All categories

2 years ago

The diagonals of a kite have lengths of 4 inches and 9 inches. Find the area of the kite. The area is square inches

Mathematics

1 answer:

elixir [45]2 years ago

7 0

Answer:

Step-by-step explanation:

area=(4×9)÷2=18 inch²

You might be interested in

Write an algebraic expression for two fifths the cube of a number

pashok25 [27]

N - the number

$\dfrac{2}{5}n^3$

7 0

2 years ago

**Spam answers will not be tolerated**

Morgarella [4.7K]

Answer:

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

Step-by-step explanation:

So we have the function:

$f(x)=\frac{4}{\sqrt x}$

And we want to find the derivative using the limit process.

The definition of a derivative as a limit is:

$\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Therefore, our derivative would be:

$\lim_{h \to 0}\frac{\frac{4}{\sqrt{x+h}}-\frac{4}{\sqrt x}}{h}$

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

$=\lim_{h \to 0}\frac{4(\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x})}{h}$

Place the 4 in front:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}$

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}(\frac{\sqrt{x+h}\sqrt x}{\sqrt{x+h}\sqrt x})$

Distribute:

$=4\lim_{h \to 0}\frac{({\sqrt{x+h}\sqrt x})\frac{1}{\sqrt{x+h}}-(\sqrt{x+h}\sqrt x)\frac{1}{\sqrt x}}{h({\sqrt{x+h}\sqrt x})}$

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

$=4 \lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }$

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

$= 4\lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }(\frac{\sqrt x +\sqrt{x+h})}{\sqrt x +\sqrt{x+h})}$

The numerator will use the difference of two squares. Thus:

$=4 \lim_{h \to 0} \frac{x-(x+h)}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Simplify the numerator:

$=4 \lim_{h \to 0} \frac{x-x-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}\\=4 \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Both the numerator and denominator have a h. Cancel them:

$=4 \lim_{h \to 0} \frac{-1}{(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Now, substitute 0 for h. So:

$=4 ( \frac{-1}{(\sqrt{x+0}\sqrt x)(\sqrt x+\sqrt{x+0})})$

Simplify:

$=4( \frac{-1}{(\sqrt{x}\sqrt x)(\sqrt x+\sqrt{x})})$

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

$=4( \frac{-1}{(x)(2\sqrt{x})})$

Multiply across:

$= \frac{-4}{(2x\sqrt{x})}$

Reduce. Change √x to x^(1/2). So:

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

Add the exponents:

$=-\frac{2}{x^\frac{3}{2}}$

And we're done!

$f(x)=\frac{4}{\sqrt x}\\f'(x)=-\frac{2}{x^\frac{3}{2}}$

5 0

2 years ago

Saj has made 7 litres of curry sauce.

Makovka662 [10]

Answer:

18 jars can be filled completely.

Step-by-step explanation:

7L=7000ml

1 jar contain 375 ml

375ml can be filled in 1 jar

375ml=1 jar

1 ml = 1/375 jar

7000 ml = 7000× 1/375 jar

7000ml= 18.67 jar

hence 18 jars can be filled completely.

3 0

2 years ago

Can anyone help me with this math question

Lynna [10]

Answer:

89 seats are not being used

Step-by-step explanation:

You subtract the seats being used by teachers

342 - 75 =267

Change 2/3 into a percentage = 66.6%

Find 66.6% of 267= 177.8 (I rounded up to 178)

Then subtract 177.8/178 from 267 to find the amount of seats not being used.

The amount of seats not being used would come down to 89 seats.

I hope this helps!

4 0

2 years ago

-7r^2= -329 square root property

Genrish500 [490]

9514 1404 393

Answer:

r = ±√47

Step-by-step explanation:

-7r^2 = -329 . . . . given

r^2 = 47 . . . . . divide both sides by -7 (multiplication property of equality)

r = ±√47 . . . . square root both sides (square root property of equality)

5 0

2 years ago

Read 2 more answers

The diagonals of a kite have lengths of 4 inches and 9 inches. Find the area of the kite. The area is square inches​

The diagonals of a kite have lengths of 4 inches and 9 inches. Find the area of the kite. The area is square inches