If y = aˣ, then y = exp(ln(aˣ)) = exp(x ln(a)). (Here I use exp(x) = eˣ.)
Then using the chain rule, the derivative of y is
dy/dx = exp(x ln(a)) • ln(a)
and undoing the rewriting, we end up with
dy/dx = ln(a) aˣ
If f(x)=7e^x, find which is the value of f(−3) rounded to the nearest hundredth.
Answer:
[tex]f(-3)\approx0.35[/tex]
Step-by-step explanation:
[tex]f(x)=7e^x[/tex]
[tex]f(-3)=7e^{-3}\approx0.35[/tex]
Someone help me click this solve it using < or >
Answer:
<
<
>
Step-by-step explanation:
To compare fractions, we need to make sure that both fractions have the same denominator. For example, for question 4, the least common multiple of 5 and 3 is 15, so we need to multiply both fractions by some numbers to get the denominators equal to 15. In this case, we will multiply the first fraction, [tex]\frac{3}{5}[/tex] by 3 to get [tex]\frac{9}{15}[/tex] and the second fraction, [tex]\frac{3}{3}[/tex] by 5 to get [tex]\frac{15}{15}[/tex].
Once we have the same denominator, we can simply compare the value of the numerators and see which one is larger. For question 4, since 9 is smaller than 15, the first fraction is smaller than the second. So the correct inequality to represent this would be "<".
To do these sums, we have to first convert them to like fractions.
For the first one:
LCM of denominators 5 and 3 is 15.[tex] \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} [/tex][tex] \frac{3}{3} = \frac{3 \times 5}{3 \times 5} = \frac{15}{15} [/tex]Since,[tex] \frac{9}{15} < \frac{15}{15} [/tex]Therefore,[tex] \frac{3}{5} < \frac{3}{3} [/tex]For the second sum:
LCM of denominators 6 and 8 is 24.[tex] \frac{4}{6} = \frac{4 \times 4}{6 \times 4} = \frac{16}{24} [/tex][tex] \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} [/tex]Since[tex] \frac{16}{24} < \frac{21}{24} [/tex]Therefore,[tex] \frac{4}{6} < \frac{7}{8} [/tex]For the third one:
LCM of denominators 10 and 5 is 10.[tex] \frac{6}{10} = \frac{6 \times 1}{10 \times 1} = \frac{6}{10} [/tex][tex] \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} [/tex]Since,[tex] \frac{6}{10} > \frac{4}{10} [/tex]Therefore,[tex] \frac{6}{10} > \frac{2}{5} [/tex]Hope you could get an idea from here.
Doubt clarification - use comment section.
A Car’s rectangular gas tank has dimensions 30 cm by 25 cm by 42 cm.
(a) Calculate the capacity in liters, of the tank.
(b) If gasoline cost $154 per liter, what is the cost of filling the tank?
Answer:
$4851
Step-by-step explanation:
rectangular prism volume = length x width x height
1 litre = 1000 cm³
cost = $per litre x litres
v = l x w x h
30cm x 25cm x 42cm = 31500cm³
litres = cm³ / 1000
31500cm³ / 1000 = 31.5 litres
31.5 x $154 = $4851
Six movie tickets cost $96 what is the cost per ticket
Cost of 6 tickets = $ 96
Cost of 1 ticket = ?
Cost of 1 ticket = 96/6
Cost per ticket = $ 16
______
Hope it helps ⚜
Step-by-step explanation:
6 tickets=$96
1 ticket =96/6
=16
the degree of the polynomial p³q²-6p²q⁵+p⁴q⁴
Answer:
idioet.
Step-by-step explanation:
what is the property of y • 0 = 0
Answer: The property of y x 0 = 0 is the Identity property.
Step-by-step explanation:
I hope this is what you were looking for, I apologize if I have been mistaken.
Directions: Given the point and slope, write the equation of the line. 3. (1,-7); slope = -1
Answer:
y=-1x-6
Step-by-step explanation:
Apply the distributive property to create an equivalent expression.
(6m -7)x4 =
Answer:
6mx^4-7x^4
Step-by-step explanation:
Find the area of the circle. Round to the nearest
tenth. Do not write units of measure.
Find the area of each circle. Use 3.14 for pi.
Answer:
452.16 cm
28.26 m
113.04 km
Step-by-step explanation:
The equation for area is r^2 π
where you square the radius and multiply by 3.14 or pi or how many digits you need to use.
For example, on the first question, you multiply the radius (12) by itself or square it to get 144.
Then you multiply 144 by 3.14 to get your first answer.
Add and simplify:
3 + 1
10 5
Answer:
I don't under stand the question can u write more clearly
Help help help help math
Answer:
158
Step-by-step explanation:
We know the supplement of angle 6 is 22, due to the fact that they are corresponding angles. Simply subtract 22 from 180 to get the answer. 180-22=158
Answer:
158 degrees
Step-by-step explanation:
Angle 6 has a same side interior relationship with the 22 degrees, so the sum of these angles are equal to 180 degrees.
To find the missing angle, subtract 180 by 22 degrees.
180-22= 158
What is the area of this figure ?
Answer:
172 in
Step-by-step explanation:
if you are in a 200 meter race and finish 19 meters ahead of your opponent, if you were to run the race again, where woild you have to start to end the race in a tie?
Answer:
i haven't done this in years but i'm pretty sure -19 meters
Step-by-step explanation:
A unique source of water pollution contributing to water quality problems in the Ganges River is: A. raw sewage. B. disease-causing organisms. C. zebra mussels. D. PCBs. E. ash from human cremations.
Evaluate the function when x = -1,0, and 4.
9. g(x) = 3 -
X
g(-1) =
g(0) =
+
g(4) =
Plz help me I need the answer
Step-by-step explanation:
what is the problem ?
as indicated you only need to use the corresponding value as "x" in the formula and then just calculate the result.
g(-1) = 3 - 1/3 × -1 = 3 + 1/3 = 3 1/3 or 10/3 or 3.333...
g(0) = 3 - 1/3 × 0 = 3
g(4) = 3 - 1/3 × 4 = 3 - 4/3 = 9/3 - 4/3 = 5/3 or 1 2/3 or 1.66666...
Answer:
g(-1) = 3/2
g(0) = 3
g(4) = 1
Solve for the value of X
Check the picture below.
Can you help me w this
x/3-2=6
+2
x/3=8
*3
x=24
x/5+1=5
-1
x/5=4
*5
x=20
Answer:
Step-by-step explanation:
a)
(x / 3) - 2 = 6
add 2 to both sides
x / 3 = 8
multiply both sides by 3
x = 24
b)
(x / 5) + 1 = 5
subtract 1 from both sides
(x / 5) = 4
multiply both sides by 5
x = 20
3. The grade-point averages of 20 college seniors selected at random from a graduating class are as follows:
3.2, 1.9 ,2.7, 2.4, 2.8, 2.9, 3.8, 3.0, 2.5, 3.3, 1.8, 2.5, 3.7, 2.8, 2.0, 3.2, 2.3, 2.1, 2.5, 1.9 Calculate the standard deviation.
The standard deviation of the grade points average of the college seniors is 0.57.
The given parameters:
3.2, 1.9 ,2.7, 2.4, 2.8, 2.9, 3.8, 3.0, 2.5, 3.3, 1.8, 2.5, 3.7, 2.8, 2.0, 3.2, 2.3, 2.1, 2.5, 1.9
The sum of the given data is calculated as follows;
∑x = 3.2 + 1.9 + 2.7 + 2.4 + 2.8 + 2.9 + 3.8 + 3.0 + 2.5 + 3.3 + 1.8 + 2.5 + 3.7 + 2.8 + 2.0 + 3.2 + 2.3 + 2.1 + 2.5 + 1.9
∑x = 53.3
The mean of the distribution is calculated as follows;
[tex]\bar x = \frac{\Sigma x}{N} \\\\\bar x = \frac{53.3}{20} \\\\\bar x = 2.665[/tex]
The square of the difference between the grade point and the mean;
[tex]\Sigma (x - \bar x)^2 = (3.2- 2.665)^2 + (1.9-2.665)^2 + (2.7- 2.665)^2 + (2.4-2.665)^2 \\\\+(2.8-2.665)^2 +(2.9 - 2.665)^2 + (3.8 - 2.665)^2 + (3-2.665)^2+ \\\\(2.5 -2.665)^2 + (3.3 - 2.665)^2 + (1.8-2.665)^2 + (2.5 - 2.665)^2 + \\\\(3.7-2.665)^2 + (2.8 - 2.665)^2 + (2-2.665)^2 + (3.2-2.665)^2 + \\\\(2.3 - 2.665)^2 + (2.1-2.665)^2 + (2.5-2.665)^2 + (1.9 - 2.665)^2\\\\\Sigma (x - \bar x)^2 = 6.5055[/tex]
The standard deviation of the grade points is calculated as follows;
[tex]\sigma = \sqrt{\frac{\Sigma (x-\bar x)^2}{N} } \\\\\sigma = \sqrt{\frac{6.5055}{20} } \\\\\sigma = 0.57[/tex]
Thus, the standard deviation of the grade points average of the college seniors is 0.57.
Learn more about standard deviation here: https://brainly.com/question/12402189
what the words corresponding to the obtained value in the box provide on your answer sheet
[tex] \sqrt{2.5 \sqrt{8} } [/tex]
Answer:
4.47Step-by-step explanation:
Hope it helps to youEvaluate. 5.8 – 3.63 = ________
Graph the function
f(x) = 3/5x - 5
Step-by-step explanation:
okay, plot a point at (0,-5) then count 3 units up and 5 units to the right and put a point there
connect the points with a straight line
add arrows to each end of the line :)
a lab has two bacterial cultures. culture a contains 4 x 10^4 and culture b contains 8x10^6 bacteria. how many times greater is culture b than culture a
Find the measure of the following: m arcTR = m arcTL = m ∠L = m ∠R = m ∠RTV =
Applying the inscribed angle theorem, the missing measures are:
measure of arc TR = 106°
measure of arc TL = 74°
m∠L = 50°
m∠R = 37°
m∠RTV = 37°
The Inscribed Angle TheoremMeasure of an inscribed angle = half the measure of the arc it intercepts
Central angle = measure of intercepted arc
We are given the following:
LR and TV are diameters of the circle O.
m∠TOR = 106° (central angle)
Find measure of arc TR:
measure of arc TR = m∠TOR
measure of arc TR = 106°
Find measure of arc TL:
measure of arc TL = 180° - m∠TOR
measure of arc TL = 180° - 106°
measure of arc TL = 74°
Find m∠L:
m∠L = ½(measure of arc TR)
m∠L = ½(106°)
m∠L = 50°
Find m∠R:
m∠R = ½(measure of arc TL)
m∠R = ½(74°)
m∠R = 37°
Find m∠RTV:
m∠RTV = ½(measure of arc RV)
m∠RTV = ½(180 - 106)
m∠RTV = ½(74)
m∠RTV = 37°
Learn more about the inscribed angle theorem on:
https://brainly.com/question/14267250
If it takes 7.1 pounds of seed to plant one acre of grass, how many acres can be planted with 7.81 pounds of seed?
Answer: make me brainlist
Step-by-step explanation: 1.1 x
A card is fresh from an ordinary deck. Find the probability that it did a diamond given that it is a jack
Answer:
1/52
Step-by-step explanation:
A deck has 52 cards and the probability of picking a specific one is 1/52, or 1.92%
If you are looking for the probability of a diamond, it is 1/4, or 25%
NEED HELP! GIVING OUT BRAINLIEST! (Need long answer)
The diagram below shows a proportional relationship between the number of cans of soup and the price.
Explain what this value means in terms of the soup.
-) Which is a valid velocity reading for an object? O 45 m/s O 45 m/s north 23 O O m/s south O 0 m/s ok Save and Exit Next Mark this and return
Answer:
Step-by-step explanation:
0 can't have a direction. It does not move. It has no speed component. Therefore 0 m/s south is not the answer.
45 m/s has no direction stated. It is just a speed, not a velocity.
45 m/s north is a velocity. It has both speed and direction.
the questions are in the pdfs i really need help
Answer:
Step-by-step explanation:
1) 11 + 11
2) 17 - n
3) x^2
4) 3^3
5) 88 / 8
6) 6 + 11
7) the quotient of 35 and 5
8) the sum of 4 and 5
9) 10 squared
10) 3 less than x
13) p^3 + qp
2^3 + 4(2)
8 + 8 + 16
14) (y^3)z / 3
(5^3)3 / 3
125(3) / 3
375 / 3
125
15) 2 + (j - h)^2
2 + (5 - 3)^2
2 + (2)^2
2 + 4
6
help me please thanks
Answer:
9.25 would be the value of x
Explanation:
Perimeter = 2(l + w)
2(13.25 + 9.25)
= 45
I need help please I'll give you 25 points
Answer:
t = 11/21
Step-by-step explanation:
Hope this helps!!