Answer: The thickness of each cookie = 0.5 inch
Step-by-step explanation:
Cácule o limite de:
lim [tex]3^{2n} + 1[/tex]
_____________________
n-∞[tex]4^{n+2} - 3[/tex]
R:∞
The limit of the expressions [tex]3^{2n} + 1[/tex] and [tex]4^{n + 2} - 3[/tex] for n to infinity is infinity
How to calculate the limits?The expressions are given as:
[tex]3^{2n} + 1[/tex]
[tex]4^{n + 2} - 3[/tex]
The limits of the expressions as they approach infinity are represented as:
[tex]\lim_{n \to \infty} 3^{2n} + 1[/tex] and [tex]\lim_{n \to \infty} 4^{n + 2} - 3[/tex]
Substitute [tex]\infty[/tex] for n in both expressions
[tex]\lim_{n \to \infty} 3^{2 * \infty} + 1[/tex] and [tex]\lim_{n \to \infty} 4^{\infty + 2} - 3[/tex]
Solve both expressions independently;
[tex]\lim_{n \to \infty} 3^{2n} + 1 = 3^{2 * \infty} + 1[/tex]
Evaluate the product
[tex]\lim_{n \to \infty} 3^{2n} + 1 = 3^{\infty} + 1[/tex]
Evaluate the exponent
[tex]\lim_{n \to \infty} 3^{2n} + 1 = \infty + 1[/tex]
Evaluate the sum
[tex]\lim_{n \to \infty} 3^{2n} + 1 = \infty[/tex]
Also, we have:
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 = 4^{\infty + 2} - 3[/tex]
Evaluate the sum
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 = 4^{\infty} - 3[/tex]
Evaluate the exponent
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 =\infty - 3[/tex]
Evaluate the difference
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 =\infty[/tex]
Hence, the limit of the expressions for n to infinity is infinity
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Give the value of x .
A. 60 degrees
B. 180 degrees
C. 120 degrees
D. 45 degrees
Answer:
x=120°
Step-by-step explanation:
sum of all angles in a triangle is equal to 180
let the unknown angle be
[tex] \alpha [/tex]
[tex]60 + 60 + \alpha = 180 \\ \alpha = 180 - 60 - 60 \\ \alpha = 60 \\ [/tex]
[tex] \alpha + x = 180 \\ x = 180 - \alpha \\ x = 180 - 60 \\ x = 120[/tex]
Rearrange the formula below to make x the subject. α y+1=2x - 10/x+1
Answer:
cross multiplication
x
Solve the problem.
A recipe calls for 6 ounces of unsweetened chocolate for 20 brownies. How much of unsweetened chocolate is needed to make 30 brownies?
Help asap pleaseeeeeeeee
Answer:
√5
Step-by-step explanation:
Given:
[tex]\displaystyle \large{5\div \sqrt{5}}[/tex]
Which can be rewritten as:
[tex]\displaystyle \large{\dfrac{5}{\sqrt{5}}}[/tex]
To find:
Simplified formTo find simplified form of the expression, keep in mind that surds should not remain as denominators. Therefore, what we have to do is to multiply both numerator & denominator by the surd itself so the denominator will be cleared as rational number.
[tex]\displaystyle \large{\dfrac{5\cdot \sqrt{5}}{\sqrt{5}\cdot \sqrt{5}}}[/tex]
We know that if same surds multiply each other, the surd will be canceled and remains only the insides. To express it in math, it can be as:
[tex]\displaystyle \large{\sqrt{a}\cdot \sqrt{a} = \left(\sqrt{a}\right )^2 =a}[/tex]
Therefore:
[tex]\displaystyle \large{\dfrac{5\sqrt{5}}{5}}[/tex]
Cancel 5:
[tex]\displaystyle \large{\sqrt{5}}[/tex]
Henceforth, the simplified expression is √5
Annie bought a package of 100 pens for $167.00. How much did each
pen cost?
Answer:
Step-by-step explanation:
167.00 / 100 = $1.67
Write an equation of the line that passes through the point (6,-9) with the given slope m= 3
Answer:
y=3x-27
Step-by-step explanation:
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Write an equation of the line passing through (6, -9) and has a slope of -3.
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
First, we need to write the equation in point-slope form:-
[tex]\hookrightarrow\sf{y-y_1=m(x-x_1)}[/tex]
Replace y₁ with -9, m with 3, and x₁ with 6:-[tex]\hookrightarrow\sf{y-(-9)=3(x-6)}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\hookrightarrow\sf{y+9=3(x-6)}[/tex]
[tex]\bigstar[/tex] On further simplification,
[tex]\hookrightarrow\sf{y+9=3x-18}[/tex]
[tex]\star[/tex] Subtract 9 from both sides, which results in:-
[tex]\hookrightarrow\sf{y=3x-27}[/tex]
So we conclude that Option B is correct.
Good luck with your studies.
[tex]\rule{300}{1}[/tex]
Pre-calc/trig
Suppose that θ=arcsin(1/7) in the first quadrant. What is cos(θ/2)? (round to 4 decimals)
Answer:
0.9974
Step-by-step explanation:
[tex]arcsin( \frac{1}{7} ) = 0.1433 \\ cos( \frac{0.1433}{2} ) = 0.9974[/tex]
solve 4(x-7)+10=-10 A=X-2 B=X=4 C=X=1 D=X=3
Answer:
A. -2
Step-by-step explanation:
Help me please I need this done quick
Someone show me step for step please!
[tex]\csc \theta \tan \theta - \tan \theta \sin \theta \\\\\\=\dfrac 1{\sin \theta} \cdot \dfrac{\sin \theta }{\cos \theta }- \dfrac{\sin \theta }{\cos \theta} \cdot \sin \theta\\\\\\=\dfrac{1}{\cos \theta}-\dfrac{\sin^2 \theta}{\cos \theta}\\\\\\=\dfrac{1- \sin^2 \theta}{\cos \theta}\\\\\\=\dfrac{\cos^2 \theta}{\cos \theta}~~~~~~~~~~~~~~;[\sin^2 \theta + \cos^2 \theta =1 ]\\\\\\=\cos \theta[/tex]
Let's write out some trigonometric identities that we can use:
[tex]tan(x)=\frac{sin(x)}{cos(x)} \\[/tex][tex]csc(x)=\frac{1}{sin(x)}[/tex][tex]sin^2(x)+cos^2(x)=1[/tex] ⇒ [tex]cos^2(x)=1-sin^2(x)[/tex]Now let's try solving them out:
[tex]csc(x)tan(x)-tan(x)sin(x)=\frac{1}{sin(x)}tan(x)-sin(x)tan(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)(\frac{1}{sin(x)}-sin(x))\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)(\frac{1}{sin(x)} -\frac{sin^2(x)}{sin(x)} )\\\\csc(x)tan(x)-tan(x)sin(x)=tan(x)*(\frac{1-sin^2(x)}{sin(x)} )\\\\csc(x)tan(x)-tan(x)sin(x)=\frac{sin(x)}{cos(x)}*\frac{cos^2(x)}{sin(x)} \\\\csc(x)tan(x)-tan(x)sin(x)=\frac{sin(x)}{sin(x)}*\frac{cos^2(x)}{cos(x)}\\\\csc(x)tan(x)-tan(x)sin(x)=1 * cos(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=cos(x)[/tex]
*I used a different variable, but that doesn't change the answer
Answer: cos(x)
Hope that helps!
A concession stand owner bought some bottles of water for $0.75 each and began selling them for $1.25 each. When he made back all the money he spent, he still had 20 bottles left to sell. What equation can be written to determine the amount of money the owner spent?
The population of a city decreases by 4.4% per year. If this year's population is
135,000, what will next year's population be, to the nearest individual?
Answer:
129060
Step-by-step explanation:
135 000 - .044(135000) = 129 060
Use the t-distribution to find a confidence interval for a difference in means μ1−μ2 given the relevant sample results. Give the best estimate for μ1−μ2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed.
A 99% confidence interval for μ1−μ2 using the sample results x⎯⎯1=535, s1=103, n1=380 and x⎯⎯2=465, s2=86, n2=200
Enter the exact answer for the best estimate and round your answers for the margin of error and the confidence interval to two decimal places.
The best estimate and the degree of freedom when the t-distribution is used to find a confidence interval is 7 and 56 respectively.
How to illustrate the research?The best estimate from the information given in the research will be:
= X1 - X2
= 53.5 - 46.5
= 7
The degree of freedom will be:
= 38 + 20 - 2
= 56
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To graph the inequality x > -3, draw an open circle on -3 and shade to the left.
TrueFalse
what plus what equals -20
How do I solve 15=3p/6 ?
I have to choose 2 tools
Answer:
scale
Step-by-step explanation:
it would be used to measure
BOOM Creations has offered to sell its balloon
bouquets for a fixed down payment of $65 and an
additional charge of $2.75 per bouquet.
Answer:
y intercept: 65
rate of change: $2.75
Step-by-step explanation:
Really quite simple lad. Your equation is y=2.75x+65. 65 is your y-intercept, and you have a rate of change of 2.75 per bouquet.
Find the vertex, axis of symmetry, and y-intercept of the quadratic function.
Answer:
See below ~
Step-by-step explanation:
Details of Graph
Maximum = 2Domain : all real numbersRange : y ≤ 2Calculate the amount of work done when moving a 567 N crate a distance of 20 meters
Answer:
W = 11340 J
Step-by-step explanation:
Given,
Force ( F ) = 567 N
Distance ( s ) = 20 N
To find : Work done ( W )
Formula : -
W = Fs
W = 567 x 20
W = 11340 J
Hence,
the amount of work done is 11340 J.
3
6
2
•
3
12
O y=2x+:
O y = 3x
O y =3x+3
O y=x+3
Which equation represents the relationship shown in the table? •
Answer:
y = 3x + 3
Step-by-step explanation:
when you check, only that equation delivers the correct x and y pairs.
x = 0, => y = 3×0 + 3 = 3
x = 1, y = 3×1 + 3 = 3+3 = 6
x = 2, y = 3×2 + 3 = 6 + 3 = 9
x = 3, y = 3×3 + 3 = 9 + 3 = 12
it all fits.
There is 1 2 of a pizza left for 4 friends to share. What fraction of a pizza will each friend get to eat? please help.
Answer:
1/3
Step-by-step explanation:
Number of pizza=12
Number of students=4
Therefore,4/12=4/4
=1/3
helppppppppppppppppppppppppppppppppppppppppppppp
Jackie has 3 brothers. Maria has 2 brothers. Keri has 1 brother. Harriet has 2 brothers. Between the four girls, what is the mean number of brothers? Median? Mode?
Answer:
mean is 2 brothers.
mean, means average
Find an equation of a line through (2, 1) and perpendicular to - 2x + 4y = 8.
y = -2x - 1
y = -2x + 5
О.
y = -2x - 3
O
y = -2x + 3
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]-2x+4y=8\implies 4y=2x+8\implies y=\cfrac{2x+8}{4} \\\\\\ y=\cfrac{2x}{4}+\cfrac{8}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x+2\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
since we know that's its slope, then
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]
so then we're really looking for the equation of a line whose slope is -2 and passes through (2 , 1)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad \qquad \stackrel{slope}{m}\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-2}(x-\stackrel{x_1}{2}) \\\\\\ y-1=-2x-4\implies y=-2x-3[/tex]
PJ is Decorating Pupcakes for Rocky´s Birthday Party. Her Color Scheme is Black, Purple, and Green. She Will use This Spinner to Determine the Color of Spinkles on each Pupcake. if Pj decorates 60 pupcakes, about how many can she expect to be purple?
A:15 pupcakes
B: 30 pupcakes
C: 20 pupcakes
D: 25 pupcakes
If there is no picture for the spinner and we assume that it is completely fair, meaning that you have an equal chance of landing on any spot: You will expect to get a certain color every 3 spins because you have 3 different colors. In this case the answer would be 20 pupcakes.
-9v -6(8-7v)
Explain please
Answer:
33v - 48
Step-by-step explanation:
- 9v - 6(8 - 7v) ← multiply each term in the parenthesis by - 6
= - 9v - 48 + 42v ← collect like terms
= 33v - 48
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: - 9v - 6(8 - 7v)[/tex]
[tex]\qquad \sf \dashrightarrow \: - 9v - [(6 \times 8) - (6 \times 7v)][/tex]
[tex]\qquad \sf \dashrightarrow \: - 9v - (48 - 42v)[/tex]
[tex]\qquad \sf \dashrightarrow \: - 9v - 48 + 42v[/tex]
[tex]\qquad \sf \dashrightarrow \:33v - 48[/tex]
Hope it helps ~
Find x. Round to the nearest tenth:
A(5, 10) and B(13,-2) are two points on the line AB.
The perpendicular bisector of the line AB has gradient
Find the equation of the perpendicular bisector of AB
Answer:
hope you understand......
