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3 years ago

2 bottles of grape juice fill 8 glasses. How many glasses can be filled from

Mathematics

1 answer:

ch4aika [34]3 years ago

5 0

Answer:

32 glasses

Step-by-step explanation:

To solve this we will first find out how many glasses one bottle of grape juice can fill.

Equation:

8/2 = 4

This means one bottle of grape juice can fill four glasses. Now all we have to do is multiply 4 glasses of grape juice by the number of bottles.

Equation:

8 * 4 = 32

32 glasses

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Are these triangles congruent or can't be determined?

Luda [366]

False. THey are congruent

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3 years ago

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A ball is thrown into the air and its position is given by h ( t ) = − 6.3 t 2 + 53 t + 24 where h is the height of the ball in

nordsb [41]

Answer:

$h'(t) = -12.6 t +53$

Now we can set up the derivate equal to 0 and we have:

$-12.6 t +53 = 0$

And solving for t we got:

$t = \frac{53}{12.6}= 4.206$

For the second derivate respect the time we got:

$h''(t) = -12.6$

So then we can conclude that t = 4.206 is a maximum for the function.

And the corresponding height would be:

$h(t=4.206) = -6.3(4.206)^2 +53*4.206+24= 135.468 ft$

So the maximum occurs at t = 4.206 s and with a height of 135.468 m

Step-by-step explanation:

For this case we have the following function:

$h(t) = -6.3t^2 +53 t+24$

In order to maximize this function we need to take the first derivate respect the time and we have:

$h'(t) = -12.6 t +53$

Now we can set up the derivate equal to 0 and we have:

$-12.6 t +53 = 0$

And solving for t we got:

$t = \frac{53}{12.6}= 4.206$

For the second derivate respect the time we got:

$h''(t) = -12.6$

So then we can conclude that t = 4.206 is a maximum for the function.

And the corresponding height would be:

$h(t=4.206) = -6.3(4.206)^2 +53*4.206+24= 135.468 ft$

So the maximum occurs at t = 4.206 s and with a height of 135.468 m

8 0

3 years ago

The Mayors of two small towns that adjoin a large community have engaged in an argument on which of their cities is safer, with

Lelu [443]

Answer:

1. City A: 150 violent crimes per 100,000 residents.

City B: 161 violent crimes per 100,000 residents.

2. City A

Step-by-step explanation:

City A:

Population = 123,000

Violent crimes = 185

Violent crimes per 100,000 people:

$V_{100k} = \frac{185*100,000}{123,000} \\V_{100k} = 150$

City B:

Population = 84,000

Violent crimes = 135

Violent crimes per 100,000 people:

$V_{100k} = \frac{135*100,000}{84,000} \\V_{100k} = 161$

1. City A: 150 violent crimes per 100,000 residents.

City B: 161 violent crimes per 100,000 residents.

2. Even though it has a bigger number of crimes, City A has the lowest crime rate since its population is larger.

5 0

3 years ago

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

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Anna [14]

Answer:

Step-by-step explanation:

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3 years ago

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