All categories

3 years ago

How many terms are in the expansion (a+b)19

Mathematics

1 answer:

astra-53 [7]3 years ago

8 0

Answer:

There are 2 ters because you would distribute the 19 to the a and the b to make it 19a + 19b, which has 2 terms

You might be interested in

Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.

max2010maxim [7]

Answer:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

Step-by-step explanation:

We want to write the trignometric expression:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0$

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

$\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)$

Take the secant of both sides:

$\displaystyle \sec(\theta)=\frac{u}{10}$

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

$\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}$

By substitutition:

$\displaystyle= \sin(2\theta)$

Using an double-angle identity:

$=2\sin(\theta)\cos(\theta)$

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

$\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)$

Simplify. Therefore:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

4 0

3 years ago

the axis of symmetry for a function in the form f(x)=x^2+4x-5 is x=-2. what are the coordinates of the vertex of the graph?

Alenkasestr [34]

Hello :
<span>f(x)=x²+4x-5
</span><span>The axis of symmetry for a function in the form f(x)=x^2+4x-5 is x=-2 :
</span>f(x) = (x+2)² + b
f(x) x²+4x+4+b= x² +4x-5
4+b= -5
b = -9
the vertex is : (2 , -9)

4 0

3 years ago

Read 2 more answers

What is 35 liters in milliliters

Evgesh-ka [11]

The answer is 35,000

6 0

3 years ago

In 2000, the population of Big Springs was 13 thousand. Use the given doubling

trasher [3.6K]

Answer:

The answer is "26179.4".

Step-by-step explanation:

Assume year 2000 as t, that is t =0.

Formula:

$A= A_0e^{rt}$

Where,

$A_0 = \ initial \ pop \\\\r= \ rate \ in \ decimal \\\\t= \ time \ in \ year$

for doubling time,

$r = \frac{log (2)}{t} \\$

$r = \frac{\log (2)}{ 40} \\\\r= \frac{0.301}{40}\\\\r= 0.007$

Given value:

$A = A_0e^{rt} \\\\$

$A_0 = 13000$

$t= 40 \ years$

when year is 2000, t=0 so, year is 2100 year as t = 100.

$A = 13000 \times e^{et}\\\\A = 13000 \times e^{e \times t}\\\\A = 13000 \times e^{0.007 \times 100}\\\\A = 13000 \times e^{0.7}\\\\A= 13000\times 2.0138\\\\A = 26179.4$

7 0

3 years ago

1. Find the mean for 2, 5, 9, 4

Reil [10]

Answer:

Answer 1. 5 Answer 2. 60 Answer 3. 37

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers