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2 months ago

Last year Boris paid £256 for his car insurance.

1 answer:

6 0

The percentage rise in Boris's car insurance costs is 249%. Step-by-step explanation: To find the percentage increase in Boris's car insurance, we need to apply a mathematical formula. The formula is {(new amount - old amount) / old amount} * 100%. Given the previous data, the old amount is £256, and the new amount is £894. Hence, the percentage increase results in (894 - 256) / 256 * 100% = 638 / 256 * 100 = 249.21875, which rounds to 249%.

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give me 3 pictures showing the application of the sum and the product of the roots of quadratic equations in real life . describ

babunello [11817]

Quadratic equations find their application in various real-world scenarios such as: sports, bridges, projectile motion, the curvature of bananas, and so on.

Here are three images representing real-world instances of quadratics:

Example 1: A cyclist travels along a parabolic trajectory to leap over obstacles.

Example 2: A person throws a basketball towards the hoop, moving in a gently upward path described by a quadratic curve.

Example 3: A football player kicks the ball upward, which follows a quadratic path as it travels a distance.

4 0

2 months ago

Read 2 more answers

Brian multiplied his average speed of 14.73 miles per hour by the amount of time he spent cross-country skiing. His product was

Leona [12618]

Yes, it was a reasonable result

Step-by-step clarification:

6 0

2 months ago

Read 2 more answers

A flat circular plate has the shape of the region x2 + y2≤1. The plate, including the boundary where x2 + y2 = 1, is heated such

Leona [12618]

Setting both partial derivatives to zero results in a single critical point at $(x,y)=\left(\dfrac12,0\right)$ , located within the unit disk.

At this given point, the derivative value of the Hessian matrix is

$|H|=\begin{vmatrix}T_{xx}&T_{xy}\\T_{yx}&T_{yy}\end{vmatrix}=\begin{vmatrix}2&0\\0&4\end{vmatrix}=8>0$

and the second-order partial derivative with respect to $x$ yields

$T_{xx}\bigg|_{(x,y)=(1/2,0)}=2>0$

This suggests that the critical point represents a local minimum, marking it as the coldest area on the plate with a temperature of $T\left(\dfrac12,0\right)=-\dfrac14$ .

To find the hottest area on the plate, it must be located along the boundary. Let $x=\cos\theta$ and $y=\sin\theta$ , so that

$T(x,y)=T(\theta)=\cos^2\theta+2\sin^2\theta-\cos\theta$
$T(\theta)=\dfrac32-\cos\theta-\dfrac12\cos2\theta$

Thus, the plate's boundary (the circle $x^2+y^2=1$ ) is treated as a single variable function $\theta$ examined over $\theta\in[0,2\pi)$ . A single differentiation gives

$T'(\theta)=\sin\theta+\sin2\theta=0$
$\implies\theta=0,\theta=\dfrac{2\pi}3,\theta=\pi,\theta=\dfrac{4\pi}3$

You will discover that $T(\theta)$ achieves three extrema on the interval $(0,2\pi)$ , with relative maxima occurring at $\theta=\dfrac{2\pi}3$ and $\theta=\dfrac{4\pi}3$ , and a relative minimum at $\theta=\pi$ (and $\theta=0$ , if you wish to include that).

Our minimum has already been identified inside the plate - which you can check to have a lower temperature than at the points noted by $T(\theta)$ - and we identify two maxima at $\theta=\dfrac{2\pi}3$ and $\theta=\dfrac{4\pi}3$ , both showing a maximum temperature of $T=\dfrac94$ .

Reverting to Cartesian coordinates, these points match up with $\left(-\dfrac12,\pm\dfrac{\sqrt3}2\right)$ .

4 0

1 month ago

Margie received her store order on 12/3/16 at 4AM. She just opened one of the

Inessa [12570]

Answer:

Expiration Date: 1/17/2017

Expiration Time: 4:00am

Preparation Date: 12/3/2016

Preparation Time: 4:00am

Initial Usage Date: 12/7/2016

Detailed Breakdown:

An illustrative depiction of the question has been provided in an image format for clarity.

From the information given, it is noted that her store order arrived on 12/3/2016 at 4am, confirming that both the prep date and time are 12/3/2016 and 4am respectively. The product has a printed expiration date of 1/17/2017, logically indicating that its expiration time is also 4am, in line with the prep time; adding 24 hours leads us back to the same time on the expiration date. Furthermore, we were informed that she utilized the product on 12/7/2016, which marks the initial use date. Based on this information, we can summarize as follows:

Expiration Date: 1/17/2017

Expiration Time: 4:00am

Preparation Date: 12/3/2016

Preparation Time: 4:00am

Initial Usage Date: 12/7/2016

8 0

3 months ago