All categories

3 years ago

PLEASE HELP!!! Find the common difference for the arithmetic sequence. -55, -50, -45, -40.....

Mathematics

1 answer:

Fed [463]3 years ago

7 0

Answer:

Step-by-step explanation:

Just grap any two consecutive terms in the sequence. lets say -55 and -50

-50-(-55) = 5

you can check this by picking two other terms

You might be interested in

What is the value of m in the equation 5m − 7 = 6m 11? 18 1 −18 −1.

riadik2000 [5.3K]

Answer: 18

Step-by-step explanation: 5m - 7 = 6m + 11

Solve for M

5m - 6m = 11+ 7

-m = 18

Divide both sides by -1

-m/-1 = 18/-1

m = -18

4 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csec%5Cleft%28x%5Cright%29%7D%7B%5Ccos%5Cleft%28x%5Cright%29%7D-%5Cfrac%7B%5Csin%5

DanielleElmas [232]

Answer:

Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that $csc(x)=1/sin(x)$ and $sec(x)=1/cos(x)$ .

Thus:

$\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}$

$=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }$

Let's do the first part first: (Recall how to divide fractions)

$\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}$

For the second term:

$\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}$

So, all together: (same denominator; combine terms)

$\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}$

Note the numerator; it can be derived from the Pythagorean Identity:

$sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)$

Thus, we can substitute the numerator:

$\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1$

Everything simplifies to 1.

7 0

3 years ago

Given a circle with radius of 2, which is the degree measure of an arc whose length is 1/2 ?

Finger [1]

180 degrees. It would be half of the circle.

3 0

3 years ago

Rewrite \sqrt((1+cos45)/(2)) using a half-angle identity

aleksklad [387]

$\stackrel{\textit{Half-Angle Identities}}{cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}}} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos\left( \cfrac{45^o}{2} \right)\implies \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos(22.5^o)$

7 0

2 years ago

A colony of bacteria is growing exponentially according to the function below, where t is in hours. How many bacteria are there

pychu [463]

The growth of the bacteria is expressed as:

B(t) = 4 e^0.8t

where t is the time in units of hours. If the bacteria is allowed to grow for 8 hours then the number of bacteria present would be,

B(t) = 4 e^0.8(8)
B(t) = 2407

5 0

3 years ago

Read 2 more answers