Answer:
[tex]f(1)=-7[/tex]
Step-by-step explanation:
We are given the derivative:
[tex]f^\prime (x) = 3 x^2 + 2x[/tex]
And the initial condition that f(2)=3.
And we want to find f(1).
So, to find our original function f(x), we will find the antiderivative of f'(x). Hence:
[tex]\displaystyle f(x)=\int f^\prime(x)\, dx=\int3x^2+2x\, dx[/tex]
By integrating, we acquire:
[tex]f(x)=x^3+x^2+C[/tex]
Since we know that f(2)=3:
[tex]3=(2)^3+(2)^2+C[/tex]
It follows that:
[tex]C=-9[/tex]
Therefore, our function is given by:
[tex]f(x)=x^3+x^2-9[/tex]
Therefore:
[tex]f(1)=(1)^3+(1)^2-9 = -7[/tex]
Here we want to solve a differential equation, we will find that our function is f(x) = x^3 + x^2 -9
Solving the differential equation.So we want to find f(x) such that we know f'(x).
We know that:
f'(x) = 3x^2 + 2x
To get f(x) we just need to integrate, we will get:
[tex]f(x) = \int\limits {3x^2 + 2x} \, dx = x^3 + x^2 + c[/tex]
Where c is a constant of integration.
Now, we know that f(2) = 3, with that we can find the value of c.
f(2) = 2^3 + 2^2 + c = 3
8 + 4 + c = 3
c = 3 - 12 = -9
So the function is:
f(x) = x^3 + x^2 -9
If you want to learn more about differential equations, you can read:
https://brainly.com/question/18760518
Find −64÷(−8) need help
Answer: The answer to -64 divided by 8 would be 8.
Someone plz help me plz T^T
a bricklayer needs to order 6300kg of building sand
Answer:
[tex]9\times 10^7\ \text{grains of sand}[/tex]
Step-by-step explanation:
Given that,
A bricklayer needs to order 6300kg of building sand.
1 grain of this sand weighs [tex]7\times 10^{-5}\ kg[/tex].
We need to find how many grains of sand are there in 6300 kg.
It can be just calculated as follows :
1 grain of sand = [tex]7\times 10^{-5}\ kg[/tex]
[tex]6300\ kg=\dfrac{6300}{7\times 10^{-5}}\\\\=9\times 10^7\ \text{grains of sand}[/tex]
or
= 90000000 grans of sand
So, 6300 kg is equal to [tex]9\times 10^7\ \text{grains of sand}[/tex].
Daria earns a profit of $22.55 selling 11 tie dye shirts at market. How much will she make if she sells 23 shirts next weekend
Answer:
$47.15
Step-by-step explanation:
22.55 divided by 11 is 2.05 so she made $2.05 on each shirt
2.05 x 23 is 47.15
HELP! HOW DO I SOLVE THIS???
4y + y to 4y2
Find the equation of the line through (-1, 3) and (5,3)
Given:
A line passes through (-1, 3) and (5,3).
To find:
The equation of the line.
Solution:
The line passes through (-1, 3) and (5,3). So, the equation of the line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-3=\dfrac{3-3}{5-(-1)}(x-(-1))[/tex]
[tex]y-3=\dfrac{0}{5+1}(x+1)[/tex]
[tex]y-3=0[/tex]
Adding 3 on both sides, we get
[tex]y-3+3=0+3[/tex]
[tex]y=3[/tex]
Therefore, the equation of the line is [tex]y=3[/tex].
A fair spinner has eight equal sections.
The sections are either yellow (Y) or green (G).
The spinner is spun 3 times.
List all the possible outcomes of the 3 spins.
One has been done for you. YYY,
2 marks
Answer:
The first one is already giving to us YYY so
the answer is GGG,YGY,GYG,YYG,GGY,YGG,GYY
Step-by-step explanation:
five times the sum of a number and two is ten
Answer:
5(x+2)=10
Step-by-step explanation:
use the PEMDAS, solve first the one inside the parenthesis and then multiply the sum to 5
put them in order from the least to greatest. You can use the number line to help!!
Will give brainliest to first right answer. Before a sale an items price was $28.00 then after being discounted the price was $14.60. What was the discount for the item? with a exact fraction
Answer:
48 percent decrease
Step-by-step explanation:
before=28 dollars
after=14.60
sorry, i cant be bothered to answer it all!!!!
The word part meaning hundred is.
a. octo-
b. penta-
c. milli-
d. centi-
Answer:
centi
Step-by-step explanation:
Hey there!
When you see/hear the word “octo-”
(or “-octa”) think of ‘octagon’ and how they have ‘EIGHT SIDES’. So this means that prefix means 8; when you see/hear the word “penta-” think of ‘pentagon’ because it ‘FIVE SIDES’. So means that prefix means 5; When you see/hear the word “milli-” think of ‘one thousandths’ (this comes in handy when you’re working with DECIMALS and SOME MEASUREMENTS); when you see/hear “centi-” think of
centigrade.. you’ll learn about that in measurements as well.. it equals 100
Now that we had to break down the meaning of the prefixes we reached our answer:
The one that has the meaning for hundred is “centi- (option D)” would most likely be your answer
Answer: D. Centi- ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
QUESTION 8
Some seventh-, and eighth-grade students.spend time at
the elementary school tutoring students. Of the students
who tutor, 21 are seventh-graders and 18 are
eighth-graders. What percent of the tutors are
seventh-graders?
A) 54%
B) 46%
C) 52%
D) 21%
simplify (4w^2 - 5w - 7) - (8w^2 + 3w -2)
what is the answer to y=x-5 and y=-7x+11 solving with substitution ????
Answer:
(2, -3)
x = 2
y = -3
Step-by-step explanation:
Answer:
y=3,x=8
Step-by-step explanation:
y=x-5
y=-7x+11
x=y+5
y=-7(y+5)+11
y=-7y-35+11
8y=24
y=3
3=x-5
x=8
what calculation can be used to find the value of p in the equation p^3 =8
Cube Root
[tex] {p}^{3} = 8 \\ p = \sqrt[3]{8} \\ p = \sqrt[3]{ 2\times 2 \times 2} \\ p = 2[/tex]
Formula
[tex] {p}^{3} - 8 = 0[/tex]
Use the following formula.
[tex] {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )[/tex]
[tex](p - 2)( {p}^{2} + 2p + 4)[/tex]
The expression p²+2p+4 has the discriminant less than 0 ( D < 0 ).
Thus, remove the expression and leave only p-2
[tex]p - 2 = 0 \\ p = 2[/tex]
Substitution
The most obvious number that multiplies itself three times and equal 8 is 2.
Substitute p = 2
[tex] {p}^{3} = 8 \\ {2}^{3} = 8 \\ 2 \times 2 \times 2 = 8 \\ 8 = 8[/tex]
The equation is true, thus 2 is the answer.
Use a graphing calculator to solve (1/4) ^ x+2 = 6:
Answer:
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
x = − 2 − ln ( 6 )/ ln ( 4 )
Decimal Form:
x = −3.29248125 …
Hope this helps!
if f(x) = 6x+2 find the value of f(2)
Answer:
14
Step-by-step explanation:
If the AREA of the rectangle at the right is 22 3/4 square inches, what is the width of the rectangle?
Answer:
3.25 or 3 1/4 inches
Step-by-step explanation:
A = lw
22.75 = 7w
w = 3.25 which is 3 1/4
Annabelle's initial balance in her checking account was $95.62. She deposited $35.79 and then withdrew $45. What is the final balance for her checking account?
A customer ordered 3 Americanos and 4 lattes for a
total of $18.00. At the same coffee shop a second
customer spends $2 less than the first customer for 5
Americanos and 2 lattes.
How much does each latte cost?
Answer:
3636
Step-by-step explanation:
Stephanie has a fish tank with 8 adult fish and 36 baby fish. What is the ratio of adult fish to baby fish in the tank?
Answer:
2:9
Step-by-step explanation:
8 adult fish:36 baby fish
To simply both, divide by 4
2 adult fish: 9 baby fish
Find the equation of the line use exact numbers.
Y=|____|x+|____|
Answer:
[tex]y=\frac{3}{4} x-2[/tex]
Step-by-step explanation:
The line has a positive slope, that much is clear. If we just count from the y-intercept up to the next clear point, we can see that it is 3 up and 4 to the right. That gives us a rise over run of 3 over 4, or [tex]\frac{3}{4}[/tex].
The y-intercept is -2, so that is the latter half of the equation.
Which is the graph of the linear equation y = -x?
Answer:
Graph the line using the slope and y-intercept, or two points.
Slope: −1
y-intercept: (0,0)
x y
0 1
0 −1
Step-by-step explanation:
a person is standing on a cliff 120 ft high looking out to the ocean there is a boat out on the ocean 300 ft from the base of the cliff if the person looks down to see the boat what is her angle of depression to the nearest tenth
Answer:
21.8°
Step-by-step explanation:
Please see the attached picture for the full solution.
URGENT PLEASE: You purchase a new guitar and take out a loan for $450. You have 18 equal monthly payments of $28 each. What is the simple interest rate for the loan? Round to the nearest tenth of a percent, if necessary.
Look at this diagram.
If QS and TV are parallel lines and m<TUR = 113°, what is m<QRP?
___°
Answer:
90
hope this helps!:)
Step-by-step explanation:
What is the value of the expression when x = 6?
a. 37
b. 59
c. 61
d. 35
Answer:
when x=6
26+x^2-1^3
26+6^2-1^3
26+36-1
61.
so the answer is.61
Please help me with the correct answer
Answer:
[tex]0.00000013=1.3*10^{-7}[/tex]
Step-by-step explanation:
Example of how scientific notation works:
[tex]150=1.50*10^{2}[/tex]
How many zeros are there?
6
How many spaces to make it 1.3?
1
6+1=7
[tex]0.00000013=1.3*10^{-7}[/tex]
The perimeter of a rectangle a picture frame is 66 inches. the length is 3 inches greater than the width the system of linear equations used to represent the situation shown below.
2X + 2Y = 66 and X +3 =Y
solve the system name dimension represented by each variable
Given:
The perimeter of a rectangular picture frame is 66 inches [2X + 2Y = 66.]The length of the frame is 3 inches greater than the width [X + 3 = Y.]To find: The dimensions.
Answer:
Formula to find the perimeter of a rectangle = 2 × (Length + Width)
We know that 2X + 2Y = 66. Simplifying it, we get:
2(X + Y) = 66
X + Y = 66/2
X + Y = 33
Now that we know the value of X + Y, and assuming X and Y to be the dimensions, let's substitute it into the formula to find the perimeter and verify it.
Perimeter = 2 × (X + Y)
66 = 2 × 33
It's verified.
Now, we also have the expression representing the length, which is X + 3 = Y.
X + Y = 33
X + 3 = Y
Let's add both expressions.
X + Y + X + 3 = 33 + Y
2X + Y + 3 = 33 + Y
2X = 33 - 3 + Y - Y
2X = 30
X = 30/2
X = 15
Hence, the width [X] is 15.
Substituting this value into the expression representing the length,
15 + 3 = Y
18 = Y
Hence, the length and breadth of the rectangular picture frame is 18 and 15 units respectively.
Hope it helps. :)
50 points and I’ll mark you brainiest if correct.
Answer:
The container can hold 18 gallons
Step-by-step explanation:
Assume the container can hold x gallons
∵ The container is [tex]\frac{2}{3}[/tex] full with water
∵ It can hold x gallons
→ Multiply [tex]\frac{2}{3}[/tex] by x to find the number of gallons in the container
∴ The number of gallons in the container = [tex]\frac{2}{3}[/tex] x
∵ 4 gallons of water pouring out
∵ It is [tex]\frac{4}{9}[/tex] full
→ Multiply [tex]\frac{4}{9}[/tex] by x to find the number of gallons left in it
∴ The number of gallons left in the container = [tex]\frac{4}{9}[/tex] x
→ The difference between the numbers of gallons is 4 gallons
∵ [tex]\frac{2}{3}[/tex] x - [tex]\frac{4}{9}[/tex] x = 4
→ Subtract the terms of the left side
∴ [tex]\frac{2}{9}[/tex] x = 4
→ Multiply both sides by 9
∴ 2x = 36
→ Divide both sides by 18
∴ x = 18
∵ x represents the full of the container
∴ The container can hold 18 gallons