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3 years ago

Quadrilateral ABCD is a square. BC = 10 What is the length of AC? A. 10 sqrt 2 B. 20 sqrt 3 C. 10 sqrt 3 D. Sqrt 100

Mathematics

1 answer:

bixtya [17]3 years ago

4 0

A is the correct answer to this question because AC and BC differ because the B must be changed to an A.

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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

3 years ago

I have 3 times as much money as my brother. Our total is $24. How much does each of us have?I have 3 times as much money as my b

musickatia [10]

Answer:

Brother's money = $6

Money I have = $18

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given:

I have 3 times as much money as my brother:

Money I have = 3x

Where x is the money that my brother has:

Brother's money = x

Our total is $24

So, 3x+x =24

Solving for x

3x+x=24

4x =24

x =24/4

x = 6

Replacing with the value of x.

Brother’s money = x = $6

Money i have = 3x =3(6) = $18

6 0

3 years ago

Which is the graph of Y = log(-x)?

hoa [83]

A++ 123456 -2 -3 -4 1

8 0

3 years ago

Help me plz! Help me plz!

erik [133]

After converting to common denominator:

8/18, 7/18, 6/18, 5/18

so the next fraction is 4/18, but if you have to simplify it’s 2/9

6 0

4 years ago

What is the solution of the equation f(x) = g(x) ?

dezoksy [38]

We are given the two functions $f(x) = x^{-\frac{1}{2} }$ and $g(x) = \sqrt{x} - \frac{3}{2}$ . Since the question is asking us for the value of x when f(x) is equal to g(x), all we need to do is equate the respective expressions together. This is what the result should be:
$x^{-\frac{1}{2}} = \sqrt{x} - \frac{3}{2}$
Now, just solve for x. If you want to save some time, you can use logic and then algebra. To do this, look at the square root. We cannot have an imaginary number, so we can rule out the first two options. Now, we are left with x = 2 and x = 4. When we plug in each x-value to the equation, only 4 works out with a result of 0.5 = 0.5. Therefore, the solution to f(x) = g(x) is D) x = 4. Hope this helps and have a great day!

4 0

3 years ago