1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Amiraneli [1.4K]
2 years ago
7

Solve for t. Express your answer in simplest and exact form.

Mathematics
1 answer:
Masteriza [31]2 years ago
8 0

Answer:

t = sqrt((2 z)/h + ((q_1)^2)/(h^2)) - q_1/h or t = -q_1/h - sqrt((2 z)/h + ((q_1)^2)/(h^2))

Step-by-step explanation:

Solve for t:

z = (h t^2)/2 + t q_1

z = (h t^2)/2 + t q_1 is equivalent to (h t^2)/2 + t q_1 = z:

(h t^2)/2 + t q_1 = z

Divide both sides by h/2:

t^2 + (2 t q_1)/h = (2 z)/h

Add q_1^2/h^2 to both sides:

t^2 + (2 t q_1)/h + q_1^2/h^2 = (2 z)/h + q_1^2/h^2

Write the left hand side as a square:

(t + q_1/h)^2 = (2 z)/h + q_1^2/h^2

Take the square root of both sides:

t + q_1/h = sqrt((2 z)/h + q_1^2/h^2) or t + q_1/h = -sqrt((2 z)/h + q_1^2/h^2)

Subtract q_1/h from both sides:

t = sqrt((2 z)/h + ((q_1)^2)/(h^2)) - q_1/h or t + q_1/h = -sqrt((2 z)/h + q_1^2/h^2)

Subtract q_1/h from both sides:

Answer: t = sqrt((2 z)/h + ((q_1)^2)/(h^2)) - q_1/h or t = -q_1/h - sqrt((2 z)/h + ((q_1)^2)/(h^2))

You might be interested in
A candy company has 150 kg of chocolate-covered nuts and 90 kg of chocolate-covered raisins to be sold as two different mixes. O
Westkost [7]

Answer:

1. 7x + 9.5y

2. 1980

Step-by-step explanation:

In Mix A, there is an equal amount of nuts and raisins.

Let x = kg of nuts = kg of raisins.

In Mix B, there is 3 times as much nuts as raisins.

Let y = kg of raisins, then 3y = kg of nuts.

We have this information:

           Nuts    Raisins   Price  

mix A    x   +   x     =  $ 7.00

mix B    3y  +  y     =  $  9.50

Total:   150   90

Hence, the number of kilograms of each mix should company prepare for the maximum revenue is = 7x + 9.5y

We have these inequalties:

{x≥0y≥0x+3y≤150x+y≤90} (equation 1)

There will be

x+x=2x kg of Mix A at $7.00 per kg.

The revenue from Mix A is:

7(2x)=14x dollars.

There will be

3y+y=4y kg of Mix B at $9.50 per kg.

The revnue from Mix B is:

9.5(4y)=38y dollars.

Hence, the total revenue is:

R=14x+38y (equation 2).

Graph the region determined by [1] and locate its vertices.

You should get:

(0,0),(90,0),(0,50),(60,30)

Test the vertices into [2] and see which vertex produces maximum revenue

(0,0): R=14(0)+38(0)=0 Minimum revenue

(90,0):R=14(90)+38(0)=1260

(0,50): R=14(0)+38(50)=1900

(60,30):R=14(60)+38(30)=1980 Maximum revenue.

3 0
3 years ago
The ingredients for making chocolate cookies are 3/4 cup of brown sugar, 1/4 cup of white sugar, 3/2 cup of butter, 11/8 cup of
Naya [18.7K]

Answer:

\frac{51}{8} cups.

Step-by-step explanation:

It is given that the ingredients for making chocolate cookies are \frac{3}{4} cup of brown sugar, \frac{1}{4} cup of white sugar, \frac{3}{2} cup of butter, \frac{11}{8} cup of flour, and \frac{5}{2} cup of chocolate chips.

Now, we have to calculate the total number of cups of ingredients needed in making chocolate cookies.

So, it will be given by

(\frac{3}{4} + \frac{1}{4} + \frac{3}{2} + \frac{11}{8} + \frac{5}{2}) cups

= \frac{3 \times 2 + 1 \times 2 + 3 \times 4 + 11 + 5 \times 4}{8} cups

= \frac{51}{8} cups. (Answer)

3 0
3 years ago
Equivalent to 7^3 × 7^-2
mixas84 [53]

Answer:

<h2><em><u>7</u></em></h2>

Step-by-step explanation:

{7}^{ - 3}  \times  {7}^{ - 2}

=  {7}^{3 - 2}

= <em><u>7 (Ans)</u></em>

3 0
3 years ago
Read 2 more answers
Nick wanted to determine the length of one blade of a windmill. He stood at a point on the ground 440 feet from the windmill's b
mafiozo [28]

Answer:There are two right triangles. You need to find the opposite side (the height) of each of them. The difference between the two is the height of the blade, x.

You know the adjacent, 440, and you are looking for the opposite, so you need to use tan for both.

tan (30) = y / 440

y = 440 * tan (30) = 254.034...

tan (38.8) = z / 440

y = 440 * tan (38.8) = 353.769.--

353.8 - 254.0 = 99.8 = 100 feet.

Step-by-step explanation:

7 0
2 years ago
According to a certain​ country's department of​ education, 39.9​% of​ 3-year-olds are enrolled in day care. what is the probabi
Yuliya22 [10]
The probability would be 39.9%

The given probability states that 39.9% of the 3 years olds are in daycare. Therefore, it would be obvious to assume that if you randomly selected a 3 year old, that would be the probability that he/she is in daycare.
8 0
3 years ago
Other questions:
  • What is 0.4 as a fraction in lowest term
    9·2 answers
  • Martha is constructing the circumscribed circle for △RST. She has already used her compass and straightedge to complete the part
    6·2 answers
  • Can someone answer this fast!!
    8·2 answers
  • Consider the function f(x) = 2x = 1 and its inverse, f-1(x) = 4x + 1
    14·2 answers
  • What is the best first step to solve the inequality 5x - 322?
    13·1 answer
  • Determine the interval(s) on which the function is (strictly) decreasing.
    8·2 answers
  • A car and a motorcycle leave at noon from the same location, heading in the same direction. The average speed of the car is 30 m
    9·2 answers
  • 15. When coffee is packed by machine into 16-ounce cans, the amount can vary. The mean weight is 16.1 ounces and the standard de
    14·1 answer
  • (x = 3)<br> Solve:<br> 5х + 6 = 21
    15·1 answer
  • ¿cuanto suman los angulos interiores de un hexagono? Escribe solo el numero que corresponda a la cantidad, sin el simbolo de gra
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!