Answer:
The equation for the curve is:
[tex]f(x) = 7*e^{2*x}[/tex]
Step-by-step explanation:
We know that for a curve defined as:
y = f(x)
The slope of the curve at the point x is:
y = f'(x)
where f'(x) = df(x)/dx
Here we know that we have a function that passes through the point (0, 7)
We also know that the slope of the curve at every point is twice the value of the y-coordinate. (remember that the y-coordinate is given by f(x))
Then we have two equations:
f(0) = 7
f'(x) = 2*f(x)
From the shape of the equation, we can assume than this is an exponential equation like:
[tex]f(x) = A*e^{k*x}[/tex]
Replacing that in the second equation, we get:
[tex]k*A*e^{k*x} = 2*A*e^{k*x}[/tex]
From that equation, we can conclude that k = 2
Then:
[tex]f(x) = A*e^{2*x}[/tex]
Now we can use the first equation:
f(0) = 7
With this, we can find the value of A.
[tex]f(0) = 7 = A*e^{2*0}\\7 = A*e^0 = A*1\\7 = A[/tex]
Then we can conclude that the equation for the curve is:
[tex]f(x) = 7*e^{2*x}[/tex]
Use two equations in two variables to solve the problem.
A merchant wants to mix peanuts and cashews, as shown in the illustration, to get 42 pounds of mixed nuts that will be sold at $6 per pound. How many pounds of each should the merchant use?
Answer:
Step-by-step explanation:
36 apples cost $6. how many apples can you buy for $1?
Answer:
16 cents
Step-by-step explanation:
6 divided by 36 = 0.16666667
Dawn has less than $60. She wants to buy 3 sweaters. What price of sweaters can she afford if all the sweaters are the same price? Let s be the price of each sweater. Write this as an inequality.
(s will be the variable)
Answer: s < $20
Step-by-step explanation:
Since Dawn has less than $60 and wants to buy 3 sweaters, then the price of sweaters that she can afford if all the sweaters are the same price will be:
(3 × s) < $60
where,
s = price of each sweater
3s < $60
Divide both side by 3
3s/3 < $60/3
s < $20
The price of each sweater is less than $20
Angles ABC and DBE are vertical angles. If m
A. 180°
B. 38°
C. 52°
D. 128°
What is the volume of the solid whose cross- sections are circular disks perpendicular to the x-axis and with diameters on the region bounded by the curves y = x and y=x^2?
Answer:
the volume of the solid is [tex]\frac{\pi }{120}[/tex]
Step-by-step explanation:
Given the data in the question;
y = x and y = x²
so
x = x²
x - x² = 0
Radius will be; r = ( x - x² )/2
Area of the circular disk πr² = π[ ( x - x² )/2 ]²
A = [tex]\frac{\pi }{4}[/tex]( x - x² )²
So, our volume will be;
V = ₀∫¹ A(x) dx
we substitute
= ₀∫¹ [tex]\frac{\pi }{4}[/tex]( x - x² )² dx
{ lets expand; ( x - x² )² = x(x-x²) -x²(x-x²) = x² - x³ - x³ + x⁴ = x² + x⁴ - 2x³ }
so we have;
= ₀∫¹ [tex]\frac{\pi }{4}[/tex]( x² + x⁴ - 2x³ ) dx
= [tex]\frac{\pi }{4}[/tex] [tex][[/tex] [tex]\frac{x^3}{3}[/tex] + [tex]\frac{x^5}{5}[/tex] - [tex]\frac{2}{4} x^4[/tex] [tex]]^1_0[/tex]
= [tex]\frac{\pi }{4}[/tex][ [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{5}[/tex] - [tex]\frac{2}{4}[/tex] ]
= [tex]\frac{\pi }{4}[/tex][ [tex]\frac{1}{30}[/tex] ]
V = [tex]\frac{\pi }{120}[/tex]
Therefore, the volume of the solid is [tex]\frac{\pi }{120}[/tex]
Is the figure line symmetric? If yes, how many lines of symmetry does the figure have?
Yes
A.No
B. Yes;3 lines of symmetry
C.Yes;6 lines of symmetry
D.Yes; 12 lines of symmetry
Please help. This is due today
Answer:
yes 6 lines are symmetry
If x = -2, y = 3 and t = 2 then (x/y)t =
Answer:
-4/3
Step-by-step explanation:
2(-2/3)
= -4/3
Answer:
[tex]( \frac{x}{y} ) \times t \\ \frac{ - 2}{3} \times 2 \\ = \frac{ - 4}{3} [/tex]
What is the value of h(2)?
0 -2
0 -11
ОО
O 3
Need help fast!!!
Please help!! This is timed!!
NO LINKS!!!!
Create a table and graph the function.
1. y = (x + 3)^2 + 2
2. y = 2(x - 2)^2 - 4
Hope this help!!!
Have a nice day!!!
Tom has a steel box that has a capacity of 5 gallons. What is the maximum amount of fluid, in quarts, that this box can hold?
A. 10 qt.
B. 15 qt.
C. 18 qt.
D. 20 qt.
Answer:
d. 20 qt.
Step-by-step explanation:
4 quarts to a gallon so 4x5= 20
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
(c) reflection about x-axis, shift right 1
Step-by-step explanation:
The transformation g(x) = p·f(x-h) causes the graph of the function f(x) to be shifted right by h units. It also causes the graph to be vertically scaled by the factor 'p'. When p is negative, the graph is also reflected across the x-axis.
Here, we have p=-2, h=1, so the graph is ...
reflected across the x-axisvertically stretched by a factor of 2shifted right 1 unitThis collection of transformations matches the 3rd choice.
_____
Additional comment
The +3 inside parentheses (square brackets) causes the graph to be shifted upward 3 units--before it is reflected and vertically scaled. The reflection across the x-axis causes that upward shift to look like a downward shift, and the vertical stretch causes that shift of 3 units to become a shift of 6 units. (All answer choices agree that the downward shift is 6 units, so we didn't really need to discuss that.)
Help please please please
Answer:
demographic
Step-by-step explanation:
Small circular disks are being cut from thin sheets of steel. The steel weighs 1.6 grams per square centimeter. The disks need to have a diameter of 5 centimeters.
(A) find the area of the disk to the nearest hundredth of a square centimeter. Show the steps in your calculation.
Answer:
[tex]A = 19.63cm^2[/tex]
Step-by-step explanation:
Given
[tex]d =5cm[/tex]
[tex]Weight = 1.6g/cm^2[/tex]
Required
The area (A) of the disk
This is calculated as:
[tex]A = \frac{\pi * d^2}{4}[/tex]
So, we have:
[tex]A = \frac{3.14 * 5^2}{4}[/tex]
[tex]A = \frac{3.14 * 25}{4}[/tex]
[tex]A = \frac{78.5}{4}[/tex]
[tex]A = 19.625[/tex]
[tex]A = 19.63cm^2[/tex] --- approximated
(120+2x)+(70+2x)=15,000
not angles, area. also foiling
Answer:
x =3702.5
Step-by-step explanation:
Given data
(120+2x)+(70+2x)=15,000
Let us open the bracket
120+2x+70+2x=15,000
Collect like terms
120+70+2x+2x=15,000
190+4x=15000
4x=15000-190
4x= 14810
Divide both sides by 4
x=14810/4
x= 3702.5
Hence the value of x =3702.5
Solve the inequality 0>_3x-2x
Answer:
x<0
Step-by-step explanation:
See image below:)
4 is a common factor of 28 and 32.
O A. True
O B. False
Answer:
True
Step-by-step explanation:
Answer:
Your answer is B
Step-by-step explanation:
To evaluate whether or not the intake of a vitamin or mineral is adequate, comparisons are made between the intake distribution and the requirement distribution. Here is some information about the distribution of vitamin C intake, in milligrams per day, for women aged 19 to 30 years:
Percentile (mg/d)
Mean 1st 5th 19th 25th 50th 75th 90th 95th 99th
84.2 31 43 47 60 79 103 126 141 180
Use the 5th, the 50th, and the 95th percentiles of this distribution to estimate the mean (±0.01) and standard deviation (±0.01) of this distribution assuming that the distribution is Normal.
μ = _________
σ = _________
Answer:
[tex]Mean=79[/tex]
[tex]\sigma=30.3951.[/tex]
Step-by-step explanation:
From the question we are told that:
[tex]Age Bracket :19-20[/tex]
[tex]5th\ percentile = 42[/tex]
[tex]50th\ percentile = 79[/tex]
[tex]95th\ percentile = 142.[/tex]
Generally the mean Median and mode of the 50th percentile is are all equal
[tex]Mean=Median=Mode[/tex]
Therefore
[tex]Mean=79[/tex]
Generally for Normal distribution
[tex]5th\ percentile\ = mean - 1.645*\sigma[/tex]
[tex]95th\ percentile\ = mean + 1.645*\sigma[/tex]
Therefore
[tex](95th\ percentile\ - 5th\ percentile) = 2*(1.645*SD).[/tex]
[tex]\sigma=(95th\ percentile\ - 5th\ percentile)/3.29[/tex]
[tex]\sigma=\frac{142-42}{3.29}[/tex]
[tex]\sigma=30.3951.[/tex]
What’s the standard form for 1,000,000+80,000+30+3
Answer:
1080033
Step-by-step explanation:
=========================================
Explanation:
1,000,000 = 1 million
80,000 = 80 thousand
Adding those two would get us
1,000,000+80,000 = 1,080,000
Then we change those last two zeros at the end of "1,080,000" to 33 instead to get the final answer 1,080,033. This is done because we're adding 30+3 = 33 at the end.
----------------------
Extra info:
The number 1,080,033 is slightly over 1.08 million1,080,033 = 1 million, 80 thousand, 331,080,033 = one million, eighty thousand, thirty-threeThe use of commas between the words is optional. It's to give a sense of the pacing or pauses when reading out the number.Find the value of the polynomial when x=1 and y=-2
Answer:
the answer is : ................
5
Name a pair of complementary angles in the diagram above.
21 and 22
Z2 and 23
24 and 25
0 27 and 29
Answer:
7&9
Step-by-step explanation:
Really, its just because, that's my explanation.
4m + 18 is called a
What expression
Constant
Term
Variable expression
Coefficient
Answer and Step-by-step explanation:
4m + 18 is an expression.
This is because it has terms and no equal/inequality sign.
#teamtrees #PAW (Plant And Water)
Answer: Constant
Step-by-step explanation: Its an Constant because every variable is different in the expression.
Giải các phương trình sau
√3x-√3=√3
Answer:
2
Step-by-step explanation:
√3x=√3+√3=2√3⇒x=2
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = 2}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \sqrt{3} x - \sqrt{3} = \sqrt{3} [/tex]
➺ [tex] \: \sqrt{3} x = \sqrt{3} + \sqrt{3} [/tex]
➺ [tex] \: \sqrt{3} x = 2 \sqrt{3} [/tex]
➺ [tex] \: x = \frac{2 \sqrt{3} }{ \sqrt{3} } [/tex]
➺ [tex] \: x = 2[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35☂}}}}⋆[/tex]
determine whether the variable is qualitative or quantitative
street name and adress
Answer:
C
Step-by-step explanation:
Street name has nothing to do with numerical values, therefore it cannot be quantitative. If we take the two qualitative answers left, one of them says something about numbers, so it cannot be that one. C is the only one left over after process of elimination.
Find the missing length indicated
Answer:
D) 20
Step-by-step explanation:
Answer:
D) 20
Step-by-step explanation:
they are asking for the longest length of the triangle. as you can see, 20 is just over 15, and from the diagram, the missing length is just over 15 so we can apply our knowledge to come to the answer of 20.
Find the margin of error for the 95% confidence interval used to estimate the population proportion. )n=460, x=60
A department store buys 100 shirts at a cost of $2000 and sells them at a selling price of $25 each. Find the percent markup.
Answer:
Mark up % = 25%
Step-by-step explanation:
Cost of 100 shirts = 2000
Cost of 1 shirt = 2000/100 = 20
Selling price of 1shirt = 25
[tex]\% mark \ up = \frac{selling \ price - cost \ price }{cost \ price } \times 100 = \frac{25- 20}{20}\times 100 = \frac{5}{20} \times 100 = 25 \%[/tex]
If f(x) is a third degree polynomial function, how many distinct imaginary roots are possible?
Answer:
1, 2, or 3
Step-by-step explanation:
if it's third degree then there must me 1 to 3 roots
hope you find this helpful :)
Answer: 0 or 2
Step-by-step explanation:
took test on edge2020
HOW COULD MAKE 7 TO BECOME EVEN NO. WITHOUT FOUR FUNDAMENTAL PRINCIPLE
LIKE :
PLUS
MINUS
SOBRACTION
DIVISION
Answer:
2,4,6,8,10,12,14,16,18,20
Answer:
How do you make the number 7 an even number without addition, subtraction or multiplication?
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22 Answers

Yogesh Rana, B.Sc. Mathematics, University of Delhi (2016)
Answered 4 years ago
You can remove alphabet S from SEVEN.
You can change the convention. Whole mathematics works like that. After all it is just a name, ie, call the numbers divisible by 2 odd and not divisible by 2 even. Everything will still work fine. You got to rename some theorems also.
Introduce and derive a new number system from the current number system, name the symbol 6 as seven and the symbol 7 as Six. Just rename the symbols.
Introducing a new number system and interchange position of 7 with an even number.
If we remove one number before 7 ( 1 - 6 ) with its name, we have again a new number system with base 9 and technically no. 7 is still no. 7 with value = 6.
These are some genuine ways rather than dividing.
ANSWERS OF DIVISION ARE TECHNICALLY WRONG AND RIDICULOUS BECAUSE DIVISION BY ‘x’ is MULTIPLICATION BY ‘1/x’ .
Use your graph to find estimates of the solutions to the equation x^2-x-6=-2
9514 1404 393
Answer:
x ≈ -1.5 or 2.6
Step-by-step explanation:
It appears as though your graph crosses the line y = -2 at approximately x = -1.5 and also at x = 2.6.
These are estimates of the solutions to the equation.
x ≈ {-1.5, 2.6}
Answer:
-2 and 3
Step-by-step explanation:
From the graph, the solution is the points where the curve cuts the x axis. From the graph, you can see that the equation cuts the x axis at two points that is at x=-2 and 3.
Hence the solutions to the equation is -2 and 3