on the volume, that means, to find the number of ounce of coffe, we need to determine the volume of the cylinder, that's why we have to replace the volume function inside the ounces function,
[tex]C(V(r))=3.2(\pi r^{3} )[/tex]
Therefore, the right answer is the last choice.
The quadratic equation x^2 - 8x = -4 is rewritten in the form (x + p)^2 = q. when q is a constant. What is the value of p ?
Answer:
-4
Step-by-step explanation:
If you multiply out the square, you can see ...
(x +p)^2 = q
x^2 +2px +p^2 = q
The coefficient of the x-term is 2p, so ...
2p = -8
p = -8/2 = -4
ESSON 3 REFINE
The rectangular prism shown below has a volume of 42 cubic
meters. What is the length of the prism? Show your work
What dim
labeled
prisma
3 m
2 m
Answer:
The length of the prism = 3m
See below for explanation
Step-by-step explanation:
The question is incomplete without the diagram stated in the question.
Since the diagram is missing, I'll show you how you can determine the length of a prism.
Volume of prism = length × width × height = l×w×h
Find attached below the diagram used in solving the question.
From the diagram,
height = 7m
Width = 2m
Given that the volume of prism = 42 cubic meters = 42m³
Length of prism = ?
Inserting the values of the variables:
42 = l×2×7
42 = 14×l
l = 42/14
l = 3
The length of the prism = 3m
How do you determine similarities in shapes?
Answer:
Step-by-step explanation:
. if every corresponding internal angles in both shapes are equal
. if all corresponding sides are equal or have same ratio.
more rules but depends on the shape also ( triangle, rectangle, hexagon,...)
The states that dropped out of the Union, became the __________________ States of America 58 POINTS!!!
Answer:
Confederate
Step-by-step explanation:
During the time that led up to the conflict known as the Civil War of America, the major cause of tension was slavery. Southern plantation owners and farmers fiercely advocated slavery because they helped with the harvest of crops and the overall southern economy. The northerners, however, resisted slavery, saying it was immorally and inhumanely wrong.
At the culmination of this tension, many southern states, led by Jefferson Davis (who later became the "president" of the Confederate states), decided to secede from the Union (break away) and establish their own entity, which they called the "Confederate States of America".
g(x) = - 3x - 8
g (____) =10
How to find the area of the seating area
Parallelogram area is base times height. Base of 14, height of 10,
Answer: A = (14 ft)(10 ft) second choice
Answer:
choice B
Step-by-step explanation:
Find the area of the triangle
Answer:
84mm
Step-by-step explanation:
Formula of a triangle:
A =bh/2
A=14(12)/2
A=168/2
A=84mm
If V = 15 cm, W = 20 cm, X = 25 cm, Y = 7 cm, and Z = 22 cm, what is the perimeter of the object?
A.
53 cm
B.
64 cm
C.
118 cm
D.
78 cm
Answer:
Sum of all the sides.
Step-by-step explanation:
Perimeter is the sum of the distance in length or width, or height or circumference of all the sides of an object.
Therefore the sum total of the given sides V, W, x ,Y, Z are;
15 +20 + 25 + 7 + 22 = 89cm
Since a picture isn't available to know which sides of the objects can be added.
an automobile traveled 21 miles north from the airport. it then turned directly west and traveled 28 miles. how far is the automobile from the airport??
The automobile is 35 miles away from the airport
1.] What is the probability of choosing a king
from a standard deck of playing cards?
Answer:
1/13
Step-by-step explanation:
there are 4 kings in a deck of 52 cards.
4/52 = 1/13
Which of the following statements is FALSE? The correlation coefficient equals the proportion of data points that lie on a straight line. The correlation coefficient will be +1.0 only if all the data lie on an upward-tilting straight line. The correlation coefficient is undefined if all the data lie on a perfectly horizontal straight line. The correlation coefficient is a unitless number and must always lie between –1.0 and +1.0, inclusive.
Answer:
The first one is False.
Step-by-step explanation:
If the correlation coefficient can also be -1 if the data lies on an upward tilting straight line.
If a sample mean is 37,which of the following is most likely the range of possible values that best describes an estimate for the population mean?
Answer:
(32, 42)
Step-by-step explanation:
Answer:
(32,42)
Step-by-step explanation:
Marco bought gifts for his family at the school gift shop for the holidays. Marco bought 10gifts and spent $11.50. How many of each item did he buy if friendship bracelets cost $1.50 and stickers cost $1?
Step-by-step explanation:
Marco bought 10 gifts = 11. 50
If 5 bracelets = 1.50 x 5 = 7.5
4 stickers = 4 x 1 = 4
So total cost = 7.5 + 4 = 11.5
6 to the power of 3 +7 times 4
Answer:
892
Step-by-step explanation:
Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
Answer:
(x - 5) (x - 7)
Step-by-step explanation:
To factor this trinomial, you must split the middle term (-12x) into two terms that can be added to get -12x, and multiplied to get 35:
[tex]x^2[/tex] - 12x + 35
[tex]x^2[/tex] -7x - 5x + 35
Group:
([tex]x^2[/tex] -7x) (-5x + 35)
Take out the GCF (Greatest Common Factor):
x(x - 7) -5(x - 7)
(x - 5) (x - 7)
Answer:
the answer is D
Step-by-step explanation:
x^2-12x+35=x^2-7x-5x+35=x*(x-7)-5(x-7)=(x-7)(x-5)
Ana has a rectangular garden with a width of 2.3 meters and a length of 2.8 meters. She makes the model below to help her determine the area of her garden. What is the area of Ana's garden?
Answer:
6.44 m2
Step-by-step explanation:
Solve for x - y = -3
Answer:
0-3=-3
Step-by-step explanation:
Solve |6k + 12| + 9=9 for k
Answer:
k= -2
Step-by-step explanation:
