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3 years ago

How to do this question? Please tell me the answer with steps

Mathematics

2 answers:

ololo11 [35]3 years ago

3 0

$\dfrac{2\cos \theta \sin \theta}{\tan(90-\theta)}=2\sin^2 \theta\\\\
\dfrac{2\cos \theta \sin \theta}{\cot \theta}=2\sin^2 \theta\\\\
\dfrac{2\cos \theta \sin \theta}{\dfrac{\cos \theta}{\sin \theta}}=2\sin^2 \theta\\\\
2\cos \theta \sin \theta\cdot\dfrac{\sin \theta}{\cos \theta}=2\sin^2 \theta\\\\
2\sin^2 \theta=2\sin^2 \theta$

Pavel [41]3 years ago

3 0

Consider a right angled triangle with hypotenuse c and legs a and b. Let sin theta = a/c .

Then cos theta = b/c and tan (90-theta) = b/a

Then 2 sin theta cos theta / tan (90 - theta)

= 2 * a/c * b/c / b/a

= 2 * ab/c^2 * a/b

= 2 a^2 / c^2 = 2 sin^2 theta

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while shopping for clothes, Tracey spent 38$ less than 3 times what Daniel spent. write and solve an equation to find how much D

alexandr1967 [171]

$\bold{\huge{\orange{\underline{Solution}}}}$

$\bold{\underline{ Given :- }}$

While shopping for clothes Tracey spent 38$ less than 3 times of what Daniel spent

$\bold{\underline{ To\: Find :- }}$

We have to determine the total cost spent by daniel

$\bold{\underline{ Let's \: Begin :- }}$

Cost spent by Tracey for her clothes = 38$

Let assume the spending by Daniel is x

$\bold{\underline{Therefore ,}}$

$\sf{ x / 3 = 38 }$

$\sf{ x = 38 × 3 }$

$\sf{ x = 114 dollar }$

$\sf{\red{ Hence,\: Daniel\: spent\: 114 \: dollars\: on \: His\: clothes }}$

7 0

3 years ago

Find the values of m and b that make the following function differentiable.

Sonbull [250]

The derivative of f(x) at x=3 is 2x=6 approaching from the left side (apply power rule to y=x^2). The derivative of f(x) at x=3 is m approaching from the right side. In order for the function to be differentiable, the limit of derivative at x=3 must be the same approaching from both sides, so m=6. Then, x^2=mx+b at x=3, plug in m=6, 9=18+b, so b=-9.

7 0

3 years ago

Read 2 more answers

In a binomial distribution, n = 8 and π=0.36. Find the probabilities of the following events. (Round your answers to 4 decimal p

skelet666 [1.2K]

Answer:

$\mathbf{P(X=5) =0.0888}$

P(x ≤ 5 ) = 0.9707

P ( x ≥ 6) = 0.0293

Step-by-step explanation:

The probability of a binomial mass distribution can be expressed with the formula:

$\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}$

$\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}$

where;

n = 8 and π = 0.36

For x = 5

The probability $\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}$

$\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =0.0887645}$

$\mathbf{P(X=5) =0.0888}$ to 4 decimal places

b. x ≤ 5

The probability of P ( x ≤ 5) $\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})$

${P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +$ $\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )$

P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888

P(x ≤ 5 ) = 0.9707

c. x ≥ 6

The probability of P ( x ≥ 6) = 1 - P( x ≤ 5 )

P ( x ≥ 6) = 1 - 0.9707

P ( x ≥ 6) = 0.0293

4 0

3 years ago

The perimeter of a triangle is 105. the lengths of all three sides are represented by three consecutive odd integers. Find the l

aev [14]

The longest side of the triangle is 37.

8 0

3 years ago

Find the solution to the following: *

Trava [24]

Answer:

First one: x = all real numbers

Second one: x = 0

Step-by-step explanation:

for the first one

given 8x+10=2(4x+5) we need to isolate the variable (x) using inverse operations

step 1 distribute the 2 to what is in the parenthesis ( 4x and 5 )

2 * 4x = 8x

5 * 2 = 10

now we have 8x + 10 = 8x + 10

step 2 subtract 8x from each side

8x - 8x = 0

now we have 10 = 10

subtract 10 from each side

10 - 10 = 0

we're left with 0 = 0 meaning that all real numbers are solutions

For the second one

given 3x-8=2(x-4) once again we need to isolate the variable using inverse operations

step 1 distribute the 2 to what is in the parenthesis (x - 4)

2 *x = 2x

2 * -4 = -8

now we have 3x - 8 = 2x - 8

step 2 add 8 to each side

-8 + 8 = 0

now we have 2x = 3x

step 3 subtract 2x from each side

3x - 2x = x

2x - 2x = 0

we're left with x = 0

5 0

3 years ago