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3 years ago

Evaluate cos0 if sin0= sqrt(5)/3 a. 9/5 b. 2/3 c. 5/9 d. 3/2

Mathematics

1 answer:

Evgesh-ka [11]3 years ago

8 0

Solution given:

$\sin( \alpha ) = \frac{\sqrt{5} }{3}$

P=√5

h=3

b= $\sqrt{3 {}^{2} - \sqrt{5} {}^{2} }$

b=2

$\cos( \alpha ) = \frac{b}{h} = \frac{2}{3}$

Note

$\alpha = 0$

b:⅔

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[TON OF POINTS] [3 QUESTIONS - Easy money :)]

kherson [118]

The correct answers are:

1/6πd³;
3; and
9 cm.

Explanation:

For the first question:

The formula for the volume of a sphere is:

$V=\frac{4}{3}\pi r^3$

We have the diameter, not the radius. The diameter is twice as much as the radius; this means to find the radius using the diameter, we divide by 2. This gives us:

$V=\frac{4}{3}\pi (\frac{d}{2})^3$

When we raise a fraction to a power, we raise both the numerator and the denominator to that power. This gives us:

$V=\frac{4}{3}\pi(\frac{d^3}{2^3})
\\
\\=\frac{4}{3}\pi(\frac{d^3}{8})$

We start multiplying this:
$V=\frac{4\pi}{3}(\frac{d^3}{8})
\\
\\=\frac{4\pi d^3}{3\times 8}
\\
\\=\frac{4\pi d^3}{24}
\\
\\=\frac{4}{24}\pi d^3
\\
\\=\frac{1}{6}\pi d^3$

For the second question:

The planes of symmetry are the planes through which we can fold the figure in half. These are in the middle horizontally through the figure; in the middle vertically (through the width) through the figure; and in the middle vertically (through the length) through the figure. This makes 3.

For the third question:

The formula for the volume of a triangular prism is:

$V=\frac{1}{3}(\frac{1}{2}bh)H$ ,

where b is the base of the triangular base of the pyramid, h is the height of the triangular base of the pyramid, and H is the height of the pyramid.

We know the volume is 90; the base of the triangle is 12 and the height is 5:

$90 = \frac{1}{3}(\frac{1}{2}\times 12\times 5)H
\\
\\90 = \frac{1}{3}(\frac{1}{2}\times 60)H
\\
\\90 = \frac{1}{3}(30)H
\\
\\90 = 10H$

We divide both sides by 10:

90/10 = 10H/10
9 = H

4 0

4 years ago

Find the equation of this line

GalinKa [24]

the Answer is:

3/4x + 1/4

6 0

3 years ago

Read 2 more answers

Evelyn went shopping with half of her monthly allowance. She spent $39.95 on a dress and 3/7 of the remainder on some accessorie

Gnoma [55]

Answer:

Evelyn monthly allowance is $187.

Step-by-step explanation:

Let the monthly allowance be 'x'.

Given:

Money taken with for shopping = $\frac{x}{2}$

Money spent of dress = $39.95

Also Given:

3/7 of the remainder on some accessories.

Money spent on accessories is equal to $\frac{3}{7}$ times Difference of monthly allowance and Money spent of dress.

framing in equation form we get;

Money spent on accessories = $\frac{3}{7}\times(\frac{x}{2}-39.95)$

Also Given:

Money left after shopping = $30.60

Now we know that;

Money taken with for shopping is equal to sum of Money spent of dress and Money spent on accessories and Money left after shopping.

framing in equation form we get;

$\frac{x}{2}=39.95+\frac{3}{7}(\frac{x}{2}-39.95)+30.60\\\\\frac{x}{2}=39.95+\frac{3x}{14}- 17.12 +30.60$

Combining like terms we get;

$\frac{x}{2}-\frac{3x}{14}=39.95-17.12+30.60\\\\\frac{x}{2}-\frac{3x}{14}= 53.43$

Now we will make denominator common using L.C.M

$\frac{x\times 7}{2\times7}-\frac{3x\times1}{14\times1}= 53.43\\\\\frac{7x}{14}-\frac{3x}{14}= 53.43\\\\\frac{7x-3x}{14}=53.43\\\\\frac{4x}{14}=53.43\\\\4x=53.43\times14\\\\x= \frac{53.43\times14}{4} = \$187$

Hence Evelyn monthly allowance is $187.

3 0

4 years ago

Mandy needs to buy 5 work shirts that are all the same price. after she uses a $20 gift certificate, she can spend no more than

SVEN [57.7K]

5x<50-20
x<10-4
x<6

x= the cost of the shirts
50= cost limit
-20= discount
5= number of shirts

4 0

3 years ago

Use linear combination 4x-9y=1 -2x+3y=-1

kirill [66]

Answer:

(x, y) = (1, 1/3)

Step-by-step explanation:

The x-coefficient in the first equation is -2 times that in the second equation, so adding twice the second equation to the first will eliminate x:

(4x -9y) +2(-2x +3y) = (1) +2(-1)

-3y = -1 . . . . simplify

y = 1/3 . . . . . divide by -3

The y-coefficient in the first equation is -3 times the y-coefficient in the second equation, so adding 3 times the second equation to the first will eliminate y:

(4x -9y) +3(-2x +3y) = (1) +3(-1)

-2x = -2 . . . . . . simplify

x = 1 . . . . . . . . . divide by -3

The solution is (x, y) = (1, 1/3).

8 0

4 years ago