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3 years ago

How to find the perimeter?

Mathematics

1 answer:

Gemiola [76]3 years ago

8 0

Answer:

Step-by-step explanation:

The angles are equal. This means that the triangle is equilateral and all the sides are equal to each other.

Set any two sides equal to each other.

2x - 3 = x + 5

x - 3 = 5

x = 8

Now substitute this x value into all the sides and add the numbers up.

2(8) - 3 = 16 - 3 = 13

So we know all 3 sides equal 13.

13 * 3 = 39

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Derive these identities using the addition or subtraction formulas for sine or cosine: sinacosb=(sin(a+b)+sin(a-b))/2

Sergeu [11.5K]

Answer:

The work is in the explanation.

Step-by-step explanation:

The sine addition identity is:

$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$ .

The sine difference identity is:

$\sin(a-b)=\sin(a)\cos(b)-\cos(a)\sin(a)$ .

The cosine addition identity is:

$\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$ .

The cosine difference identity is:

$\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)$ .

We need to find a way to put some or all of these together to get:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$ .

So I do notice on the right hand side the $\sin(a+b)$ and the $\sin(a-b)$ .

Let's start there then.

There is a plus sign in between them so let's add those together:

$\sin(a+b)+\sin(a-b)$

$=[\sin(a+b)]+[\sin(a-b)]$

$=[\sin(a)\cos(b)+\cos(a)\sin(b)]+[\sin(a)\cos(b)-\cos(a)\sin(b)]$

There are two pairs of like terms. I will gather them together so you can see it more clearly:

$=[\sin(a)\cos(b)+\sin(a)\cos(b)]+[\cos(a)\sin(b)-\cos(a)\sin(b)]$

$=2\sin(a)\cos(b)+0$

$=2\sin(a)\cos(b)$

So this implies:

$\sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)$

Divide both sides by 2:

$\frac{\sin(a+b)+\sin(a-b)}{2}=\sin(a)\cos(b)$

By the symmetric property we can write:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$

3 0

3 years ago

Calculus: Help ASAP

Serggg [28]

$\bf \displaystyle \int\limits_{-1}^{0}~(4x^6+2x)^3(12x^5+1)\cdot dx\\\\
-------------------------------\\\\
u=4x^6+2x\implies \cfrac{du}{dx}=24x^5+2\implies \cfrac{du}{2(12x^5+1)}=dx\\\\
-------------------------------\\\\
\displaystyle \int\limits_{-1}^{0}~u^3\underline{(12x^5+1)}\cdot\cfrac{du}{2\underline{(12x^5+1)}}\implies \cfrac{1}{2}\int\limits_{-1}^{0}~u^3\cdot du\\\\
-------------------------------\\\\$

$\bf \textit{now, we'll change the bounds, using u(x)}
\\\\\\
u(-1)=4(-1)^6+2(-1)\implies u(-1)=2
\\\\\\
u(0)=4(0)^6+2()\implies u(0)=0\\\\
-------------------------------\\\\
\displaystyle \cfrac{1}{2}\int\limits_{2}^{0}~u^3\cdot du\implies \left. \cfrac{1}{2}\cdot \cfrac{u^4}{4} \right]_{2}^{0}\implies \left. \cfrac{u^4}{8} \right]_{2}^{0}\implies [0]-[2]\implies -2$

5 0

3 years ago

A TV that usually sells for $195.72 is on sale for 20% off. If sales tax on the TV is 9%, what is the price of the TV, including

Nuetrik [128]

The total cost of the TV is: $181.57

Work: 195.72 x 0.20 (20%) = 39.14

195.72 - 39.14 = 166.58 <-- Was for the discount now you have to do the tax.

Now Tax, 166.58 + 14.99 = 181.57

Hope this helps!

7 0

3 years ago

Read 2 more answers

What is the answer?

alexgriva [62]

Answer:

Area = (2-3x)(2x+5)(x-1)

= -6x³-5x²+21x-10

Step-by-step explanation:

6 0

4 years ago

John Sullivan bought a new Brunswick boat for $17,000. He made a $2,500 down payment on it. The bank's loan was for 60 months, a

Rudiy27

John has 17000 - 2500 = 14500 left to pay after the down payment

Then add on the finance charges 14500 + 4900 = 19400

The total of $19400 is to be paid over 60 monthly instalments, so John will be paying 19400÷60 = $323.30 per month

6 0

3 years ago