Answer:
Step-by-step explanation:
The heights of neither the rectangular prism nor the triangular prism are given, so we don't know the volume of either.
If h is the height of the rectangular prism, then its volume is
6×8×h = 48
if the height of the triangular prism is h/2, then its volume is
(1/2)×24×8×(h/2) = 48
So we know the volumes are the same -- but we don't know what that volume is.
Answer:
1/10 per sec
Step-by-step explanation:
When he's walked x feet in the eastward direction, the angle Θ that the search light makes has tangent
tanΘ = x/18
Taking the derivative with respect to time
sec²Θ dΘ/dt = 1/18 dx/dt.
He's walking at a rate of 18 ft/sec, so dx/dt = 18.
After 3seconds,
Speed = distance/time
18ft/sec =distance/3secs
x = 18 ft/sec (3 sec)
= 54ft. At this moment
tanΘ = 54/18
= 3
sec²Θ = 1 + tan²Θ
1 + 3² = 1+9
= 10
So at this moment
10 dΘ/dt = (1/18ft) 18 ft/sec = 1
10dΘ/dt = 1
dΘ/dt = 1/10 per sec
The answer is 2023 ...so my guess would be 2000
The best answer (and only correct answer) among the answer choices given is:
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[C]: y⁻¹ = (x+6) / 3 .
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Explanation:
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Given the original function: y = 3x - 6 ;
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To find the "inverse equation" of said function; we change the "x" to a y"; and the "y" to an "x"; and rewrite:
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x = 3y <span>− 6 ;
Now, rewrite in "slope-intercept form" ; or y = mx + b ;
that is, with y as "single, isolated" variable on the left-hand side of the equation (with an "implied coefficient of positive one", only); then an "equal sign, then "mx + b" ; in which: "m" is the coefficient of the variable, "x"; and in which "m" refers to the "slope"; and "b" refers to the 'y-intercept".
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So,we have the inverse function:
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x = 3y − 6 ; we want to write in slope-intercept form;
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Add "6" to each side of the equation:
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x + 6 = 3y − 6 + 6 ;
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x + 6 = 3y ;
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↔ Rewrite as: 3y = x + 6 ;
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Divide EACH side of the equation by "3" ; to isolate "y" one side of the equation; specifically, the left-hand side of equation; and to write in "slope-intercept form:
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3y / 3 = (x + 6) / 3 ;
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to get:
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y = (x + 6) / 3 ;
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y = (x/3) + (6/3) ;
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y = (x/3 ) + 2 ;
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or; write as: y = (1/3)x + 2 ;
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Now, let us examine the answer choices given:
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Note that all the answer choices begin with "y-1" ;
(except "answer choice: [B]" , which begins with "x-1"). This seems confusing; however, in reality, this does not mean, "y minus 1"; or "x minus 1". Rather, it mean y⁻¹ or x⁻¹ as notation for the "inverse" (not to be confused with the exponent notation. The confusion stems from the fact that it can be difficult to make such notations on the "Brainly" system.
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That being said, we can write the aforementioned "rewritten equations" (see above in THIS VERY ANSWER) as:
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y⁻¹ = (x + 6) / 3 ;
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y⁻¹ = (x/3) + (6/3) ;
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y⁻¹ = (x/3 ) + 2 ;
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or; write as: y⁻¹ = (1/3)x + 2
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That being said:
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The best answer (and only correct answer) among the answer choices given is: Answer choice: [C]: y⁻¹ = (x+6) / 3 .
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There are two types of interest: Simple interest and compounding interest:
Simple interest: F = P(1+in)
Compounding interest: F = P(1+i)ⁿ
The compounding interest is always bigger than simple interest for a given amount of n time. The effective interest rate is
Effective interest rate = 1.5%/year * 1 yr/12 months = 0.125% per month
Since there are 12 months in 1 year, n= 12. Then i = 0.125/100 = 0.00125
Difference = Compounded Interest - Simple Interest
Difference = P(1+i)ⁿ - P(1+in) = 1000(1+0.00125)¹² - 1000(1+0.00125*12)
Difference = $0.104
You will only have $0.104 more money than the simple interest.
