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2 years ago

What's

Mathematics

1 answer:

Iteru [2.4K]2 years ago

8 0

Answer:

374/105.

Step-by-step explanation:

1/3 of 8 * 2/7

= 1/3 * 8 * 2/7

= 8/3 * 2/7

= 16/21.

2/5 of 7

= 2/5 * 7

= 14/5.

Adding 16/21 + 14/5

= 80 / 105 + (14*21) / 105

= 80/105 + 294/105

= 374/105.

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You notice a hot air balloon descending. The elevation h (in feet) of the balloon is modeled by the function h(x)=−11x+330, wher

Mars2501 [29]

Answer:

1) Please find attached, the graph of the function

The domain of the function is 0 ≤ x ≤ 30

The range of the function is 330 ≥ x ≥ 0

2) The slope of the given equation, shows that the elevation decreases, by (-)11 feet for each increase in time by one second

3) The y-intercept gives the initial elevation of the balloon at time t = 0 seconds

The x-intercept gives the final elevation of the balloon when it lands at time t = 30 seconds

Step-by-step explanation:

1) The function modelling the height of the balloon is h(x) = -11x + 330

Where;

x = The time of elevation of the balloon

The data for the graphing derived from Microsoft Excel are as follows

x ${}$ h(x)

0 ${}$ 330

5 ${}$ 275

10 ${}$ 220

15 ${}$ 165

20 ${}$ 110

25 ${}$ 55

30 ${}$ 0

Please find attached, the graph of the function

The domain of the function is 0 ≤ x ≤ 30

The range of the function is 330 ≥ x ≥ 0

Comparing the given function to the general equation of a straight line, y = m·x + c, we have that the slope, m = -11

2) The slope of a straight line graph gives the rate of change of the dependent variable, per unit change in the independent variable

Therefore, the slope of the given equation, -11 gives the rate of change of the function per unit increase in the independent variable x

Therefore, the elevation decreases, by (-)11 feet for each increase in time by one second

3) The y-intercept gives the initial elevation of the balloon at time t = 0 seconds

The x-intercept gives the final elevation of the balloon when it lands at time t = 30 seconds

8 0

2 years ago

Read 2 more answers

Simplify (square root 2)( square root of 2^3)

steposvetlana [31]

Answer:

$\large\boxed{(\sqrt2)(\sqrt{2^3})=4}$

Step-by-step explanation:

$(\sqrt2)(\sqrt{2^3})\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{2\cdot2^3}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt{2^{1+3}}=\sqrt{2^4}\\\\(1)=\sqrt{2^{2\cdot2}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(2^2)^2}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=2^2=4\\\\(2)=\sqrt{2\cdot2\cdot2\cdot2}=\sqrt{16}=6\ \text{because}\ 4^2=16$

8 0

3 years ago

Write the following phrase as an expression<br> "the product of 6 and n"

Kamila [148]

Answer:

Step-by-step explanation:

A product refers to the multiplication of two or more numbers.

6n is the equivalent of 6*n

4 0

1 year ago

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

3 years ago

ernie thinks he is being stalked by his own shadow. if the ratio of ernie's height to his shadow's height is 1.5 to 1, and ernie

Anna71 [15]

The height of Ernies shadow is 4 feet when his height is 6 feet.

<h3>equation</h3>

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the length of his shadow. Given that the ratio of ernie's height to his shadow's height is 1.5 to 1. Hence:

(1.5/2.5) * y = 6
y = 10 feet

(1/2.5) * 10 = x

x = 4 feet

The height of Ernies shadow is 4 feet when his height is 6 feet.

Find out more on equation at: brainly.com/question/13763238

7 0

2 years ago