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3 years ago

X-70/x<-3 solve for x under the assumption that x>0

1 answer:

4 0

Simplifying 0x + 7 + 5x = 2x + 30 + 40 Anything times zero is zero. 0x + 7 + 5x = 2x + 30 + 40 Combine like terms: 0 + 7 = 7 7 + 5x = 2x + 30 + 40 Reorder the terms: 7 + 5x = 30 + 40 + 2x Combine like terms: 30 + 40 = 70 7 + 5x = 70 + 2x Solving 7 + 5x = 70 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. 7 + 5x + -2x = 70 + 2x + -2x Combine like terms: 5x + -2x = 3x 7 + 3x = 70 + 2x + -2x Combine like terms: 2x + -2x = 0 7 + 3x = 70 + 0 7 + 3x = 70 Add '-7' to each side of the equation. 7 + -7 + 3x = 70 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 70 + -7 3x = 70 + -7 Combine like terms: 70 + -7 = 63 3x = 63 Divide each side by '3'. x = 21 Simplifying x = 21

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Find the function y = f(t) passing through the point (0, 18) with the given first derivative.

monitta

Answer:

$\displaystyle y = \frac{t^2}{16} + 18$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Functions
Function Notation
Coordinates (x, y)

Calculus

Derivatives

Derivative Notation

Antiderivatives - Integrals

Integration Constant C

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Step-by-step explanation:

Step 1: Define

Identify

Point (0, 18)

$\displaystyle \frac{dy}{dt} = \frac{1}{8} t$

Step 2: Find General Solution

Use integration

[Derivative] Rewrite: $\displaystyle dy = \frac{1}{8} t\ dt$
[Equality Property] Integrate both sides: $\displaystyle \int dy = \int {\frac{1}{8} t} \, dt$
[Left Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle y = \int {\frac{1}{8} t} \, dt$
[Right Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle y = \frac{1}{8}\int {t} \, dt$
[Right Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle y = \frac{1}{8}(\frac{t^2}{2}) + C$
Multiply: $\displaystyle y = \frac{t^2}{16} + C$

Step 3: Find Particular Solution

Substitute in point [Function]: $\displaystyle 18 = \frac{0^2}{16} + C$
Simplify: $\displaystyle 18 = 0 + C$
Add: $\displaystyle 18 = C$
Rewrite: $\displaystyle C = 18$
Substitute in C [Function]: $\displaystyle y = \frac{t^2}{16} + 18$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Integration

Book: College Calculus 10e

4 0

2 years ago

a cubic box has a side length of 2 feet. How many of these boxes could fit inside a larger cubic box whose base has a perimeter

kap26 [50]

So if a cubic box has a side length of 2 ft in order to find the volume we need to cube it or multiply the length times 3 times. so it would be 2x2x2=8. that is the volume of the fiest cube. in order to find the volume of the larger cube first you need to know the length of one of the sides. the base has 4 sides to it that are all equal so you divide 24 by 4 and get 6. then to find the volume you multiply 6 three times since it is also a cubic cube so it would be 6x6x6=216. now you know the volume of each cube so you divide 216 by 8 to find how many times the volume of the small cube would go into the volume of the larger cube and get 27 times.

6 0

3 years ago

Find the dot product of the position vectors whose terminal points are (14, 9) and (3, 6).

erma4kov [3.2K]

Answer:

Step-by-step explanation:

The formula for the dot product of vectors is

u·v = |u||v|cosθ

where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.

$|u|=\sqrt{14^2+9^2}$ which is $\sqrt{277}$

$|v|=\sqrt{3^2+6^2}$ which is $\sqrt{45}$

I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.

We also need the angle, which of course has its own formula.

$cos\theta=\frac{uv}{|u||v|}$ where uv has ITS own formula:

uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.

uv = 96.

To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:

$cos^{-1}\theta=\frac{96}{111.64676}$ which returns an angle measure of 30.7. Plugging that all into the dot product formula:

$u*v=\sqrt{277}*\sqrt{45}cos(30.7)$ gives you a dot product of 96

6 0

3 years ago

I don´t understand this: Lin’s father is paying for a $20 meal. a) He has a 15%-off coupon for the meal. How much is the discoun

Naddika [18.5K]

You'll have to set this up as two separate problems. First, we want to take 15% off the original $20 bill. To do this, you're going to multiply 20 by .15, which gives you $3. So, 15% off $20 is $17.

Now, we want to find 7% of the new bill, so we're going to multiply 17 by .07 to get $1.19, and add it to the $17, making the final bill $18.19. You could also multiply $17 by 1.07 to get your final total without the extra step in the middle, but only do that once you're comfortable with the math.

Pls give brainiest

7 0

3 years ago

What is 7000000000+7000000000

gogolik [260]

Answer:14,000,000,000

Step-by-step explanation: all u have to do i 7+7 then add your zeros so

5 0

2 years ago

Read 2 more answers