9514 1404 393
Answer:
c = -3; d = 5
Step-by-step explanation:
The function is differentiable if it is continuous and the derivative is continuous.
This function will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
5(3^2) +c = 45 +c
From the right, the limit is ...
d(3^2) -3 = 9d -3
__
The derivative will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
f'(x) = 10x
= 10(3) = 30
From the right, the limit is ...
f'(x) = 2dx
= 2d(3) = 6d
__
This gives us a pair of simultaneous equations in 'c' and 'd':
45 +c = 9d -3
6d = 30
The latter tells us d = 5. Then the former tells us ...
45 +c = 9(5) -3 ⇒ c = -3
The function is differentiable if c = -3 and d = 5.
_____
Additional comment
With these values, the function becomes ...
[tex]f(x)=\begin{cases}5x^2-3&\text{if }x\le 3\\5x^2-3&\text{if }x>3\end{cases}[/tex]
I know the answer to the question but what is 45292062 + 64829162629 + 123146 =
Answer:
64874577837
Step-by-step explanation:
you simply add the numbers
45292062 + 64829162629 + 123146 =
64874454691 +123146
64874577837Trevor found that a circle has a circumference of 15 ft. What is the diameter & radius of the circle? Write & solve an equation. Leave your answer as a decimal.
Answer: R = 2.38732415 D = 4.7746482927568605
If you put $6.57 into a savings account that earns 6%, how much interests
will you receive at the end of seven years?
Answer:
817.51
Step-by-step explanation:
Please help me finish my math homework
Answer:
x³+y³+z³=k
Explanation:
I talk, he talk, why you middle talk? You rotate the ground 4 times. You go and understand the tree. I'll give you clap on your cheeks. Bring your parents and your mother and especially your father. Close the window airforce is coming. I have two daughters and both are girls. Stand in a straight circle. Don't stand in front of my back
1. The order of the angles from smallest to greatest is PQR, QRP, PRQ.
2. The value of x + y is (2x + 179)/7.
3. Triangle GHK is isosceles because angles H and K are congruent.
4. The hypotenuse is always the longest side of a right triangle.
1. To determine the order of the angles in the given triangle, we can use the fact that the largest angle will be opposite the longest side. Let's compare the lengths of the sides:
- PQ = 5.6
- PR = 6.1
- QR = 5.2
From the given lengths, we can see that PR is the longest side. Therefore, angle PRQ will be the largest angle. Now we need to compare the remaining two angles, PQR and QRP. Since QR is the shortest side, angle PQR will be the smallest angle. This means that the order of the angles from smallest to greatest is: PQR, QRP, PRQ.
2. In a triangle, the sum of the interior angles is always 180 degrees. Given the angles in terms of y and x, we can set up an equation:
(4y - 8) + (3y + 9) + 5x = 180
Combining like terms:
7y + 5x + 1 = 180
To find the value of x + y, we need to solve for y in terms of x first. Let's isolate y:
7y = 180 - 5x - 1
7y = 179 - 5x
y = (179 - 5x)/7
Now, we can substitute this expression for y into the equation x + y:
x + y = x + (179 - 5x)/7
To simplify further, we can distribute the division:
x + y = (7x + 179 - 5x)/7
x + y = (2x + 179)/7
Therefore, the value of x + y is (2x + 179)/7.
3. To prove that triangle GHK is isosceles, we need to show that two of its sides are congruent. Given that angle H is 56 degrees, and angles IKJ and H are alternate interior angles, we know that angle IKJ is also 56 degrees. Since angle IKJ is 68 degrees, this implies that angle KJI is 112 degrees (180 - 68 = 112).
Now, considering triangle GHK, we have:
- Angle G = 180 - (angle H + angle K) = 180 - (56 + 112) = 180 - 168 = 12 degrees
Since angle G is 12 degrees, and angles G and H are alternate interior angles, we know that angle H is also 12 degrees.
Therefore, we have two angles in triangle GHK that are congruent, namely angle H and angle K, making it an isosceles triangle.
4. Proof that the hypotenuse is always the longest side of a right triangle:
Let's consider a right triangle with sides a, b, and c, where c is the hypotenuse.
According to the Pythagorean theorem, which is a fundamental property of right triangles, we have:
[tex]c^2 = a^2 + b^2[/tex]
To compare the lengths of a, b, and c, let's square all the sides:
[tex]a^2, b^2, and c^2[/tex] are all positive since they are the squares of real numbers.
Now, if we examine the inequality [tex]a^2 + b^2 < c^2[/tex], we can see that the sum of the squares of the shorter sides is less than the square of the hypotenuse.
Since [tex]c^2 = a^2 + b^2[/tex], the inequality becomes [tex]a^2 + b^2 < a^2 + b^2[/tex], which is not possible.
Therefore, we can conclude that in a right triangle, the hypotenuse (side c) is always the longest side.
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IVE BEEN WORKING ON THIS ALL DAY
Two arithmetic sequences A and B both begin with 30. Sequence A has common difference 9 and sequence B has common difference 4. What is the difference between the 51st term of A and the 51st term of B?
The n-th term of an arithmetic sequence with first term a and common difference d is
a + (n - 1) d
So, the 51st term of A is
30 + 9 (51 - 1) = 480
while the 51st term of B is
30 + 4 (51 - 1) = 230
The difference between them 480 - 230 = 250.
A movie theater used Y=KX to calculate how much money
they made selling 9 buckets of popcorn. They determined they
made 45.99 dollars. How much was it for each bucket?
you need to do 300 hours of community service for a scholarship. you have served 135 hours so far. write and solve an inequality that represents the number of hours h that you have left to work.
3p - 8 = -23
What value of p makes this equation true
A. p= -6
B. p= -5
C. p= 5
D. p= 7
1. Cheryl is planning to spend $15 on a Christmas gift for her father. He needs new socks and ties. A store has socks on sale for $3 and ties for $5. Write an equation in standard form that
represents this situation.
Answer:
4 dollars in total
Step-by-step explanation:
its 75 after the spend
If
m ≤ f(x) ≤ M
for
a ≤ x ≤ b,
where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then
m(b − a) ≤
b
If
m ≤ f(x) ≤ M
for
a ≤ x ≤ b,
where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then m(b − a) ≤ f(x) dx ≤ M(b − a).
f(x) dx ≤ M(b − a).
Use this property to estimate the value of the integral.
8
(10x − 20 sin(x)) dx
7
Use the fact that -1 ≤ sin(x) ≤ 1.
Then
20 ≥ -20 sin(x) ≥ -20 … … … (multiply each side by -20)
-20 ≤ -20 sin(x) ≤ 20 … … … (swap the endpoints)
10x - 20 ≤ 10x - 20 sin(x) ≤ 10x + 20 … … … (add 10x to each side)
and over the interval [7, 8], we have
7 ≤ x ≤ 8
70 ≤ 10x ≤ 80 … … … (multiply each side by 10)
so that the whole integrand is bounded by
70 - 20 ≤ 10x - 20 sin(x) ≤ 80 + 20
50 ≤ 10x - 20 sin(x) ≤ 100
Take m = 50 and M = 100. It follows that
[tex]50(8-7) \le \displaystyle \int_7^8 (10x-20\sin(x)) \, dx \le 100(8-7)[/tex]
which places the value of the integral between 50 and 100.
A barge traveled 30 miles up a river in 5 hours What was the average rate of travel, in miles
per hour, of the barye?
Answer:
6 miles per hour
does this help??
Step-by-step explanation:
Average speed = distance/time = 30/5 = 6 miles/hour
Which of the following equations has the same solutions as the equation 3x+2y=-12? Check all that apply.
Answer number 10 no links
Answer: 6
Step-by-step explanation:if you add -5 1/3 plus (-2/3) that equals to -6 and if you are adding you gotta add a positive 6 to the negative 6 and that makes 0
[tex] - 5 \frac{1}{3} + ( - \frac{ 2}{3} ) + ? = 0[/tex]
To findThe missing term
Taking the missing term as "x"
Solution[tex] - 5 \frac{1}{3} + ( - \frac{ 2}{3} ) + ? = 0 \\ \\ \implies - \frac{ 16}{3} - \frac{2}{3} + x = 0 \\ \\ \implies \frac{ - 16 - 2}{3} + x = 0 \\ \\ \implies \frac{ - 18}{3} + x = 0 \\ \\ \implies \cancel \frac{ - 18}{3} + x = 0 \\ \\ \implies - 6 + x = 0 \\ \\ \implies x = 0 + 6 \\ \\ \implies x = \red6[/tex]
[tex] \therefore \tt{The \: \: missing \: \: term= 6}[/tex]
Hope This HelpsWhich rule explains why these scalene triangles are similar?
A. SSS
B. SAS
C. AA
D. None of the above; the triangles cannot be proven similar
Answer:
D. none of the above
Step-by-step explanation:
no side lengths given
no angles are the same in both triangles
helppppppppppppppppp meeeeeeeee
Answer:
WHEN THE BIRDS FLYING IN THE FIRE COZ THE MOON IS RECTANGLE I LIKE COLOR YELLOW COZ MY POP IS CIRCLE
Please help ... need help
Answer:
c maybe
Step-by-step explanation:
There were 82 goldfish in the tank at Jeremy’s birthday party. If this was 20% of the fish in the tank, how many fish were in the tank
Answer:
410 i think
Step-by-step explanation:
The graph below shows the height through which an elevator travels, y, in x seconds:
What is the rate of change for the relationship represented in the graph?
1 over 15
1 over 14
14
15
Help!
I do not understand a single thing lol I’m sorry<3
= 8
step-by-step explanation:
evaluate
-8c⁴ d +4c² d² + 16c - 2d
when c =-1 ,d=4
=8
hope it helps!#carry on learning
Sorry if I am incorrect.....
What is 184.24 to 4 significant figures
(-1,-1) has a slope of -6
Answer:
y=-6x+5
Step-by-step explanation:
can somebody please help me
I tried to solve it but I still don't get it
Answer:
x^3 - 4x^2 - 6x + 3
Step-by-step explanation:
Divide using polynomial division.
In all but the worst weather, Sarah and three coworkers meet each day at 4:45 to walk the river trail behind their office building. The four coworkers are an example of a(n)
The coworkers meet each day after the official work hours, then they are an example of an informal group. An informal group is a group made up of people to discuss non-official matters.
The two major types of groups relating to official function are formal and informal. Formal groups are groups formed by the management for a specific or official purpose. This type of groups discuss official matters and issues, and probably are dissolved after achieving the purpose of forming the group.
Informal groups are groups formed by a set of workers( which may sometimes include an external person) formed to discuss non-official maters. The members meet at the non-official hours to deliberate, gist or discuss personal and other relating issues.
Therefore, the four coworkers mentioned in the given question are an example of an informal group.
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10X10
yesssssssssssssssss
Answer:
100
Step-by-step explanation:
Answer:
100
Step-by-step explanation:
A 4-card poker hand is dealt at random from a standard 52-card deck. What is the total number of possible hands
Answer:
Step-by-step explanation:
The first choice is 1 out of 52
The second choice is 1 out of 51 because 1 card went with the first choice
The third is 1 out of 50
The fourth is 1 out of 49
Number of hands = 52*51*50*49
Number of hands = 6497400
Solve the math problem
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The slope of the given line is Undefined because it is parallel to y - axis ~
Answer:
zero
Step-by-step explanation:
Write the slope-intercept form of the equation of a line parallel to y=-2/3x+12 that has a y-intercept of -13 (step by step)
Answer:
y = -2/3x - 13
Step-by-step explanation:
The slope remains the same, but the y-intercept changes to -13
No one i don't know use this
Answer:
Lol
Step-by-step explanation:
Function or not a Function
Answer:
Function; Not a function
Step-by-step explanation:
Write the ordered pair in the first set (x, y): (1, 11), (2, 7) , (3, 2)
Write the ordered pair in the second set (x, y): (1, 3), (1, 4), (2, 4) , (3, 2)
The first set in a function because no ordered pair has the same x value.
The second set in not a function because the x value is the same in two of the ordered pairs.
