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3 years ago

Hi please help with this maths question URGENT!!! Thank you.

Mathematics

2 answers:

seropon [69]3 years ago

4 0

Y = 20T + 16C

this is 20 * the cost of one cinema ticket, and 16 * the cost of one theatre ticket. i assume the answer was to be in slope intercept form by the style of question.. i hope this helps!

Sedaia [141]3 years ago

3 0

Answer:

$\large\boxed{\pounds(20T+16C)}$

Step-by-step explanation:

$\text{The expression for the cost of 20 theatre tickets:}\ 20(\pounds T)\\\\\text{The expression for the cost of 16 cinema tickets:}\ 16(\pounds C)\\\\\text{The expression for the total cost of 20 theatre tickets and 16 cinema tickets:}\\\\20(\pounds T)+16(\pounds C)=\pounds(20T+16C)$

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B) Let g(x) =x/2sqrt(36-x^2)+18sin^-1(x/6)<br><br> Find g'(x) =

jolli1 [7]

I suppose you mean

$g(x) = \dfrac x{2\sqrt{36-x^2}} + 18\sin^{-1}\left(\dfrac x6\right)$

Differentiate one term at a time.

Rewrite the first term as

$\dfrac x{2\sqrt{36-x^2}} = \dfrac12 x(36-x^2)^{-1/2}$

Then the product rule says

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 x' (36-x^2)^{-1/2} + \dfrac12 x \left((36-x^2)^{-1/2}\right)'$

Then with the power and chain rules,

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12\left(-\dfrac12\right) x (36-x^2)^{-3/2}(36-x^2)' \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} - \dfrac14 x (36-x^2)^{-3/2} (-2x) \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12 x^2 (36-x^2)^{-3/2}$

Simplify this a bit by factoring out $\frac12 (36-x^2)^{-3/2}$ :

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-3/2} \left((36-x^2) + x^2\right) = 18 (36-x^2)^{-3/2}$

For the second term, recall that

$\left(\sin^{-1}(x)\right)' = \dfrac1{\sqrt{1-x^2}}$

Then by the chain rule,

$\left(18\sin^{-1}\left(\dfrac x6\right)\right)' = 18 \left(\sin^{-1}\left(\dfrac x6\right)\right)' \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac x6\right)'}{\sqrt{1 - \left(\frac x6\right)^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac16\right)}{\sqrt{1 - \frac{x^2}{36}}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{3}{\frac16\sqrt{36 - x^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18}{\sqrt{36 - x^2}} = 18 (36-x^2)^{-1/2}$

So we have

$g'(x) = 18 (36-x^2)^{-3/2} + 18 (36-x^2)^{-1/2}$

and we can simplify this by factoring out $18(36-x^2)^{-3/2}$ to end up with

$g'(x) = 18(36-x^2)^{-3/2} \left(1 + (36-x^2)\right) = \boxed{18 (36 - x^2)^{-3/2} (37-x^2)}$

5 0

2 years ago

Joey is creating a rectangular garden. The garden is 9 feet long and 7 feet wide. Joey calculated he needs feet of fencing to cl

Crazy boy [7]

Answer:

Amount of fencing: 32 feet

Amount of soil: 63 square feet

Step-by-step explanation:

Fencing: In a rectangle, the opposite side is the same length. So we do:

9+7+9+7 = <u>32 feet</u>

Soil: The soil is the area. Area is equal to length times width. Length is 9 and width is 7, so we do:

9 x 7 = <u>63 feet squared</u>

8 0

3 years ago

Find the exact value of the composition. arccos (cos pi/2)

Genrish500 [490]

<span>arccos (cos pi/2)=?
</span>cos pi/2=0, arccos (0)=?, we know that cos pi/2=0, so cos^-1 (o)= Pi/2, but cos^-1 (o)=arccos (0), so arccos (cos pi/2)=Pi/2

6 0

3 years ago

Diego inicia un viaje por carretera de 12 horas con la batería de su teléfono al 75%. Dado su uso normal, ¿su teléfono durará to

faltersainse [42]

Based on Diego's normal usage of his phone, if the battery is at 75%, the phone will not last the whole trip.

<h3>How long will the phone battery last?</h3>

First find out how long each percentage of battery life lasts:

= 15 / 100

= 0.15 hours

If Diego is going on a 12 hour trip with 75%, the length of time it would last is:

= 0.15 x 75

= 11.25 hours

This is less than the 12 hours required so the phone will not last the whole trip.

Rest of question:

At 100%, the battery can go for 15 hours.

Find out more on rate of use at brainly.com/question/16140581.

#SPJ1

3 0

2 years ago

can anyone help me with this ??

Mars2501 [29]

Answer:

A. 336

B. Arranging 3 people in 8 chairs.

C. 42

B. Arranging 2 people in 7 chairs.

Step-by-step explanation:

$P(n, r) = P(8, 3)$

Formula for Permutation is given as:

$P(n, r) = \dfrac{n!}{(n-r)!}$

Putting the value of $n$ = 8 and $r =3$ , we get:

$P(8, 3) = \dfrac{8!}{(8-3)!} \\\Rightarrow \dfrac{8\times 7 \times 6 \times 5\times 4 \times 3 \times 2\times 1}{5\times 4 \times 3\times 2\times 1}\\\Rightarrow 8\times 7 \times 6 \\\Rightarrow 336$

B. Real world situation for part A:

Arranging 3 people on 8 chairs.

First person has 8 options.

Second person has 7 options.

Third person has 6 options.

$P(n, r) = P(7, 2)$

Formula for Permutation is given as:

$P(n, r) = \dfrac{n!}{(n-r)!}$

Putting the value of $n$ = 7 and $r$ = 2 , we get:

$P(7, 2) = \dfrac{7!}{(7-2)!} \\\Rightarrow \dfrac{7 \times 6 \times 5\times 4 \times 3 \times 2\times 1}{5\times 4 \times 3\times 2\times 1}\\\Rightarrow 7 \times 6 \\\Rightarrow 42$

D. Real world situation for part AC:

Arranging 2 people on 7 chairs.

First person has 7 options.

Second person has 6 options.

4 0

3 years ago