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1 day ago

A plane ticket barcelona costs £175 the price decreases by 6% work out the new price

Mathematics

2 answers:

Svet_ta [4.3K]1 day ago

6 0

Answer: £164.50

Reducing 175 by 6% results in 164.5.

The absolute change is:

164.5 - 175 = -10.5

Step-by-step explanation:

The calculation is as follows:

175 - Percentage decrease =

175 - (6% × 175) =

175 - 6% of 175 =

(1 - 0.06) × 175 =

0.94 × 175 =

94 ÷ 100 × 175 =

94 × 175 divided by 100 =

16,450 ÷ 100 =

164.5

So, the final amount is £164.50

Zina [3.9K]1 day ago

3 0

Answer: £164.5

Step-by-step explanation:

The initial ticket price is £175.

The reduction of 6% amounts to 6/100 × £175

giving £10.5.

To find the new ticket price, we subtract the 6% reduction from the original price:

= £175 - £10.5 equals

= £164.5

I trust this assists you.

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Find the point on the circle x^2+y^2 = 16900 which is closest to the interior point (30,40)

Leona [4166]

Response-

(78,104) represents the point closest to the interior.

Explanation-

The equation defining the circle,

$\Rightarrow x^2+y^2 = 16900$

$\Rightarrow y^2 = 16900-x^2$

$\Rightarrow y = \sqrt{16900-x^2}$

Since the point lies on the circle, its coordinates must be,

$(x,\sqrt{16900-x^2})$

The distance "d" from the point to (30,40) can be calculated as,

$=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$=\sqrt{(x-30)^2+(\sqrt{16900-x^2}-40)^2}$

$=\sqrt{x^2+900-60x+16900-x^2+1600-80\sqrt{16900-x^2}}$

$=\sqrt{9400-60x-80\sqrt{16900-x^2}}$

Next, we need to determine the value of x for which d is minimized. The minimum distance occurs when $9400-60x-80\sqrt{16900-x^2}$ is at its lowest value.

Let’s set up the equation,

$\Rightarrow f(x)=9400-60x-80\sqrt{16900-x^2}$

$\Rightarrow f'(x)=-60+80\dfrac{x}{\sqrt{16900-x^2}}$

$\Rightarrow f''(x)=\dfrac{1352000}{\left(16900-x^2\right)\sqrt{16900-x^2}}$

We find the critical points,

$\Rightarrow f'(x)=0$

$\Rightarrow-60+80\dfrac{x}{\sqrt{16900-x^2}}=0$

$\Rightarrow 80\dfrac{x}{\sqrt{16900-x^2}}=60$

$\Rightarrow 80x=60\sqrt{16900-x^2}$

$\Rightarrow 80^2x^2=60^2(16900-x^2)$

$\Rightarrow 6400x^2=3600(16900-x^2)$

$\Rightarrow \dfrac{16}{9}x^2=16900-x^2$

$\Rightarrow \dfrac{25}{9}x^2=16900$

$\Rightarrow x=\sqrt{\dfrac{16900\times 9}{25}}=78$

$\Rightarrow x=78$

Then,

$\Rightarrow f''(78)=\dfrac{1352000}{\left(16900-78^2\right)\sqrt{16900-78^2}}=\dfrac{125}{104}=1.2$

Since f''(x) is positive, the function f(x) achieves its minimum at x=78

When x is set to 78, the corresponding y value will be

$\Rightarrow y = \sqrt{16900-x^2}=\sqrt{16900-78^2}=104$

This leads us to conclude that the closest point is (78,104)

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8 days ago

Lines m and n are cut by transversal l. Lines m and n are cut by transversal l. On line m where it intersects line l, 4 angles a

babunello [3635]

∠1 and ∠8 are alternate exterior angles while ∠3 and ∠6 are alternate interior angles.

step-by-step explanation:

When transversal l intersects lines m and n, the angles formed outside each line on the opposite side of the transversal constitute alternate angles (like ∠1 and ∠8). In contrast, alternate interior angles appear on opposite sides but are located between the two lines (like ∠3 and ∠6).

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Keywords: Transversal, angles

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12 days ago

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If x3=64 and y3=125, what is the value of y−x?

Zina [3914]

Answer: We start with equation 1

x=64/3

Next, we solve equation 2

y=125/3

Now, we combine equations 1 and 2

y-x=125/3 -64/3

=61/3

Step-by-step explanation:

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5 days ago

In a certain town, 60 families own tv sets, 85 own scooters, 70th own refrigerators, and 95 own radio sets. One hundred and thir

tester [3916]

Answer:

310

Step-by-step explanation:

The highest possible number is achieved when each household has just one appliance. When calculating the total, we find ...

60 + 85 + 70 + 95 = 310

The maximum possible number of families is 310.

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17 days ago

What is the concentration of a new solution obtained by mixing 25ml of water with 125ml of a 20% salt solution in water?

babunello [3635]

Given that the salt concentration in a 125 ml salt solution is at 20%, it indicates a salt to water ratio of 20:80, which simplifies to 1:4.

Consequently, the salt quantity in the 125 ml 20% solution can be calculated as 20% of 125, yielding 0.2 x 125 = 25 ml, and therefore, the water content amounts to 125 - 25 = 100 ml.

When adding 25 ml of water to this 20% salt solution, the total water becomes 100 + 25 = 125 ml while the salt quantity remains at 25 ml.

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