The equation of the line tangent to the curve at the points , y = 8ex cos(x), (0, 8) as calculated is y' = 0.
We will differentiate y = 4ex cos(x) so as to find the required equation.
we get the differential as ,
y' = - 8eˣsin(x)
given the value of x as 0 and y as 8
y' = -8e⁰sin(0)
Now as we know that the value of sin( 0 ) is 0 , therefore the equation becomes,
y'= 0
Differentiation is a branch of calculus which is used to calculate the rate of change in a given object in a specified time. The other branch of calculus is integration.
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Graph the line through the given point with the given slope.
(0, 5), m = - 5
(basically what coordinate points would there be?)
Answer:
The equation would be
y =-5x + 5
Step-by-step explanation:
Use the x of 0 from the point given (0,5)
Use the y of 5 from the point given (0,5)
Use the slope that is given: -5
Use all of the above to solve for the y-intercept (b).
y = mx + b
5 = -5(0) + b
5 = 0 + b
5 = b
y =mx + b
y = -5x + 5
In the graph, the line crosses the y axis at (0,5) . The is the y -intercept or the "b" of the equation.
From that points move down 5 and one to the right. This is the slope. Once we have two points we can draw a line.
I need the answer to the second question in the picture, but can you also say if the one above it is correct or not?
The area of shaded region of standard normal distribution is 0.1292
what is standard normal distribution?
A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.
Any normal distribution can be transformed into the common normal distribution by converting the individual values into z-scores. Z-scores indicate the number of standard deviations that each value in a z-distribution is from the mean.
solution:
For - 3.39 to 0
The standard deviation value is : 0.00035
For 0 to 1.13
The standard deviation value is : 0.3708
Then for - 3.39 to + 1.13 :
The area of the given shaded area is 0.1292
Hence,the area of shaded region of standard normal distribution is 0.1292
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State a and d for the arithmetic sequence below:
1, 3, 5, 7...
a=
d=
Answer:a,9 b,11
Step-by-step explanation:
Evaluate the quantity of x cubed minus 2x squared plus 3x minus 7 end quantity divided by the quantity of x minus 1 end quantity period.
Our final resulting answer will be -5.
To calculate the remainder, first divide the polynomials.
Set up the polynomials to be divided. if there is not a term for every exponent, insert one with a value of 0.
[tex]\sqrt[x-1]{x^{3}-2x^{2} +3x-7 }[/tex]
Divide the highest order term in the dividend [tex]x^{3}[/tex] by the highest order term in divisor x.
Multiply the new quotient term by the divisor.
The expression needs to be subtracted from the dividend, so change all the signs [tex]x^{3}[/tex]+[tex]x^{2}[/tex].
After changing the signs, add the last dividend from the multiplied polynomials to find the new dividend.
Pull the next terms from the original dividend down into the current dividend.
Divide the highest order term in the dividend -[tex]x^{2}[/tex] by the highest order term in divisor x.
Multiply the new quotient term by the divisor.
The expression needs to be subtracted from the dividend, so change all the signs in -[tex]x^{2}[/tex]-x.
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
Pull the next terms from the original dividend down into the current dividend.
Divide the highest order term in the dividend 2x by the highest order in divisor x.
Multiply the new quotient term by the divisor.
The expression needs to be subtracted from the dividend, so change all the signs in -2x+2.
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
The final answer is the quotient plus the remainder over the divisor.
[tex]x^{2}[/tex]-x+2-[tex]\frac{5}{x-1}[/tex]
Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.
So, our final answer will be -5.
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Why is 1 not a square number?
According to square numbers , 1 is a square number while 2 is not .
What does Squaring mean ?
In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9.
When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.
Thus , 1 is a square number while 2 is not .
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If a1 = 3, an+1 = 2an, find a2.
Answer:
a2=0Step-by-step explanation:
a=2
n=0.5
2a=0
2.2=0
4=0
2a=0
Describe a real world situation that could be modeled by the expression Y equals 1/20 XP transcribe what is
The required real-world situation has been written in the solution part which could be modeled by the expression Y equals 1/20 XP.
A real-world situation that could be modeled by the expression Y = 1/20XP is the relationship between the distance a person runs and the number of calories they burn.
In this situation, Y represents the number of calories burned and X represents the distance run in miles. The constant 1/20 represents the rate at which calories are burned per mile.
For example, if a person runs 5 miles, we can substitute 5 for X in the expression to find the number of calories they burn:
Y = 1/20 × 5X
Y = 1/4
Thus, the person burns 1/4 calorie for every mile they run.
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What is domain simple answer?
A domain is a component of the nomenclature used in web addresses to identify your website or a particular page of your website online.
What is domain ?A function's authorized range of values is known as its domain. For a function like f, this set contains of the x values (x). The set of those values represents the possible range of values that a function can take as input. The function's response to our x value entry is this group of values.
here ,
A domain is typically a sphere of knowledge or an area under one's control.
Users find it much easier to recall and search for online because it is a string of text linked to a website's numerical IP address.
Both the internet's architecture and the way a company's network resources are set up fall under the umbrella term "domain."
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Find the missing number in this proportion. ?/8=16/64
A.0
B.1
C.2
D.3
Evaluation:
We are required to find the equivalent fraction here. When simplifying 16/64, we divide both sides by 16:
16 ÷ 16 = 1
64 ÷ 16 = 4
16/64 in its simplest form is 1/4. When we multiply both the numerator and denominator by 2, we will find that:
1/4 = 2/8
Verification:
To verify this, we can multiply both parts of the fraction by 8:
2 × 8 = 16
8 × 8 = 64
Hence, we know our answer is correct.
Where are the asymptotes for the following function located?
f (x) = startfraction 7 over x squared minus 2 x minus 24 endfraction
The asymptotes for the given function f(x) = 7/(x^2-2x-24) are located at
x = -3 and x = 8.
The asymptotes of a function are the lines that the graph approaches, but never touches as it continues to infinity. In the given function, f(x) = 7/(x^2-2x-24), the asymptotes are located at x = -3 and x = 8.
To find the asymptotes of a function, you first need to factor the denominator of the function. In this case, the denominator is[tex]x^2-2x-24,[/tex]which can be factored into (x+3)(x-8). This means that there are two potential zeroes in the denominator, x=-3 and x=8. These two points are the two asymptotes of the graph of the given function.
To explain further, the two asymptotes divide the x-axis into three intervals. On the interval (-infinity, -3), the graph of the function will approach negative infinity as x approaches -3 from the left. On the interval (-3, 8), the graph of the function will approach positive infinity as x approaches 8 from the right. On the interval (8, infinity), the graph of the function will approach negative infinity as x approaches 8 from the right.
In summary, the asymptotes for the given function f(x) = 7/(x^2-2x-24) are located at x = -3 and x = 8.
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2. The total surface area of a square based pyramid is 900 sq. cm. If the lateral surface area of the pyramid is three times the base area, find the length of the base. Also find the volume of the pyramid.
Answer:
Length of the base = 15 cm
Volume = 1125√2 cm³ = 1590.99 cm³ (2 d.p.)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.6cm}\underline{Lateral Surface Area of a square pyramid}\\\\$LSA=a \sqrt{a^2+4h^2}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{6.6cm}\underline{Base Area of a square pyramid}\\\\$BA=a^2$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\end{minipage}}[/tex]
If the lateral surface area (LSA) of the pyramid is three times the base area (BA):
[tex]\implies a \sqrt{a^2+4h^2}=3a^2[/tex]
Rearrange the equation to isolate h²:
[tex]\implies \sqrt{a^2+4h^2}=3a[/tex]
[tex]\implies (\sqrt{a^2+4h^2})^2=(3a)^2[/tex]
[tex]\implies a^2+4h^2=9a^2[/tex]
[tex]\implies 4h^2=8a^2[/tex]
[tex]\implies h^2=2a^2[/tex]
[tex]\boxed{\begin{minipage}{6.6cm}\underline{Total Surface Area of a square pyramid}\\\\$SA=a^2+a \sqrt{a^2+4h^2}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]
Given:
SA = 900 cm²h² = 2a²Substitute these values into the formula for the total surface area and solve for a:
[tex]\implies a^2+a\sqrt{a^2+4(2a^2)}=900[/tex]
[tex]\implies a^2+a\sqrt{a^2+8a^2}=900[/tex]
[tex]\implies a^2+a\sqrt{9a^2}=900[/tex]
[tex]\implies a^2+a(3a)=900[/tex]
[tex]\implies a^2+3a^2=900[/tex]
[tex]\implies 4a^2=900[/tex]
[tex]\implies a^2=225[/tex]
[tex]\implies a=15[/tex]
Therefore, the length of the base of the square based pyramid is:
a = 15 cmTo find the height (h), substitute the found value of a into the formula for h² and solve for h:
[tex]\implies h^2=2(15)^2[/tex]
[tex]\implies \sqrt{h^2}=\sqrt{2(15)^2}[/tex]
[tex]\implies h=\sqrt{2}\sqrt{(15)^2}[/tex]
[tex]\implies h=15\sqrt{2}[/tex]
Therefore, the height of the square based pyramid is:
h = 15√2 cm[tex]\boxed{\begin{minipage}{5cm}\underline{Volume of a square pyramid}\\\\$V=\dfrac{1}{3}a^2h$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]
Given:
a = 15h = 15√2Substitute the values into the formula and solve for volume:
[tex]\implies V=\dfrac{1}{3}(15)^2 \cdot 15\sqrt{2}[/tex]
[tex]\implies V=\dfrac{225}{3} \cdot 15\sqrt{2}[/tex]
[tex]\implies V=75\cdot 15\sqrt{2}[/tex]
[tex]\implies V=1125\sqrt{2}[/tex]
[tex]\implies V=1590.99[/tex]
Therefore, the volume of the square based pyramid is:
1590.99 cm³ (2 d.p.)What type of discontinuity is a hole?
A removable discontinuity is when a function has an isolated point where it is not defined, and the function can be made continuous by removing that point. A hole is an example of a removable discontinuity.
In mathematics, a discontinuity is a point or set of points where a function does not behave as expected or fails to exist. There are three types of discontinuities: removable discontinuities, jump discontinuities, and infinite discontinuities. A removable discontinuity is when a function has an isolated point where it is not defined, and the function can be made continuous by removing that point. In other words, the function can be made continuous by “filling in” the discontinuity. An example of a removable discontinuity is a hole, where the graph has a gap that can be filled in. Jump discontinuities occur when the left-hand and right-hand limits of the function do not agree at a point, and the function “jumps” from one value to another at that point. An example of a jump discontinuity is a cusp, where the graph has a sharp point. Finally, an infinite discontinuity is when the function does not exist at a point, such as a vertical asymptote. In all three cases, the discontinuity can be easily identified by looking at the graph of the function.
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If sinA + sin² A = 1, then the value of the expression (cos²A + cos¹A) is
(a) 1 (6) 1/2 (c) 2 (d) 3
Using trigonometric identities, If sinA + sin² A = 1, then the value of the expression (cos²A + cos⁴A) is; 1
How to solve trigonometric identities?We are told that sinA + sin² A = 1.
Now, we want to find (cos²A + cos⁴A).
From trigonometric identities, we know that;
cos²A = 1 - sin² A
Thus;
cos²A + cos⁴A = 1 - sin² A + cos⁴A
Similarly, using trig identities on the given expression;
From sinA + sin² A = 1, we can say that;
sinA = 1 - sin² A
Since cos²A = 1 - sin² A, then we can say that;
sinA = cos²A
Thus;
sin²A = cos⁴A
Thus;
cos²A + cos⁴A = 1 - sin² A + sin²A
= sinA + sin²A= 1
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Correct question is;
If sinA + sin² A = 1, then the value of the expression (cos²A + cos⁴A) is
May I ask what’s the answer to this MC question because what I've calculated is 36 to the power 222 which giant matched the above choices
Answer:
B
Step-by-step explanation:
16 = 2⁴
9 = 3²
(2⁴)¹¹¹ × (3²)²²² = 2⁴⁴⁴ × 3⁴⁴⁴ = (2×3)⁴⁴⁴ = 6⁴⁴⁴
you can only combine the exponents of the same bases, or the bases of the same exponent.
in our case here the latter is used.
and indeed
6⁴⁴⁴ = (6²)²²² = 36²²²
so, essentially you were right. but you still needed to transform this into the form of the given answer option.
What mode of observation is 5'7 8?
The mode for a particular set of observations is 5 since it occurs the majority of the time.
What is mode?The mode formula is described in statistics as the formula for calculating the mode of a given collection of data. The value that occurs most frequently in a particular set is referred to as the mode, and the mode differs across grouped and ungrouped data sets. The mode may be calculated quite easily. Put all of the numbers in a given set in order, either lowest to highest or highest to lowest, and then count how many times each number appears in the set. The mode is the one that appears the most.
Here,
given set of observation:
5, 7, 8, 5, 7, 6, 9, 5, 10, 6
Mode is the number which occurs the highest time.
So here 5 occurs the highest times(3 times).
So,5 is the mode.
The mode for given set of observation is 5 as it occurs most time.
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Classifying Triangles Maze! Directions: Glven each set of side lengths, determine if the triangle is acute. obluse, night, or not a triangle. Use your solutions to navigate through the moze End! Start! Acute 6,10,17 Obtuse 26, 28, 38 Nota a 10, 17, 23 Obtuse Not a Right Not a A Obtuse Acute Right 13, 18, 29 Not a A 9,13, 20 Acute 15,19,25 Not A 4, 11, 13 Acute Right Obtuse Not a A Right Acute Obtuse 16,16, 22 Nota A 4,7,8 Acute 20, 21, 29 Obtuse 3,16,25 Obtuse Obtuse Right Not a Δ Not a Acute Not a A 5, 16, 24 Acute 19,24,39 Right 9,40,41 Obtuse 12, 35, 37 Right Not a A Acute Not a A Acute Right Acute 7,34,45 Not a 4,13,16 Right 23, 30, 37 Obtuse 14, 21, 37 on 1 Gino Won A Things Algebra LLC. 2016
Classifying triangles maze's path formed from the starting point is 3 - 10 - 17, 9 - 13 - 20, 4 - 7 - 8, 20 - 21 - 29, 15 - 19 - 25, 26 - 28 - 38, 4 - 11 - 13, 3 - 16 - 25, 12 - 35 - 37, 23 - 30 - 37, 9 - 40 - 41, 19 - 24 - 39, 16 - 16 - 22, and 13 - 18 - 29.
The full question is in the attachment. According to the Pythagorean theorem if there are three sides a, b, and c, where a ≤ b < c
a² + b² < c² an obtuse triangle is formeda² + b² = c² a right triangle is formeda² + b² > c² an acute triangle is formedBut if a + b < c then a triangle cannot be formed
From point start
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passes through (6,3) and (14,-5)
Answer:
Slope: m = (y2 - y1)/(x2 - x1) = (-5 - 3)/(14 - 6) = -8/8 = -1
The equation of the line is y = -x + b
Substitute (6,3) into the equation:
3 = -6 + b
b = 9
Therefore, the equation of the line is y = -x + 9
Step-by-step explanation:
What is the horizontal asymptote of f/x )= 4 x?
The given equation of the horizontal asymptote is y=0
Because there is not a rational expression so there is no horizontal asymtotes.The given equation would be linear because degree of given function is 1.
what is an Asymptote?An asymtote is a line being approached by a curve but never touching the curve at any finite distance.It is a line that the graph approaches as either x or y in positive or negative infinity.
How do you find horizontal asymptotes?The horizontal asympototes of a function can be determined by looking at the degree of the numerator and denominator.if we say N is the degree of numerator and Dis the degree of denominator.So it will be N<D.Then horizontal asymptotes will be y=0
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I can't seem to figure out what it means by characteristics for these equations, It might be more simple than I think, but I honestly don't know.
Explanation:
Characteristics about an equation are slope, intercepts, and things like that.
Part D of each problem is just referring to part a, b, and c
So, Part D is basically asking you to show your work, to explain slope-intercept equation, make observations about the problem, etc.
Hope I helped! :)
What are the 4 tests of congruency?
The 4 tests of congruency are:
Side - Side - Side (S.S.S. congruency)
Side - Angle - Side (S.A.S. congruency)
Angle - Angle - Side (A.A.S congruency)
Right - Hypotenuse - Side (R.H.S. congruency)
Tests of congruency:
Side - Side - Side (S.S.S. congruency)
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
Side - Angle - Side (S.A.S. congruency)
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
Angle - Angle - Side (A.A.S congruency)
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
Right - Hypotenuse - Side (R.H.S. congruency)
If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.
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How do you know what method SSS SAS ASA AAS to use when proving triangle congruence?
We can find out which method SSS, SAS, ASA, and AAS can be used to prove similarity by observing what three components are given.
If it is given that three sides are equal then we will use side side side(SSS) postulate.
If it is given that two sides and one angle is given then we will use the side angle side(SAS) postulate.
If two angles and one side is given then we will use the angle side angle (ASA) postulate.
To find which postulate will suit for that we will have to observe which components are given that are equal.
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A new bank customer with $2,500 wants to open a money market account. The bank is offering a simple interest rate of 1.6%.
a. How much interest will the customer earn in 20 years?
b. What will the account balance be after 20 years?
a) The customer will earn $800 as interest in 20 years.
b) The account balance after 20 years will be - $ 3300.
Principle = $2500
Rate of simple interest = 1.6%
Time = 20 yrs
The simple interest is expressed as :
S.I = [tex]\frac{PRT}{100}[/tex]
⇒ S.I = [tex]\frac{2500 * 1.6 * 20}{100}[/tex]
⇒ S.I = 25 * 20 *1.6
⇒ S.I = 800
The simple interest after 20 years = $800
The account balance after 20 years is -
= principle + simple interest
= 2500 + 800
= 3300
a) The customer will earn $800 as interest in 20 years.
b) The account balance after 20 years will be - $ 3300.
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1800 ounces of a radioactive substance are stored in a radioactive container.
ounces, of the substance that is left after t years can be modeled by the equation y = 1800e-0.00052t
where y is the amount of the substance left after t years.
Approximately how many years will it take until 80 ounces of this substance remains?
According to the given statement 2.622 years will it take until 80 ounces of this substance remains.
How much does one ounce weigh?Use a test tube holder that has an ounce marker or can be converted quickly to ounces (like cups). As you take the measuring cup from the ingredient, let it overflow. You may try and reduce measurement afterwards. Use a knife to level the measuring cup.
Briefing:The equation may be used to predict how much of the chemical is still present after t years, measured in ounces.
y=1800e -0.00052t
In the equation above, we substitute y = 80 ounce to obtain the time.
80= 1800e -0.00052t
80/1800=e -0.00052t
2/45= e -000.52t
Considering both ends of the aforementioned equation
In(2/45)= In(e -000.52t)
In(2)-In(45)= In(e -000.52)
0.3010-1.653= -000.52t
-1.352= -000.52t
dividing by 000.52 on both side
1.352/000.52= t
t= 2.622 years
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How do we get negative infinity?
Negative infinity is obtained by taking the limit of a decreasing sequence of negative real numbers as they approach negative infinity.
Negative infinity is an abstract concept that is used to represent a value that is less than the lowest possible number. To get negative infinity, one must take the limit of a decreasing sequence of negative real numbers. This means that the sequence of numbers must get closer and closer to negative infinity as it continues to decrease. For example, if you take the sequence of numbers -1, -2, -3, -4, -5, -6, and so on, the limit of this sequence is -∞. As the sequence continues to decrease, it eventually reaches a point where the numbers become so small that they cannot be measured. At this point, the limit of the sequence is -∞.
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9. Find the measure of angle B. Round to the nearest tenth. (show work)
The measure of angle 55 degrees Celsius
What is the explanation?In order to get the measure of the unknown angle A, we are given a right-angled triangle with two known side lengths for the perpendicular and base.
To do that, we may use the tan formula, which uses the two provided side lengths.
the nearest tenth:
To get the solution in this case, we must apply the tan ratio.
tan = Adjacent or Opposite
tan = Opposite / Adjacent
Given: Opposite equals 4, adjacent equals 13.
Given: Adjacent = 13, opposite = 12.
tan θ = 12/13
θ = tan^-1 (12/13)
55 degrees.
55 degrees, please.
The measure of angle 55 degrees Celsius
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s = ut + 1/2 at2
u = 10 a = -2 t= 1/2
Answer:
Step-by-step explanation:
12 pencils cost 1.80 pounds. How many pencils can be bought for 6 pounds?
Answer:
Step-by-step explanation:i think to answer is either 90p or 9p
Answer:
90p or 9p
Step-by-step explanation:
Determine the domain and range for the function below.
Answer:
Domain: (-∞, ∞); Range: [1, ∞)
Step-by-step explanation:
Domain is the set/interval of x-values that the function spans while the range is the set or interval of y-values that the function spans.
Domain
We can see that the arrows point towards negative and positive infinity for x and also see there are no holes or asymptotes for this graph. Therefore, the domain is (-∞, ∞) or {x | x is any real number}
Range
We can see that the arrows both point towards infinity for y-values and that the lowest y-value this graph touches is y = 1 (inclusive, meaning this y-value is included in the range). Thus, the range is [1, ∞) or {y | y ≥ 1}
Find the distance between two numbers on a number line -4 7/12 and -3 1/6
Answer: -17/12 or -1 5/12 or 1 5/12
Step-by-step explanation:
convert both equations into improper fractions
− 55/12 - (-19/6)
-55/12+19/6
find the common factor of the denominators
-55/12 + 38/12
-17/12
-1 5/12
Given:
CD CB CA CE and
Prove:
A E
You may use any style proof you prefer.
The alternate angles between two parallel lines are equal, therefore, ∠ A = ∠ E.
What is rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.
Given:
CD ≅ CB and CA ≅ CE
As you can see from the diagram, on joining BE and AD the figure will represent a rectangle ABED because the diagonals of the rectangle are equal and bisect each other.
Thus, DE || AB (Rectangle property)
∠ A = ∠ E, because the alternate angle of parallel lines is equal.
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