The possibility of the other two numbers in the given data set is 3.
What do we mean by a number?An object that can be counted, measured, and given a name is a number. The initial examples are the natural numbers 1, 2, 3, 4, and so forth. In language, numbers can be expressed using number words. The symbols referred to as numerals can be used to represent specific numbers in a more general way; for instance, the numeral "5" stands for the number five. Due to the limited amount of symbols that can be learned, fundamental numbers are typically arranged in a numeral system, which is a systematic manner of representing any number. The Hindu-Arabic numeral system, which enables any number to be expressed using a combination of 10 fundamental numeric symbols known as digits, is the most widely used numeral system.So, by observing the data, we can simply conclude that:
As the mode is 3, the remaining two numbers are 3.Therefore, the possibility of the other two numbers in the given data set is 3.
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An order is received for 180 mL of a 2.5% solution to be prepared from diluting a 15% solution with water. How much of the stock 15% solution is needed?
a.
20 mL
b.
25 mL
c.
30 mL
d.
35 mL
We need 30 ml of the 15 percent solution to complete the order.
Here, we are given that we need to prepare 180 mL of a 2.5% solution by diluting a 15% solution with water.
the 180 ml 2.5% solution will contain-
2.5% pf 180 ml acid
= 2.5/100 × 180
= 25/1000 × 180
= 1/40 × 180
= 18/4
= 9/2
= 4.5 ml
Water in the 180 ml solution will be = 180 - 4.5 = 175.5
Now, we have say x ml of 15% solution
It must contain 4.5 ml of acid
Thus-
15% of x = 4.5
15/100 × x = 4.5
x = 4.5 × 100/15
x = 450/15
x = 30
Thus, we need 30 ml of the 15 percent solution, hence, option C.
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in the diagram below angle E congruent angle H enter the segments in tye blanks provided that would result in a true equation
ANSWER
DF/GF or DE/GH
EXPLANATION
We know that angle H and angle E are congruent. We also know that angles HFG and EFD are congruent too because they are vertical angles. Thus, by the AA postulate, triangles HGF and EDF are similar.
If two figures are similar, the ratio between corresponding sides must be constant. Of these two triangles, the corresponding sides are
• EF and HF
,• DF and GF
,• DE and GH
So the ratio between corresponding sides is,
[tex]\frac{EF}{HF}=\frac{DF}{GF}=\frac{DE}{GH}[/tex]The answers could be DF/GF or DE/GH
Harrison Heights Elementary School has 3 fourth grade classrooms. Each classroom has 28 students. Howmany fourth grade students attend Harrison Heights Elementary?
Harrison Heights Elementary School has 3 fourth grade classrooms. Each classroom has 28 students.
From the given statement;
Number of four grade classrooms = 3
Number of student in each classromm = 28
So,
for total number of students in 3 four grade students = 3 x (number of student in one class)
= 3 x (28)
= 84 students
Answer : 84 students
The perimeter of a parallelogram is 120cm. If one of the sides is greater than the other by 10cm,
find the length of all the sides of the parallelogram
Answer:
Two of the sides are 25cm and the other two sides are 35cm.
Step-by-step explanation:
The perimeter is the distance all the way around the shape.
The shape is a parallelogram, so two sides across from each other are the same length. And the other two sides are also the same as each other. See image.
The shorter sides can be labelled x and the longer sides can be labelled x + 10. This is because the question said the long side is 10cm more than the short side.
see image.
Add up all the sides to make them equal to the perimeter. Set it equal to 120. See image.
Solve for x.
x + x+10 + x + x+10 = 120
4x + 20 = 120
Subtract 20.
4x = 100
Divide by 4.
x = 25
The short sides are 25cm and the long sides are 35cm.
Check:
25+35+25+35=
120 Check!
What are the missing reasons in the proof?
50 points!
The missing reasons in the proof that shows that the triangles are congruent by SSS are:
3. Definition or parallelogram
4. Alternate interior angles theorem
5. Reflexive property of congruency
6. SSS Congruence Theorem
What is the SSS Congruence Theorem?The SSS congruence theorem is applicable when two triangles have three pair of corresponding side lengths that are congruent to each other. The SSS congruence theorem states that they are congruent to each other. This theorem can be used in proof where it is established that the three sides of two triangles are equal to each other.
What is the Reflexive Property of Congruency?A side is congruent to itself according to the reflexive property of congruency. This means that if two triangles share a common side, the two angles therefore have a pair of corresponding congruent sides in a proof.
Therefore, the missing reasons for the proof are explained below:
Statements Reasons
1. AD║BC 1. Definition or parallelogram
2. ∠ADB ≅ ∠CBD 2. Alternate interior angles theorem
3. AB║CD 3. Definition or parallelogram
4. ∠ABD ≅ ∠CDB 4. Alternate interior angles theorem
5. DB ≅ DB 5. Reflexive property of congruency
6. ΔABD ≅ ΔCDB 6. SSS Congruence Theorem
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Rectangle A measures 20 cm by 4 cm. Rectangle B is a scaled copy of Rectangle A. Select ALL of the measurement pairs that could be the
dimensions of Rectangle B.
100 cm by 20 cm
15 cm by 5 cm
12.5 cm by 2.5 cm
20 cm by 5 cm
5 cm by 1 cm
The measurement pairs that could be the dimensions of rectangle B are 100 cm by 20 cm, 12.5 cm by 2.5 cm, and 5 cm by 1 cm.
The rectangle A measures 20 cm by 4 cm.
The ratio of the dimensions of rectangle A is 20:4 = 5.
Rectangle B is a scaled copy of rectangle A.
The dimensions of rectangle B must be in the same ratio as those of rectangle A.
The first set of dimensions is 100 cm by 20 cm.
The ratio of dimensions is 100:20 = 5.
Thus, these could be the dimensions of the rectangle B.
The second set of dimensions is 15 cm by 5 cm.
The ratio of dimensions is 15:5 = 3.
Thus, these cannot be the dimensions of the rectangle B.
The third set of dimensions is 12.5 cm by 2.5 cm.
The ratio of dimensions is 12.5:2.5 = 5.
Thus, these could be the dimensions of the rectangle B.
The fourth set of dimensions is 20 cm by 5 cm.
The ratio of dimensions is 20:5 = 4.
Thus, these cannot be the dimensions of the rectangle B.
The fifth set of dimensions is 5 cm by 1 cm.
The ratio of dimensions is 5:1 = 5.
Thus, these could be the dimensions of the rectangle B.
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Write a formula for the function obtained when the graph is shifted as described.
The given function is
f(x) = x^3
Recall, if a function, f(x) is shifted c units upwards, the new function would be f(x) + c. This means that if we translate the given function 3 units upwards, the new function would be x^3 + 3
Also, if a function, f(x) is shifted d units to the left, the new function would be
f(x + d). This means that if we translate x^3 + 3 7 units to the left, the new function would be (x + 7)^3 + 3
The function is
f(x) = (x + 7)^3 + 3
f(x)=2x^3+6x^2-5x-3
Find (f-g)(x)
The solution to the function expression, (f - g)(x) is: D. 2x³ + 6x² - 8x + 1.
How to Subtract Functions?To evaluate or subtract functions that has polynomials, all we simply need to do is to pair like terms together and combine them.
Given the following:
f(x) = 2x³ + 6x² – 5x – 3 and g(x) = 3x – 4
Therefore:
(f - g)(x) = f(x) - g(x)
Substitute
(2x³ + 6x² – 5x – 3) – (3x – 4)
2x³ + 6x² - 5x - 3 - 3x + 4
Combine like terms
2x³ + 6x² - 5x - 3x - 3 + 4
2x³ + 6x² - 8x + 1
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Complete Question:
f(x) = 2x³ + 6x² – 5x – 3
g(x) = 3x – 4
Find (f - g)(x).
O A. (f - g)(x) = 2x³ + 6x² – 2x – 7
O B. (f - g)(x) = 2x³ + 6x² – 2x + 1
O c. (f - g)(x) = 2x³ + 6x² – 8x – 7
O D. (f - g)(x) = 2x³ + 6x² – 8x + 1
Instructions: Find the area of the sector with the red outline. Round your answer to the nearest tenth.
HeHeThe area of a sector is given as:
[tex]A=\frac{\theta}{360^0}\times\pi r^2[/tex][tex]\begin{gathered} r\rightarrow radius,\theta\rightarrow angle\text{ at the centre} \\ r=14ft \\ \theta=210^0 \end{gathered}[/tex][tex]\begin{gathered} A=\frac{210^0}{360^0}\times\pi\times14^2 \\ A=\frac{7}{12}\times196\times\pi \\ A=359.2ft^2 \end{gathered}[/tex]Hence, the area in the nearest tenth is
can someone help me with this
The exact values of the sine of the addition and subtraction of two angles are 576 / 1105 and 264 / 1105, respectively.
How to find the exact value of the sine of the addition and the subtraction of two angles
Since angle A is in the fourth quadrant and B is in the second quadrant, then we find the following inequalities:
cos A > 0, sin A < 0
cos B < 0, sin B > 0
If we know that cos A = 13 / 85 and sin B = 12 / 13, then the missing trigonometric functions according to the fundamental trigonometric formula are:
sin A = - √(1 - cos² A)
sin A = - √[1 - (13 / 85)²]
sin A = - 84 / 85
cos B = - √(1 - sin² B)
cos B = - √[1 - (12 / 13)²]
cos B = - 5 / 13
And the exact value of the sine of the addition and subtraction of two angles is found by the following formula:
sin (A + B) = sin A · cos B + cos A · sin B
sin (A + B) = (- 84 / 85) · (- 5 / 13) + (13 / 85) · (12 / 13)
sin (A + B) = 576 / 1105
sin (A - B) = sin A · cos B - cos A · sin B
sin (A - B) = (- 84 / 85) · (- 5 / 13) - (13 / 85) · (12 / 13)
sin (A - B) = 264 / 1105
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look at this diagram. if TV and WY are parallel lines and m
The measure of the angle ∠YXU is 138°.
We are given that the lines TV and WY are parallel to each other. Parallel lines in geometry are two lines in the same plane that are at an equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. We are given two angles in the diagram. The measure of the angle ∠VUS is 138°. We can see that the angles ∠VUS and ∠YXU are corresponding angles. Corresponding angles are any pair of angles that are both on the same side of a transversal. So, the angles must be equal to each other.
∠YXU = ∠VUS = 138°
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Step 1 of 2: Red the rational expression to its lowest terms 2 - 2x^2/2x^2 - 2Step 2 of 2: Find the restricted values of X, if any, for the given rational expression.
Step1
we can factor the numerator and denominator because we have a square subtract
[tex]\begin{gathered} \frac{(\sqrt[]{2}+\sqrt[]{2}x)(\sqrt[]{2}-\sqrt[]{2}x)}{(\sqrt[]{2}x-\sqrt[]{2})(\sqrt[]{2}x+\sqrt[]{2})} \\ \\ \frac{(\sqrt[]{2}+\sqrt[]{2}x)}{\sqrt[]{2}x+\sqrt[]{2})}\cdot\frac{(\sqrt[]{2}-\sqrt[]{2}x)}{(\sqrt[]{2}x-\sqrt[]{2})} \\ \\ 1\cdot-1 \\ \\ =-1 \end{gathered}[/tex]step 2
restricted values of X are when the denominator is 0
then
[tex]2x^2-2=0[/tex]factor this
[tex](\sqrt[]{2}x-\sqrt[]{2})(\sqrt[]{2}x+\sqrt[]{2})=0[/tex]and find the value of x what make each parenthesis 0
[tex]\begin{gathered} \sqrt[]{2}x-\sqrt[]{2}=0 \\ \sqrt[]{2}x=\sqrt[]{2} \\ x=1 \end{gathered}[/tex]first restricted value is x=1
[tex]\begin{gathered} \sqrt[]{2}x+\sqrt[]{2}=0 \\ \sqrt[]{2}x=-\sqrt[]{2} \\ x=-1 \end{gathered}[/tex]
and the other restricted value is x=-1
Question 2: Attached in screenshot below: If chart from question 1 is needed just tell me.
EXPLANATION
The slope field can be obtained by applying a graph drawing as shown as follows:
find:For f(x) = 5x – 2 and g(2) = 4xa) (f - g)(x) =wb) (f-9)(-3) =
We have functions f and g defined as:
f(x) = 5x - 2
g(x) = 4x - 2
We can subtract both functions:
f(x) - g(x) = (5x - 2) - (4x - 2) = 5x - 2 - 4x + 2
Then:
f(x) - g(x) = x
But, by definition, we know that:
(f - g)(x) = f(x) - g(x)
Putting these together:
(f - g)(x) = x
Now, if x = -3:
(f - g)(-3) = -3
given the following system identify the type of system x+y=4x-y=6
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given system of equation
[tex]\begin{gathered} x+y=4----equation\text{ 1} \\ x-y=6-----equation\text{ 2} \end{gathered}[/tex]STEP 2: Solve the given equation
Subtract equation 2 from equation 1
[tex]\begin{gathered} (x-x)+(y-(-y))=4-6 \\ y+y=-2 \\ 2y=-2 \\ Divide\text{ both sides by 2} \\ \frac{2y}{2}=-\frac{2}{2} \\ y=-1 \end{gathered}[/tex]STEP 3: Solve for x
[tex]\begin{gathered} Substitute\text{ -1 for y in equation 1} \\ x+(-1)=4 \\ x-1=4 \\ x=4+1 \\ x=5 \end{gathered}[/tex]The values of x and y are 5 and -1 respectively meaning that the system has one solution, hence the type of system of equation given is a CONSISTENT system of linear equation.
Why are lysosomes important to the health of cells?(1 point)
Responses
They break down worn-out cell parts that are no longer needed.
They break down worn-out cell parts that are no longer needed.
They move proteins around the cell.
They move proteins around the cell.
They allow cell organelles to move freely through the cell as needed.
They allow cell organelles to move freely through the cell as needed.
They create cell boundaries and make cells rigid.
They create cell boundaries and make cells rigid.
PLEASE HELP ME!!!
Lysosomes are important to the health of cells of the following reason:
They break down worn-out cell parts that are no longer needed.What are Lysosomes?Lysosomes can be defined as protective organelles that contain enzymes that can be used to break down negative microorganisms that invade the body. The Lysosomes are very important to the health of cells because they protect the cells from being damaged by viruses and bacteria that can limit the growth of the body.
So, the option that explains why lysosomes are important to the health of cells is that they break down worn-out cell parts that are no longer needed. Option A is accurate.
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Solve for points please
One loaf of bread and six rolls cost $1.80. At the same prices, two loaves of bread and four rolls cost $2.40. How much does one loaf of bread cost?
We have to find the price of one loaf of bread.
With the information we have, we can construct a system of equations.
Let B be the price of one loaf of bread and R the price of a roll.
Then, if one loaf of bread and six rolls cost $1.80, we can write:
[tex]B+6R=1.80[/tex]We also know that two loaves of bread and four rolls cost $2.40, so we can write:
[tex]2B+4R=2.40[/tex]We can solve for B with the method of elimination: we can substract the first equation from 1.5 times the second equation.
This can be express in mathematica terms as:
[tex]\begin{gathered} 1.5(2B+4R)-(B+6R)=1.5\cdot2.40-1.80 \\ 3B+6R-B-6R=3.60-1.80 \\ (3-1)B+(6-6)R=1.80 \\ 2B=1.80 \\ B=\frac{1.80}{2} \\ B=0.90 \end{gathered}[/tex]Then, we have just calculated that the loaf of bread costs $0.90.
Answer: the cost of a loaf of bread is $0.90.
An individual borrowed 84000 at an APR of 3% which will be paid off with monthly payments of $422 for 23 years
If an individual borrowed 84000 the Starting loan principal is $84,000; Interest rate is 3%; Number of payment per year is 12 payments per year; Loan term is 23 years; Payment amount is $422.
Principal loana. Identifying the starting loan principal, the interest rate, the number of payments per year, the loan term, and the payment amount.
Starting loan principal = $84,000
Interest rate =3%
Number of payment per year = 12 payments per year
Loan term = 23 years
Payment amount = $422
b. Total payment
There are 12 payments every year for 23 years, so
12 × 23 = 276
c. Total amount
Total amount 276× $422
Total amount = $116,472
d. Toward principal and interest
Toward Principal = $84,000
Toward Interest = $116,472 - $84,000
Toward Interest = $32,472
Therefore the starting loan principal is $84,000.
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The complete question is:
An individual borrowed 84000 at an APR of 3% which will be paid off with monthly payments of $422 for 23 years
a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.
A. The amount borrowed is
The annual interest rate is
The number of payments per year is
The loan term is
The payment amount is
B. How many total payments does the loan require? What is the total amount paid over the full term of the loan?
C. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?
The percentage paid toward the principal is
and the percentage paid for interest is:
24) j(h - 9) + 2; use h=9, and j = 8
Answer:
The value of the expression at h=9 and j=8 is;
[tex]2[/tex]Explanation:
Given the expression;
[tex]j(h-9)^3+2[/tex]At;
[tex]\begin{gathered} h=9 \\ j=8 \end{gathered}[/tex]substituting the given values of the variables;
[tex]\begin{gathered} j(h-9)^3+2 \\ 8(9-9)^3+2 \\ 8(0)+2 \\ =2 \end{gathered}[/tex]Therefore, the value of the expression at h=9 and j=8 is;
[tex]2[/tex]Answer:
2
Step-by-step explanation:
j(h - 9) + 2
Let h=9 and j=8
8(9 - 9) + 2
Parentheses first
8(0) + 2
Multiply
0+2
Add
2
The cost of providing water bottles at a high school football game is $35 for the
rental of the coolers and $0.50 per bottle of water.
A. What does $35 represent in the function for this situation?
B. What does $0.50 represent in the function for this situation?
C. Write a function for the amount 'C, in dollars, of providing b water bottles.
D. What is an appropriate domain for the function?
E. Graph the function over the appropriate domain.
Answer:
Step-by-step explanation:
A.
35 dollars represents the cost of renting the coolers (I think it's a constant since it does not say it is the cost per cooler).
B.
0.50 cent represents the cost per water bottle in the function (the coefficient in front of b, the amount of water bottles being purchased).
C.
C is the total cost.
C = 0.50b + 35
D.
I'm not sure what this is asking. Y = 0.50x + 35's domain is all real numbers but I'm not sure what it means by "appropriate domain for the function" unless the problem is using the average statistics from actual high school football games based on how many water bottles are purchased or something else.
E.
The graph would be all real numbers unless I'm wrong. Which is very possible on d and e but I think I provided the correct info on the others.
If cos x= √2/2 and x is a fourth quadrant angle, evaluate tan x
Given that;
[tex]\begin{gathered} \cos x=\frac{\sqrt[]{2}}{2} \\ and\text{ x is a fourth angle quadrant.} \end{gathered}[/tex]Note that cosine is positive on the fourth angle quadrant while tangent is negative.
From;
[tex]\begin{gathered} \cos x=\frac{\sqrt[]{2}}{2} \\ \text{adjacent}=\sqrt[]{2},\text{ hypotenuse= 2} \\ \text{opposite}=\text{ }\sqrt[]{2^2-(\sqrt[]{2})^2} \\ \text{opposite}=\sqrt[]{4-2} \\ \text{opposite}=\sqrt[]{2} \\ \end{gathered}[/tex]Thus, the tangent is;
[tex]\begin{gathered} \tan x=\frac{-\sqrt[]{2}}{\sqrt[]{2}} \\ \tan x=-1 \end{gathered}[/tex]There are different types of proofs: two-column, paragraph and flow chart. Which of these type of proofs do you prefer? Why?
I prefer the two-column proof since it is the most common format in high school textbooks. One can easily find each of the steps of the proof, and one can correct any step so you can continue the next one step by step in a chronological list of them.
It is easy to audit this type of proof, and I am very comfortable using it.
Decide whether it is an even function, an odd function, or neither
Given:
There are 2 graphs and 2 functions given in the question
Required:
We need to identify that which are even and which are odd
Explanation:
Even function:
f(-x) = f(x)
The graph of an even function is symmetric with respect to the y-axis.
Odd function:
f(-x) = -f(x)
The graph of an odd function is symmetric with respect to the origin
Here 1st graph is neither even nor odd function because it is not symmetric with respect to the y-axis and also not symmetric with respect to the origin
2nd graph is even because it is
1st function is neither even nor odd because
[tex]f(-x)=-6(-x)^5+7x^2=6x^5+7x^2\ne-f(x)[/tex]2nd function is
what is the average rate of change of the equation f(x)=x^2+3x-5 from x=2 to x=4
The formula to calculate the average rate of change is as follows:
[tex]R=\frac{f(b)-f(a)}{b-a}[/tex]Where "a" represents the starting point and "b" the ending point.
So, a = 2 and b = 4 in this case, so we have:
[tex]\begin{gathered} a=2 \\ f(a)=f(2)=2^2+3\cdot2-5=4+6-5=5 \\ b=4 \\ f(b)=f(4)=4^2+3\cdot4-5=16+12-5=23 \end{gathered}[/tex]Thus:
[tex]R=\frac{23-5}{4-2}=\frac{18}{2}=9[/tex]The average rate of change is 9.
5. Alex's friend Pablo comes
up with
an exact equation to find out how many bags he needs. Use his equation to find out how many bags will actually be needed if B=x(2x+7)+3(2x+7)+(x+4)(2x+7), where the quantity (2x + 7) equals 4. Show how you arrive at your answer.
8.5 bags will actually be needed if B=x(2x+7)+3(2x+7)+(x+4)(2x+7), where the quantity (2x + 7) equals 4
What is an Expression?Expression: An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) Expressions can be thought of as similar to phrases. In language, a phrase on its own may include an action, but it doesn't make a complete sentence.
Number of bags needed B=x(2x+7)+3(2x+7)+(x+4)
where the quantity (2x+7)=4
2x+7=4
2x=4-7
2x=-3
x=-3/2
now we are given the no. of bags needed
B=x(2x+7)+3(2x+7)+(x+4)
substitute the value of x which is found above x=-3/2
B=(-3/2)(2(-3/2)+7)+3(2(-3/2)+7)+((-3/2)+4)
B=8.5
hence 8.5 bags are needed
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What are the missing reasons for the proof?
URGENT
△ABD is congruent to △CDB (△ABD ≅ △CDB) under the SAS congruency condition.
What is the congruency of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. The relationship between equality and congruence is established by three key theorems. If and only if two angles have equal measures, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.So, △ABD ≅ △CDB:
AD || BD (Definition of parallelogram: Given)∠ADB ≅ ∠CDB (Alernate interior angles throrem: Given)AB || CD (Definition of parallelogram)∠ABD ≅ ∠CDB (Alternate interior angles throrem)DB ≅ DB (Common line)△ABD ≅ △CDB (SAS condition)Therefore, △ABD is congruent to △CDB (△ABD ≅ △CDB) under the SAS congruency condition.
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which has the larger 15th term when comparing the arithmetric and geometric sequences below? show evidence that support your answer Arithmetic sequence: 150, 650, 1150, 1650Geometric sequence:4,12, 36, 108
Answer
For the arithmetic sequence,
15th term = 7,500
For the geometric sequence,
15th term = 19,131,876
We can see that the geometric sequence has the larger 15th term.
Explanation
The general formula for an arithmetic progression is
f(n) = a + (n - 1)d
where
a = first term = 150
n = number of terms
d = common difference
= (Second term) - (First term)
= (Third term) - (Second term)
= Difference between consecutive terms
= 650 - 150
= 500
f(n) = 150 + (n - 1)500
f(n) = 150 + 500n - 500
f(n) = -350 + 500n
For the 15th term, n = 15
f(n) = -350 + 500n
f(15) = -350 + 500(15)
f(15) = -350 + 7500
f(15) = 7,150
For the geometric sequence,
[tex]f(n)=ar^{n-1}[/tex]where
a = first term = 4
n = number of terms
r = common ratio
= (Second term)/(First term)
= (Third term)/(Second term)
= Ratio of consecutive terms
= (12/4)
= 3
For the 15th term, n = 15
[tex]\begin{gathered} f(n)=ar^{n-1} \\ f(15)=4\times3^{15-1} \\ f(15)=4\times3^{14} \\ f(15)=19,131,876 \end{gathered}[/tex]Hope this Helps!!!
A construction crew is lengthening a road. The road started with a length of 54 miles, and the crew is adding 2 miles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then us
this equation to find the total length of the road after the crew has worked 32 days.
Equation:
Total length of the road after 32 days: ___ miles
Answer: 456 Miles
Step-by-step explanation:
Find the equation of the tangent line e^-4t at t=0
Given -
y = e^-4t
To Find -
The equation of the tangent =?
Step-by-Step Explanation -
y = e^-4t
So, dy/dx =
y' = -4e^-4t
also,
m = y'(0) = -4e^-4(0)
= -4
So,
when x = 0, y = e^0 = 1
So, point of tangency is (0,1)
Slope of tangent is -4
Using point-slope form:
y - 1 = -4(x - 0)
y = -4x +1
Final Answer -
The equation of the tangent =
y = -4x +1 or at x = t
y = -4t +1
