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3 years ago

What is the value of the power 7³

Mathematics

2 answers:

Virty [35]3 years ago

8 0

7^3 means 7 cubed, or 7*7*7.

7 times 7 is 49. 49 times 7 is 343.

Hope this helps! :)

zalisa [80]3 years ago

6 0

Answer:

343

Step-by-step explanation:

$7^3 = 7 * 7 * 7$
$7 * 7 * 7 = 49 * 7$
$49 * 7 = 343$

Therefore, the answer is 343.

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Whats is equivanlent fractions of 24/84

Aloiza [94]

Answer:

2/7

Step to step explanation:

This question is in other words, asking you to simplify the fraction.

Find the GCF and divide both the denominator and numeratior by the GCF.

The GCF of 24/84 is 12.

24/12 = 2

84/12 = 7.

3 0

3 years ago

If I decline by 23%, what percent would be remaining?

egoroff_w [7]

Answer: 77%

Step-by-step explanation:

100-23=77

Hope it helps!

4 0

3 years ago

Commission: 10 percent on first $5,000; 15% over $5,000. Find the total graduate commission on $22,000.

natta225 [31]

Based on the information about the percentage, the commission that will be paid will be $3050.

<h3>How to solve percentage</h3>

From the information given, it was stated that there's a 10 percent on first $5,000 and 15% over $5,000.

The total graduate commission on $22,000 will be:

= (10% × $5000) + (15% × $17000)

= (0.1 × $5000) + (0.15 × $17000)

= $500 + $2550

= $3050

Learn more about percentages on:

brainly.com/question/24304697

8 0

2 years ago

Let f(x) = 1/x^2 (a) Use the definition of the derivatve to find f'(x). (b) Find the equation of the tangent line at x=2

Verdich [7]

Answer:

(a) $f'(x)=-\frac{2}{x^3}$

(b) $y=-0.25x+0.75$

Step-by-step explanation:

The given function is

$f(x)=\frac{1}{x^2}$ .... (1)

According to the first principle of the derivative,

$f'(x)=lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{x^2-(x+h)^2}{x^2(x+h)^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{x^2-x^2-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-h(2x+h)}{hx^2(x+h)^2}$

Cancel out common factors.

$f'(x)=lim_{h\rightarrow 0}\frac{-(2x+h)}{x^2(x+h)^2}$

By applying limit, we get

$f'(x)=\frac{-(2x+0)}{x^2(x+0)^2}$

$f'(x)=\frac{-2x)}{x^4}$

$f'(x)=\frac{-2)}{x^3}$ .... (2)

Therefore $f'(x)=-\frac{2}{x^3}$ .

(b)

Put x=2, to find the y-coordinate of point of tangency.

$f(x)=\frac{1}{2^2}=\frac{1}{4}=0.25$

The coordinates of point of tangency are (2,0.25).

The slope of tangent at x=2 is

$m=(\frac{dy}{dx})_{x=2}=f'(x)_{x=2}$

Substitute x=2 in equation 2.

$f'(2)=\frac{-2}{(2)^3}=\frac{-2}{8}=\frac{-1}{4}=-0.25$

The slope of the tangent line at x=2 is -0.25.

The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).

Using point slope form the equation of tangent is

$y-y_1=m(x-x_1)$

$y-0.25=-0.25(x-2)$

$y-0.25=-0.25x+0.5$

$y=-0.25x+0.5+0.25$

$y=-0.25x+0.75$

Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.

5 0

3 years ago

John made a rectangle pen for his dog using 28 feet of fencing. If the width of the pen is 2 feet more than one-half the length,

kati45 [8]

Okay, so you know that the perimeter of the pen is 28 feet. Now we need the separate side lengths.

P = 28 ft.
Length = x
Width = (1/2)x + 2

So now we can plug in the little equations of length and width into a perimeter formula:
2(x) + 2((1/2)x + 2) = 28
Distribute the 2's and solve as needed.
2x + x + 4 = 28
3x + 4 = 28
3x = 24
x = 8

To find the width, just plug in 8 for x in our little equation:
(1/2)(8) + 2
= 6

So, the length is 8 feet and the width is 6 feet.

5 0

3 years ago

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What is the value of the power 7³​

What is the value of the power 7³