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sattari [20]
2 years ago
13

Sandra throws an object straight up into the air with an initial velocity of 38 ft/s from a platform that is 30 ft above the gro

und. Use the formula h(t)=−16t2+v0t+h0 , where v0 is the initial velocity and h0 is the initial height. How long will it take for the object to hit the ground?
A. 1 s

B. 2 s

C. 3 s

D. 4 s
Mathematics
2 answers:
Makovka662 [10]2 years ago
6 0

Answer:

The answer is C.

Step-by-step explanation:

Given formula h(t)=−16t2+v0t+h0 , where v0 is the initial velocity and h0 is the initial height.

In this case, the initial postion is a platform 30ft above ground so h0=+30

The initial velocity is 38 ft/s straight up into the air so v0=+38

h(t)=-16t2+38t+30

When the object hits the ground, h=0.

h=-16t2+38t+30=0

Simplifying 8t2-19t-15=0

(8t+5)(t-3)=0

t=-5/8 or 3

As time cannot be -ve, t=3s. The answer is C.

Vikentia [17]2 years ago
4 0

Answer:

C

Step-by-step explanation:

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One size of pizza served at Joe’s Pizza Parlor is 10in. in diameter. What is the area of this particular (circular) size pizza?
abruzzese [7]

Answer:

78.5 in.²

Explanation:

Formula For Area Of Circle: Area = πr²

π: 3.14

r (Half Of Diameter): 5

r²: 25

3.14 · 25 = 78.5

6 0
3 years ago
One of the vertices of an equilateral triangle is on the vertex of a square and two other vertices are on the not adjacent sides
Elina [12.6K]
<h2>Answer:</h2>

<em> The side of the triangle is either 38.63ft or 10.35ft</em>

<h2>Step-by-step explanation:</h2>

This problem can be translated as an image as shown in the Figure below. We know that:

  • The side of the square is 10 ft.
  • One of the vertices of an equilateral triangle is on the vertex of a square.
  • Two other vertices are on the not adjacent sides of the same square.

Let's call:

Since the given triangle is equilateral, each side measures the same length. So:

x: The side of the equilateral triangle (Triangle 1)

y: A side of another triangle called Triangle 2.

That length is the hypotenuse of other triangle called Triangle 2. Therefore, by Pythagorean theorem:

\mathbf{(1)} \ x^2=100+y^2

We have another triangle, called Triangle 3, and given that the side of the square is 10ft, then it is true that:

y+(10-y)=10

Therefore, for Triangle 3, we have that by Pythagorean theorem:

(10-y)^2+(10-y)^2=x^2 \\ \\ 2(10-y)^2=x^2 \\ \\ \\ \mathbf{(2)} \ x^2=2(10-y)^2

Matching equations (1) and (2):

2(10-y)^2=100+y^2 \\ \\ 2(100-20y+y^2)=100+y^2 \\ \\ 200-40y+2y^2=100+y^2 \\ \\ (2y^2-y^2)-40y+(200-100)=0 \\ \\ y^2-40y+100=0

Using quadratic formula:

y_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ y_{1,2}=\frac{-(-40) \pm \sqrt{(-40)^2-4(1)(100)}}{2(1)} \\ \\ \\ y_{1}=37.32 \\ \\ y_{2}=2.68

Finding x from (1):

x^2=100+y^2 \\ \\ x_{1}=\sqrt{100+37.32^2} \\ \\ x_{1}=38.63ft \\ \\ \\ x_{2}=\sqrt{100+2.68^2} \\ \\ x_{2}=10.35ft

<em>Finally, the side of the triangle is either 38.63ft or 10.35ft</em>

5 0
3 years ago
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Find the common denominator for these two rational numbers<br><br>​
nevsk [136]

Answer:

Step-by-step explanation:

n²,5n

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8 0
3 years ago
Write a story problem to go with the multiplication problem 3 x 7/8
Mariulka [41]

Answer:

Elias Nebiyu gives seven breads for his eight friends and he continues this give away for three days.

Step-by-step explanation:

3x 7/8 result is attached above.

4 0
2 years ago
The ratio of students to teachers at a school is 19 to 1 how many students are there in each total number of people
vladimir2022 [97]

<u>Question</u>:

The ratio of students to teachers at a school is 19 : 1. How many students are there in each total number of people?

A: 100 people

b. 280 people

c.440 people

d.760 people

<u>Answer</u>:

A )95 students  and 5 teachers

B)266 students  and 14 teachers

C)418 students  and 22 teachers

D)722 students  and 38 teachers

<u>Step-by-step explanation:</u>

<u><em>A: 100 people</em></u>

Ratio  =  19  :  1

The sum of the ratio is 19 + 1 = 20

Scale factor  = \frac{100}{20}

scale factor  = 5

The number students is 19 \times 5 = 95

The number of teachers is 1 \times 5 = 5

<em><u>b. 280 people </u></em>

Ratio  =  19  :  1

The sum of the ratio is 19 + 1 = 20

Scale factor  = \frac{280}{20}

scale factor  = 14

The number students is 19 \times 14 = 266

The number of teachers is 1 \times 14 =  14

<em><u>c.440 people</u></em>

Ratio  =  19  :  1

The sum of the ratio is 19 + 1 = 20

Scale factor  = \frac{440}{20}

scale factor  = 22

The number students is 19 \times 22 = 418

The number of teachers is 1 \times 22 =  22

<em><u>d.760 people</u></em>

Ratio  =  19  :  1

The sum of the ratio is 19 + 1 = 20

Scale factor  = \frac{760}{20}

scale factor  = 38

The number students is 19 \times 38 = 722

The number of teachers is 1 \times 38 =  38

5 0
3 years ago
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