[tex]\sf{\dfrac{a^x}{log(a)} }[/tex]
(OR)[tex]\sf{\dfrac{a^x}{ln(a)} }[/tex]
[tex]\large\bold{\underline{\underline{Solution:-}}}[/tex][tex]\sf{Let\ y=\dfrac{a^x}{ln(a)} }[/tex]
[tex]\sf{=\dfrac{d}{dx}\bigg[\dfrac{a^x}{ln(a)} \bigg] }[/tex]
(Linear differentiation)[tex]\sf{=\dfrac{1}{ln(a)}.\dfrac{d}{dx}(a^x) }[/tex]
[tex]\sf{=\dfrac{ln(a)a^x}{ln(a)} }[/tex]
[tex]\boxed{\sf{=a^x}}[/tex]
[tex]\large\bold{\underline{\underline{Applied:-}}}[/tex]✭ Linear differentiation→ [tex]\sf{[a.b(x)+c.d(x)]'=a.b'(x)+c.d'(x)}[/tex]
✭ Exponential function rule
→ [tex]\sf{(a^x)'=ln(a).a^x}[/tex]
Answer:
a^x.
Step-by-step explanation:
y = a^x / log a
Assuming the log is to the base e:
y = (1/ log a) * a^x
Derivative of a^x:
Let u = a^x
log u = log a^x
log u = x log a
1/u * du/dx = log a
du/dx = = u * log a
y = (1 / log a) * u
so dy/du = 1/log a
and dy/dx = dy/du * du/dx
= (1/log a )* log a u
= u
= a^x.
The base of a right triangle is 2 meters greater than the height. If the area of the triangle is 100 m2, what are the dimensions of the base and the height?
Answer:
b = 15.2 m
h = 13.2 m
Step-by-step explanation:
The area of a right triangle is given by:
[tex] A = \frac{bh}{2} [/tex] (1)
Where:
b: is the base
h: is the height
If the base is 2 meters greater than the height we have:
[tex]b = h + 2[/tex] (2)
And if the area of the triangle is 100 m², the dimensions of the base can be found by entering equation (2) into (1):
[tex]100 m^{2} = \frac{(h + 2)*h}{2}[/tex]
[tex] 200 m^{2} = h^{2} + 2h [/tex]
[tex] h^{2} + 2h - 200 m^{2} = 0 [/tex]
By solving the above quadratic equation we have:
[tex] h = 13.2 m [/tex]
And by entering the above value into equation (2) we have:
[tex]b = 13.2 + 2 m = 15.2 m[/tex]
Therefore, the dimensions of the base and the height are 15.2 m and 13.2 m respectively.
I hope it helps you!
Identify the two factors that were multiplied together to form the array of tiles. Then identify the product of the two factors. Use the variable x in your expressions.
Answer:
[tex]Terms: 3\ and\ x + 2[/tex]
[tex]Product = 3x + 6[/tex]
Step-by-step explanation:
See attachment for complete question.
From the attachment, there are 3 columns and 3 rows
The 3 columns represent the first factor
To get the second factor, we have to analyze the 3 rows in the attachment.
Notice that the first row is bigger than the other two rows.
This big row will be represented with variable x
Notice that the boxes in second row are smaller than the first row and the + sign is written on each of the boxes.
This is represented with + 1
Also, notice that the boxes in third row are smaller than the first row and the + sign is written on each of the boxes.
This is also represented with + 1
Hence, the expression for the rows is x + 1 + 1 = x + 2
The product is then calculated as:
[tex]Product = 3 * (x + 2)[/tex]
[tex]Product = 3 * x + 3*2[/tex]
[tex]Product = 3x + 6[/tex]
Write a function in any form that would match the graph shown below. please help :)
Answer:
0, -4
2,0
-4,0
-2,-8
Step-by-step explanation:
I chose the points that were most visable
what is 11÷132?? anwser please
Answer:
11÷132= 0.0833333333
but i think u wanted this answer
132÷11= 12
the sum of two numbers is 10 and their difference is 6
Writing Linear Equations from Key Information slope = 3, y-intercept = −1
Answer:
y = 3x - 1
Step-by-step explanation:
ANSWER ASAP look at pic and answer #18
Answer:
Four
Step-by-step explanation:
5TH GRADE MATH 15 POINTS GIVEN HELP
Answer:
The question?
Step-by-step explanation:
we need question to answer
M<2=12x+5 and m<7 4x+19 find m<2
Ana mixed 1 cup of lemonade with 4 cups of cranberry juice to make her favorite punch. How much cranberry juice will she use for 5 cups of lemonade. PLEASE HELP ME ASAPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
20
Step-by-step explanation:
since for every 1 lemonade there is 4 cranberry you have 5 lemonade now so you need 4 cranberry for every one of the 5 lemonade, which gives you 20
Can people help me on this please I need it!!! It’s really important
Answer:
62
Step-by-step explanation:
The total of a triangle is 180
so 78+48 is 118
180-118=62
The seniors on the student council bought a total of 36 plants to use in landscaping the front of the school. They bought some azaleas that cost $6
each and some lilles that cost $5 each. They spent a total of $196 on these plants. How many azaleas did the students buy?
Answer:
The students bought 16 azaleas plants.
Step-by-step explanation:
Given that:
Total plants bought by student council = 36
Cost of each azaleas plant = $6
Cost of each lily plant = $5
Total amount spent = $196
Let,
x be the number of azaleas
y be the number of lilies
x+y = 36 Eqn 1
6x+5y=196 Eqn 2
Multiplying Eqn 1 by 6
6(x+y=36)
6x+6y=216 Eqn 3
Subtracting Eqn 2 from Eqn 3
(6x+6y)-(6x+5y)=216-196
6x+6y-6x-5y=20
y=20
Putting y=20 in Eqn 1
x+20=36
x=36-20
x=16
Hence,
The students bought 16 azaleas plants.
Slove by using elimination
3x+7y=27
-3x+y=21
Answer:
x = -5
y = 6
Step-by-step explanation:
3x + 7y = 27 --------------(I)
-3x + y = 21 -----------(II)
Add equation (I) & (II) and so x will be eliminated and we can find the value of y.
(I) 3x + 7y = 27
(II) -3x + y = 21 {add}
8y = 48
y = 48/8
y = 6
Plugin y = 6 in equation (I)
3x +7*6 = 27
3x + 42 = 27
3x = 27 - 42
3x = -15
x = -15/3
x = -5
GIVING BRAINLIEST PLZZ HELP ASAP
Answer:
D
Step-by-step explanation:
x and y go up at a constant rate (or you can say it has a CROC or constant rate of chacge) y going up 5 for every one x
with our equation being y = 5x + 5
hope this helps <3
Answer:
Step-by-step explanation:
It would be D because to know if its linear, x has to increase by 1 and y by a constant rate.
X increases by 1 and y increases by 5
I've attached a graph for you to see
If you have any further questions, don't be afraid to reach out! I hope this helps!
John sells forty funnel cakes at the fair in five hours. How
many funnel cake did he sell per hour?
Answer:
John sold 8 funnel cakes in 1 hour
Step-by-step explanation:
Hope I helped
Answer:
An average of 8 funnel cakes an hour
Step-by-step explanation:
40/5=8 but we don't know if he sold the same amount every hour.
Write an equation of the line that passes through the points (0,4) and (2, 10).
Answer:
y=3x+4
Step-by-step explanation:
one bucket of gravel has a mass of 7.05 kg. what is the mass of 20 buckets of gravel in kilograms?
The weight of 20 buckets is 141 Kg.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
weight of 1 bucket of gravel = 7.05
weight of 20 buckets = 7.05 x 20
= 141 Kg
Hence, the weight of 20 buckets is 141 Kg.
Learn more about unitary method here:
https://brainly.com/question/22056199
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I ONLY NEED THE ANSWER FOR C. THE OTHER TWO ARE CORRECT. PLEASE HELP :(
Answer:
1.2 I think sorry if I'm wrong double check to see
Step-by-step explanation:
This is what I thought of oof so sorry if it incorrect
-4.8 (6.3x-4.18)=-58.56 what is x?
Answer:
x = 2.825
Step-by-step explanation:
-4.3(6.3x + -4.18) = -58.56
-4.3(-4.18 + 6.3x) = -58.56
(-4.18 * -4.3 + 6.3x * -4.3) = -58.56
(17.974 + -27.09x) = -58.56
17.974 + -27.09x = -58.56
17.974 + -17.974 + -27.09x = -58.56 + -17.974
0.000 + -27.09x = -58.56 + -17.974
-27.09x = -58.56 + -17.974
-27.09x = -76.534
x = 2.825175341
Determine if the function is even, odd, or neither.
Answer:
It is an even function.
f(t) = 2 cos πt
Thank you and please rate me as brainliest as it will help me to level up
Answer:
I think its odd as I guess.
URGENT
The measure of one of the acute angles in a right triangle is 24. what is the measure of the other angle?
Answer:
do you have pictures and more measurements so i can solve the problem for you?
Step-by-step explanation:
Write the number that is 3 million more than 648 000 000.
Answer:
651,000,000
Step-by-step explanation:
Answer:
651,000,000
I think u knew this already tho :)
Which lines have a y-intercept of 5? Check all that apply.
A: y=5x-1
B: 4x-8y=40
C: x-y=5
D: x-3y=15
E: 2x-y=10
F: 6x+4y=20
Answer:
F: 6x+4y=20
Step-by-step explanation:
Only line representing the equation 6x+4y=20 has y-intercept of 5.
The line that has the y-intercept = 5 is 6x + 4y = 20
What are intercepts?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
The standard slope intercept form:
y = mx + b
Comparing the options A,C,D and E with standard form and none of the options have b = 5.
So these options are out.
Now the options B,
Simplify, y = x/2 - 5
Compare with slope intercept form, and this equation also does not have
the y intercept as 5.
Now option F;
simplify, 6x + 4y = 20
y = -3x/2 + 5
Comparing with standard form,
And b= 5
Therefore, The line that has the y-intercept = 5 is 6x + 4y = 20
To learn more about the intercepts;
https://brainly.com/question/14180189
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Plss Someone answer!!!!
Answer:
50 hours
Step-by-step explanation:
if it takes 5 hours for 2 inches to fall, then you multiply 2 by ten to get 20, you do the same thing to the other half of the equation, or five, to get 50 hours.
55 pages in 25 minutes
Write the point-slope form of the line that has a slope of -7 and passes through the point (10,4).
Answer:
y=10/4-7
Step-by-step explanation:
120% of __________ is 78
120% of 65 is 78.
This means that 120 times what equals 78.
120*65=78
Answer:
65
Step-by-step explanation:
thianamccornell1 no one else
Answer:
Oh I see, that’s weird
Step-by-step explanation:
Maybe you have to wait a while or wait for somebody else to answer because that’s what happens to me sometimes
sara ordered 2 eggs, a slice of bacon, and a glass of orange juice for breakfast. the sales tax for the order was $0.48. she paid for her breakfast with a $10 bill.
one egg = $1.69
slice of bacon = $1.49
glass of orange juice = $1.09
how much change should sara receive from the $10 bill?
Answer:
She should receive $3.56 from paying with a $10 bill
Step-by-step explanation:
The total cost of all her items including sales tax is
$6.44
You have to deduct this total cost from what she paid with.
$10.00 - $6.44 = $3.56
Therefore,
Sara should receive $3.56 from paying with a $10 bill.
Answer: $3.56
Step by step explanation:
1. Figure out how much the eggs cost. (1.69×2=3.38)
2. Add the price of the eggs, bacon, O.J., and sales tax together. (3.38+1.49+1.09+0.48=6.44)
3. Subtract the total ($6.44) by the amount you paid ($10). (10-6.44=3.56)
Pleas help! I'll give brainliest!!!
Which of the following statements is true?
A material with randomly oriented atoms is not magnetic.
All materials are magnetic.
Electrons are atoms that are magnetic.
Electrons are atoms that re magnetic
Answer:
Electrons are atoms that are magnetic.
Step-by-step explanation:
Answer:
Electrons are atoms that are magnetic