Answer:
90°
Step-by-step explanation:
The angle between the vectors can be found any of several ways. Here, we observe that the segments from the origin to the two points are at right angles to each other. (Their slopes are opposite reciprocals.) Hence the angle between the vectors is 90°.
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The slope to point 'a' is y/x = 2/1 = 2.
The slope to point 'b' is y/x = (-1/2)/1 = -1/2.
The product of these slopes is (2)(-1/2) = -1, indicating the vectors are perpendicular. The angle between them is 90°.
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We can also use the trig formula for the tangent of the difference of angles.
tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))
The tangents are the slopes, calculated above, so we have ...
tan(α -β) = (2 -(-1/2))/(1 +(2)(-1/2)) = (5/2)/0 = <em>undefined</em>
The tangent is <em>undefined</em> for angles that are odd multiples of 90°. The angle between the vectors is 90°.
Answer:
175 miles
Step-by-step explanation:
Hillary has travelled
320 + 350 = 670 miles
in the first two weeks.
Therefore, Hillary starts with 670 miles and needs to add a certain number of miles "x" to get 845 in total.
670 + x = 845
And if we subtract 670 from both sides:
x = 845 - 670 = 175
175 miles
<span>assume the graduate put the purchase on his card.thenInitial balance = $8000 on the first statement (+fees and interest charges, if any)That means he owes the card issuer $8000.Credit balance is what the issuer owes the card holder, which is zero
</span> option "c. $8000" is your answer
The ostrich can run 20 miles in 40 minutes.
<u>Solution:</u>
Given that, An ostrich run 6 mile in 12 minutes
We have to find how far he could come in 40 minutes
Now, according to the given information
Ostrich runs 6 miles ⇒ 12 minutes
Then, “n” miles ⇒ 40 minutes
Now, by criss cross multiplication we get,
Hence, the ostrich can run 20 miles in 40 minutes
Answer:
4.36 in
Step-by-step explanation:
To solve this problem we first find the volume of the sphere using the volume formula, after this we set this volume equal to the volume container which is a rectangular prism. After this we simple solve for the height by dividing the volume of the sphere by 12*10 to get the height
So the steps should look like
(4/3)*π*5³=523.599 in³
523.599 in³=12*10*Height
(523.599/(12*10))=4.36 in
