The square in the figure has two sides tangent to the circle. If area of the circle is 9a^2pi^2, find the area of the square. (A=6, pi=3.14, please estimate the answer two places after decimal)
Answers
As the square has two sides tangent to the circle, the lenght of the side will be de diameter of the circle.
The area of a circle, which is pi*r², in this case is 9a²pi², given that a=6.
So:
\(\begin{gathered} \pi r^2=9\cdot a^2\cdot\pi^2\text{ (dividing both sides by pi)} \\ \pi r^2=9\cdot36\cdot3.14^{2} \\ \pi r^{2}=3,194,51 \\ r^{2}=1017,36 \\ r=31,89 \end{gathered}\)Once r=31.89,, the diameter will be 2*r= 63.78
The area of the square is (63.78)² = 4,067.89u²
Related Questions
6 x (12-2) + 2 to the power of 2
Answers
Answer:
84x
Step-by-step explanation:
need help here is screenshot fast pls
Answers
The equation that models the zombie population is the one in option D.
\(y = 50*(2)^{x/4}\)
Which equation describes the zombie population?We know that the zombie population will be described by an exponential equation, these are of the form:
\(y = A*(b)^{kx}\)
Where A is the initial population, in this case we know that:
A = 50
b is the rate of growth, we know that the population is doubled every 4 days, so:
b = 2
And k is a factor that is defined by in how many days the population is doubled, here we know that the population is doubled every 4 days, then k = 1/4
And the population equation is.
\(y = 50*(2)^{x/4}\)
So the correct option is D.
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I need help NUMBER 181.Find the GCF2.Write the GCF 3.Rewrite expression factor out the GCF4. Write the final factored expression!
Answers
Answer:
1. Find the GCF:
16 y | 5
1
2. Write the GCF: 1
3. Rewrite expression factor out the GCF: 16y + 5
4. Write the final factored expression: 16y + 5
Explanation:
The initial expression is:
16y + 5
So, we have two terms: 16y and 5
The factors of these terms are:
16y: 1, 2, 4, 16, y, 2y, 4y, 16y
5: 1, 5
So, the greatest common factor is 1
Then, the expression factor out the GCF is:
\(\frac{16y+5}{1}=16y+5\)Therefore, the final factored expression is:
1*(16y + 5) = 16y + 5
The number of Calories burned while running varies directly with the number of miles run. Francesca burns 816 Calories on her 8-mile run. Write a direct variation equation to represent this relationship.
Answers
Answer:
y = 102*x
Step-by-step explanation:
y=a*x
x: distance
y: calories
816=a*8
a= 816/8= 102
Rocio deposits $3,200 in a one year CD at
3.1% interest, compounded daily. What is
her APY to the nearest hundredth of a
percent?
Answers
The annual percentage yield (APY) of Rocio is 3.11 %
What is Annual Percentage Yield?
The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest.
Given data ,
Deposit amount of Russ = $ 3200
Interest rate R = 3.1 %
And it is given that the interest rate is compounded daily , so
Interest rate R = 3.1 % / 365
= 0.031 / 365
= 0.000084
Now , The annual percentage yield (APY) is calculated as
The interest amount = 3200 x ( 1 + 0.000084 )³⁶⁵
= 3200 x ( 1.000084 )³⁶⁵
= 3200 x 1.031133
= 3299.6272
≈ 3299.627
Therefore , the interest will be
= 3299.627 - 3200
= $ 99.627
Now , the annual percentage yield (APY) is given by
= Interest / Deposit
= 99.627 / 3200
= 0.03113
≈ 3.11 %
Hence , annual percentage yield (APY) of Rocio is 3.11 %
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write and equivalent expression by combining like terms 12x+6y-3y+9
Answers
Answer:
12x + 3y + 9
Step-by-step explanation:
Im not sure if you can add constants to variables so here is my simplified expression.
answerrrr plssssssssss
Answers
Answer:
no solution
Step-by-step explanation:
Why is 2(7^0)=2 correct?
Answers
Least common multiples of two- digit numbers. I need two examples. SHOW WORK
Answers
9514 1404 393
Answer:
LCM(21, 51) = 357LCM(42, 90) = 630Step-by-step explanation:
For a pair of numbers, I find it convenient to think in terms of factors unique to the number, and factors shared with the other number.
Consider the numbers 21 and 51, for example.
21 = 3·7
51 = 3·17
The factor 3 is shared by both numbers. The factors 7 and 17 are unique to one number or the other.
If we group these factors like this ...
(factors unique to 1 [ shared factors ) factors unique to 2]
= (7 [3 ) 17]
The numbers in ( ) parentheses are the factors of 21, and the numbers in [ ] brackets are the factors of 51.
The LCM (least common multiple) is the product of the factors in those brackets:
LCM(21, 51) = 7 × 3 × 17 = 357
__
The unique factors of the numbers don't have to be prime (as in the above example); they just cannot be shared. Here's another example for the numbers 42 and 90
(7 [ 3·2 ) 3·5 ] = (7 [ 6 ) 15] . . . . factors of (42) and [90]
Then the LCM is ...
LCM(42, 90) = 7 × 6 × 15 = 630
_____
Additional comment
What we have called "shared factors" here is the same as the "greatest common divisor"(GCD) or "greatest common factor" (GCF).
If we divide our little diagram so it shows the product of the two numbers:
(42)[90] = (7×6)·[6×15]
we can see that the LCM is the quotient of the product and the GCD.
LCM(A, B) = A·B/GCD(A, B)
This is an occasionally handy relationship, as it is not difficult to find the GCD of a pair of numbers using Euclid's algorithm.
Find the weight of one square in hanger a and the weight of a pentagon in hanger b
Answers
Answer:
the first and second M is undefined because we have no information to make an equation
Evaluate f(3) whenf(x)=(x^2+4x-7
Answers
Answer:
14
Step-by-step explanation:
(3)^2 + 4(3) - 7
9 + 12 - 7
21 - 7
14
the surface area of the pyramid. The side lengths of the base are equal.
Triangular pyramid with base edge of 8 inches, and a slant height measuring 14 inches, on a triangular face. Apothem goes from the vertex to the midpoint of a base edge and measures 6.9 inches.
Answers
First, let's find the length of the altitude of the triangle formed by the base edge and apothem. We can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the legs of the right triangle and c is the hypotenuse (slant height).
a = 4 (half of the base edge)
b = 6.9 (apothem)
c = 14 (slant height)
Substituting values:
4^2 + 6.9^2 = 14^2
16 + 47.61 = 196
63.61 = 196 - 16
63.61 = 180.00
√63.61 = 7.98
So the altitude of the triangle formed by the base edge and apothem is approximately 7.98 inches.
Now we can find the area of each triangular face:
Area of one triangular face = 1/2 x base x height
Area of one triangular face = 1/2 x 8 x 7.98
Area of one triangular face = 31.92 square inches
Since there are four triangular faces, the total surface area of the pyramid is:
Total surface area = 4 x 31.92
Total surface area = 127.68 square inches
Therefore, the surface area of the pyramid is approximately 127.68 square inches.
Answer:
the surface area of the triangular pyramid is 227.6 square inches.
Step-by-step explanation:
To find the surface area of the triangular pyramid, we need to calculate the area of the triangular base and the area of each triangular face, and then add them together.
The area of the triangular base can be found using the formula:
Base Area = (1/2) x Base Edge Length x Apothem
Substituting the given values, we get:
Base Area = (1/2) x 8 x 6.9 = 27.6 square inches
To find the area of each triangular face, we can use the formula:
Face Area = (1/2) x Base Edge Length x Slant Height
Substituting the given values, we get:
Face Area = (1/2) x 8 x 14 = 56 square inches
Since the triangular pyramid has 4 faces, we need to multiply the area of each face by 4 to get the total surface area. Therefore, the surface area of the triangular pyramid is:
Total Surface Area = 4 x Face Area + Base Area
= 4 x 56 + 27.6
= 227.6 square inches
So the surface area of the triangular pyramid is 227.6 square inches.
PLEASE HELP FAST !!!!!
The distribution of pitches thrown in the
80 at-bats in a baseball game is as follows.
Pitches 1 2 3 4 5
Frequency 12 16 32 12 8
Find the relative frequency that the pitcher
will throw exactly 4 pitches in an at-bat.
?
Relative Frequency =
Do NOT simplify your answer.
Answers
The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:
3/20.
How to calculate a relative frequency?A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of at bats in this problem is given as follows:
80.
In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:
12/80 = 3/20.
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Find the equation of the line
Answers
The equation of the graph is y = 3x + 7
How to determine the equation of a lineThe equation of a line is composed of;
The y- interceptThe slopeThe y and x variablesThe formula for the equation of line is written this;
y = m x + c
Where;
m is the slopec is the intercept on the y axisFrom the graph shown, we can see that the intercept on y is 7, thus, c = 7
The formula for slope is given as;
m = y2 - y1/x2 - x1
m = 7 - 1/ 2 - 0
m = 6/2
m = 3
The slope of the graph is 3
Now, let's substitute into the equation for the line
y = 3x + 7
Thus, the equation of the line is y = 3x + 7
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Find the measure of < 1.
Answers
The multipliers that will create opposite terms of the y-variable for this system have been determined. Use the equivalent system of equations to solve the system. 4(3x − 1 4 y = 15) → 12x − y = 60 −6(2 3 x − 1 6 y = 6) → − 4x + y = − 36 What is the solution to the system of equations? ( , )
Answers
Answer:
The answer to the multipliers that will create opposite terms of the y-variable for this system have been determined. Use the equivalent system of equations to solve the system. is (3, -24)
Step-by-step explanation:
Answer:
3 -24
Step-by-step explanation:
got it right
What is the percent change from 310 to 155?
Answers
Answer: 50% decrease
Step-by-step explanation:
50% of 310 = 155
310-155=155
50% decrease :)
ANSWER: 50% decrease
SOLUTION:
50% of 310 = 155
310-155=155
So in all the answer is.......
50% decrease :)))))
-XOXOXO:)
find two polynomials whose difference is 2x^2 + x + 4
Answers
The two polynomials whose difference is 2x^2 + x + 4 are
6x² + 3x + 5 and 4x² + 2x + 1.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The difference between the two polynomials is 2x² + x + 4.
The two polynomials are:
6x² + 3x + 5 _____(1)
4x² + 2x + 1 ______(2)
The difference between (1) and (2)
6x² + 3x + 5 - 4x² - 2x - 1
2x² + x + 4
Thus,
The two polynomials are 6x² + 3x + 5 and 4x² + 2x + 1.
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Find the quotient of 3/5 3/7. Write your answer in the simplest form.
Answers
\(\cfrac{3}{5}\div\cfrac{3}{7}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5}\cdot \cfrac{7}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{7}{5}\implies 1\frac{2}{5}\)
Brianna made 9 1/4 bags of popcorn for a movie night with some friends. Together they ate 4 bags of it. How much popcorn was left?
Answers
There were 5 1/4 bags of popcorn left after eating 4 bags.
To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.
Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:
9 1/4 = (4 * 9 + 1) / 4 = 37/4
Now, let's subtract the 4 bags eaten from the total:
37/4 - 4
To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:
37/4 - 4/1
Now, let's find a common denominator and subtract the fractions:
37/4 - 16/4 = (37 - 16) / 4 = 21/4
The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:
21/4 = 5 1/4
Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.
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A Bernoulli differential equation is one of the formsdy/dx + P(x)y = Q(x)y^n (*) Observe that, if n 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y^(1-n) transforms the Bernoulli equation into the linear equation du/dx + (1 - n)P(x)u = (1 - n)Q(x). Consider the initial value problem xy’ + y = 2xy^2, y(1) = 4. (a) This differential equation can be written in the form (*) with P(x) = ___,Q(x) =___, and n = ___.(b) The substitution u = ___ will transform it into the linear equation Du/dx + ___ u = ___(c) Using the substitution in part (b), we rewrite the initial condition in part (c) u(1) = ____(d) Now solve the linear equation in part (b). and find the solution that satisfies the initial condition in part (c) U(x) = ____(e) Finally, solve for yy(x) = ____
Answers
the answer for this question is i don't know
So , bye
(a) This differential equation can be written in the form (*) with P(x) = 1, Q(x) = 2x, and n = 2.
(b) The substitution u = 1/y will transform it into the linear equation Du/dx + 0u = -2x
(c)Using the substitution in part (b), we rewrite the initial condition in part u(1) = 1/y(1) = 1/4.
(d) the linear equation in part (b) is y = 1/(C - x) and the solution that satisfies the initial condition in part (c) U(x) = -y⁻¹ = -x + C,
(e) Finally, solve for y(x) = 1/(1/4 + 1 - x) = 4/(5 - x).
What is Bernoulli differential equation?
A Bernoulli differential equation is a type of non-linear ordinary differential equation of the form:
dy/dx + P(x)y = Q(x)yⁿ
where P(x) and Q(x) are functions of x and n is a constant. The equation is named after the Swiss mathematician Jakob Bernoulli.
These types of differential equations are important in various fields of science, such as physics, engineering, and economics. They are non-linear, meaning that the dependent variable y appears in both linear and non-linear terms, making them difficult to solve in general.
a) This differential equation can be written in the form (*) with P(x) = x, Q(x) = 2x, and n = 2.
b) The substitution u = y⁻¹ will transform it into the linear equation du/dx - xu = -2x.
c) Using the substitution in part (b), we rewrite the initial condition as u(1) = 1/4.
d) Now we solve the linear equation in part (b). The characteristic equation is given by d/dx(e\(\mathrm{(\int -xdx))}\) = -xe\(\mathrm{(\int -xdx))}\) which has the general solution u(x) = Ce\((-x^2/2)\).
Using the initial condition, we find C = 1/4, so u(x) = 1/4e\((-x^2/2)\).
e) Finally, we solve for y. From u = y⁻¹, we have y = 1/u = 4e\((-x^2/2)\).
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HCF of 560 and 729 :)
Answers
The HCF of 560 and 729 is 1.
To find the HCF of 560 and 729, we use the Euclidean algorithm as follows;HCF of 560 and 729:Step 1: Divide the larger number by the smaller number, then find the remainder.729 ÷ 560 = 169 remainder 169Step 2: Divide the smaller number (i.e., 560) by the remainder (i.e., 169).560 ÷ 169 = 3 remainder 53.
Step 3: Divide the remainder from step 1 (i.e., 169) by the remainder from step 2 (i.e., 53).169 ÷ 53 = 3 remainder 10Step 4: Divide the remainder from step 2 (i.e., 53) by the remainder from step 3 (i.e., 10).53 ÷ 10 = 5 remainder 3Step 5: Divide the remainder from step 3 (i.e., 10) by the remainder from step 4 (i.e., 3).10 ÷ 3 = 3 remainder 1.
Step 6: Divide the remainder from step 4 (i.e., 3) by the remainder from step 5 (i.e., 1).3 ÷ 1 = 3 remainder 0The HCF of 560 and 729 is the last non-zero remainder, which is 1.
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Solve this question
(7w^7)k³
Answers
The value of the variable 'w' for the given equation 7 ( w + 7 )³ = 7(6³) is equal to w = -1.
As given in the question,
Given equation is equal to :
7 ( w + 7 )³ = 7(6³)
Divide both the side of the equation by 7 we get,
⇒ 7 ( w + 7 )³ / 7 = 7(6³) /7
⇒( w + 7 )³ = (6³)
Take cube root both the side of the equation we get,
⇒∛( w + 7 )³ = ∛(6³)
⇒ w + 7 = 6
Now subtract 7 from both the side of the equation we get,
⇒w + 7 - 7 = 6 - 7
⇒ w = -1
Therefore, the value of the variable 'w' for the given equation is equal to w = -1.
The complete question is:
Solve this equation:
7 ( w + 7 )³ = 7(6³)
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How much of a premium do you pay for a steel house worth $190,000 with $49,000 worth of content in a suburban area?
A. $1258.70
B. $1372.70
C. $1589.90
D. $2304.70
Answers
Answer:
D. $2304.70
Step-by-step explanation:
a typical 2000 square foot house may cost anything from $200000 to $300000
Hope it helps!!!brainliest pls!!!!Step-by-step explanation:
How much of a premium do you pay for a steel house worth $190,000 with $49,000 worth of content in a suburban area?
B. $1372.70
Evaluate.
-|-7 + 3|
-4
4
-10
Answers
Answer: -4
Step-by-step explanation:
Place a negative in front
Solution: it would be -4
what is the distance between x=-2 and x=10
Answers
Answer:
12 prob
Step-by-step explanation:
Explanation: Look on a number line and count how many numbers it takes you to get to 10.
50 Points! Multiple choice algebra question. Photo attached. Which represents the correct synthetic division of (x^2-4x+7) divided by (x-2)? Thank you!
Answers
Option D is the correct synthetic division of (x^2-4x+7) divided by (x-2)
What is the synthetic division?Synthetic division is a shorthand procedure used to divide a polynomial by a linear factor of (x - a) form, in which "a" is constant. This method gives an expedient way to locate the quotient and remainder without carrying out long division.
x - 2 | x^2 - 4x + 7
x^2 - 2x
---------
-2x + 7
-2x + 4
-------
3
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Plz help!!
Write the equation that represents the graph shown.
Answers
.....................................
A family drives 509 miles to their vacation destination. It takes them 8.6 hours to get there. What was their average velocity in miles per hour?
Answers
Answer:
Their average velocity during their trip was 59.19 miles per hour.
Step-by-step explanation:
To calculate the average velocity of the family's trip, we divide the total distance traveled by the time it took to travel that distance:
Average velocity = total distance ÷ time
In this case, the total distance traveled is 509 miles and the time it took to travel that distance is 8.6 hours. So, we can plug these values into the formula:
Average velocity = 509 miles ÷ 8.6 hours
Simplifying this equation, we get:
Average velocity = 59.19 miles per hour (rounded to two decimal places)
Therefore, the family's average velocity during their trip was 59.19 miles per hour.
Solve for x.
8.x + 2
70°
60°
X =
Answers
Answer:
180
Step-by-step explanation: