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3 years ago

6

Ellie and her family are driving to her grandmother’s house. The drive takes 2 4/5 h total. Ellie and her family have completed

3/5 of the drive.
About how many hours have Ellie and her family been driving?

1 answer:

Westkost [7]3 years ago

3 0

She has driven for about 1 hour and 28 minutes

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Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

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3 years ago

What is 73×28 in multiply with regrouping

klio [65]

First, u multiply 8x3. Only the 4 can go in the ones place so put the four beneath the line and put the 2 over the 7.
Multiply 8x7 and add 2.
Move to the tens place, do 2x3 then 2x7.
Add the products and put the comma. Then ur done

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2 years ago

A single six-sided die is rolled. Find the probability of rolling a seven

suter [353]

Answer:

0

Step-by-step explanation:

according to the mathematical encyclopedia written by Albert Einstien, if a single six sided die is rolled, the probability of rolling a seven is 0 because the dice has six sides. 1,2,3,4,5,6. NO SEVEN!!!

3 0

3 years ago

Read 2 more answers

Brian rides his bicycle 24 miles in 2 hours. Write a ratio of Brain's miles per hour. Use the ratio from #1 to determine how far

Sati [7]

Answer:Ratio in miles per hour is 12 miles per hour.

Distance travelled is 60miles

Step-by-step explanation:

Speed=distance/time taken

24/2=12miles per hour

Therefore, distance travelled in 5 hours is 12*5=60miles

6 0

3 years ago

If g(x) = x+1/ x-2 and h (x) =4 - x , what is the value of ( g*h) (-3)?

Lapatulllka [165]

<u>Answer:</u>

g (h (x) ) = 5/8

<u>Step-by-step explanation:</u>

We are given the following two functions and we are to find the value of $g ( h ( - 3 ) )$ :

$g ( x ) = \frac { x + 1 } { x + 2 }$

$h ( x ) = 4 - x$

Firstly, we need to find the function :

$g ( h ( x ) ) = \frac { ( 4 - x + 1 ) } { ( 4 - x - 2 ) } = \frac { 5 - x } { 2 - x }$

Now substituting the value $x=-3$ in it:

$g ( h ( x ) ) = \frac { 5 - (-3) } { 2 - (-3) }$

g (h (x) ) = 5/8

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2 years ago