A juice container is a square prism with base edge length 4 inches. When an 8-inch straw is inserted into the container as shown
, exactly 1 inch remains outside the container. The length of AB is ___ inches, to the nearest inch. (Enter only the number.)
1 answer:
Assuming AB is the height because we are given it has a square base with 4 by 4
so draw a diagram ( see attachment)
given tha the 8 inch straw ha 1 inch sticking out, the diagonal is 7
use pythagorean theorem twice since 2 right triangles
a^2+b^2=c^2
4^2+4^2=c^2
16+16=c^2
32=c^2
sqrt both sides
4√2=c
the bottom diagonal is 4√2
bottom^2+height^2=7^2
(4√2)^2+(AB)^2=7^2
32+(AB)^2=47
minus 32 both sides
(AB)^2=15
sqrt both sides
AB=√15
if AB is the height
so draw a diagram ( see attachment)
given tha the 8 inch straw ha 1 inch sticking out, the diagonal is 7
use pythagorean theorem twice since 2 right triangles
a^2+b^2=c^2
4^2+4^2=c^2
16+16=c^2
32=c^2
sqrt both sides
4√2=c
the bottom diagonal is 4√2
bottom^2+height^2=7^2
(4√2)^2+(AB)^2=7^2
32+(AB)^2=47
minus 32 both sides
(AB)^2=15
sqrt both sides
AB=√15
if AB is the height
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The domain of the given graph is [−3, ∞) and the range is (−∞, 4].
We need to find the domain and range of the given graph.
<h3>What are the domain and range of the function?</h3>The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values that it can take.
We can observe that the graph extends horizontally from −3 to the right without a bound, so the domain is [−3, ∞). The vertical extent of the graph is all range values 4 and below, so the range is (−∞, 4].
Therefore, the domain of the given graph is [−3, ∞) and the range is (−∞, 4].
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Answer:
.
Step-by-step explanation:
Here in this problem, we have to rewrite a radical expression as an equivalent exponential expression.
The radical expression is 2(4√3)
Now, 2 ( 4√3)
=( 2 × 4) √3 {Since all the terms are in product form so, we can rearrange it}
= ( 2× 2²) × √3
=2³√3 {Since we know the formula from the property of exponent, xᵃ . xᵇ = x⁽ᵃ⁺ᵇ⁾ }
=.
Therefore, is the required equivalent exponential form. (Answer)