Answer:
[tex]\large\boxed{a_n=5\left(\dfrac{1}{10}\right)^{n-1}}[/tex]
Step-by-step explanation:
Check:
[tex]n=1\\\\a_1=5\left(\dfrac{1}{10}\right)^{1-1}=5\left(\dfrac{1}{10}\right)^0=5(1)=5\qquad\bold{CORRECT}\ (1,\ 5)\\\\n=2\\\\a_2=5\left(\dfrac{1}{10}\right)^{2-1}=5\left(\dfrac{1}{10}\right)^1=5\left(\dfrac{1}{10}\right)=\dfrac{5}{10}=0.5\qquad\bold{CORRECT}\ (2,\ 0.5)\\\\n=3\\\\a_3=5\left(\dfrac{1}{10}\right)^{3-1}=5\left(\dfrac{1}{10}\right)^2=5\left(\dfrac{1}{100}\right)=\dfrac{5}{100}=0.05\qquad\bold{CORRECT}\ (3,\ 0.05)[/tex]
[tex]a_{n}[/tex] [tex]= 5 (\frac {1}{10} )^{n-1}[/tex]
Mathematical sequences are the set of numbers that makes a pattern or can be simple and complicated, finite and infinite. Explore sequences, terms in a sequence, and the different kinds of mathematical sequences, including the famous Fibonacci sequence.
Check:
n=1
[tex]a_{1} = 5 (\frac {1}{10} )^{1-1} = 5 (\frac {1}{10} )^{0} = 5 (1)=5[/tex] True (1,5)
n=2
[tex]a_{2} = 5 (\frac {1}{10} )^{2-1} = 5 (\frac {1}{10} )^{1} = 5 \frac{1}{10} = 0.5[/tex] True (2, 0.5)
n=3
[tex]a_{3} = 5 (\frac {1}{10} )^{3-1} = 5 (\frac {1}{10} )^{2} = 5 \frac{1}{100} = 0.05\\[/tex] True (3, 0.05)
sequence chart is a series of the events and actions set in the order in which they take place. this is considered to be a fantastic way to represent the necessary steps taken to reach to the outcome.
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Solve x 2 + 8x + 7 = 0 {-1, -7} {1, 7} {}
Answer:
Step-by-step explanation:
The y value has to be 0, so neither of those 2 answers look correct.
factor the quadratic
x^2 + 8x +7 = 0
(x + 7)(x + 1) = 0
x + 7 = 0
x = - 7
========
x + 1 = 0
x = - 1
========
The two points that solve this equation are
(-1,0)
(-7,0)
Answer:
The answer for the equation is {-1,-7}
Step-by-step explanation:
This is found by using the quadratic equation.
_____ are ______ midsegments of ΔWXY.
What is the perimeter of ΔWXY?
11.57 cm
12.22 cm
12.46 cm
14.50 cm
Answer:
The perimeter of Δ WXY is 14.50 cm ⇒ the last answer
Step-by-step explanation:
* Lets explain how to solve the problem
- There is a fact in any triangle; the segment joining the midpoints of
two side of a triangle is parallel to the 3rd side and half its length
* Lets use this fact to solve the problem
- In Δ WXY
∵ Q is the midpoint of WX
∵ R is the midpoint of XY
∵ S is the midpoint of YW
- By using the fact above
∴ QR = 1/2 WY
∴ RS = 1/2 WX
∴ SQ = 1/2 XY
- Lets calculate the length of the sides of Δ WXY
∵ QR = 1/2 WY
∵ QR = 2.93
∴ 2.93 = 1/2 WY ⇒ multiply both sides by 2
∴ WY = 5.86 cm
∵ RS = 1/2 WX
∵ RS = 2.04
∴ 2.04 = 1/2 WX ⇒ multiply both sides by 2
∴ WX = 4.08 cm
∵ SQ = 1/2 XY
∵ SQ = 2.28
∴ 2.28 = 1/2 XY ⇒ multiply both sides by 2
∴ XY = 4.56 cm
- Lets find the perimeter of Δ WXY
∵ The perimeter of Δ WXY = WX + XY + YW
∴ The perimeter of Δ WXY = 5.86 + 4.08 + 4.56 = 14.50
* The perimeter of Δ WXY is 14.50 cm
In this exercise we have to use the knowledge of the perimeter of a figure to calculate its value, and then:
Letter D
So from some information given in the statement and in the image, we can say that:
Q is the midpoint of WXR is the midpoint of XYS is the midpoint of YWSo solving, you will have to:
[tex]QR = 1/2 WY\\RS = 1/2 WX\\SQ = 1/2 XY[/tex]
Now with both information we can calculate the perimeter value as:
[tex]QR = 1/2 WY\\QR = 2.93\\2.93 = 1/2 WY\\ WY = 5.86 cm\\RS = 1/2 WX\\ RS = 2.04\\2.04 = 1/2 WX\\WX = 4.08 cm\\SQ = 1/2 XY\\SQ = 2.28\\2.28 = 1/2 XY \\XY = 4.56 cm\\ WXY = WX + XY + YW\\WXY = 5.86 + 4.08 + 4.56 = 14.50[/tex]
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What is the value of f (x)=16^x when x=1/2 ? A. 2 B. 4 C. 8 D. 32
Answer:
B
Step-by-step explanation:
Using the rule of exponents
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]
Given
f(x) = [tex]16^{x}[/tex], then when x = [tex]\frac{1}{2}[/tex]
f([tex]\frac{1}{2}[/tex] ) = [tex]16^{\frac{1}{2} }[/tex] = [tex]\sqrt[2]{16}[/tex] = 4
Last year you mowed grass and shoveled snow for 10 households. You earned $200 per household
mowing for the entire season and $180 per household shoveling for the entire season. You earn a total of
$1880 last year. Write and solve an algebraic model to determine the number of households you mow and
shovel for
Answer:
what ever it said above
Step-by-step explanation:
Find the slope and the y-intercept of the equation y-36x - 1) = 0
Answer:
the slope: m = 36the y-intercept: b = 1Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation
[tex]y-36x-1=0[/tex] add 36x and 1 to both sides
[tex]y-36x+36x-1+1=36x+1[/tex]
[tex]y=36x+1[/tex]
Therefore
the slope: m = 36
the y-intercept: b = 1
Average of 6 numbers is 4, if the average of 2 numbers is 2 what is the average of other 4
Answer:
5
Step-by-step explanation:
Let's just pretend the 6 numbers are: a,b,c,d,e,f.
Then (a+b+c+d+e+f)/6 =4 (given by first statement.)
Let's pretend the average of 2 numbers is 2 means they are talking about the a and b.
So (a+b)/2=2.
Now we want to find (c+d+e+f)/4 as requested by their question.
So first step multiply both sides of our first equation by 6 giving us:
a+b+c+d+e+f=24
So the second step multiply both sides of our second equation by 2 giving us:
a+b=4.
Now if a+b+c+d+e+f=24 and a+b=4, then c+d+e+f=20 since 20+4=24.
So the average of the four numbers c,d,e, and f is 20/4=5.
which of the two functions below has the smallest minimum y-value f(x)=4(x-6)^4+1 g(x)2x^3+28
Answer:
The function g(x) has smallest minimum y-value.
Step-by-step explanation:
The given functions are
[tex]f(x)=4(x-6)^4+1[/tex]
[tex]g(x)=2x^3+28[/tex]
The degree of f(x) is 4 and degree of g(x) is 3.
The value of any number with even power is always greater than 0.
[tex](x-6)^4\geq 0[/tex]
Multiply both sides by 4.
[tex]4(x-6)^4\geq 0[/tex]
Add 1 on both the sides.
[tex]4(x-6)^4+1\geq 0+1[/tex]
[tex]f(x)\geq 1[/tex]
The value of f(x) is always greater than 1, therefore the minimum value of f(x) is 1.
The minimum value of a 3 degree polynomial is -∞. So, the minimum value of g(x) is -∞.
Since -∞ < 1, therefore the function g(x) has smallest minimum y-value.
The function f(x)=4(x-6)^4+1 has the smallest minimum y-value as its minimum value can be directly located at y=1 while g(x)=2x^3+28, being a cubic function, continues infinitely in the negative direction.
Explanation:In this mathematical problem, we are tasked to determine which of the functions, f(x)=4(x-6)^4+1 or g(x)=2x^3+28, has the smallest minimum y-value. Each of these functions represent distinct types of polynomials which have different properties. The function f(x) is a quartic function that is even, or symmetric around the y-axis, while g(x) is a cubic function.
The minimum value of f(x) can be determined directly by setting the expression (x - 6)^4 to 0, yielding the minimum value 1 because any real number to the power of 4 is always non-negative and the smallest non-negative number is 0. For cubic functions like g(x), they do not have absolute minimum or maximum. They go from negative to positive infinity as x ranges over all real numbers. Therefore, the function f(x)=4(x-6)^4+1 has a smaller minimum y-value.
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What is the equation of the line (in slope-intercept form) that passes through the point (5,−1) and is parallel to the line y=2x−7
Answer:
y = 2x - 11Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\==========================[/tex]
[tex]\text{We have the equation of a line:}\ y=2x-7\to m_1=2.\\\\\text{The slope of a parallel line:}\ m_2=m_1=2.\\\\\text{We have the equation:}\\\\y=2x+b\\\\\text{Put the coordinates of the point (5, -1) o the equation:}\\\\-1=2(5)+b\\-1=10+b\qquad\tex\text{subtract 10 from both sides}\\-11=b\to b=-11\\\\\text{Finally:}\\\\y=2x-11[/tex]
how do you rewrite the equation V=1/3s^2h in terms of s
[tex]\bf V=\cfrac{1}{3}s^2h\implies V=\cfrac{s^2h}{3}\implies 3V=s^2 h\implies \cfrac{3V}{h}=s^2\implies \sqrt{\cfrac{3V}{h}}=s[/tex]
Answer:
s = sqrt(3V/h)
Step-by-step explanation:
To put this in terms of s, we must first isolate the s^2. So we can multiply by 3/h on both sides. So we get s^2 = 3V/h. Taking the square roots of both sides, we get s = sqrt(3V/h).
which of the following are necessary when proving that the diagonals of a rectangle are congruent check all that apply
Answer:
Opposite sides are congruent; All right angles are congruent
Step-by-step explanation:
Henry buys a large boat for the summer, however he cannot pay the full amount of $32,000 at
once. He puts a down payment of $14,000 for the boat and receives a loan for the rest of the
payment of the boat. The loan has an interest rate of 5.5% and is to be paid out over 4 years.
What is Henry’s monthly payment, and how much does he end up paying for the boat overall?
Answer:
Monthly Payment = $457.5
Total amount Henry end up paying for the boat overall = $35,960
Step-by-step explanation:
Total Amount to be paid = $32,000
Down Payment = $ 14,000
Interest rate = 5.5%
Total time for Amount to be paid = 4 years
Rest of the payment to be paid = 32,000 - 14,000
= 18000
Amount of interest = P*r*t
P= Principal Amount
r = rate
t = time
Putting values
Amount of interest= 0.055 *18000*4 = 3960
Total Remaining payment = 18000+3960 = 21,960
As Payment to be paid in 4 years, So number of months = 4*12 = 48 months
Monthly payment = Total Payment / Months = 21,960/48 = 457.5
So, Monthly Payment = $457.5
Total amount Henry end up paying for the boat overall = Down Payment + Remaining Payment
=14,000+21960
= 35960
So, Total amount Henry end up paying for the boat overall = $35,960
2sqrt 27 + sqrt12 - 3 sqrt 3 -2 sqrt 12 what is the simplified form of the following expression
Simplified form of expression is,
⇒ - 3√3
We have to given that,
An expression is,
⇒ 2√27 + √12 - 3√3 - 2√12
We can simplify it as,
⇒ 2√27 + √12 - 3√3 - 2√12
⇒ 2 √9×3 + √3×4 - 3√3 - 2√3×4
⇒ 2 × 3 √3 - 2√3 - 3√3 - 2 × 2√3
⇒ 6√3 - 2√3 - 3√3 - 4√3
⇒ - 3√3
Therefore, Simplified form of expression is,
⇒ - 3√3
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Final answer:
The expression simplifies to 4sqrt(3) after breaking down the square roots of 27 and 12 into 3√(3) and 2√(3), respectively, and combining like terms.
Explanation:
To simplify the expression 2√(27) + √(12) - 3√(3) - 2√(12), we should first simplify √(27) and √(12) individually.
Square root of 27 can be written as √(9*3). Since 9 is a perfect square, we get 3√(3). Similarly, √(12) can be simplified to √(4*3). As 4 is a perfect square, this simplifies to 2√(3).
Now, substituting back into the original expression, we get 2(3√(3)) + 2√(3) - 3√(3) - 2(2√(3)), which simplifies to 6√(3) + 2√(3) - 3√(3) - 4√(3).
Combining like terms, we obtain 6√(3) - 2√(3), which simplifies further to 4√(3).
Therefore, the simplified form of the original expression is 4√(3).
Using the horizontal line test, which of the following can be concluded about
the inverse of the graph of the function below?
A horizontal line test on the inverse of a function yields the same results as a vertical line test on the function itself, and the conclusion is the same as in paragraph two.
A vertical line test looks for one or more intersections with a specified set of relations. We can conclude that the relation is a function if there is only one intersection with the relation at ANY point in its domain. If a VERTICAL line intersects the function several times, it is not a function.
Here, we see that the vertical line test on the depicted relation produces just one intersection at any point in the domain of the relation, hence we infer that the graph depicts a function.
A function's inverse is a reflection of the function about the y=x line. The outcome is the same as swapping the x and y axes.
As a result, a horizontal line test on the inverse of a function yields the same results as a vertical line test on the function itself, and the conclusion is the same as in paragraph two.
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What are the solutions of the equation (x + 2)2 + 12(x + 2) - 14 = 0? Use u substitution and the quadratic formula to solve
x=-8+55
x--653
X=-45_2
x = -2+52
Answer:
[tex]\large\boxed{x=-8\pm5\sqrt2}[/tex]
Step-by-step explanation:
[tex](x-2)^2+12(x+2)-14=0\\\\\text{Substitute}\ (x+2)=t:\\\\t^2+12t-14=0\qquad\text{add 14 to both sides}\\\\t^2+2(t)(6)=14\qquad\text{add}\ 6^2=36\ \text{to both sides}\\\\\underbrace{t^2+2(t)(6)+6^2}=14+36\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(t+6)^2=50\Rightarrow t+6=\pm\sqrt{50}\qquad\text{subtract 6 from both sides}\\\\t=-6\pm\sqrt{25\cdot2}\\\\t=-6\pm5\sqrt2[/tex]
[tex]\text{we're going back to substitution}\\\\x+2=-6\pm5\sqrt2\qquad\text{subtract 2 from both sides}\\\\x=-8\pm5\sqrt2[/tex]
BRAINLIST HELP PLEASE
Answer:
B 3 ^ (1/9)
Step-by-step explanation:
We know that a^b^c = a ^ (b*c)
3 ^ (2/3)^1/6
3^ (2/3*1/6)
3^ (2/18)
3^(1/9)
two numbers are in the ratio of 4:11. their sum is 60. What is the greater of those two numbers?
Answer:
The numbers are 44 (greater) and 16 ( smaler)
Step-by-step explanation:
4x+11x =60
15x = 60
x=4
4*4=16
11*4=44
44+16 = 60
4/11 =0.363636......
16/44= 0.363636......
Kareem walks 6 blocks east and 2 blocks north to school. After school, he walks 3 blocks west and 3 blocks north to the library. Now how many blocks is he far from his home?
Answer:
Yep your correct, 3 east 5 north.
Step-by-step explanation:
He first walks 6 east and 2 north
He then walks 3 west and 3 north
East and west are opposites so 6-3=3 east (not west because he walked more blocks east than west)
North and north are the same so 2+3=5 north
PLEASE GIVE BRAINLIEST
False rational statement?
A. Every rational number is also an integer
B. No rational number is irrational
C. Every irrational number is also real
D. Every integer is also a rational number
Answer:
D. Every integer is also a rational number
Step-by-step explanation:
Every integer is also a rational number would be FALSE about a rational statement.
If the equation of a circle is (x + 5)2 + (y - 7)2 = 36, its center point is
A(5.7)
B(-5,7)
C(5-7)
the correct answer is B) (-5, 7), which represents the center point of the circle.
The equation of a circle in standard form is given by:
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
Where:
- (h, k) is the center of the circle
- r is the radius of the circle
Comparing this standard form to the given equation [tex]\( (x + 5)^2 + (y - 7)^2 = 36 \)[/tex], we can identify the center and radius of the circle.
For the given equation:
- Center of the circle: (-5, 7) because the term [tex]\( (x + 5)^2 \)[/tex] means the x-coordinate of the center is -5, and the term [tex]\( (y - 7)^2 \)[/tex]means the y-coordinate of the center is 7.
- Radius of the circle: [tex]\( r = \sqrt{36} = 6 \)[/tex] because the equation is already in the form [tex]\( r^2 = 36 \), so \( r = 6 \).[/tex]
So, the correct answer is B) (-5, 7), which represents the center point of the circle.
A baseball diamond is actually a square with sides of 90 feet. If a runner tries to steal second base how far must the catcher at home plate throw to get the runner out given this information explain why runners more often try to steal second base than third
Answer:
126.5 ft
Step-by-step explanation:
It's further for the catcher to throw to
The catcher must throw approximately 127.3 feet to get a runner out at second base on a square baseball diamond. The Pythagorean theorem is used to calculate the diagonal from home plate to second base. Runners often try to steal second base due to the longer throw required and being in scoring position.
Explanation:The question involves calculating the distance a catcher must throw the ball to get a runner out at second base on a baseball diamond, which is a square with sides of 90 feet. To find this distance, we must determine the diagonal of the square, as the catcher throws the ball from one corner (home plate) to the opposite corner (second base). Applying the Pythagorean theorem to the square, the diagonal distance D is given by D = √(90² + 90²). So, D = √(8100 + 8100) = √16200 feet, which approximately equals 127.3 feet. Runners are inclined to steal second base more often because it is generally easier to steal with the catcher having to make a longer throw, and once on second base, the runner is in scoring position with two bases potentially available to advance.
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is x^2 = 55 irrational or rational
Answer
I think its Rational
Step-by-step explanation:
Answer:
Irrational
Step-by-step explanation:
A rational number can be expressed in the form
[tex]\frac{a}{b}[/tex] where a and b are integers
Given
x² = 55 ( take the square root of both sides )
x = ± [tex]\sqrt{55}[/tex] ← irrational
[tex]\sqrt{55}[/tex] cannot be expressed as a rational number
the radius of the Outer Circle is 2x cm and the radius of the inside circle is 6 cm the area of the Shaded region is 288 Pi centimeters squared. What is the value of x
For this case we have that by definition, the area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
r: It is the radius of the circle.
So, we have that the area of the shaded region is given by:
[tex]\pi * (2x) ^ 2- \pi * 6 ^ 2 = 288 \pi\\4x ^ 2-36 = 288\\4x ^ 2 = 288 + 36\\4x ^ 2 = 324[/tex]
We divide between 4 on both sides of the equation:
[tex]x ^ 2 = 81[/tex]
We apply root to both sides:
[tex]x = \pm \sqrt {81}[/tex]
We choose the positive value of the root:
[tex]x = \sqrt {81}\\x = 9[/tex]
Finally, the value of "x" is 9
Answer:
[tex]x = 9[/tex]
The vertices of a quadrilateral in the coordinate plans are known. How can the perimeter of the figure be found?
Answer:
The perimeter can be found by calculating lengths of sides using distance formula and then adding up the lengths
Step-by-step explanation:
If the vertices of a quadrilateral are known in the coordinate plane, the vertices can be used to determine the lengths of sides of quadrilateral. The distance formula is used for calculating the distance between two vertices which is the length of the side
[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
after calculating all the lengths of four sides using their vertices, they can be summed up to find the perimeter ..
3. Find all the zeroes of the polynomial x4 + 2x3 - 8x2 - 18x - 9, if two of its zeroes are 3
and -3.
Answer:
2b2t
Step-by-step explanation:
2b2t
Answer:
x = 3, x = - 3, x = - 1 with multiplicity 2
Step-by-step explanation:
Given that x = 3 and x = - 3 are zeros then
(x - 3) and (x + 3) are factors and
(x - 3)(x + 3) = x² - 9 ← is a factor
Using long division to divide the polynomial by x² - 9 gives
quotient = x² + 2x + 1 = (x + 1)² and equating to zero
(x + 1)² = 0 ⇒ x + 1 = 0 ⇒ x = - 1 with multiplicity 2
Hence the zeros of the polynomial are
x = 3, x = - 3, x = - 1 with multiplicity 2
Simplify the following expression.
x4 + 3x2 - 2x* -5x2 - x + x2 + x +1+7x4
Answer: 8x^4+x^3-4x^2+1
Step-by-step explanation:
To simplify this polynomial expression, we first combine like terms. The simplified expression will be 8x^4 - x + 1.
Explanation:The expression provided in your question is a polynomial that contains terms with variables raised to different powers. In simplifying this kind of polynomial, you first need to combine like terms, which are those terms that have the same variable and the same exponent.
Therefore, let's organize and combine like terms: x4 - 2x + x and 3x2 - 5x2 + x2 and . As a result, we get 8x4, or 8x to the power of 4, -x, and 1. Thus, the final simplified expression is: 8x4 - x + 1
Hope this helps in your understanding of simplifying polynomials!
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Find the values for m and n that would make the following equation true.
(7z^m) (nz^3) = -14z^7
m= ?
n= ?
Answer:
m=4
n=-2
Step-by-step explanation:
(7z^m) (nz^3) = -14z^7
7*n z^(m+3) = -14 z^7
We know the constants have to be the same
7n = -14
Divide each side by 7
7n/7 = -14/7
n = -2
And the exponents have to be the same
m+3 = 7
Subtract 3 from each side
m+3-3 = 7-3
m =4
The values that satisfy the equation (7z^m) (nz^3) = -14z^7 are m = 4 and n = -2, found by equating coefficients and exponents.
Explanation:To find the values for m and n that would make the given equation true, we need to equate the coefficients and the exponents of the similar terms on both sides of the equation. The original equation is (7zm) (nz3) = -14z7.
First, let's look at the coefficients: 7 * n should equal -14. This gives us the value of n directly, n = -2.
Now, let's look at the exponents of z. To equate the exponents, we use the property that when multiplying similar bases, the exponents are added: m + 3 equals 7. Solving for m gives us m = 4.
Therefore, the values that satisfy the equation are m = 4 and n = -2.
A cylindrial hole is cut through the cylinder below.
below. The larger Cylinder has a diameter of 14 mm and a height of 25 mm. If the diameter of the hole is 10 mm, find the volume of the solid.
Answer:
V=1884 Cubic mm
Step-by-step explanation:
We know that the volume of the Sphere is given by the formula
[tex]V= \pi r^2h[/tex]
Where r is the radius and h is the height of the cylinder
We are asked to determine the radius of the hollow cylinder , which will be the difference of the solid cylinder and the cylinder being carved out.
[tex]V=V_1-V_2[/tex]
[tex]V=\pi r_1^2 \times h-\pi r_2^2 \times h[/tex]
[tex]V=\pi \times h \times (r_1^2-r_2^2)[/tex]
Where
[tex]V_1[/tex] is the the volume of solid cylinder with radius [tex]r_1[/tex] and height h
[tex]V_2[/tex] is the volume of the cylinder being carved out with radius [tex]r_2[/tex] and height h
where
[tex]r_1 = 7[/tex] mm ( Half of the bigger diameter )
[tex]r_2 = 5[/tex] mm ( Half of the inner diameter )
[tex]h=25[/tex] mm
Putting these values in the formula for V we get
[tex]V=\pi \times 25\times (7^2-5^2)[/tex]
[tex]V=3.14 \times 25 \times(49-25)[/tex]
[tex]V=3.14 \times 25 \times 24[/tex]
[tex]V= 1884[/tex]
The graph represents function 1, and the equation represents function 2:
Function 2
y = 8x + 12
How much more is the rate of change of function 2 than the rate of change of function 1?
3
If there was a graphical representation, I would be happy to assist you.
Martin builds a right square pyramid using
straws. A diagram of the pyramid and its net
are shown.
What is the surface area of the pyramid?
Enter the answer in the box.
Answer:
360 ft^2
Step-by-step explanation:
The surface area of a right square pyramid can be found using the formula: [tex]a^2+2a\sqrt{\frac{a^2}{4}+h^2}[/tex]
In this formula:
a = base edge (the length of the sides of the square)h = height of the pyramidIn this diagram, the base edge length is 10 ft and the height of the square pyramid is 12 ft. Substitute these values into the formula to find the surface area.
[tex]a^2+2a\sqrt{\frac{a^2}{4}+h^2}[/tex][tex](10)^2+2(10)\sqrt{\frac{(10)^2}{4}+(12)^2[/tex]Simplify this expression. Start by evaluating the exponents then rewrite the expression.
[tex](100)+2(10)\sqrt{\frac{(100)}{4}+(144)[/tex]Now evaluate inside the radical sign.
[tex](100)+2(10)\sqrt{(25)+(144)[/tex][tex](100)+2(10)\sqrt{169[/tex]Multiply 2 and 10 together (we're following the rules of PEMDAS).
[tex](100)+(20)\sqrt{169[/tex]Find the square root of 169 then multiply that by 20.
[tex](100)+(20)(13)[/tex][tex](100)+(260)[/tex]Finish the problem by adding 100 and 260 together.
[tex]100 +260=360[/tex]The surface area of the pyramid is [tex]\boxed{\text {360 ft}^2}[/tex].
What is the x-intercept of the line with the equation y= 1/2 x-3
Answer:
The x intercept is 6
Step-by-step explanation:
To find the x intercept, set y =0 and solve for x
y= 1/2 x-3
0 = 1/2x -3
Add 3 to each side
0+3 = 1/2 x-3+3
3 =1/2x
Multiply each side by 2
2*3 =1/2x*2
6 =x
The x intercept is 6