The base of a right pyramid with apex V is a square ABCD of side 10cm. The length of each slant edge is 15cm. Calculate:

1) You can depend solely on your braking system, as the vehicle will only travel 250ft from when you apply the brakes until it completely stops, leaving it 50ft away from the cow. 2) Refer to the attached image. j(t) represents the distance from the brake application point after t seconds in feet. j'(t) indicates the car's speed t seconds after braking, expressed in ft/s. j"(t) shows the car's acceleration t seconds post-braking in

. 3) Any time beyond t=5.28 will not accurately reflect the car's path, because at that moment, it will have reached a speed of 0ft/s, and without an external force, the car will remain stationary past that point. 4)

(refer to attached image for the graph). Step-by-step breakdown: 1) Here, we need to determine when the vehicle's speed becomes 0, indicating a complete stop. We achieve that by deriving the position function:

. Setting the first derivative to zero gives us:

95-18t=0, from which we solve for t: -18t=-95, leading to t=5.28s. Now we will calculate the position of the vehicle after 5.28 seconds:

This results in the vehicle stopping 250.69ft after brake application, leaving approximately 50ft between the vehicle and the cow when it halts completely, allowing reliance solely on the brakes. 2) For part 2, I derive the function again to obtain:

j"(t)=-18 and then graph them (see attached image). Here, j(t) illustrates the distance post-brake application t seconds later in feet, j'(t) signifies the velocity t seconds after brakes were applied in ft/s, while j"(t) indicates the car's acceleration post-braking in

. 3) Yes, after t=5.28, the models in part (ii) won't accurately represent the vehicle's trajectory, as at that instance the car's speed would be 0ft/s and if no additional force acts on it, the vehicle won't move beyond that point. 4)

(refer to the attached image for the graph).

<span>A typical door measures about 80 inches tall by 36 inches wide. The width in that pair is 36 inches, so Hank's reasonable estimate for the classroom door width would be 36 inches. Converting inches to feet uses 12 inches = 1 foot, and 36 ÷ 12 = 3, so the width is about 3 feet.</span>

A college admissions office employs the formula to forecast the GPA of prospective students:

z = 0.003x + 0.8y − 4,

with z representing the predicted GPA on a scale of 0 to 4.3, x being the combined student's SAT Math and Verbal scores scaling from 400 to 1600, and y as the student's high school GPA on a 0 to 4.3 scale. The college accepts applicants whose predicted GPA meets or exceeds 2.3.

In the case of a student with SATs of 1050 and a high school GPA of 3.0, will they be granted admission?

Answer:

A. No, since Z = 1.55, which falls short of the 2.3 minimum GPA required for acceptance.

Step-by-step reasoning:

Z = 0.003x + 0.8y - 4

X = SAT score

Y = high school GPA

Z = predicted college GPA

X = 1050

Y = 3.0

Z =.003 *(1050) + 0.8*(3.0) -4

Z = 1.55, which is below the required admission GPA of 2.3.

To solve this problem, we need to convert the measurements so we can carry out the necessary calculations. A ton equals 2000 pounds, therefore, 3/4 ton translates to 1500 pounds. Since there are 16 ounces in a pound, 4 pounds and 14 ounces amounts to 4.875 pounds. To find the number of bricks, we divide:
                                     number of bricks = 1500 lbs / 4.875 lbs
                                                            = 307.7

Consequently, this is the number of bricks required. The final answer is approximately.

Response:

2.33 $

Detailed breakdown:

10x14=140 cents / 2.33$