All categories

3 years ago

Please help me please help with just one question at least

Mathematics

1 answer:

Anton [14]3 years ago

3 0

Answer:

1.A

2.C

3.D

4.C

Step-by-step explanation:

HOPE IT HELP

BRAINLIEST PLEASE

You might be interested in

Find the exact value of the expression.<br> tan( sin−1 (2/3)− cos−1(1/7))

Sonja [21]

Answer:

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

Step-by-step explanation:

I'm going to use the following identity to help with the difference inside the tangent function there:

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

Let $a=\sin^{-1}(\frac{2}{3})$ .

With some restriction on $a$ this means:

$\sin(a)=\frac{2}{3}$

We need to find $\tan(a)$ .

$\sin^2(a)+\cos^2(a)=1$ is a Pythagorean Identity I will use to find the cosine value and then I will use that the tangent function is the ratio of sine to cosine.

$(\frac{2}{3})^2+\cos^2(a)=1$

$\frac{4}{9}+\cos^2(a)=1$

Subtract 4/9 on both sides:

$\cos^2(a)=\frac{5}{9}$

Take the square root of both sides:

$\cos(a)=\pm \sqrt{\frac{5}{9}}$

$\cos(a)=\pm \frac{\sqrt{5}}{3}$

The cosine value is positive because $a$ is a number between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ because that is the restriction on sine inverse.

So we have $\cos(a)=\frac{\sqrt{5}}{3}$ .

This means that $\tan(a)=\frac{\frac{2}{3}}{\frac{\sqrt{5}}{3}}$ .

Multiplying numerator and denominator by 3 gives us:

$\tan(a)=\frac{2}{\sqrt{5}}$

Rationalizing the denominator by multiplying top and bottom by square root of 5 gives us:

$\tan(a)=\frac{2\sqrt{5}}{5}$

Let's continue on to letting $b=\cos^{-1}(\frac{1}{7})$ .

Let's go ahead and say what the restrictions on $b$ are.

$b$ is a number in between 0 and $\pi$ .

So anyways $b=\cos^{-1}(\frac{1}{7})$ implies $\cos(b)=\frac{1}{7}$ .

Let's use the Pythagorean Identity again I mentioned from before to find the sine value of $b$ .

$\cos^2(b)+\sin^2(b)=1$

$(\frac{1}{7})^2+\sin^2(b)=1$

$\frac{1}{49}+\sin^2(b)=1$

Subtract 1/49 on both sides:

$\sin^2(b)=\frac{48}{49}$

Take the square root of both sides:

$\sin(b)=\pm \sqrt{\frac{48}{49}$

$\sin(b)=\pm \frac{\sqrt{48}}{7}$

$\sin(b)=\pm \frac{\sqrt{16}\sqrt{3}}{7}$

$\sin(b)=\pm \frac{4\sqrt{3}}{7}$

So since $b$ is a number between $0$ and $\pi$ , then sine of this value is positive.

This implies:

$\sin(b)=\frac{4\sqrt{3}}{7}$

So $\tan(b)=\frac{\sin(b)}{\cos(b)}=\frac{\frac{4\sqrt{3}}{7}}{\frac{1}{7}}$ .

Multiplying both top and bottom by 7 gives:

$\frac{4\sqrt{3}}{1}= 4\sqrt{3}$ .

Let's put everything back into the first mentioned identity.

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

$\tan(a-b)=\frac{\frac{2\sqrt{5}}{5}-4\sqrt{3}}{1+\frac{2\sqrt{5}}{5}\cdot 4\sqrt{3}}$

Let's clear the mini-fractions by multiply top and bottom by the least common multiple of the denominators of these mini-fractions. That is, we are multiplying top and bottom by 5:

$\tan(a-b)=\frac{2 \sqrt{5}-20\sqrt{3}}{5+2\sqrt{5}\cdot 4\sqrt{3}}$

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

4 0

3 years ago

The differnce between a number divide by 3 and 4 is 20

Talja [164]

Answer:

(n/3)/4 =20

Step-by-step explanation:

i think this is what your looking for if not im sorry

have a blessed day :)

3 0

3 years ago

In the xy- plane, the graph of the equation y + 3x + 5 is a line that intersects the y-axis at (0,b) what is the value of b?

maxonik [38]

Answer:

$b=5$

Step-by-step explanation:

The given equation is:

$y=3x+5$

To find the point where this line intersect the y-axis, we put x=0 into the given equation.

When x=0, we have $y=3(0)+5$ .

This implies that; y=5.

The y-intercept is (0,5).

Comparing (0,5) to (0,b), we can conclude that; b=5

8 0

3 years ago

Please help me <br><br> 6th grade math

Marta_Voda [28]

Answer:

Late response, sorry. It is 750 meters.

Step-by-step explanation:

An easy method to save time is to just divide the distance by time to find what amount per second it can run. In this case, you have 120 and 4 to work with. Divide and you'll get 30 meters per second. Then, multiply 25(your seconds) by 30(the meters it runs per second) to get your answer.

5 0

3 years ago

The floor of a gazebo is in the shape of a regular octagon. The perimeter of the floor is 72 feet. The distance from the center

Katyanochek1 [597]

The length of one side of the octagon is given by:
$L = 72/8

L = 9$
Then, the apothem can be determined using the Pythagorean theorem in the following way:
$11.8 ^ 2 = (9/2) ^ 2 + a ^ 2
$
Clearing to have:
$a ^ 2 = 11.8 ^ 2 - (9/2) ^ 2$
$a = \sqrt{11.8 ^ 2 - (9/2) ^ 2}$
$a = 10.91$
Then, the area is given by:
$A = (8) * (1/2) * (L) * (a)
$
Where,
L: length of the octagon sides
a: apotema
Substituting values:
$A = (8) * (1/2) * (9) * (10.91)

A = 392.76 feet ^ 2$
Answer:
the approximate length of the apothem is:
a = 10.91 feet
The approximate area of the floor of the gazebo is:
A = 392.76 feet ^ 2

8 0

3 years ago

Read 2 more answers