Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]?

The position function for a free-falling object is s(t) = -16t^2 + vt +5. A ball is thrown upward from the top of a 400-foot bui

mixer [17]

Answer:

6.21 seconds

Step-by-step explanation:

The position function of a free-falling object is,

$s(t) = -16t^2+v_0t+s_0$

Where,

$s_0$ = initial height of the object,

$v_0$ = initial velocity of the object,

Here,

$s_0=400\text{ feet}$

$v_0=35\text{ feet per sec}$

Hence, the height of the ball after t seconds,

$s(t)=-16t^2+35t+400$

When s(t) = 0,

$\implies -16t^2+35t+400=0$

$t=\frac{-35\pm \sqrt{35^2-4\times -16\times 400}}{2\times -16}$

$t=\frac{-35\pm \sqrt{1225+25600}}{-32}$

$\implies t\approx -4.02\text{ or }t\approx 6.21$

∵ Time cannot be negative,

Hence, after 6.21 seconds the ball will reach the ground.

4 0

3 years ago

Angle mIJK=180, angle mIJU = 3x-7, and angle mUJK=17x + 7 find angle mIJU

Andrej [43]

Answer:

The measure of angle IJU is 20 degrees.

Step-by-step explanation:

In order to find that, we need to add the two angles together and set equal to 180 degrees. Then we can solve for x.

(3x - 7) + (17x + 7) = 180 ----> Combine like terms

20x = 180 -----> Divide by 20

x = 9

Now that we have this, we can stick the value into the equation and solve for IJU.

IJU = 3x - 7

IJU = 3(9) - 7

IJU = 27 - 7

IJU = 20

3 0

3 years ago

5x + 3 - 2x = 12 + 7x - 2 solution ??? SOMEONE HELPPP PLEASE !!

tensa zangetsu [6.8K]

Answer:

x = -7/4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

5x + 3 - 2x = 12 + 7x - 2

Step 2: Solve for x

Combine like terms: 3x + 3 = 7x + 10
[SPE] Subtract 3x on both sides: 3 = 4x + 10
[SPE] Subtract 10 on both sides: -7 = 4x
[DPE] Divide 4 on both sides: -7/4 = x
Rewrite: x = -7/4

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: 5(-7/4) + 3 - 2(-7/4) = 12 + 7(-7/4) - 2
Multiply: -35/4 + 3 + 7/2 = 12 - 49/4 - 2
Add: -23/4 + 7/2 = 12 - 49/4 - 2
Add: -9/4 = 12 - 49/4 - 2
Subtract: -9/4 = -1/4 - 2
Subtract: -9/4 = -9/4

Here we see that -9/4 does indeed equal -9/4.

∴ x = -7/4 is the solution to the equation.

8 0

3 years ago

A binomial probability distribution has p = .20 and n = 100.

AleksAgata [21]

Answer:

Mean = 0.2(100) = 20

Variance = 0.2×0.8×100 = 16

Standard deviation = 4

Yes, np > 5 & nq > 5

3 0

3 years ago

Read 2 more answers

Evaluate the determinant for the following matrix [144] [522] [155]

WARRIOR [948]

Matrix :

1    4    4

5 2    2

1    5    5

=> Determinant =

1 * (2*5 - 2*5) - 4 * (5*5 - 1*2) + 4 * ( 5*5 - 2*1)

= 1*(10 - 10) - 4*(25 - 2) + 4*(25 -2) = 1*0 + 4* 23 + 4*(25 - 2) = 0 - 4*23 + 4*23 = 0

Answer: 0

8 0

3 years ago