Three pens cost £1.80 total. Work out the cost in 1 pen. Give your answer in pence

Use the following written description to write the equation for the situation.

elena55 [62]

How I understand it’s 5x+y

7 0

2 years ago

Read 2 more answers

Find the least common denominator for these two rational expressions. B/b^2 -64 -7b/b^2+7b-8

san4es73 [151]

Answer:

The least common denominator is (b-8)(b+8)(b-1)

Step-by-step explanation:

We are given expression as

$\frac{b}{b^2-64}-\frac{7b}{b^2+7b-8}$

Firstly, we will factor both denominators

$b^2-64=b^2-8^2=(b-8)(b+8)$

$b^2+7b-8=(b+8)(b-1)$

so, we can plug it back

$\frac{b}{(b-8)(b+8)}-\frac{7b}{(b+8)(b-1)}$

First term denominator is

(b-8)(b+8)

Second term denominator is

(b+8)(b-1)

So,

Least common denominator will be

(b-8)(b+8)(b-1)

So, we get

$LCD=(x-8)(x+8)(x-1)$

3 0

2 years ago

Triangle is 18 in high 36 in across ....how much fabric to make 5

Korolek [52]

Answer:

A=324

Step-by-step explanation:

formual to Solve for area

A=h*b/2 so 18*36/2= a = 324

3 0

3 years ago

Hi can you help me with this problem i dont understand it

Romashka-Z-Leto [24]

Answer:

Answer is d - x = $\frac{y + z}{4}$

Step-by-step explanation:

Step 1: Add 'z' to both sides

4x -z (+z) = y + z

4x = y + z

Step 2: To solve for x, divide both sides by 4

$\frac{4x}{4}$ = $\frac{y + z}{4}$

x = $\frac{y + z}{4}$

5 0

2 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cint%20t%5E2%2B1%20%5C%20dt" id="TexFormula1" title="\frac{d}{dx} \

Kisachek [45]

Answer:

$\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2$

Step-by-step explanation:

$\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} = \ ?$

We can use Part I of the Fundamental Theorem of Calculus:

$\displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}$

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

$\displaystyle\int\limits^b_a \text{f(t) dt} + \int\limits^c_b \text{f(t) dt} = \int\limits^c_a \text{f(t) dt}$

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

$\displaystyle \frac{d}{dx} \int\limits^0_{2x} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}$

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

$\displaystyle\int\limits^b_a \text{f(t) dt}\ = -\int\limits^a_b \text{f(t) dt}$

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

$\displaystyle \frac{d}{dx} -\int\limits^{2x}_{0} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}$

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

$\displaystyle \frac{d}{dx} \int\limits^u_a \text{f(t) dt} = \text{f(u)} \cdot \frac{d}{dx} [u]$
where u represents any function other than a variable

For the first term, replace $\text{t}$ with $2x$ , and apply the chain rule to the function. Do the same for the second term; replace

$\displaystyle-[(2x)^2+1] \cdot (2) \ + \ [(x^2)^2 + 1] \cdot (2x)$

Simplify the expression by distributing $2$ and $2x$ inside their respective parentheses.

$[-(8x^2 +2)] + (2x^5 + 2x)$
$-8x^2 -2 + 2x^5 + 2x$

Rearrange the terms to be in order from the highest degree to the lowest degree.

$\displaystyle2x^5-8x^2+2x-2$

This is the derivative of the given integral, and thus the solution to the problem.

6 0

2 years ago