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3 years ago

For an angle Θ with the point (12, −5) on its terminating side, what is the value of cosine?

1 answer:

5 0

Given that the point (12,-5) which takes the form (x,y), This implies that:
opposite=-5
adjacent=12
thus using using Pythagorean theorem, the hypotenuse will be:
c^2=a^2+b^2
plugging the values we obtain:
c^2=(12)^2+(-5)^2
c^2=144+15
c^2=169
thus
c=13
but
cos θ=adjacent/ hypotenuse
therefore:
cos θ=12/13

Answer is option . D

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determine the diameter to the nearest inch of a large can of tuna that has a volume 6068 inches and a height of 3.3 inches

anyanavicka [17]

Answer:

The diameter of can is 48 inches.

Step-by-step explanation:

Given:

Volume of can = 6068 inches.

And height(h) = 3.3 inches.

Now, to find the diameter.

Diameter = 2 × radius

Let radius be $r.$

So, by putting the formula of volume we get the radius:

$Volume =\pi r^2h$

$6068=3.14\times r^2\times 3.3$ (taking the value of π=3.14)

$6068=10.362\times r^2$

Dividing both sides by 10.362 we get:

$585.60=r^2$

Using square root on both sides we get:

$24.199=r$

Radius = 24.199 inches.

Then, we get the diameter:

Diameter = 2 × radius

Diameter = 2 × 24.199 = 48.398 inches.

Diameter = 48 inches (rounding to nearest, inch as in the place of tenth it is 3 which is less than 5.)

Therefore, the diameter of can is 48 inches.

7 0

3 years ago

What number is 2 * 10 ^100

Studentka2010 [4]

Answer:

2.00000000e+100

Step-by-step explanation:

$2 \times {10}^{100} = \\ 2 \times 1.00000000e + 100= \\ 2.00000000e + 100$

8 0

3 years ago

Jasmine mixes 37 ounces of grape juice and 13 ounces of apple juice to make a fruit punch. She will pour the punch into 6-ounce

Anastaziya [24]

First we have to figure out how much fruit punch Jasmine has.
To do this, we just have to add the number of ounces of grape juice she mixes with the number of ounces of apple juice.

37 + 13 = 50.

Jasmine is pouring the punch into 6 ounce cups. To find out how many cups of punch she can make, you have to divide the number of ounces of punch she has (50) by the number of ounces she can put in a cup (6).

50/6 ≈ 8.33

Therefore, Jasmine can

A. make 8 full cups of punch with the apple juice and grape juice.

and

B. Yes, there will be juice left over, because the amount of cups Jasmine could fill had a decimal, or a remainder.

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3 years ago

Graph the following lines and using the graph determine several values of x for which the graph is positive (negative): y=−4x+3

True [87]

Answer:

Step-by-step explanation:

Given line is,

y=-4x+3

when, x=-1 , y=-4(-1)+3=4+3=7

when, x=0 , y=-4(0)+3=0+3=3

when, x=1 , y=-4(1)+3=-4+3=-1

So, we got the points (-1,7) , (0,3) , (1,-1)

Now, putting the points in the graph and adding them , we will get the graph of given line.

Please check image for the graph.

Now for the second part-

The graph is positive means- it will be above the x-axis, that is y value will be positive.

From the graph we can see that, if x<0 , then y is positive.

So, any value of x which is less than 0 , will give the positive graph here.

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3 years ago

explain how to use missing pieces strategy to compare two fractions. include a diagram with your explanation

Artemon [7]

The missing pieces strategy is another method to compare two fractions. To tell which number is larger, you ned to see which one is missing less. For example you have ¾ versus 4/5. Each of these fraction needs 1 to complete the whole. You need to subtract the numerator with one to compare them. For ¾ we have ¼ and for 4/5 we have 1/5. You know that if you complete 4/5 you will get 5 and for ¾ you will get 4. You know that 5 is greater than four. Therefore, 4/5 is larger than ¾.

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3 years ago