1. The function f(x) = –0.05(x2 – 26x – 120) represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent? (1 point)
2. What do the zeros of this function represent? Remember the zeros are where f(x) = 0. (1 point)
3. Will the zeros tell you where the net should be placed? Why or why not? (1 point)
4. To find the zeros, set the function equal to 0, and then factor the polynomial. Start by setting the function equal to 0. (1 point)
Factor the polynomial.
The polynomial (x2 – 26x – 120) is in the form x2 + bx + c which can be factored as (x + p)(x + q) .
5. Next factor the polynomial x2 – 26x – 120. To identify the factors, complete the table: Note: This table does not contain all the factors of –120, but it has enough to let you factor the polynomial. (2 points: 0.5 points for each row)
p q p + q
10 –12
–10 12
30 –4
4 –30
6. Which values of p and q give the correct factors? (1 point)
7. Factor the polynomial completely: (2 points: 1 point for each factor)
0 = –0.05(x2 – 26x – 120)
8. Find the roots of the equation by setting each factor equal to 0 and solving for x.
Hint: There are three factors, but the constant factor, –0.05, does not equal zero. Solve for x with the other two factors. (2 points: 1 point for each factor)
9. Identify the roots. (2 points: 1 point for each root)
10. What are the zeros of this function? Circle them on the graph. (1 point)
11. Are these zeros the same as the roots you found? (1 point)
12. What does a negative zero mean in terms of this problem? (1 point)
13. Following this trajectory, will Nik hit a net that is 30 feet from the cannon? How do you know? (1 point)
Answers
f(x) represents the distance of the cannon from the ground
Question 2
When f(x) = 0, there will two values of 'x'. The point on the positive x-axis where the graph crosses represent the point where the cannon hits the ground.
Question 3
Yes, it would. By knowing the spot where the cannon will hit the ground, we can set the net at the spot.
Question 4
f(x) = 0
-0.05 (x² - 26x -120) = 0
x² - 26x - 120 = 0
Question 5
Please refer to the table attached below
Question 6
The value of p and q that gives the correct factors are -30 and 4 since it gives p+q = -26
Question 7
Factorising the equation completely
-0.05 (x² - 26x - 120) = 0
-0.05 (x+4) (x-30) = 0
(x+4) (x-30) = 0
Question 8
Solving the equation
x+4 = 0 and x-30=0
x=-4 and x=30
Question 9
The roots of the equation is x = -4 and x = 30
Question 10
Please refer to the third graph
Question 11
Yes
Question 12
The negative zero means the initial distance of the cannon, where it was fired from
Question 13
The distance between x = -4 and x = 30 is 34 units. If the cannon was fired from the point when x = -4, the cannon will hit the ground again 34 units from the point it was fired from. If Nik put a net 30 units from the firing point, the cannon will fly pass it.
The motion of the projectile (cannonball), given by the (quadratic)
polynomial function is the path of a parabola.
Response:
Vertical heightThe point the projectile is at ground levelYes, because is it where the projectile will landx² - 26·x - 120 = 0(x - 30)·(x + 4) = x² - 26·x - 120 p = -30, and q = 4-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4) x - 30 = 0 and x + 4 = 0 Which gives; x = 30 or x = -4x = 30 or x = -4The zeros of the function are x = 30, and x = -4YesThe negative zero (x = -4) means that the ground level is a point before the location at which the cannonball is launched (x = 0). It also means that the cannonball was launched above ground level.Yes, because the projectile hits the ground 30 feet from the cannonWhich methods can be used to evaluate the polynomial?1. f(x) is the output of the projectile function, where;
x = The input which is the distance
Therefore;
f(x) = The vertical distance (height) of the cannonball at point x.2. The zeros are the points where the height, f(x) = 0
Therefore;
The zeros represent the points at which the cannonball is at ground level3. The net should be placed where the cannonball is expected to reach ground level.
Therefore;
The zeros indicates where the net should be placed4. The given polynomial can be equated to 0 as follows;
x² - 26·x - 120 = 0
5. x² - 26·x - 120 = x² - 30·x + 4·x- 120
Which gives;
x·(x - 30) + 4·(x- 30) = (x - 30)·(x + 4)
(x - 30)·(x + 4) = x² - 26·x - 1206. Where; (x + p)·(x + q) = a·x² + b·x + c
We have;
The values of p and q that give the correct factors are;
p = -30, and q = 47. The polynomial, -0.05·(x² - 26·x - 120) = 0 in factored form is therefore;
-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4)8. From the factors, we have;
-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4)
The roots of the equations, are given as follows;
x - 30 = 0 and x + 4 = 0
Which gives;
x = 30 or x = -49. The roots of the equation are therefore;
x = 30, and x = -410. The zeros for the function, are the values of x at which f(x) = 0
At x = 30 f(30) = -0.05 × (30² - 26 × 30 - 120) = 0
At x = -4, f(-4) = -0.05 × ((-4)² - 26 × (-4) - 120) = 0
The zeros of the function are x = 30, and x = -411. Yes. The zeros are the same as the roots found given that at the roots, f(x) = 0
12. The zeros of the function are x = 30 and x = -4, which are points at
which the projectile (cannonball) is at ground level. The negative zero, x
= -4, means that, apart from the point x = 30, the projectile can (also/only)
be at ground level at a point before the location where the projectile is
launched, (-4) which means that at the point at which the cannonball is
launched, which is at x = 0, the cannonball was not on the ground, but
at the lip of the barrel or at a more elevated position.
What the negative zero means are therefore;
It is a location before the point where the cannonball is launchedThe cannonball is launched from a height above ground level13. At 30 feet, x = 30, which is a zero of the function, and the cannonball
is at ground level, such that a net placed at 30 feet from the cannon
will be hit by the cannonball.
Therefore;
Yes Nik will hit a net that is 30 feet from the cannonLearn more about quadratic functions and projectiles here:
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Related Questions
What are the values of a1 and r of the geometric series?
2 – 2 + 2 – 2 + 2
Answers
Answer: For the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]
Step-by-step explanation: We are given to find the values of [tex]a_1[/tex] and [tex]r[/tex] of the following geometric series:
[tex]2-2+2-2+2-~.~.~..[/tex]
We know that
[tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio of the given geometric series.
We can see that the first term of the given geometric series is 2.
So. we must have
[tex]a_1=2.[/tex]
Also, common ratio is found by dividing a term by its preceding term.
Therefore, the common ratio [tex]r[/tex] of the given geometric series is
[tex]r=\dfrac{-2}{2}=\dfrac{2}{-2}=~.~.~.~=-1.[/tex]
Thus, for the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]
The rounding rule for the correlation coefficient requires three decimal places true or false
Answers
Answer:
Round the value of r to three decimal places.
Step-by-step explanation:
The rounding rule for the correlation coefficient requires three decimal places
this statement is true.
The correlation coefficient in statistics is a parameter which measures the degree of strength of relation between two variables .
Its value lies between -1 to +1 .
The closer the correlation coefficient will be near to 1 the stronger the correlation will be.
The correlation between two variables can be positive or negative
Correlation coefficients are helpful in determining the functional relationships among the variables
So higher magnitude of correlation coefficients lead to accurate functional relation among variables.
The rounding rule for the correlation coefficient requires three decimal places
this statement is true.
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The infinite sequence –1, –2, –3, –4, –5, ... can be generated with which explicit formula?
Answers
Answer:
An = (-1)* n
Step-by-step explanation:
An = ( -1) * n
A2 = (-1 ) * 2 = -2
A3= ( -1 ) * 3 = -3
A4= ( -1 ) * 4 = -4
A5= ( -1 ) * 5 = -5
An explicit formula also known as an exact formula is a mathematical formula used to find the nth term in a series or sequence . hence the explicit formula used to find the nth term of this sequence can be represented as
An = ( -1 ) * n where n = number of the next term
Answer:
A
Step-by-step explanation:
i got it right
If sin θ = 2 over 7 and tan θ > 0, what is the value of cos θ?
Answers
[tex]\bf sin(\theta )=\cfrac{2}{7}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}\qquad \textit{let's find the adjacent side} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{7^2-2^2}=a\implies \pm\sqrt{45}=a\implies \pm 3\sqrt{5}=a[/tex]
but.... which is it? the + or the -? well, we know that tan(θ) > 0, is another way to say that the tangent of the angle is positive, now, for the tangent to be positive, since it's opposite/adjacent both opposite and adjacent have to be the same exact sign, now, we know the opposite is +2, so that means the adjacent has to be the same sign, thus is the positive version 3√(5)
thus [tex]\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad \qquad cos(\theta )=\cfrac{3\sqrt{5}}{7}[/tex]
Which of the following is not one of the three ways to express a ratio A 3/4 B 3:4 C 3 of 4 D 3 to 4
Answers
A population of flies grows according to the function p(x) = 2(4)x, where x is measured in weeks. A local spider has set up shop and consumes flies according to the function s(x) = 2x + 5. What is the population of flies after two weeks with the introduced spider?
Answers
now, after two weeks, x = 2
[tex]\bf P(x)-s(x)\implies 2(4)^2-[2(2)+5]\implies 32-9[/tex]
Answer:
answer is 23
Step-by-step explanation:
If a new car is valued at $13,200 and 6 years later it is valued at $3000, then what is the average rate of change of its value during those six years?
Answers
Which are the roots of the quadratic function f(q) = q2 – 125? Check all that apply. q = 5 q = –5 q = 3 q = –3 q = 25 q = –25
Answers
Answer:
q=5 sqrt 5 and q=-5 sqrt 5
Step-by-step explanation:
got it right on edge :)
The roots of the quadratic function f(q) = q^2 − 125 are q = -5 and q = 5. Other options listed do not satisfy the function. The roots are found by factoring the equation as a difference of squares.
Explanation:The roots of the quadratic function f(q) = q2 − 125 can be found by solving the equation q2 − 125 = 0. To find the roots, we need to factor the quadratic or use the square root property since the equation is already set to zero.
We can see that this is a difference of squares equation, so it factors to (q + 5)(q - 5) = 0. Setting each factor equal to zero gives us q = -5 and q = 5.
So, the roots of the quadratic function are q = -5 and q = 5. The other options given (q = 3, q = -3, q = 25, q = -25) do not satisfy the equation f(q) = q2 − 125 = 0, hence they are not roots of this function.
Let g(x) = x - 3 and h(x) = x2 + 6. What is (h o g)(1)?
Answers
Paula has 3 bananas. She wants to divide each of them into sections. How many 's are there in 3 bananas?
Answers
Answer:
B IS 21
Step-by-step explanation:
Evaluate the surface integral. ∫∫s (x2 + y2 + z2) ds s is the part of the cylinder x2 + y2 = 16 that lies between the planes z = 0 and z = 5, together with its top and bottom disks.
Answers
[tex]\mathbf r_1(u,v)=\begin{cases}x(u,v)=4\cos u\\y(u,v)=4\sin u\\z(u,v)=v\end{cases}[/tex]
where [tex]0\le u\le2\pi[/tex] and [tex]0\le v\le5[/tex],
[tex]\mathbf r_2(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=0\end{cases}[/tex]
where [tex]0\le u\le4[/tex] and [tex]0\le v\le2\pi[/tex], and
[tex]\mathbf r_3(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=5\end{cases}[/tex]
where [tex]0\le u\le4[/tex] and [tex]0\le v\le2\pi[/tex].
For the cylinder, we have
[tex]\dfrac{\partial\mathbf r_1}{\partial u}\times\dfrac{\partial\mathbf r_1}{\partial v}=\langle4\cos u,4\sin u,0\rangle\implies\left\|\dfrac{\partial\mathbf r_1}{\partial u}\times\dfrac{\partial\mathbf r_1}{\partial v}\right\|=4[/tex]
and the integral over this surface is
[tex]\displaystyle\iint_{\text{cyl}}(x^2+y^2+z^2)\,\mathrm dS=4\int_{v=0}^{v=5}\int_{u=0}^{u=2\pi}((4\cos u)^2+(4\sin u)^2+v^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle320\int_{u=0}^{u=2\pi}\mathrm du+8\pi\int_{v=0}^{v=5}v^2\,\mathrm dv[/tex]
[tex]=640\pi+\dfrac83\pi(125)[/tex]
[tex]=\dfrac{2920\pi}3[/tex]
Bottom disk:
[tex]\dfrac{\partial\mathbf r_2}{\partial u}\times\dfrac{\partial\mathbf r_2}{\partial v}=\langle0,0,u\rangle\implies\left\|\dfrac{\partial\mathbf r_2}{\partial u}\times\dfrac{\partial\mathbf r_2}{\partial v}\right\|=u[/tex]
and the integral over the bottom disk is
[tex]\displaystyle\iint_{z=0}(x^2+y^2+z^2)\,\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=4}u((u\cos v)^2+(u\sin v)^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle2\pi\int_{u=0}^{u=4}u^3\,\mathrm du[/tex]
[tex]=128\pi[/tex]
The setup for the integral along the top disk is similar to that for the bottom disk, except that [tex]z=5[/tex]:
[tex]\displaystyle\iint_{z=5}(x^2+y^2+z^2)\,\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=4}u((u\cos v)^2+(u\sin v)^2+5^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle2\pi\int_{u=0}^{u=4}(u^3+25u)\,\mathrm du[/tex]
[tex]=528\pi[/tex]
Finally, the value of the integral over the entire surface is the sum of the integrals over the component surfaces:
[tex]\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\frac{2920\pi}3+128\pi+528\pi=\dfrac{4888\pi}3[/tex]
Evaluate the given surface integral by parameterizing the surface and computing the integral on each surface separately. Take the antiderivatives of both dimensions defining the area, from the bounds of the integral for an accurate solution.
Explanation:The problem you've presented is a surface integral in the field of calculus, specifically relating to multivariable calculus. To solve this, we need to evaluate the integral over the specified parts of the cylinder and the top and bottom disks. We start by parameterizing the surface. Given that our cylinder is x² + y² = 16 between z = 0 and z = 5, we can use cylindrical coordinates with the parameterization: r(θ, z) = <4cos(θ), 4sin(θ), z> for 0 ≤ θ ≤ 2π and 0 ≤ z ≤ 5. With this parameterization, you can derive the equation for the surface integral and solve it.
When working with surface integrals, it's essential to remember that you are totaling up the quantity across the entire surface of an object. In such a situation, we could handle this problem by separating it into three parts: the side of the cylinder, the top disk, and the bottom disk, and compute the integral on each surface separately.
The integral can be solved by taking the antiderivatives of both dimensions defining the area, with the edges of the surface in question being the bounds of the integral. You can apply this approach to all the separate parts of this question.
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Simplify: 4x^2+36/4x•1/5x
Answers
Answer:
Step-by-step explanation:
The given equation is:
[tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex]
On solving the above equation, we get
=[tex]\frac{4x^2+36}{(4x)(5x)}[/tex]
=[tex]\frac{4(x^2+9)}{(4x)(5x)}[/tex]
=[tex]\frac{x^2+9}{(x)(5x)}[/tex]
=[tex]\frac{x^2+9}{(5x^2)}[/tex]
which is the required simplified form.
Thus, the simplified form of the given equation [tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex] is [tex]\frac{x^2+9}{(5x^2)}[/tex].
A deposit of $1,295 at 7% for 180 days what is the interest earned
Answers
To find the simple interest on a deposit of $1,295 at a 7% rate for 180 days, we use the formula I = P × r × t. With 180 days being roughly 0.5 years, the interest earned is approximately $45.33.
Explanation:Calculating Simple Interest for a Deposit
To calculate the simple interest earned on a deposit, we can use the simple interest formula which is Interest (I) = Principal (P) × Rate (r) × Time (t).
In this case, a student wants to know the interest earned on a deposit of $1,295 at 7% for 180 days. Since simple interest is usually calculated on an annual basis, we need to adjust the time to reflect a portion of the year. 180 days is equivalent to ½ year (since 180/365 ≈ 0.493). Now we can plug in the values into the formula:
I = P × r × t
I = $1,295 × 0.07 × 0.5
So, the interest earned would be:
I = $1,295 × 0.07 × 0.5I = $45.325
The student will earn approximately $45.33 in interest (rounded to the nearest cent).
Complete the pattern ___, ___, ___, 0, 2, 4, 6
Answers
Answer:-6, -4, -2, 0, 2, 4, 6. They continue in increments of +2.
Step-by-step explanation:
The law of cosines is a2+b2 - 2abcosC = c^2 find the value of 2abcosC .... A. 40 B. -40 C. 37 D. 20
(The sides are 2,4, and 5; A to B is 2, B to C is 4, and A to C is 5.)
Answers
Аngle C lies opposite to the side AB, so "c" in the formula it is AB in your triangle
4² + 5² - 2abcosC = 2²
16 + 25 - 2abcosC = 4
41 - 4 = 2abcosC
2abcosC = 37
Given the Law of Cosines, the value of 2abcosC after plugging in the values of a, b, and c is: [tex]\mathbf{2abcosC = 37}[/tex]
Law of Cosines is given as: [tex]a^2+b^2 - 2abcosC = c^2[/tex]
Given also are the sides of a triangle:
a = 4 (side B to C)b = 5 (side A to C)c = 2 (side A to B)Plug in the values into the Law of Cosines, [tex]a^2+b^2 - 2abcosC = c^2[/tex] to find [tex]\mathbf{2abcosC}[/tex]
Thus:[tex]4^2+5^2 - 2abcosC = 2^2\\\\16 + 25 - 2abcosC = 4\\\\41 - 2abcosC = 4[/tex]
Subtract 41 from both sides[tex]41 - 2abcosC - 41 = 4-41\\\\-2abcosC = -37[/tex]
Divide both sides by -1[tex]\mathbf{2abcosC = 37}[/tex]
Therefore, given the Law of Cosines, the value of 2abcosC after plugging in the values of a, b, and c is: [tex]\mathbf{2abcosC = 37}[/tex]
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which expression is equivalent to (4h^7k^2)^4?
A: 16h^11k^6
B: 16h^28k^8
C; 256h^11k^6
D: 256h^28k^8
Answers
The answer is D.
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
[tex](4h^7k^2)^4[/tex]
We need to simplify this :
Here we go:
We will apply :
[tex](a^m)^n=a^{mn}[/tex]
[tex](4h^7k^2)^4\\\\=4^4\times (h^7)^4\times (k^2)^4\\\\=256h^{28}k^8[/tex]
Hence, option 'D' is correct.
Write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (a) x4 + 5 / x5 + 2x3
Answers
Factor 2x^2-128 completely
Answers
2(x² - 64), but (x² - 64) = x² - 8² (difference of 2 squares),[a²-b²=(a-b)(a+b)]
2(x² - 64) = 2(x² - 8²) = 2(x-8)(x+8)
Andrew estimated the weight of his dog to be 60 lb. The dog’s actual weight was 68 lb. What was the percent error in Andrew’s estimate? Round your answer to the nearest tenth of a percent. __________ %
Answers
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 68&100\\ 8&x \end{array}\implies \cfrac{68}{8}=\cfrac{100}{x}[/tex]
Which measure of variability is the most appropriate for this set of values?
13, 42, 104, 36, 28, 6, 17
Answers
Answer:
in other words that guy said E
Step-by-step explanation:
Lily is standing at horizontal ground level with the base of the Sears Tower. The angle formed by the ground and the line segment from her position to the top of the building is 15.7°. The Sears Tower is 1450 feet tall. Find Lily's distance from the Sears Tower to the nearest foot.
Answers
tan theta=[opposite]/[adjacent]
opposite=1450 ft
adjacent=x ft
theta=15.7
thus;
1450/x=tan15.7
hence;
x=1450/tan15.7
x=5,158.54 ft
x=5,159 (to the nearest foot)
the quadratic formula gives which roots for the equation 2x^2+x-6=0
Answers
a=2, b=1, c=-6
x = -b+_ /(b^2 - 4ac) ÷ 2a
+_ (plus minus) / ( square root)
X = -1 +_ /1^2 - 4(2)(-6) ÷ 2(2)
= -1 +_ /49 ÷ 4
= -1 +_ 7 ÷ 4
= 6/4 or -8/4
= 3/2 or -2
Hope it helped!
The quadratic formula gives two roots for a quadratic equation. The roots of the equation 2x²+x-6=0 are 1.5 and -2.
Explanation:The quadratic formula gives the roots of a quadratic equation of the form ax²+bx+c=0. For the equation 2x²+x-6=0, the values of a, b, and c are 2, 1, and -6, respectively.
Using the quadratic formula, we can calculate the roots:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula:
x = (-1 ± √(1² - 4*2*(-6))) / (2*2)
Simplifying the expression:
x = (-1 ± √(1 + 48)) / 4
x = (-1 ± √49) / 4
x = (-1 ± 7) / 4
Therefore, the roots of the equation 2x²+x-6=0 are:
x = (-1 + 7) / 4 = 3/2 = 1.5
x = (-1 - 7) / 4 = -8/4 = -2
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How many minutes does it take an athlete to run a 10.0 kilometer race? assume the athlete's pace is 6.50 minutes per mile. (1 mi = 1.609 km)?
Answers
To find out how many minutes it takes an athlete to run a 10.0 kilometer race using a pace of 6.50 minutes per mile, we can set up a proportion and solve for x. The athlete takes approximately 40.33 minutes to run the race.
Explanation:To convert the athlete's pace from minutes per mile to minutes per kilometer, we will use the conversion factor 1 mile = 1.609 kilometers. Therefore, the athlete's pace is 6.50 minutes per 1.609 kilometers. To find out how many minutes it takes the athlete to run a 10.0 kilometer race, we can set up a proportion:
6.50 minutes / 1.609 kilometers = x minutes / 10.0 kilometers
Using cross multiplication, we can solve for x:
x = (6.50 minutes × 10.0 kilometers) / 1.609 kilometers
x = 40.33 minutes (rounded to two decimal places)
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Determine the angular velocity, in radians per second, of 4.3 revolutions in 9 seconds. Round the answer to the nearest tenth.
Answers
simplify away.
John has taken out a loan for college. He started paying off the loan with the first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he payed the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of the first 20 payments using complete sentences.
Answers
month 1: $100
month 2: $100*(1.1)
month 3: $100*(1.1)²
month 4: $100*(1.1)³
...
The payments form the geometric sequence
a, ar, ar², ..., arⁿ
where
a = $100
r = 1.1
The sum of the first n terms is
[tex]S_{n} = \frac{a(1-r^{n})}{1-r} [/tex]
Therefore the sum of the first 20 payments is
S₂₀ = [$100(1 - 1.1²⁰)]/(1 - 1.1)
= $5727.50
John makes a total of $5727.50 in the first 20 payments.
Ohm’s Law states that the electrical current, I in amperes, through a resistor is given by the formula 644-14-04-00-00_files/i0210000.jpg where V is the voltage in volts and R is the resistance in ohms. If the current is 6 amperes and the resistance is 18 ohms, what is the voltage?
Answers
Your Answer is 108 volts
Answer:
The correct answer is D., or "108 volts".
In the figure below, segment AC is congruent to segment AB:
Triangle ABC with a segment joining vertex A to point D on side BC. Side AB is congruent to side AC
Which statement is used to prove that angle ABD is congruent to angle ACD?
Answers
the answer is A. segment AD bisects angle CAB. I just took the exam and I got it right. hope this helps!
Answer: Isosceles triangle theorem
Step-by-step explanation:
In the given picture, there a triangle whose two sides are equal AB=AC.
Therefore it is an isosceles triangle.
Now, the isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.
Therefore by isosceles triangle theorem in ΔABC we have
[tex]\angle{B}=\angle{C}[/tex]
Since [tex]\angle{ACD}=\angle{C}[/tex] [Reflexive]
[tex]\angle{ABD}=\angle{B}[/tex] [Reflexive]
Therefore, [tex]\angle{ACD}=\angle{ABD}=[/tex]
Two standard number cubes are thrown, one after the other. What is the probability that the first cube lands showing a 1 and the second cube lands showing a number that is not 1? Round the answer to the nearest thousandth.
Answers
Let B be the probability that you don't throw 1
A and B are independent events
P(A)= 1/6 and P(B)= 5/6
Because they are independent you multiply them: 1/6 x 5/6 = 0.138888...
Rounded to the nearest thousandth is 0.139
Answer:
B on edge
Step-by-step explanation:
whats the value of the equation
Answers
13x-2(x+4) = 8x+1 =
13x-2x-8 = 8x+1=
11x-8 = 8x+1
-8 =-3x+1=
-9 = -3x
x = -9/-3 = 3
x = 3
The circle will be dilated by a scale factor of 6. What is the value for n if the expression nPI represents the circumference of the circles in inches?
Answers
So basically N = 12r. You haven't given me any original radius, so I can't give you a constant for N, but if you do have that original radius you can just plug that into 12r.
Based on your comment, N = 12 * 9 = 108 inches
The value of n is 12 .
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.
According to the question
The circle will be dilated by a scale factor of 6 .
so,
New radius of the circle R = 6r
As is it dilated by a scale factor of 6
Now ,
The circumference of the new circles = 2πR
= 2.6π
= [tex]12\pi r[/tex] -------------------- (1)
and given circumference of the new circles = nπ ---------------------(2)
when we compare both n = 12
Hence, the value of n is 12 .
To know more about scale factor here:
https://brainly.com/question/22312172
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